CINXE.COM

<!DOCTYPE html> <html class="client-nojs vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available" lang="zh" dir="ltr"> <head> <meta charset="UTF-8"> <title>逻辑运算符 - 维基百科，自由的百科全书</title> <script>(function(){var className="client-js vector-feature-language-in-header-enabled vector-feature-language-in-main-page-header-disabled vector-feature-sticky-header-disabled vector-feature-page-tools-pinned-disabled vector-feature-toc-pinned-clientpref-1 vector-feature-main-menu-pinned-disabled vector-feature-limited-width-clientpref-1 vector-feature-limited-width-content-enabled vector-feature-custom-font-size-clientpref-1 vector-feature-appearance-pinned-clientpref-1 vector-feature-night-mode-enabled skin-theme-clientpref-day vector-toc-available";var cookie=document.cookie.match(/(?:^|; )zhwikimwclientpreferences=([^;]+)/);if(cookie){cookie[1].split('%2C').forEach(function(pref){className=className.replace(new RegExp('(^| )'+pref.replace(/-clientpref-\w+$|[^\w-]+/g,'')+'-clientpref-\\w+( |$)'),'$1'+pref+'$2');});}document.documentElement.className=className;}());RLCONF={"wgBreakFrames":false,"wgSeparatorTransformTable":["",""],"wgDigitTransformTable":["",""],"wgDefaultDateFormat":"zh", "wgMonthNames":["","1月","2月","3月","4月","5月","6月","7月","8月","9月","10月","11月","12月"],"wgRequestId":"8b7c01f0-f59c-4b39-a69a-088f5dc47bb0","wgCanonicalNamespace":"","wgCanonicalSpecialPageName":false,"wgNamespaceNumber":0,"wgPageName":"逻辑运算符","wgTitle":"逻辑运算符","wgCurRevisionId":74670111,"wgRevisionId":74670111,"wgArticleId":18306,"wgIsArticle":true,"wgIsRedirect":false,"wgAction":"view","wgUserName":null,"wgUserGroups":["*"],"wgCategories":["自2018年12月缺少来源的条目","布尔代数","邏輯聯結詞"],"wgPageViewLanguage":"zh","wgPageContentLanguage":"zh","wgPageContentModel":"wikitext","wgRelevantPageName":"逻辑运算符","wgRelevantArticleId":18306,"wgUserVariant":"zh","wgIsProbablyEditable":true,"wgRelevantPageIsProbablyEditable":true,"wgRestrictionEdit":[],"wgRestrictionMove":[],"wgNoticeProject":"wikipedia","wgCiteReferencePreviewsActive":true,"wgMediaViewerOnClick":true,"wgMediaViewerEnabledByDefault":true,"wgPopupsFlags":0, "wgVisualEditor":{"pageLanguageCode":"zh","pageLanguageDir":"ltr","pageVariantFallbacks":["zh-hans","zh-hant","zh-cn","zh-tw","zh-hk","zh-sg","zh-mo","zh-my"]},"wgMFDisplayWikibaseDescriptions":{"search":true,"watchlist":true,"tagline":true,"nearby":true},"wgWMESchemaEditAttemptStepOversample":false,"wgWMEPageLength":9000,"wgRelatedArticlesCompat":[],"wgEditSubmitButtonLabelPublish":true,"wgULSPosition":"interlanguage","wgULSisCompactLinksEnabled":false,"wgVector2022LanguageInHeader":true,"wgULSisLanguageSelectorEmpty":false,"wgWikibaseItemId":"Q211790","wgCheckUserClientHintsHeadersJsApi":["brands","architecture","bitness","fullVersionList","mobile","model","platform","platformVersion"],"GEHomepageSuggestedEditsEnableTopics":true,"wgGETopicsMatchModeEnabled":false,"wgGEStructuredTaskRejectionReasonTextInputEnabled":false,"wgGELevelingUpEnabledForUser":false};RLSTATE={"ext.gadget.large-font":"ready","ext.globalCssJs.user.styles":"ready","site.styles":"ready","user.styles":"ready", "ext.globalCssJs.user":"ready","user":"ready","user.options":"loading","ext.math.styles":"ready","skins.vector.search.codex.styles":"ready","skins.vector.styles":"ready","skins.vector.icons":"ready","jquery.makeCollapsible.styles":"ready","ext.wikimediamessages.styles":"ready","ext.visualEditor.desktopArticleTarget.noscript":"ready","ext.uls.interlanguage":"ready","wikibase.client.init":"ready","ext.wikimediaBadges":"ready"};RLPAGEMODULES=["site","mediawiki.page.ready","jquery.makeCollapsible","skins.vector.js","ext.centralNotice.geoIP","ext.centralNotice.startUp","ext.gadget.edit0","ext.gadget.WikiMiniAtlas","ext.gadget.UnihanTooltips","ext.gadget.Difflink","ext.gadget.pseudonamespace-UI","ext.gadget.SpecialWikitext","ext.gadget.switcher","ext.gadget.VariantAlly","ext.gadget.AdvancedSiteNotices","ext.gadget.hideConversionTab","ext.gadget.internalLinkHelper-altcolor","ext.gadget.noteTA","ext.gadget.NavFrame","ext.gadget.collapsibleTables","ext.gadget.scrollUpButton", "ext.urlShortener.toolbar","ext.centralauth.centralautologin","mmv.bootstrap","ext.popups","ext.visualEditor.desktopArticleTarget.init","ext.visualEditor.targetLoader","ext.echo.centralauth","ext.eventLogging","ext.wikimediaEvents","ext.navigationTiming","ext.uls.interface","ext.cx.eventlogging.campaigns","ext.cx.uls.quick.actions","wikibase.client.vector-2022","ext.checkUser.clientHints","ext.quicksurveys.init","ext.growthExperiments.SuggestedEditSession","wikibase.sidebar.tracking"];</script> <script>(RLQ=window.RLQ||[]).push(function(){mw.loader.impl(function(){return["user.options@12s5i",function($,jQuery,require,module){mw.user.tokens.set({"patrolToken":"+\\","watchToken":"+\\","csrfToken":"+\\"}); }];});});</script> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=ext.math.styles%7Cext.uls.interlanguage%7Cext.visualEditor.desktopArticleTarget.noscript%7Cext.wikimediaBadges%7Cext.wikimediamessages.styles%7Cjquery.makeCollapsible.styles%7Cskins.vector.icons%2Cstyles%7Cskins.vector.search.codex.styles%7Cwikibase.client.init&only=styles&skin=vector-2022"> <script async="" src="/w/load.php?lang=zh&modules=startup&only=scripts&raw=1&skin=vector-2022"></script> <meta name="ResourceLoaderDynamicStyles" content=""> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=ext.gadget.large-font&only=styles&skin=vector-2022"> <link rel="stylesheet" href="/w/load.php?lang=zh&modules=site.styles&only=styles&skin=vector-2022"> <meta name="generator" content="MediaWiki 1.44.0-wmf.5"> <meta name="referrer" content="origin"> <meta name="referrer" content="origin-when-cross-origin"> <meta name="robots" content="max-image-preview:standard"> <meta name="format-detection" content="telephone=no"> <meta name="viewport" content="width=1120"> <meta property="og:title" content="逻辑运算符 - 维基百科，自由的百科全书"> <meta property="og:type" content="website"> <link rel="preconnect" href="//upload.wikimedia.org"> <link rel="alternate" media="only screen and (max-width: 640px)" href="//zh.m.wikipedia.org/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" type="application/x-wiki" title="编辑本页" href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=edit"> <link rel="apple-touch-icon" href="/static/apple-touch/wikipedia.png"> <link rel="icon" href="/static/favicon/wikipedia.ico"> <link rel="search" type="application/opensearchdescription+xml" href="/w/rest.php/v1/search" title="Wikipedia (zh)"> <link rel="EditURI" type="application/rsd+xml" href="//zh.wikipedia.org/w/api.php?action=rsd"> <link rel="canonical" href="https://zh.wikipedia.org/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh" href="https://zh.wikipedia.org/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh-Hans" href="https://zh.wikipedia.org/zh-hans/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh-Hans-CN" href="https://zh.wikipedia.org/zh-cn/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh-Hans-MY" href="https://zh.wikipedia.org/zh-my/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh-Hans-SG" href="https://zh.wikipedia.org/zh-sg/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh-Hant" href="https://zh.wikipedia.org/zh-hant/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh-Hant-HK" href="https://zh.wikipedia.org/zh-hk/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh-Hant-MO" href="https://zh.wikipedia.org/zh-mo/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="zh-Hant-TW" href="https://zh.wikipedia.org/zh-tw/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="alternate" hreflang="x-default" href="https://zh.wikipedia.org/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"> <link rel="license" href="https://creativecommons.org/licenses/by-sa/4.0/deed.zh"> <link rel="alternate" type="application/atom+xml" title="Wikipedia的Atom feed" href="/w/index.php?title=Special:%E6%9C%80%E8%BF%91%E6%9B%B4%E6%94%B9&feed=atom"> <link rel="dns-prefetch" href="//meta.wikimedia.org" /> <link rel="dns-prefetch" href="//login.wikimedia.org"> </head> <body class="skin--responsive skin-vector skin-vector-search-vue mediawiki ltr sitedir-ltr mw-hide-empty-elt ns-0 ns-subject mw-editable page-逻辑运算符 rootpage-逻辑运算符 skin-vector-2022 action-view"><a class="mw-jump-link" href="#bodyContent">跳转到内容</a> <div class="vector-header-container"> <header class="vector-header mw-header"> <div class="vector-header-start"> <nav class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-dropdown" class="vector-dropdown vector-main-menu-dropdown vector-button-flush-left vector-button-flush-right" > <input type="checkbox" id="vector-main-menu-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-main-menu-dropdown" class="vector-dropdown-checkbox " aria-label="主菜单" > <label id="vector-main-menu-dropdown-label" for="vector-main-menu-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-menu mw-ui-icon-wikimedia-menu"></span> <span class="vector-dropdown-label-text">主菜单</span> </label> <div class="vector-dropdown-content"> <div id="vector-main-menu-unpinned-container" class="vector-unpinned-container"> <div id="vector-main-menu" class="vector-main-menu vector-pinnable-element"> <div class="vector-pinnable-header vector-main-menu-pinnable-header vector-pinnable-header-unpinned" data-feature-name="main-menu-pinned" data-pinnable-element-id="vector-main-menu" data-pinned-container-id="vector-main-menu-pinned-container" data-unpinned-container-id="vector-main-menu-unpinned-container" > <div class="vector-pinnable-header-label">主菜单</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-main-menu.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">隐藏</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> 导航 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage-description" class="mw-list-item"><a href="/wiki/Wikipedia:%E9%A6%96%E9%A1%B5" title="访问首页[z]" accesskey="z"><span>首页</span></a></li><li id="n-indexpage" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%88%86%E7%B1%BB%E7%B4%A2%E5%BC%95" title="以分类索引搜寻中文维基百科"><span>分类索引</span></a></li><li id="n-Featured_content" class="mw-list-item"><a href="/wiki/Portal:%E7%89%B9%E8%89%B2%E5%85%A7%E5%AE%B9" title="查看中文维基百科的特色内容"><span>特色内容</span></a></li><li id="n-currentevents" class="mw-list-item"><a href="/wiki/Portal:%E6%96%B0%E8%81%9E%E5%8B%95%E6%85%8B" title="提供当前新闻事件的背景资料"><span>新闻动态</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Special:%E6%9C%80%E8%BF%91%E6%9B%B4%E6%94%B9" title="列出维基百科中的最近修改[r]" accesskey="r"><span>最近更改</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Special:%E9%9A%8F%E6%9C%BA%E9%A1%B5%E9%9D%A2" title="随机载入一个页面[x]" accesskey="x"><span>随机条目</span></a></li> </ul> </div> </div> <div id="p-help" class="vector-menu mw-portlet mw-portlet-help" > <div class="vector-menu-heading"> 帮助 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-help" class="mw-list-item"><a href="/wiki/Help:%E7%9B%AE%E5%BD%95" title="寻求帮助"><span>帮助</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:%E7%A4%BE%E7%BE%A4%E9%A6%96%E9%A1%B5" title="关于本计划、你可以做什么、应该如何做"><span>维基社群</span></a></li><li id="n-policy" class="mw-list-item"><a href="/wiki/Wikipedia:%E6%96%B9%E9%87%9D%E8%88%87%E6%8C%87%E5%BC%95" title="查看维基百科的方针和指引"><span>方针与指引</span></a></li><li id="n-villagepump" class="mw-list-item"><a href="/wiki/Wikipedia:%E4%BA%92%E5%8A%A9%E5%AE%A2%E6%A0%88" title="参与维基百科社群的讨论"><span>互助客栈</span></a></li><li id="n-Information_desk" class="mw-list-item"><a href="/wiki/Wikipedia:%E7%9F%A5%E8%AF%86%E9%97%AE%E7%AD%94" title="解答任何与维基百科无关的问题的地方"><span>知识问答</span></a></li><li id="n-conversion" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%AD%97%E8%AF%8D%E8%BD%AC%E6%8D%A2" title="提出字词转换请求"><span>字词转换</span></a></li><li id="n-IRC" class="mw-list-item"><a href="/wiki/Wikipedia:IRC%E8%81%8A%E5%A4%A9%E9%A2%91%E9%81%93"><span>IRC即时聊天</span></a></li><li id="n-contact" class="mw-list-item"><a href="/wiki/Wikipedia:%E8%81%94%E7%BB%9C%E6%88%91%E4%BB%AC" title="如何联络维基百科"><span>联络我们</span></a></li><li id="n-about" class="mw-list-item"><a href="/wiki/Wikipedia:%E5%85%B3%E4%BA%8E" title="查看维基百科的简介"><span>关于维基百科</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Wikipedia:%E9%A6%96%E9%A1%B5" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="维基百科" src="/static/images/mobile/copyright/wikipedia-wordmark-zh.svg" style="width: 6.5625em; height: 1.375em;"> <img class="mw-logo-tagline" alt="自由的百科全书" src="/static/images/mobile/copyright/wikipedia-tagline-zh.svg" width="103" height="14" style="width: 6.4375em; height: 0.875em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Special:%E6%90%9C%E7%B4%A2" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="搜索维基百科[f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>搜索</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="搜索维基百科" aria-label="搜索维基百科" autocapitalize="sentences" title="搜索维基百科[f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Special:搜索"> </div> <button class="cdx-button cdx-search-input__end-button">搜索</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="个人工具"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="更改页面字体大小、宽度和颜色的外观" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="外观" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">外观</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=zh.wikipedia.org&uselang=zh" class=""><span>资助维基百科</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="我们推荐您创建账号并登录，但这不是强制性的" class=""><span>创建账号</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="建议你登录，尽管并非必须。[o]" accesskey="o" class=""><span>登录</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="更多选项" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="个人工具" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">个人工具</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="用户菜单" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=zh.wikipedia.org&uselang=zh"><span>资助维基百科</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E5%88%9B%E5%BB%BA%E8%B4%A6%E6%88%B7&returnto=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="我们推荐您创建账号并登录，但这不是强制性的"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>创建账号</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Special:%E7%94%A8%E6%88%B7%E7%99%BB%E5%BD%95&returnto=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="建议你登录，尽管并非必须。[o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>登录</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> 未登录编辑者的页面 <a href="/wiki/Help:%E6%96%B0%E6%89%8B%E5%85%A5%E9%97%A8" aria-label="了解有关编辑的更多信息"><span>了解详情</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%B4%A1%E7%8C%AE" title="来自此IP地址的编辑列表[y]" accesskey="y"><span>贡献</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Special:%E6%88%91%E7%9A%84%E8%AE%A8%E8%AE%BA%E9%A1%B5" title="对于来自此IP地址编辑的讨论[n]" accesskey="n"><span>讨论</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="站点"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="目录" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">目录</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">隐藏</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">序言</div> </a> </li> <li id="toc-基本運算符" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#基本運算符"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>基本運算符</span> </div> </a> <ul id="toc-基本運算符-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-二元邏輯聯結詞表" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#二元邏輯聯結詞表"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>二元邏輯聯結詞表</span> </div> </a> <button aria-controls="toc-二元邏輯聯結詞表-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>开关二元邏輯聯結詞表子章节</span> </button> <ul id="toc-二元邏輯聯結詞表-sublist" class="vector-toc-list"> <li id="toc-圖-{}-示" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#圖-{}-示"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>圖示</span> </div> </a> <ul id="toc-圖-{}-示-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">开关目录</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">逻辑运算符</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。39种语言可用" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-39" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">39种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D8%A9_%D9%85%D9%86%D8%B7%D9%82%D9%8A%D8%A9" title="رابطة منطقية – 阿拉伯语" lang="ar" hreflang="ar" data-title="رابطة منطقية" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/M%C9%99ntiqi_%C9%99m%C9%99liyyat" title="Məntiqi əməliyyat – 阿塞拜疆语" lang="az" hreflang="az" data-title="Məntiqi əməliyyat" data-language-autonym="Azərbaycanca" data-language-local-name="阿塞拜疆语" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Логическа операция – 保加利亚语" lang="bg" hreflang="bg" data-title="Логическа операция" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Connectiva_l%C3%B2gica" title="Connectiva lògica – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Connectiva lògica" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Logisk_operator" title="Logisk operator – 丹麦语" lang="da" hreflang="da" data-title="Logisk operator" data-language-autonym="Dansk" data-language-local-name="丹麦语" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Logische_Verkn%C3%BCpfung" title="Logische Verknüpfung – 德语" lang="de" hreflang="de" data-title="Logische Verknüpfung" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CE%B3%CE%B9%CE%BA%CE%AD%CF%82_%CF%83%CF%85%CE%BD%CE%B1%CF%81%CF%84%CE%AE%CF%83%CE%B5%CE%B9%CF%82" title="Λογικές συναρτήσεις – 希腊语" lang="el" hreflang="el" data-title="Λογικές συναρτήσεις" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Conet%C3%AEv_l%C3%B2gic" title="Conetîv lògic – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Conetîv lògic" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Logical_connective" title="Logical connective – 英语" lang="en" hreflang="en" data-title="Logical connective" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Conectiva_l%C3%B3gica" title="Conectiva lógica – 西班牙语" lang="es" hreflang="es" data-title="Conectiva lógica" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Konnektor_(keeleteadus)" title="Konnektor (keeleteadus) – 爱沙尼亚语" lang="et" hreflang="et" data-title="Konnektor (keeleteadus)" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Lokailu_logiko" title="Lokailu logiko – 巴斯克语" lang="eu" hreflang="eu" data-title="Lokailu logiko" data-language-autonym="Euskara" data-language-local-name="巴斯克语" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%D8%A8%D8%B7_%D9%85%D9%86%D8%B7%D9%82%DB%8C" title="رابط منطقی – 波斯语" lang="fa" hreflang="fa" data-title="رابط منطقی" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Connecteur_logique" title="Connecteur logique – 法语" lang="fr" hreflang="fr" data-title="Connecteur logique" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A9%D7%A8_%D7%9C%D7%95%D7%92%D7%99" title="קשר לוגי – 希伯来语" lang="he" hreflang="he" data-title="קשר לוגי" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Logikai_m%C5%B1velet" title="Logikai művelet – 匈牙利语" lang="hu" hreflang="hu" data-title="Logikai művelet" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D6%80%D5%A1%D5%B4%D5%A1%D5%A2%D5%A1%D5%B6%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A3%D5%B8%D6%80%D5%AE%D5%B8%D5%B2%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Տրամաբանական գործողություն – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Տրամաբանական գործողություն" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Operator_logika" title="Operator logika – 印度尼西亚语" lang="id" hreflang="id" data-title="Operator logika" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/R%C3%B6ka%C3%B0ger%C3%B0" title="Rökaðgerð – 冰岛语" lang="is" hreflang="is" data-title="Rökaðgerð" data-language-autonym="Íslenska" data-language-local-name="冰岛语" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Connettivo_logico" title="Connettivo logico – 意大利语" lang="it" hreflang="it" data-title="Connettivo logico" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%AB%96%E7%90%86%E6%BC%94%E7%AE%97" title="論理演算 – 日语" lang="ja" hreflang="ja" data-title="論理演算" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D0%BF%D0%BE%D0%B7%D0%B8%D1%86%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D3%A9%D0%B7%D0%B0%D1%80%D0%B0_%D2%9B%D0%B0%D1%82%D1%8B%D0%BD%D0%B0%D1%81" title="Пропозициялық өзара қатынас – 哈萨克语" lang="kk" hreflang="kk" data-title="Пропозициялық өзара қатынас" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%85%BC%EB%A6%AC_%EC%97%B0%EC%82%B0" title="논리 연산 – 韩语" lang="ko" hreflang="ko" data-title="논리 연산" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%BA%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Логичка операција – 马其顿语" lang="mk" hreflang="mk" data-title="Логичка операција" data-language-autonym="Македонски" data-language-local-name="马其顿语" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pengoperasi_logik" title="Pengoperasi logik – 马来语" lang="ms" hreflang="ms" data-title="Pengoperasi logik" data-language-autonym="Bahasa Melayu" data-language-local-name="马来语" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Logisk_konstant" title="Logisk konstant – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Logisk konstant" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Funktor_zdaniotw%C3%B3rczy" title="Funktor zdaniotwórczy – 波兰语" lang="pl" hreflang="pl" data-title="Funktor zdaniotwórczy" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Conectivo_l%C3%B3gico" title="Conectivo lógico – 葡萄牙语" lang="pt" hreflang="pt" data-title="Conectivo lógico" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Conector_logic" title="Conector logic – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Conector logic" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Логическая операция – 俄语" lang="ru" hreflang="ru" data-title="Логическая операция" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/V%C3%BDrokov%C3%A1_spojka" title="Výroková spojka – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Výroková spojka" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Logisk_operator" title="Logisk operator – 瑞典语" lang="sv" hreflang="sv" data-title="Logisk operator" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8F%E0%AE%B0%E0%AE%A3_%E0%AE%87%E0%AE%A3%E0%AF%88%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BF" title="ஏரண இணைப்பி – 泰米尔语" lang="ta" hreflang="ta" data-title="ஏரண இணைப்பி" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%BC%D0%B0%D0%BB%D2%B3%D0%BE%D0%B8_%D0%BC%D0%B0%D0%BD%D1%82%D0%B8%D2%9B%D3%A3" title="Амалҳои мантиқӣ – 塔吉克语" lang="tg" hreflang="tg" data-title="Амалҳои мантиқӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="塔吉克语" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%94%E0%B8%B3%E0%B9%80%E0%B8%99%E0%B8%B4%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%95%E0%B8%A3%E0%B8%A3%E0%B8%81%E0%B8%B0" title="ตัวดำเนินการตรรกะ – 泰语" lang="th" hreflang="th" data-title="ตัวดำเนินการตรรกะ" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Mant%C4%B1k_ba%C4%9Flac%C4%B1" title="Mantık bağlacı – 土耳其语" lang="tr" hreflang="tr" data-title="Mantık bağlacı" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D1%96%D1%87%D0%BD%D0%B8%D0%B9_%D1%81%D0%BF%D0%BE%D0%BB%D1%83%D1%87%D0%BD%D0%B8%D0%BA" title="Логічний сполучник – 乌克兰语" lang="uk" hreflang="uk" data-title="Логічний сполучник" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D9%86%D8%B7%D9%82%DB%8C_%D8%B9%D8%A7%D9%85%D9%84" title="منطقی عامل – 乌尔都语" lang="ur" hreflang="ur" data-title="منطقی عامل" data-language-autonym="اردو" data-language-local-name="乌尔都语" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%82%8F%E8%BC%AF%E9%80%A3%E6%8E%A5%E8%A9%9E" title="邏輯連接詞 – 粤语" lang="yue" hreflang="yue" data-title="邏輯連接詞" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q211790#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="命名空间"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Talk:%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" rel="discussion" title="关于此页面的讨论[t]" accesskey="t"><span>讨论</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown " > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="更改语言变体" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">不转换</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-varlang-0" class="selected ca-variants-zh mw-list-item"><a href="/zh/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh" hreflang="zh"><span>不转换</span></a></li><li id="ca-varlang-1" class="ca-variants-zh-Hans mw-list-item"><a href="/zh-hans/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh-Hans" hreflang="zh-Hans"><span>简体</span></a></li><li id="ca-varlang-2" class="ca-variants-zh-Hant mw-list-item"><a href="/zh-hant/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh-Hant" hreflang="zh-Hant"><span>繁體</span></a></li><li id="ca-varlang-3" class="ca-variants-zh-Hans-CN mw-list-item"><a href="/zh-cn/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh-Hans-CN" hreflang="zh-Hans-CN"><span>大陆简体</span></a></li><li id="ca-varlang-4" class="ca-variants-zh-Hant-HK mw-list-item"><a href="/zh-hk/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh-Hant-HK" hreflang="zh-Hant-HK"><span>香港繁體</span></a></li><li id="ca-varlang-5" class="ca-variants-zh-Hant-MO mw-list-item"><a href="/zh-mo/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh-Hant-MO" hreflang="zh-Hant-MO"><span>澳門繁體</span></a></li><li id="ca-varlang-6" class="ca-variants-zh-Hans-MY mw-list-item"><a href="/zh-my/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh-Hans-MY" hreflang="zh-Hans-MY"><span>大马简体</span></a></li><li id="ca-varlang-7" class="ca-variants-zh-Hans-SG mw-list-item"><a href="/zh-sg/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh-Hans-SG" hreflang="zh-Hans-SG"><span>新加坡简体</span></a></li><li id="ca-varlang-8" class="ca-variants-zh-Hant-TW mw-list-item"><a href="/zh-tw/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" lang="zh-Hant-TW" hreflang="zh-Hant-TW"><span>臺灣正體</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="查看"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"><span>阅读</span></a></li><li id="ca-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=history" title="本页面的早前版本。[h]" accesskey="h"><span>查看历史</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="工具" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">工具</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">工具</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">隐藏</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="更多选项" > <div class="vector-menu-heading"> 操作 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6"><span>阅读</span></a></li><li id="ca-more-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=edit" title="编辑该页面[e]" accesskey="e"><span>编辑</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=history"><span>查看历史</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> 常规 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%85%A5%E9%A1%B5%E9%9D%A2/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="列出所有与本页相链的页面[j]" accesskey="j"><span>链入页面</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Special:%E9%93%BE%E5%87%BA%E6%9B%B4%E6%94%B9/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" rel="nofollow" title="页面链出所有页面的更改[k]" accesskey="k"><span>相关更改</span></a></li><li id="t-upload" class="mw-list-item"><a href="/wiki/Project:%E4%B8%8A%E4%BC%A0" title="上传图像或多媒体文件[u]" accesskey="u"><span>上传文件</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Special:%E7%89%B9%E6%AE%8A%E9%A1%B5%E9%9D%A2" title="全部特殊页面的列表[q]" accesskey="q"><span>特殊页面</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&oldid=74670111" title="此页面该修订版本的固定链接"><span>固定链接</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=info" title="关于此页面的更多信息"><span>页面信息</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Special:%E5%BC%95%E7%94%A8%E6%AD%A4%E9%A1%B5%E9%9D%A2&page=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&id=74670111&wpFormIdentifier=titleform" title="有关如何引用此页面的信息"><span>引用此页</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Special:URL%E7%BC%A9%E7%9F%AD%E7%A8%8B%E5%BA%8F&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E9%2580%25BB%25E8%25BE%2591%25E8%25BF%2590%25E7%25AE%2597%25E7%25AC%25A6"><span>获取短链接</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Special:QrCode&url=https%3A%2F%2Fzh.wikipedia.org%2Fwiki%2F%25E9%2580%25BB%25E8%25BE%2591%25E8%25BF%2590%25E7%25AE%2597%25E7%25AC%25A6"><span>下载二维码</span></a></li> </ul> </div> </div> <div id="p-electronpdfservice-sidebar-portlet-heading" class="vector-menu mw-portlet mw-portlet-electronpdfservice-sidebar-portlet-heading" > <div class="vector-menu-heading"> 打印/导出 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=show-download-screen"><span>下载为PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="本页面的可打印版本[p]" accesskey="p"><span>打印页面</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 在其他项目中 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Logical_connectives" hreflang="en"><span>维基共享资源</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q211790" title="链接到连接的数据仓库项目[g]" accesskey="g"><span>维基数据项目</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="页面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="外观"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">外观</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移至侧栏</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">隐藏</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> <div id="mw-indicator-noteTA-60ef224e" class="mw-indicator"><div class="mw-parser-output"><span class="skin-invert" typeof="mw:File"><span title="本页使用了标题或全文手工转换"><img alt="本页使用了标题或全文手工转换" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/35px-Zh_conversion_icon_m.svg.png" decoding="async" width="35" height="22" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/53px-Zh_conversion_icon_m.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cd/Zh_conversion_icon_m.svg/70px-Zh_conversion_icon_m.svg.png 2x" data-file-width="32" data-file-height="20" /></span></span></div></div> </div> <div id="siteSub" class="noprint">维基百科，自由的百科全书</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="zh" dir="ltr"><style data-mw-deduplicate="TemplateStyles:r83732972">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}html.client-js body.skin-minerva .mw-parser-output .mbox-text-span{margin-left:23px!important}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media screen{html.skin-theme-clientpref-night .mw-parser-output .ambox{border-left-color:#36c!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-night .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-night .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .ambox{border-left-color:#36c!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy,html.skin-theme-clientpref-os .mw-parser-output .ambox-delete{border-left-color:#b32424!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-speedy{background-color:#300!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-Unreferenced plainlinks metadata ambox ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/File:Tango-nosources.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Tango-nosources.svg/45px-Tango-nosources.svg.png" decoding="async" width="45" height="45" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Tango-nosources.svg/68px-Tango-nosources.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4e/Tango-nosources.svg/90px-Tango-nosources.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">此條目<b>没有列出任何<a href="/wiki/Wikipedia:%E5%88%97%E6%98%8E%E6%9D%A5%E6%BA%90" title="Wikipedia:列明来源">参考或来源</a></b>。<span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2018年12月5日</span>)</i></small><span class="hide-when-compact"><br /><small>維基百科所有的內容都應該<a href="/wiki/Wikipedia:%E5%8F%AF%E4%BE%9B%E6%9F%A5%E8%AD%89" title="Wikipedia:可供查證">可供查證</a>。请协助補充<a href="/wiki/Wikipedia:%E5%8F%AF%E9%9D%A0%E6%9D%A5%E6%BA%90" title="Wikipedia:可靠来源">可靠来源</a>以<a class="external text" href="https://zh.wikipedia.org/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=edit">改善这篇条目</a>。无法查证的內容可能會因為異議提出而被移除。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <div id="noteTA-60ef224e" class="noteTA"><div class="noteTA-group"><div data-noteta-group-source="module" data-noteta-group="IT"></div><div data-noteta-group-source="module" data-noteta-group="Math"></div></div></div> <p>在<a href="/wiki/%E5%BD%A2%E5%BC%8F%E9%80%BB%E8%BE%91" class="mw-redirect" title="形式逻辑">形式逻辑</a>中，<b>逻辑运算符</b>或<b>逻辑联结词</b>把语句连接成更复杂的复杂语句。例如，假设有两个逻辑<a href="/wiki/%E5%91%BD%E9%A2%98" title="命题">命题</a>，分别是“正在下雨”和“我在屋里”，我们可以将它们组成复杂命题“正在下雨，<b>并且</b>我在屋里”或“<b>没有</b>正在下雨”或“<b>如果</b>正在下雨，<b>那么</b>我在屋里”。一个将两个语句组成的新的语句或命题叫做<b>复合语句</b>或<b>复合命题</b>。又称逻辑操作符（Logical Operators）。 </p> <div class="mw-heading mw-heading2"><h2 id="基本運算符"><span id=".E5.9F.BA.E6.9C.AC.E9.81.8B.E7.AE.97.E7.AC.A6"></span>基本運算符</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=edit&section=1" title="编辑章节：基本運算符"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>基本的操作符有：“<a href="/wiki/%E9%80%BB%E8%BE%91%E9%9D%9E" title="逻辑非">非</a>”（¬）、“<a href="/wiki/%E9%80%BB%E8%BE%91%E5%90%88%E5%8F%96" class="mw-redirect" title="逻辑合取">与</a>”（∧）、“<a href="/wiki/%E9%80%BB%E8%BE%91%E6%9E%90%E5%8F%96" class="mw-redirect" title="逻辑析取">或</a>”（∨）、“<a href="/wiki/%E5%AE%9E%E8%B4%A8%E6%9D%A1%E4%BB%B6" title="实质条件">条件</a>”（→）以及“<a href="/wiki/%E5%8F%8C%E6%9D%A1%E4%BB%B6" class="mw-redirect" title="双条件">双条件</a>”（↔）。“非”是一个一元操作符，它只操作一项（¬ P）。剩下的是二元操作符，操作两项来组成复杂语句（P ∧ Q, P ∨ Q, P → Q, P ↔ Q）。 </p><p>注意，符号“与”（∧）和<a href="/wiki/%E4%BA%A4%E9%9B%86" title="交集">交集</a>（∩），“或”（∨）和<a href="/wiki/%E5%B9%B6%E9%9B%86" title="并集">并集</a>（∪）的相似性。这不是巧合：交集的定义使用“与”，并集的定义是用“或”。 </p><p>这些连接符的<a href="/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8" title="真值表">真值表</a>: </p> <table class="wikitable" style="text-align:center"> <tbody><tr> <th><i>P</i></th> <th><i>Q</i></th> <th>¬<i>P</i></th> <th><i>P</i> ∧ <i>Q</i></th> <th><i>P</i> ∨ <i>Q</i></th> <th><i>P</i> → <i>Q</i></th> <th><i>P</i> ↔ <i>Q</i> </th></tr> <tr> <th>T</th> <th><b>T</b></th> <th>F</th> <th>T</th> <th>T</th> <th>T</th> <th>T </th></tr> <tr> <th>T</th> <th><b>F</b></th> <th>F</th> <th>F</th> <th>T</th> <th>F</th> <th>F </th></tr> <tr> <th>F</th> <th><b>T</b></th> <th>T</th> <th>F</th> <th>T</th> <th>T</th> <th>F </th></tr> <tr> <th>F</th> <th><b>F</b></th> <th>T</th> <th>F</th> <th>F</th> <th>T</th> <th>T </th></tr></tbody></table> <p>为了减少需要的括号的数量，有以下的优先规则：¬高于∧，∧高于∨，∨高于→。例如，P ∨ Q ∧ ¬ R → S是 (P ∨ (Q ∧ (¬ R)) → S的简便写法。 </p> <div class="mw-heading mw-heading2"><h2 id="二元邏輯聯結詞表"><span id=".E4.BA.8C.E5.85.83.E9.82.8F.E8.BC.AF.E8.81.AF.E7.B5.90.E8.A9.9E.E8.A1.A8"></span>二元邏輯聯結詞表</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=edit&section=2" title="编辑章节：二元邏輯聯結詞表"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>下面是在輸入P和Q上的16個二元<a href="/wiki/%E5%B8%83%E6%9E%97%E5%87%BD%E6%95%B8" class="mw-redirect" title="布林函數">布林函數</a>。 </p> <table style="background:transparent;text-align:center;"> <tbody><tr> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E7%9F%9B%E7%9B%BE" title="矛盾">永假</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊥</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f282c7bc331cc3bfcf1c57f1452cc23c022f58de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \bot }"></span> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> ¬<i>P</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn0000.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Venn0000.svg/100px-Venn0000.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Venn0000.svg/150px-Venn0000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Venn0000.svg/200px-Venn0000.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E6%81%86%E7%9C%9F%E5%BC%8F" title="恆真式">永真</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \top }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊤</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \top }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf12e436fef2365e76fcb1034a51179d8328bb33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \top }"></span> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vee }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vee }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b76220c6805c9b465d6efbc7686c624f49f3023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \vee }"></span> ¬<i>P</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn1111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Venn1111.svg/100px-Venn1111.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Venn1111.svg/150px-Venn1111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/ca/Venn1111.svg/200px-Venn1111.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td></tr> <tr> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E9%80%BB%E8%BE%91%E5%90%88%E5%8F%96" class="mw-redirect" title="逻辑合取">合取</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span> <i>Q</i><br /><i>P</i> & <i>Q</i><br /><i>P</i> <b>·</b> <i>Q</i><br /><i>P</i> AND <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb95f3f5a9898c871045935a253d1d23e0e2644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \rightarrow }"></span>¬<i>Q</i> <br /> ¬<i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acf12661d69611db01ff7f036bf8c5b5dfec902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftarrow }"></span> <i>Q</i> <br /> ¬<i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \downarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↓</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \downarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4618f22b0f780805eb94bb407578d9bc9487947a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \downarrow }"></span> ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn0001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/100px-Venn0001.svg.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/150px-Venn0001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/99/Venn0001.svg/200px-Venn0001.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E8%B0%A2%E8%B4%B9%E5%B0%94%E7%AB%96%E7%BA%BF" title="谢费尔竖线">與非</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> ↑ <i>Q</i><br /><i>P</i> | <i>Q</i> <br /><i>P</i> NAND <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> → ¬<i>Q</i> <br /> ¬<i>P</i> ← <i>Q</i><br />¬<i>P</i> ∨ ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn1110.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Venn1110.svg/100px-Venn1110.svg.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Venn1110.svg/150px-Venn1110.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/cb/Venn1110.svg/200px-Venn1110.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td></tr> <tr> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E5%AE%9E%E8%B4%A8%E9%9D%9E%E8%95%B4%E6%B6%B5" title="实质非蕴涵">非蘊涵</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb95f3f5a9898c871045935a253d1d23e0e2644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \rightarrow }"></span> <i>Q</i> <br /> <i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \supset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊅</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \supset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0066ef658b08a8a21cf267a4e5bec61bc03fcb73" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.676ex;" alt="{\displaystyle \not \supset }"></span> <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> & ¬<i>Q</i> <br /> ¬<i>P</i> ↓ <i>Q</i> <br /> ¬<i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acf12661d69611db01ff7f036bf8c5b5dfec902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftarrow }"></span> ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn0100.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Venn0100.svg/100px-Venn0100.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Venn0100.svg/150px-Venn0100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e6/Venn0100.svg/200px-Venn0100.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E5%AE%9E%E8%B4%A8%E6%9D%A1%E4%BB%B6" title="实质条件">蘊涵</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> → <i>Q</i> <br /> <i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \supset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊃</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \supset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27bfe0828a2ed4c9c6b70987a85c02a1f005843c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle \supset }"></span> <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> ↑ ¬<i>Q</i> <br /> ¬<i>P</i> ∨ <i>Q</i> <br /> ¬<i>P</i> ← ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn1011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Venn1011.svg/100px-Venn1011.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Venn1011.svg/150px-Venn1011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1e/Venn1011.svg/200px-Venn1011.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td></tr> <tr> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E5%91%BD%E9%A2%98" title="命题">命題P</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn0101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Venn0101.svg/100px-Venn0101.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/10/Venn0101.svg/150px-Venn0101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/10/Venn0101.svg/200px-Venn0101.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E5%90%A6%E5%AE%9A" class="mw-redirect" title="否定">非P</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;">¬<i>P</i><br />~<i>P</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn1010.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Venn1010.svg/100px-Venn1010.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Venn1010.svg/150px-Venn1010.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Venn1010.svg/200px-Venn1010.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td></tr> <tr> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E5%8F%8D%E9%9D%9E%E8%95%B4%E6%B6%B5" class="mw-redirect" title="反非蕴涵">反非蘊涵</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acf12661d69611db01ff7f036bf8c5b5dfec902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftarrow }"></span> <i>Q</i> <br /> <i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \subset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊄</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \subset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5b8e16e392d3856efb6355f906bf3d7b35f7f2ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.676ex;" alt="{\displaystyle \not \subset }"></span> <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> ↓ ¬<i>Q</i> <br /> ¬<i>P</i> & <i>Q</i> <br /> ¬<i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb95f3f5a9898c871045935a253d1d23e0e2644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \rightarrow }"></span> ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn0010.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Venn0010.svg/100px-Venn0010.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Venn0010.svg/150px-Venn0010.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Venn0010.svg/200px-Venn0010.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E5%8F%8D%E8%95%B4%E6%B6%B5" class="mw-redirect" title="反蕴涵">反蘊涵</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftarrow }"></span> <i>Q</i> <br /> <i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \subset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊂</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \subset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f51f0eeff0c2a9dcb9c856f87ca0359e701ef01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle \subset }"></span> <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> ∨ ¬<i>Q</i> <br /> ¬<i>P</i> ↑ <i>Q</i> <br /> ¬<i>P</i> → ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn1101.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Venn1101.svg/100px-Venn1101.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/35/Venn1101.svg/150px-Venn1101.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/35/Venn1101.svg/200px-Venn1101.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td></tr> <tr> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E5%91%BD%E9%A2%98" title="命题">命題Q</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn0011.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Venn0011.svg/100px-Venn0011.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Venn0011.svg/150px-Venn0011.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/76/Venn0011.svg/200px-Venn0011.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E5%90%A6%E5%AE%9A" class="mw-redirect" title="否定">非Q</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;">¬<i>Q</i><br />~<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn1100.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Venn1100.svg/100px-Venn1100.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/31/Venn1100.svg/150px-Venn1100.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/31/Venn1100.svg/200px-Venn1100.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td></tr> <tr> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E9%80%BB%E8%BE%91%E5%BC%82%E6%88%96" title="逻辑异或">異或</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363ed81fd02da85c658dde9f17737c13b7263e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftrightarrow }"></span> <i>Q</i> <br /> <i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \equiv }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≢</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \equiv }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d130bfc3eff6deb5c732a636f866cd9e373c197" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.676ex;" alt="{\displaystyle \not \equiv }"></span> <i>Q</i> <br /> <i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b16e2bdaefee9eed86d866e6eba3ac47c710f60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \oplus }"></span> <i>Q</i><br /><i>P</i> XOR <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> ↔ ¬<i>Q</i> <br /> ¬<i>P</i> ↔ <i>Q</i> <br /> ¬<i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363ed81fd02da85c658dde9f17737c13b7263e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftrightarrow }"></span> ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn0110.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Venn0110.svg/100px-Venn0110.svg.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/46/Venn0110.svg/150px-Venn0110.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/46/Venn0110.svg/200px-Venn0110.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E9%80%BB%E8%BE%91%E5%8F%8C%E6%9D%A1%E4%BB%B6" class="mw-redirect" title="逻辑双条件">雙條件</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> ↔ <i>Q</i> <br /> <i>P</i> ≡ <i>Q</i><br /><i>P</i> XNOR <i>Q</i><br /> <i>P</i> IFF <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363ed81fd02da85c658dde9f17737c13b7263e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftrightarrow }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↮</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/363ed81fd02da85c658dde9f17737c13b7263e49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftrightarrow }"></span> <i>Q</i> <br /> ¬<i>P</i> ↔ ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn1001.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Venn1001.svg/100px-Venn1001.svg.png" decoding="async" width="100" height="73" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Venn1001.svg/150px-Venn1001.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Venn1001.svg/200px-Venn1001.svg.png 2x" data-file-width="410" data-file-height="299" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td></tr> <tr> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E9%80%BB%E8%BE%91%E6%9E%90%E5%8F%96" class="mw-redirect" title="逻辑析取">析取</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> ∨ <i>Q</i><br /><i>P</i> <sub>∨</sub> <i>Q</i><br /><i>P</i> OR <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftarrow }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> → <i>Q</i> <br /> ¬<i>P</i> ↑ ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn0111.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/100px-Venn0111.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/150px-Venn0111.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/30/Venn0111.svg/200px-Venn0111.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td> <td> <table style="border-collapse: collapse; margin-left: auto; margin-right: auto; border: 1px solid black; margin-bottom: 1em;"> <tbody><tr> <td colspan="4" style="text-align: center; font-weight: bold; background-color: #ccccff;"><a href="/wiki/%E9%80%BB%E8%BE%91%E6%88%96%E9%9D%9E" title="逻辑或非">或非</a> </td></tr> <tr> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">符號 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em; width: 1in;" nowrap="">等價公式 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">真值表 </td> <td style="text-align: center; border: 1px solid black; background-color: #eee; padding-left: 1em; padding-right: 1em;" nowrap="">文氏圖 </td></tr> <tr> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> ↓ <i>Q</i><br /><i>P</i> NOR <i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4acf12661d69611db01ff7f036bf8c5b5dfec902" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \leftarrow }"></span> ¬<i>Q</i> <br /> ¬<i>P</i> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb95f3f5a9898c871045935a253d1d23e0e2644b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \not \rightarrow }"></span> <i>Q</i> <br /> ¬<i>P</i> ∧ ¬<i>Q</i> </td> <td style="border: 1px solid black; padding: 0.5em; background-color: white; padding-left: 1em; padding-right: 1em;"> <table style="border-collapse: collapse; text-align: center;"> <tbody><tr> <td rowspan="2" colspan="2" style="border: 1px solid black;">  </td> <td colspan="2" style="text-align:center;"><b>Q</b> </td></tr> <tr> <td style="padding: 4pt;">0 </td> <td style="padding: 4pt;">1 </td></tr> <tr> <td rowspan="2" style="vertical-align: middle;"><b>P</b> </td> <td>0   </td> <td style="border: 1px solid black; padding: .75em; background: #ffaaaa;"> 1  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr> <tr> <td style="padding: 4pt;">1   </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td> <td style="border: 1px solid black; padding: .75em;"> 0  </td></tr></tbody></table> </td> <td style="border: 1px solid black; padding: 0.5em; text-align: center; background-color: white; padding-left: 1em; padding-right: 1em;"><span typeof="mw:File"><a href="/wiki/File:Venn1000.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Venn1000.svg/100px-Venn1000.svg.png" decoding="async" width="100" height="74" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Venn1000.svg/150px-Venn1000.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3c/Venn1000.svg/200px-Venn1000.svg.png 2x" data-file-width="380" data-file-height="280" /></a></span> </td></tr></tbody></table> <p><br /> </p><p><br /> </p><p><br /> </p> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="圖-{}-示"><span id=".E5.9C.96-.7B.7D-.E7.A4.BA"></span>圖示</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&action=edit&section=3" title="编辑章节：圖示"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><table style="background:transparent;text-align:center;"> <tbody><tr> <th><a href="/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8" title="真值表">真值表</a> </th> <th> </th> <th><a href="/wiki/%E5%93%88%E6%96%AF%E5%9C%96" title="哈斯圖">哈斯圖</a> </th></tr> <tr> <td><figure class="noresize" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/380px-Logical_connectives_table.svg.png" decoding="async" width="380" height="493" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/570px-Logical_connectives_table.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/760px-Logical_connectives_table.svg.png 2x" data-file-width="547" data-file-height="710" usemap="#ImageMap_51764bf5fcc3702a" /></span><map name="ImageMap_51764bf5fcc3702a"><area href="/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8" shape="rect" coords="277,1,376,27" alt="input A" title="input A" /><area href="/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8" shape="rect" coords="278,27,375,51" alt="input B" title="input B" /><area href="/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8" shape="rect" coords="278,89,376,490" alt="output f(A,B)" title="output f(A,B)" /><area href="/wiki/%E7%9F%9B%E7%9B%BE%E5%BC%8F" shape="rect" coords="2,89,276,113" alt="X and ¬X" title="X and ¬X" /><area href="/wiki/%E9%80%BB%E8%BE%91%E4%B8%8E" shape="rect" coords="2,113,276,138" alt="A and B" title="A and B" /><area href="/wiki/%E5%8F%8D%E9%9D%9E%E8%98%8A%E6%B6%B5" shape="rect" coords="2,138,276,163" alt="¬A and B" title="¬A and B" /><area href="/wiki/%E5%91%BD%E9%A2%98" shape="rect" coords="3,163,277,190" alt="B" title="B" /><area href="/wiki/%E5%AE%9E%E8%B4%A8%E9%9D%9E%E8%95%B4%E6%B6%B5" shape="rect" coords="2,190,276,215" alt="A and ¬B" title="A and ¬B" /><area href="/wiki/%E5%91%BD%E9%A2%98" shape="rect" coords="1,214,276,239" alt="A" title="A" /><area href="/wiki/%E9%80%BB%E8%BE%91%E5%BC%82%E6%88%96" shape="rect" coords="1,239,275,263" alt="A xor B" title="A xor B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E6%88%96" shape="rect" coords="1,263,276,288" alt="A or B" title="A or B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E6%88%96%E9%9D%9E" shape="rect" coords="2,291,275,315" alt="¬A and ¬B" title="¬A and ¬B" /><area href="/wiki/%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93" shape="rect" coords="2,315,274,340" alt="A xnor B" title="A xnor B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E9%9D%9E" shape="rect" coords="2,340,275,365" alt="¬A" title="¬A" /><area href="/wiki/%E5%AE%9E%E8%B4%A8%E6%9D%A1%E4%BB%B6" shape="rect" coords="2,365,275,389" alt="¬A or B" title="¬A or B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E9%9D%9E" shape="rect" coords="2,391,276,417" alt="¬B" title="¬B" /><area href="/wiki/%E5%8F%8D%E8%98%8A%E6%B6%B5" shape="rect" coords="1,417,274,442" alt="A or ¬B" title="A or ¬B" /><area href="/wiki/%E8%B0%A2%E8%B4%B9%E5%B0%94%E7%AB%96%E7%BA%BF" shape="rect" coords="1,440,276,466" alt="¬A or ¬B" title="¬A or ¬B" /><area href="/wiki/%E9%87%8D%E8%A8%80%E5%BC%8F" shape="rect" coords="2,465,276,490" alt="X or ¬X" title="X or ¬X" /></map><figcaption></figcaption></figure> </td> <td width="50pt"> </td> <td><figure class="noresize" typeof="mw:File"><span><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/350px-Logical_connectives_Hasse_diagram.svg.png" decoding="async" width="350" height="495" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/525px-Logical_connectives_Hasse_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/700px-Logical_connectives_Hasse_diagram.svg.png 2x" data-file-width="744" data-file-height="1052" usemap="#ImageMap_b748e3b7f2340c02" /></span><map name="ImageMap_b748e3b7f2340c02"><area href="/wiki/%E9%87%8D%E8%A8%80%E5%BC%8F" shape="rect" coords="153,13,196,94" alt="X or ¬X" title="X or ¬X" /><area href="/wiki/%E8%B0%A2%E8%B4%B9%E5%B0%94%E7%AB%96%E7%BA%BF" shape="rect" coords="38,110,78,192" alt="¬A or ¬B" title="¬A or ¬B" /><area href="/wiki/%E5%8F%8D%E8%98%8A%E6%B6%B5" shape="rect" coords="122,109,164,192" alt="A or ¬B" title="A or ¬B" /><area href="/wiki/%E5%AE%9E%E8%B4%A8%E6%9D%A1%E4%BB%B6" shape="rect" coords="185,108,226,192" alt="¬A or B" title="¬A or B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E6%88%96" shape="rect" coords="270,109,312,192" alt="A or B" title="A or B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E9%9D%9E" shape="rect" coords="6,205,48,290" alt="¬B" title="¬B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E9%9D%9E" shape="rect" coords="69,206,111,290" alt="¬A" title="¬A" /><area href="/wiki/%E9%80%BB%E8%BE%91%E5%BC%82%E6%88%96" shape="rect" coords="131,207,173,290" alt="A xor B" title="A xor B" /><area href="/wiki/%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93" shape="rect" coords="176,207,218,290" alt="A xnor B" title="A xnor B" /><area href="/wiki/%E5%91%BD%E9%A2%98" shape="rect" coords="239,207,280,290" alt="A" title="A" /><area href="/wiki/%E5%91%BD%E9%A2%98" shape="rect" coords="301,206,344,290" alt="B" title="B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E6%88%96%E9%9D%9E" shape="rect" coords="37,304,79,389" alt="¬A and ¬B" title="¬A and ¬B" /><area href="/wiki/%E5%AE%9E%E8%B4%A8%E9%9D%9E%E8%95%B4%E6%B6%B5" shape="rect" coords="122,304,164,389" alt="A and ¬B" title="A and ¬B" /><area href="/wiki/%E5%8F%8D%E9%9D%9E%E8%98%8A%E6%B6%B5" shape="rect" coords="184,304,227,389" alt="¬A and B" title="¬A and B" /><area href="/wiki/%E9%80%BB%E8%BE%91%E4%B8%8E" shape="rect" coords="270,304,312,389" alt="A and B" title="A and B" /><area href="/wiki/%E7%9F%9B%E7%9B%BE%E5%BC%8F" shape="rect" coords="154,401,196,487" alt="X and ¬X" title="X and ¬X" /></map><figcaption></figcaption></figure> </td></tr></tbody></table></dd></dl> <div style="clear:both;"></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r84265675">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output .hlist .mw-empty-li{display:none}.mw-parser-output .hlist dt::after{content:" :"}.mw-parser-output .hlist dd::after,.mw-parser-output .hlist li::after{content:" · ";font-weight:bold}.mw-parser-output .hlist-pipe dd::after,.mw-parser-output .hlist-pipe li::after{content:" | ";font-weight:normal}.mw-parser-output .hlist-hyphen dd::after,.mw-parser-output .hlist-hyphen li::after{content:" - ";font-weight:normal}.mw-parser-output .hlist-comma dd::after,.mw-parser-output .hlist-comma li::after{content:"、";font-weight:normal}.mw-parser-output .hlist dd:last-child::after,.mw-parser-output .hlist dt:last-child::after,.mw-parser-output .hlist li:last-child::after{content:none}.mw-parser-output .hlist ol{counter-reset:listitem}.mw-parser-output .hlist ol>li{counter-increment:listitem}.mw-parser-output .hlist ol>li::before{content:" "counter(listitem)"\a0 "}.mw-parser-output .hlist dd ol>li:first-child::before,.mw-parser-output .hlist dt ol>li:first-child::before,.mw-parser-output .hlist li ol>li:first-child::before{content:"（"counter(listitem)"\a0 "}.mw-parser-output ul.cslist,.mw-parser-output ul.sslist{margin:0;padding:0;display:inline-block;list-style:none}.mw-parser-output .cslist li,.mw-parser-output .sslist li{margin:0;display:inline-block}.mw-parser-output .cslist li::after{content:"，"}.mw-parser-output .sslist li::after{content:"；"}.mw-parser-output .cslist li:last-child::after,.mw-parser-output .sslist li:last-child::after{content:none}</style><style data-mw-deduplicate="TemplateStyles:r84261037">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{text-align:center;padding-left:1em;padding-right:1em}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output .navbox-subgroup{background-color:#fdfdfd}.mw-parser-output .navbox-list{border-color:#fdfdfd}.mw-parser-output .navbox-list-with-group{text-align:left;border-left-width:2px;border-left-style:solid}.mw-parser-output tr+tr>.navbox-abovebelow,.mw-parser-output tr+tr>.navbox-group,.mw-parser-output tr+tr>.navbox-image,.mw-parser-output tr+tr>.navbox-list{border-top:2px solid #fdfdfd}.mw-parser-output .navbox-title{background-color:#ccf;position:relative}.mw-parser-output .navbox-abovebelow,.mw-parser-output .navbox-group,.mw-parser-output .navbox-subgroup .navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em;width:auto;padding-left:0.2em;position:absolute;left:1em}.mw-parser-output .navbox .mw-collapsible-toggle{margin-left:0.5em;position:absolute;right:1em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="逻辑联结词" style="padding:3px"><table class="nowraplinks hlist mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84244141">.mw-parser-output .navbar{display:inline;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:110%;margin:0 8em}.mw-parser-output .navbar-ct-mini{font-size:110%;margin:0 5em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E9%80%BB%E8%BE%91%E8%81%94%E7%BB%93%E8%AF%8D" title="Template:逻辑联结词"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/w/index.php?title=Template_talk:%E9%80%BB%E8%BE%91%E8%81%94%E7%BB%93%E8%AF%8D&action=edit&redlink=1" class="new" title="Template talk:逻辑联结词（页面不存在）"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E9%80%BB%E8%BE%91%E8%81%94%E7%BB%93%E8%AF%8D" title="Special:编辑页面/Template:逻辑联结词"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="逻辑联结词" style="font-size:110%;margin:0 5em"><a class="mw-selflink selflink">逻辑联结词</a></div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%81%86%E7%9C%9F%E5%BC%8F" title="恆真式">恆真</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \top }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊤</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \top }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf12e436fef2365e76fcb1034a51179d8328bb33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \top }"></span>）</li></ul> </div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Logical_connectives_Hasse_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/100px-Logical_connectives_Hasse_diagram.svg.png" decoding="async" width="100" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/150px-Logical_connectives_Hasse_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/200px-Logical_connectives_Hasse_diagram.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%B0%A2%E8%B4%B9%E5%B0%94%E7%AB%96%E7%BA%BF" title="谢费尔竖线">与非</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \uparrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↑</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \uparrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddb20b28c74cdaa09e1f101d426441da1996072f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \uparrow }"></span>）</li> <li><a href="/wiki/%E5%AE%9E%E8%B4%A8%E6%9D%A1%E4%BB%B6" title="实质条件">反蕴涵</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftarrow }"></span>）</li> <li><a href="/wiki/%E5%AE%9E%E8%B4%A8%E6%9D%A1%E4%BB%B6" title="实质条件">蕴涵</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e574cc3aa5b4bf5f3f5906caf121a378eef08b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightarrow }"></span>）</li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E6%88%96" title="逻辑或">或</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span>）</li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%80%BB%E8%BE%91%E9%9D%9E" title="逻辑非">非</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa78fd02085d39aa58c9e47a6d4033ce41e02fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.204ex; margin-bottom: -0.376ex; width:1.55ex; height:1.176ex;" alt="{\displaystyle \neg }"></span>）</li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E5%BC%82%E6%88%96" title="逻辑异或">异或</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \oplus }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊕</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \oplus }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8b16e2bdaefee9eed86d866e6eba3ac47c710f60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \oplus }"></span>）</li> <li><a href="/wiki/%E5%BD%93%E4%B8%94%E4%BB%85%E5%BD%93" title="当且仅当">双条件</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"></span>）</li> <li><a href="/wiki/%E5%91%BD%E9%A2%98%E9%80%BB%E8%BE%91" title="命题逻辑">命题</a></li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%80%BB%E8%BE%91%E6%88%96%E9%9D%9E" title="逻辑或非">或非</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \downarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↓</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \downarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4618f22b0f780805eb94bb407578d9bc9487947a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \downarrow }"></span>）</li> <li><a href="/wiki/%E5%AE%9E%E8%B4%A8%E9%9D%9E%E8%95%B4%E6%B6%B5" title="实质非蕴涵">非蕴涵</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c458d67617e028ed10948d2dbcfef80e9e060a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \nrightarrow }"></span>）</li> <li><a href="/wiki/%E5%AE%9E%E8%B4%A8%E9%9D%9E%E8%95%B4%E6%B6%B5" title="实质非蕴涵">反非蕴涵</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nleftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nleftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7694c9fc8eebe8a57c8156dd3c2caf022a619439" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \nleftarrow }"></span>）</li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E4%B8%8E" title="逻辑与">与</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span>）</li></ul> </div></td></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%9F%9B%E7%9B%BE" title="矛盾">恆假</a>（<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \bot }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊥</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \bot }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f282c7bc331cc3bfcf1c57f1452cc23c022f58de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \bot }"></span>）</li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"></div><div role="navigation" class="navbox" aria-labelledby="数理逻辑" style="padding:3px"><table class="nowraplinks mw-collapsible expanded navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91" title="Template:数理逻辑"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91" title="Template talk:数理逻辑"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91" title="Special:编辑页面/Template:数理逻辑"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="数理逻辑" style="font-size:110%;margin:0 5em"><a href="/wiki/%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91" title="数理逻辑">数理逻辑</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%">基本概念</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%85%AC%E7%90%86" title="公理">公理</a> <ul><li><a href="/wiki/%E5%85%AC%E7%90%86%E5%88%97%E8%A1%A8" title="公理列表">列表</a></li></ul></li> <li><a href="/wiki/%E5%8A%BF_(%E6%95%B0%E5%AD%A6)" title="势 (数学)">势</a></li> <li><a href="/wiki/%E4%B8%80%E9%98%B6%E9%80%BB%E8%BE%91" title="一阶逻辑">一阶逻辑</a></li> <li><span class="ilh-all" data-orig-title="形式证法" data-lang-code="en" data-lang-name="英语" data-foreign-title="Formal proof"><span class="ilh-page"><a href="/w/index.php?title=%E5%BD%A2%E5%BC%8F%E8%AF%81%E6%B3%95&action=edit&redlink=1" class="new" title="形式证法（页面不存在）">形式证法</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Formal_proof" class="extiw" title="en:Formal proof"><span lang="en" dir="auto">Formal proof</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%82%8F%E8%BC%AF%E8%AA%9E%E7%BE%A9%E5%AD%B8" title="邏輯語義學">邏輯語義學</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%9F%BA%E7%A1%80" title="数学基础">数学基础</a></li> <li><a href="/wiki/%E4%BF%A1%E6%81%AF%E8%AE%BA" title="信息论">信息论</a></li> <li><a href="/wiki/%E8%95%B4%E6%B6%B5" title="蕴涵">蕴涵</a></li> <li><a href="/wiki/%E7%BB%93%E6%9E%84_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)" title="结构 (数理逻辑)">结构</a></li> <li><a href="/wiki/%E9%9B%86%E5%90%88_(%E6%95%B0%E5%AD%A6)" title="集合 (数学)">集合</a></li> <li><a href="/wiki/%E5%AE%9A%E7%90%86" title="定理">定理</a></li> <li><a href="/wiki/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F" title="公理系统">形式理论</a></li> <li><a href="/wiki/%E7%B1%BB%E5%9E%8B%E8%AE%BA" title="类型论">类型论</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">定理<br />（<span class="ilh-all" data-orig-title="Category:数学基础定理" data-lang-code="en" data-lang-name="英语" data-foreign-title="Category:Theorems in the foundations of mathematics"><span class="ilh-page"><a href="/w/index.php?title=Category:%E6%95%B0%E5%AD%A6%E5%9F%BA%E7%A1%80%E5%AE%9A%E7%90%86&action=edit&redlink=1" class="new" title="Category:数学基础定理（页面不存在）">列表</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Category:Theorems_in_the_foundations_of_mathematics" class="extiw" title="en:Category:Theorems in the foundations of mathematics"><span lang="en" dir="auto">Category:Theorems in the foundations of mathematics</span></a></span>）</span></span>及<span class="ilh-all" data-orig-title="集合论悖论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Paradoxes of set theory"><span class="ilh-page"><a href="/w/index.php?title=%E9%9B%86%E5%90%88%E8%AE%BA%E6%82%96%E8%AE%BA&action=edit&redlink=1" class="new" title="集合论悖论（页面不存在）">悖论</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Paradoxes_of_set_theory" class="extiw" title="en:Paradoxes of set theory"><span lang="en" dir="auto">Paradoxes of set theory</span></a></span>）</span></span>）</th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="nowrap"><a href="/wiki/%E5%93%A5%E5%BE%B7%E5%B0%94%E5%AE%8C%E5%A4%87%E6%80%A7%E5%AE%9A%E7%90%86" title="哥德尔完备性定理">哥德尔完备性定理</a>及<a href="/wiki/%E5%93%A5%E5%BE%B7%E5%B0%94%E4%B8%8D%E5%AE%8C%E5%A4%87%E5%AE%9A%E7%90%86" title="哥德尔不完备定理">哥德尔不完备定理</a></span></li> <li><a href="/wiki/%E5%A1%94%E6%96%AF%E5%9F%BA%E4%B8%8D%E5%8F%AF%E5%AE%9A%E7%BE%A9%E5%AE%9A%E7%90%86" title="塔斯基不可定義定理">塔斯基不可定義定理</a></li> <li><a href="/wiki/%E5%B7%B4%E6%8B%BF%E8%B5%AB-%E5%A1%94%E6%96%AF%E5%9F%BA%E5%AE%9A%E7%90%86" title="巴拿赫-塔斯基定理">巴拿赫-塔斯基定理</a></li> <li><span class="nowrap">康托尔 <a href="/wiki/%E5%BA%B7%E6%89%98%E5%B0%94%E5%AE%9A%E7%90%86" title="康托尔定理">定理</a>、<a href="/wiki/%E5%BA%B7%E6%89%98%E5%B0%94%E6%82%96%E8%AE%BA" title="康托尔悖论">悖论</a>和<a href="/wiki/%E5%B0%8D%E8%A7%92%E8%AB%96%E8%AD%89%E6%B3%95" title="對角論證法">對角論證法</a></span></li> <li><a href="/wiki/%E7%B4%A7%E8%87%B4%E6%80%A7%E5%AE%9A%E7%90%86" title="紧致性定理">紧致性定理</a></li> <li><a href="/wiki/%E5%81%9C%E6%9C%BA%E9%97%AE%E9%A2%98" title="停机问题">停机问题</a></li> <li><span class="ilh-all" data-orig-title="林德斯特伦定理" data-lang-code="en" data-lang-name="英语" data-foreign-title="Lindström's theorem"><span class="ilh-page"><a href="/w/index.php?title=%E6%9E%97%E5%BE%B7%E6%96%AF%E7%89%B9%E4%BC%A6%E5%AE%9A%E7%90%86&action=edit&redlink=1" class="new" title="林德斯特伦定理（页面不存在）">林德斯特伦定理</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Lindstr%C3%B6m%27s_theorem" class="extiw" title="en:Lindström's theorem"><span lang="en" dir="auto">Lindström's theorem</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%8B%92%E6%96%87%E6%B5%B7%E5%A7%86%E2%80%93%E6%96%AF%E7%A7%91%E4%BC%A6%E5%AE%9A%E7%90%86" title="勒文海姆–斯科伦定理">勒文海姆–斯科伦定理</a></li> <li><a href="/wiki/%E7%BD%97%E7%B4%A0%E6%82%96%E8%AE%BA" title="罗素悖论">罗素悖论</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%80%BB%E8%BE%91" title="逻辑">逻辑</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="传统逻辑" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E4%BC%A0%E7%BB%9F%E9%80%BB%E8%BE%91" title="传统逻辑">传统逻辑</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%82%8F%E8%BC%AF%E7%9C%9F%E7%90%86" title="邏輯真理">邏輯真理</a></li> <li><a href="/wiki/%E6%81%86%E7%9C%9F%E5%BC%8F" title="恆真式">恆真式</a></li> <li><a href="/wiki/%E5%91%BD%E9%A2%98" title="命题">命题</a></li> <li><a href="/wiki/%E6%8E%A8%E7%90%86" title="推理">推理</a></li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E7%AD%89%E4%BB%B7" title="逻辑等价">逻辑等价</a></li> <li><a href="/wiki/%E4%B8%80%E8%87%B4%E6%80%A7_(%E9%82%8F%E8%BC%AF)" title="一致性 (邏輯)">一致性</a> <ul><li><span class="ilh-all" data-orig-title="相同一致性" data-lang-code="en" data-lang-name="英语" data-foreign-title="Equiconsistency"><span class="ilh-page"><a href="/w/index.php?title=%E7%9B%B8%E5%90%8C%E4%B8%80%E8%87%B4%E6%80%A7&action=edit&redlink=1" class="new" title="相同一致性（页面不存在）">相同一致性</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Equiconsistency" class="extiw" title="en:Equiconsistency"><span lang="en" dir="auto">Equiconsistency</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E8%AE%BA%E8%AF%81" title="逻辑论证">逻辑论证</a></li> <li><a href="/wiki/%E5%8F%AF%E9%9D%A0%E6%80%A7%E5%AE%9A%E7%90%86" title="可靠性定理">可靠性定理</a></li> <li><a href="/wiki/%E6%9C%89%E6%95%88%E6%80%A7" title="有效性">有效性</a></li> <li><a href="/wiki/%E7%9B%B4%E8%A8%80%E4%B8%89%E6%AE%B5%E8%AE%BA" title="直言三段论">直言三段论</a></li> <li><a href="/wiki/%E5%AF%B9%E7%AB%8B%E5%9B%9B%E8%BE%B9%E5%BD%A2" title="对立四边形">对立四边形</a></li> <li><a href="/wiki/%E6%96%87%E6%B0%8F%E5%9B%BE" title="文氏图">文氏图</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%91%BD%E9%A2%98%E9%80%BB%E8%BE%91" title="命题逻辑">命题逻辑</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%80%BB%E8%BE%91%E4%BB%A3%E6%95%B0" title="逻辑代数">逻辑代数</a></li> <li><a href="/wiki/%E5%B8%83%E5%B0%94%E5%87%BD%E6%95%B0" title="布尔函数">布尔函数</a></li> <li><a class="mw-selflink selflink">逻辑运算符</a></li> <li><a href="/wiki/%E5%91%BD%E9%A2%98%E9%80%BB%E8%BE%91" title="命题逻辑">命题逻辑</a></li> <li><a href="/wiki/%E5%85%AC%E5%BC%8F_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)" title="公式 (数理逻辑)">命题公式</a></li> <li><a href="/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8" title="真值表">真值表</a></li> <li><a href="/wiki/%E5%A4%9A%E5%80%BC%E9%80%BB%E8%BE%91" title="多值逻辑">多值逻辑</a> <ul><li><a href="/wiki/%E4%B8%89%E5%80%BC%E9%80%BB%E8%BE%91" title="三值逻辑">三值</a></li> <li><span class="ilh-all" data-orig-title="有限值逻辑" data-lang-code="en" data-lang-name="英语" data-foreign-title="Finite-valued logic"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%89%E9%99%90%E5%80%BC%E9%80%BB%E8%BE%91&action=edit&redlink=1" class="new" title="有限值逻辑（页面不存在）">有限值</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Finite-valued_logic" class="extiw" title="en:Finite-valued logic"><span lang="en" dir="auto">Finite-valued logic</span></a></span>）</span></span></li> <li><a href="/wiki/%E6%97%A0%E9%99%90%E5%80%BC%E9%80%BB%E8%BE%91" title="无限值逻辑">无限值</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%BB%8F%E5%85%B8%E9%80%BB%E8%BE%91" title="经典逻辑">经典逻辑</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%BB%8F%E5%85%B8%E9%80%BB%E8%BE%91" title="经典逻辑">经典逻辑</a></li> <li><a href="/wiki/%E4%B8%80%E9%98%B6%E9%80%BB%E8%BE%91" title="一阶逻辑">一阶逻辑</a></li> <li><a href="/wiki/%E4%BA%8C%E9%9A%8E%E9%82%8F%E8%BC%AF" title="二階邏輯">二階邏輯</a> <ul><li><span class="ilh-all" data-orig-title="一元二阶逻辑" data-lang-code="en" data-lang-name="英语" data-foreign-title="Monadic second-order logic"><span class="ilh-page"><a href="/w/index.php?title=%E4%B8%80%E5%85%83%E4%BA%8C%E9%98%B6%E9%80%BB%E8%BE%91&action=edit&redlink=1" class="new" title="一元二阶逻辑（页面不存在）">一元</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Monadic_second-order_logic" class="extiw" title="en:Monadic second-order logic"><span lang="en" dir="auto">Monadic second-order logic</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E9%AB%98%E9%98%B6%E9%80%BB%E8%BE%91" title="高阶逻辑">高阶逻辑</a></li> <li><a href="/wiki/%E8%87%AA%E7%94%B1%E9%80%BB%E8%BE%91" title="自由逻辑">自由逻辑</a></li> <li><a href="/wiki/%E9%87%8F%E5%8C%96_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)" title="量化 (数理逻辑)">量化</a></li> <li><span class="ilh-all" data-orig-title="谓词 (数理逻辑)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Predicate (mathematical logic)"><span class="ilh-page"><a href="/w/index.php?title=%E8%B0%93%E8%AF%8D_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)&action=edit&redlink=1" class="new" title="谓词 (数理逻辑)（页面不存在）">谓词</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Predicate_(mathematical_logic)" class="extiw" title="en:Predicate (mathematical logic)"><span lang="en" dir="auto">Predicate (mathematical logic)</span></a></span>）</span></span></li> <li><a href="/wiki/%E4%B8%80%E5%85%83%E8%B0%93%E8%AF%8D%E6%BC%94%E7%AE%97" title="一元谓词演算">一元谓词演算</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9B%86%E5%90%88%E8%AE%BA" title="集合论">集合论</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%9B%86%E5%90%88_(%E6%95%B0%E5%AD%A6)" title="集合 (数学)">集合</a> <ul><li><span class="ilh-all" data-orig-title="遗传集" data-lang-code="en" data-lang-name="英语" data-foreign-title="Hereditary set"><span class="ilh-page"><a href="/w/index.php?title=%E9%81%97%E4%BC%A0%E9%9B%86&action=edit&redlink=1" class="new" title="遗传集（页面不存在）">遗传集</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Hereditary_set" class="extiw" title="en:Hereditary set"><span lang="en" dir="auto">Hereditary set</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E7%B1%BB_(%E6%95%B0%E5%AD%A6)" title="类 (数学)">类</a></li> <li>（<a href="/wiki/%E5%9F%BA%E6%9C%AC%E5%85%83%E7%B4%A0" title="基本元素">基本</a>）<a href="/wiki/%E5%85%83%E7%B4%A0_(%E6%95%B8%E5%AD%B8)" title="元素 (數學)">元素</a></li> <li><a href="/wiki/%E6%9C%89%E5%BA%8F%E5%AF%B9" title="有序对">有序对</a></li> <li><a href="/wiki/%E5%BA%8F%E6%95%B0" title="序数">序数</a></li> <li><a href="/wiki/%E5%AD%90%E9%9B%86" title="子集">子集</a></li> <li><a href="/wiki/%E7%9B%B8%E7%AD%89" title="相等">相等</a></li> <li><a href="/wiki/%E5%A4%96%E5%BB%B6%E6%80%A7" title="外延性">外延性</a></li> <li><a href="/wiki/%E5%8A%9B%E8%BF%AB" title="力迫">力迫</a></li> <li><a href="/wiki/%E5%85%B3%E7%B3%BB_(%E6%95%B0%E5%AD%A6)" title="关系 (数学)">关系</a> <ul><li><a href="/wiki/%E7%AD%89%E4%BB%B7%E5%85%B3%E7%B3%BB" title="等价关系">等价关系</a></li> <li><a href="/wiki/%E9%9B%86%E5%90%88%E5%88%92%E5%88%86" title="集合划分">集合划分</a></li></ul></li> <li>集合运算 <ul><li><a href="/wiki/%E4%BA%A4%E9%9B%86" title="交集">交集</a></li> <li><a href="/wiki/%E5%B9%B6%E9%9B%86" title="并集">并集</a></li> <li><a href="/wiki/%E8%A1%A5%E9%9B%86" title="补集">补集</a></li> <li><a href="/wiki/%E7%AC%9B%E5%8D%A1%E5%84%BF%E7%A7%AF" title="笛卡儿积">笛卡儿积</a></li> <li><a href="/wiki/%E5%86%AA%E9%9B%86" title="冪集">冪集</a></li> <li><span class="ilh-all" data-orig-title="集合的同一性和关系列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="List of set identities and relations"><span class="ilh-page"><a href="/w/index.php?title=%E9%9B%86%E5%90%88%E7%9A%84%E5%90%8C%E4%B8%80%E6%80%A7%E5%92%8C%E5%85%B3%E7%B3%BB%E5%88%97%E8%A1%A8&action=edit&redlink=1" class="new" title="集合的同一性和关系列表（页面不存在）">同一性</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/List_of_set_identities_and_relations" class="extiw" title="en:List of set identities and relations"><span lang="en" dir="auto">List of set identities and relations</span></a></span>）</span></span></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9B%86%E5%90%88_(%E6%95%B0%E5%AD%A6)" title="集合 (数学)">集合</a>种类</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8F%AF%E6%95%B8%E9%9B%86" title="可數集">可數集</a></li> <li><a href="/wiki/%E4%B8%8D%E5%8F%AF%E6%95%B8%E9%9B%86" title="不可數集">不可數集</a></li> <li><a href="/wiki/%E7%A9%BA%E9%9B%86" title="空集">空集</a></li> <li><span class="ilh-all" data-orig-title="居集" data-lang-code="en" data-lang-name="英语" data-foreign-title="Inhabited set"><span class="ilh-page"><a href="/w/index.php?title=%E5%B1%85%E9%9B%86&action=edit&redlink=1" class="new" title="居集（页面不存在）">居集</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Inhabited_set" class="extiw" title="en:Inhabited set"><span lang="en" dir="auto">Inhabited set</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%8D%95%E5%85%83%E7%B4%A0%E9%9B%86%E5%90%88" title="单元素集合">单元素集合</a></li> <li><a href="/wiki/%E6%9C%89%E9%99%90%E9%9B%86%E5%90%88" title="有限集合">有限集合</a></li> <li><a href="/wiki/%E6%97%A0%E9%99%90%E9%9B%86%E5%90%88" title="无限集合">无限集合</a></li> <li><a href="/wiki/%E4%BC%A0%E9%80%92%E9%9B%86%E5%90%88" title="传递集合">传递集合</a></li> <li><span class="ilh-all" data-orig-title="超滤子 (集合论)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ultrafilter (set theory)"><span class="ilh-page"><a href="/w/index.php?title=%E8%B6%85%E6%BB%A4%E5%AD%90_(%E9%9B%86%E5%90%88%E8%AE%BA)&action=edit&redlink=1" class="new" title="超滤子 (集合论)（页面不存在）">超滤子</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ultrafilter_(set_theory)" class="extiw" title="en:Ultrafilter (set theory)"><span lang="en" dir="auto">Ultrafilter (set theory)</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%80%92%E5%BD%92%E9%9B%86%E5%90%88" title="递归集合">递归集合</a></li> <li><a href="/wiki/%E6%A8%A1%E7%B3%8A%E9%9B%86" title="模糊集">模糊集</a></li> <li><a href="/wiki/%E5%85%A8%E9%9B%86" title="全集">全集</a> <ul><li><span class="ilh-all" data-orig-title="哥德尔可构造全集" data-lang-code="en" data-lang-name="英语" data-foreign-title="Constructible universe"><span class="ilh-page"><a href="/w/index.php?title=%E5%93%A5%E5%BE%B7%E5%B0%94%E5%8F%AF%E6%9E%84%E9%80%A0%E5%85%A8%E9%9B%86&action=edit&redlink=1" class="new" title="哥德尔可构造全集（页面不存在）">可构造全集</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Constructible_universe" class="extiw" title="en:Constructible universe"><span lang="en" dir="auto">Constructible universe</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="格伦迪克全集" data-lang-code="en" data-lang-name="英语" data-foreign-title="Grothendieck universe"><span class="ilh-page"><a href="/w/index.php?title=%E6%A0%BC%E4%BC%A6%E8%BF%AA%E5%85%8B%E5%85%A8%E9%9B%86&action=edit&redlink=1" class="new" title="格伦迪克全集（页面不存在）">格伦迪克全集</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Grothendieck_universe" class="extiw" title="en:Grothendieck universe"><span lang="en" dir="auto">Grothendieck universe</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%86%AF%C2%B7%E8%AF%BA%E4%BC%8A%E6%9B%BC%E5%85%A8%E9%9B%86" title="冯·诺伊曼全集">冯·诺伊曼全集</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%98%A0%E5%B0%84" title="映射">映射</a>与<a href="/wiki/%E5%8A%BF_(%E6%95%B0%E5%AD%A6)" title="势 (数学)">势</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%87%BD%E6%95%B0" title="函数">函数</a>、<a href="/wiki/%E6%98%A0%E5%B0%84" title="映射">映射</a> <ul><li><a href="/wiki/%E5%AE%9A%E4%B9%89%E5%9F%9F" title="定义域">定义域</a></li> <li><a href="/wiki/%E5%88%B0%E8%BE%BE%E5%9F%9F" title="到达域">到达域</a></li> <li><a href="/wiki/%E5%83%8F_(%E6%95%B8%E5%AD%B8)" title="像 (數學)">像</a></li></ul></li> <li><a href="/wiki/%E5%8D%95%E5%B0%84" title="单射">单射</a>、<a href="/wiki/%E6%BB%A1%E5%B0%84" title="满射">满射</a>、<a href="/wiki/%E5%8F%8C%E5%B0%84" title="双射">双射</a></li> <li><a href="/wiki/%E5%BA%B7%E6%89%98%E5%B0%94-%E4%BC%AF%E6%81%A9%E6%96%AF%E5%9D%A6-%E6%96%BD%E7%BD%97%E5%BE%B7%E5%AE%9A%E7%90%86" title="康托尔-伯恩斯坦-施罗德定理">康托尔-伯恩斯坦-施罗德定理</a></li> <li><a href="/wiki/%E5%90%8C%E6%9E%84" title="同构">同构</a></li> <li><a href="/wiki/%E5%93%A5%E5%BE%B7%E5%B0%94%E6%95%B0" title="哥德尔数">哥德尔数</a></li> <li><a href="/wiki/%E5%88%97%E4%B8%BE%E6%B3%95_(%E9%9B%86%E5%90%88%E8%AE%BA)" title="列举法 (集合论)">列举法</a></li> <li><a href="/wiki/%E5%A4%A7%E5%9F%BA%E6%95%B0" title="大基数">大基数</a> <ul><li><a href="/wiki/%E4%B8%8D%E5%8F%AF%E9%81%94%E5%9F%BA%E6%95%B8" title="不可達基數">不可達基數</a></li></ul></li> <li><a href="/wiki/%E9%98%BF%E5%88%97%E5%A4%AB%E6%95%B8" title="阿列夫數">阿列夫數</a></li> <li><a href="/wiki/%E8%BF%90%E7%AE%97" title="运算">运算</a> <ul><li><a href="/wiki/%E4%BA%8C%E5%85%83%E8%BF%90%E7%AE%97" title="二元运算">二元运算</a></li></ul></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">集合理论</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%AD%96%E6%A2%85%E6%B4%9B-%E5%BC%97%E5%85%B0%E5%85%8B%E5%B0%94%E9%9B%86%E5%90%88%E8%AE%BA" title="策梅洛-弗兰克尔集合论">策梅洛-弗兰克尔 (ZFC)</a> <ul><li><a href="/wiki/%E9%80%89%E6%8B%A9%E5%85%AC%E7%90%86" title="选择公理">选择公理</a></li> <li><a href="/wiki/%E8%BF%9E%E7%BB%AD%E7%BB%9F%E5%81%87%E8%AE%BE" title="连续统假设">连续统假设</a></li></ul></li> <li><span class="ilh-all" data-orig-title="广义集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="General set theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%B9%BF%E4%B9%89%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="广义集合论（页面不存在）">广义集合论 (GST)</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/General_set_theory" class="extiw" title="en:General set theory"><span lang="en" dir="auto">General set theory</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="克里普克-普拉克集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Kripke–Platek set theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%85%8B%E9%87%8C%E6%99%AE%E5%85%8B-%E6%99%AE%E6%8B%89%E5%85%8B%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="克里普克-普拉克集合论（页面不存在）">克里普克-普拉克 (KP)</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Kripke%E2%80%93Platek_set_theory" class="extiw" title="en:Kripke–Platek set theory"><span lang="en" dir="auto">Kripke–Platek set theory</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="莫尔斯-凯利集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Morse–Kelley set theory"><span class="ilh-page"><a href="/w/index.php?title=%E8%8E%AB%E5%B0%94%E6%96%AF-%E5%87%AF%E5%88%A9%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="莫尔斯-凯利集合论（页面不存在）">莫尔斯-凯利集合论 (MK)</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Morse%E2%80%93Kelley_set_theory" class="extiw" title="en:Morse–Kelley set theory"><span lang="en" dir="auto">Morse–Kelley set theory</span></a></span>）</span></span></li> <li><a href="/wiki/%E6%9C%B4%E7%B4%A0%E9%9B%86%E5%90%88%E8%AE%BA" title="朴素集合论">朴素集合论</a></li> <li><a href="/wiki/%E6%96%B0%E5%9F%BA%E7%A1%80%E9%9B%86%E5%90%88%E8%AE%BA" title="新基础集合论">新基础集合论</a></li> <li><span class="ilh-all" data-orig-title="塔斯基-格罗滕迪克集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Tarski–Grothendieck set theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%A1%94%E6%96%AF%E5%9F%BA-%E6%A0%BC%E7%BD%97%E6%BB%95%E8%BF%AA%E5%85%8B%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="塔斯基-格罗滕迪克集合论（页面不存在）">塔斯基-格罗滕迪克 (TG)</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Tarski%E2%80%93Grothendieck_set_theory" class="extiw" title="en:Tarski–Grothendieck set theory"><span lang="en" dir="auto">Tarski–Grothendieck set theory</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%86%AF%E8%AF%BA%E4%BC%8A%E6%9B%BC-%E5%8D%9A%E5%86%85%E6%96%AF-%E5%93%A5%E5%BE%B7%E5%B0%94%E9%9B%86%E5%90%88%E8%AE%BA" title="冯诺伊曼-博内斯-哥德尔集合论">冯·诺伊曼-博内斯-哥德尔 (NBG)</a></li> <li><span class="ilh-all" data-orig-title="建构式集合论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Constructive set theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%BB%BA%E6%9E%84%E5%BC%8F%E9%9B%86%E5%90%88%E8%AE%BA&action=edit&redlink=1" class="new" title="建构式集合论（页面不存在）">建构式集合论</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Constructive_set_theory" class="extiw" title="en:Constructive set theory"><span lang="en" dir="auto">Constructive set theory</span></a></span>）</span></span></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><span class="ilh-all" data-orig-title="语法 (逻辑)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Syntax (logic)"><span class="ilh-page"><a href="/w/index.php?title=%E8%AF%AD%E6%B3%95_(%E9%80%BB%E8%BE%91)&action=edit&redlink=1" class="new" title="语法 (逻辑)（页面不存在）">句法</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Syntax_(logic)" class="extiw" title="en:Syntax (logic)"><span lang="en" dir="auto">Syntax (logic)</span></a></span>）</span></span>及<a href="/wiki/%E5%BD%A2%E5%BC%8F%E8%AF%AD%E8%A8%80" title="形式语言">语言</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%AD%97%E6%AF%8D%E8%A1%A8_(%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%A7%91%E5%AD%A6)" title="字母表 (计算机科学)">字母表</a></li> <li><a href="/wiki/%E5%85%83%E6%95%B0" title="元数">元数</a></li> <li><a href="/wiki/%E8%87%AA%E5%8B%95%E6%A9%9F%E7%90%86%E8%AB%96" title="自動機理論">自動機理論</a></li> <li><a href="/wiki/%E5%85%AC%E7%90%86%E6%A8%A1%E5%BC%8F" title="公理模式">公理模式</a></li> <li><a href="/wiki/%E8%A1%A8%E9%81%94%E5%BC%8F" title="表達式">表達式</a> <ul><li><span class="ilh-all" data-orig-title="基础表达式" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ground expression"><span class="ilh-page"><a href="/w/index.php?title=%E5%9F%BA%E7%A1%80%E8%A1%A8%E8%BE%BE%E5%BC%8F&action=edit&redlink=1" class="new" title="基础表达式（页面不存在）">基础表达式</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ground_expression" class="extiw" title="en:Ground expression"><span lang="en" dir="auto">Ground expression</span></a></span>）</span></span></li></ul></li> <li><span class="ilh-all" data-orig-title="通过新的常数和函数名称进行扩展" data-lang-code="en" data-lang-name="英语" data-foreign-title="Extension by new constant and function names"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%9A%E8%BF%87%E6%96%B0%E7%9A%84%E5%B8%B8%E6%95%B0%E5%92%8C%E5%87%BD%E6%95%B0%E5%90%8D%E7%A7%B0%E8%BF%9B%E8%A1%8C%E6%89%A9%E5%B1%95&action=edit&redlink=1" class="new" title="通过新的常数和函数名称进行扩展（页面不存在）">扩展</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Extension_by_new_constant_and_function_names" class="extiw" title="en:Extension by new constant and function names"><span lang="en" dir="auto">Extension by new constant and function names</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%85%B3%E7%B3%BB_(%E6%95%B0%E5%AD%A6)" title="关系 (数学)">关系</a></li> <li>形式 <ul><li><a href="/wiki/%E5%BD%A2%E5%BC%8F%E6%96%87%E6%B3%95" title="形式文法">文法</a></li> <li><a href="/wiki/%E5%BD%A2%E5%BC%8F%E8%AF%AD%E8%A8%80" title="形式语言">语言</a></li> <li><a href="/wiki/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F" title="公理系统">证明</a></li> <li><a href="/wiki/%E5%BD%A2%E5%BC%8F%E7%B3%BB%E7%B5%B1" title="形式系統">系统</a></li> <li><a href="/wiki/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F" title="公理系统">理论</a></li></ul></li> <li><span class="ilh-all" data-orig-title="形成规则" data-lang-code="en" data-lang-name="英语" data-foreign-title="Formation rule"><span class="ilh-page"><a href="/w/index.php?title=%E5%BD%A2%E6%88%90%E8%A7%84%E5%88%99&action=edit&redlink=1" class="new" title="形成规则（页面不存在）">形成规则</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Formation_rule" class="extiw" title="en:Formation rule"><span lang="en" dir="auto">Formation rule</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%90%88%E5%BC%8F%E5%85%AC%E5%BC%8F" title="合式公式">合式公式</a> <ul><li><a href="/wiki/%E5%8E%9F%E5%AD%90%E5%85%AC%E5%BC%8F" title="原子公式">原子公式</a></li> <li><a href="/wiki/%E5%8F%A5%E5%AD%90_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)" title="句子 (数理逻辑)">封闭式</a></li> <li><span class="ilh-all" data-orig-title="基本式" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ground formula"><span class="ilh-page"><a href="/w/index.php?title=%E5%9F%BA%E6%9C%AC%E5%BC%8F&action=edit&redlink=1" class="new" title="基本式（页面不存在）">基本式</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ground_formula" class="extiw" title="en:Ground formula"><span lang="en" dir="auto">Ground formula</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%BC%80%E6%94%BE%E5%8F%A5%E5%AD%90" title="开放句子">开放式</a></li></ul></li> <li><a href="/wiki/%E8%87%AA%E7%94%B1%E5%8F%98%E9%87%8F%E5%92%8C%E7%BA%A6%E6%9D%9F%E5%8F%98%E9%87%8F" title="自由变量和约束变量">自由变量和约束变量</a></li> <li><a href="/wiki/%E5%85%83%E8%AA%9E%E8%A8%80" title="元語言">元語言</a></li> <li><a class="mw-selflink selflink">逻辑运算符</a> <ul><li><a href="/wiki/%E9%80%BB%E8%BE%91%E9%9D%9E" title="逻辑非">¬</a></li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E6%88%96" title="逻辑或">∨</a></li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E4%B8%8E" title="逻辑与">∧</a></li> <li><a href="/wiki/%E5%AE%9E%E8%B4%A8%E6%9D%A1%E4%BB%B6" title="实质条件">→</a></li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E5%8F%8C%E6%9D%A1%E4%BB%B6" class="mw-redirect" title="逻辑双条件">↔</a></li> <li><span class="ilh-all" data-orig-title="逻辑相等" data-lang-code="en" data-lang-name="英语" data-foreign-title="Logical equality"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E7%9B%B8%E7%AD%89&action=edit&redlink=1" class="new" title="逻辑相等（页面不存在）">逻辑相等</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Logical_equality" class="extiw" title="en:Logical equality"><span lang="en" dir="auto">Logical equality</span></a></span>）</span></span></li></ul></li> <li><span class="ilh-all" data-orig-title="谓词 (数理逻辑)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Predicate (mathematical logic)"><span class="ilh-page"><a href="/w/index.php?title=%E8%B0%93%E8%AF%8D_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)&action=edit&redlink=1" class="new" title="谓词 (数理逻辑)（页面不存在）">谓词</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Predicate_(mathematical_logic)" class="extiw" title="en:Predicate (mathematical logic)"><span lang="en" dir="auto">Predicate (mathematical logic)</span></a></span>）</span></span> <ul><li><a href="/wiki/%E6%B3%9B%E5%87%BD%E8%B0%93%E8%AF%8D" title="泛函谓词">泛函谓词</a></li> <li><a href="/wiki/%E8%B0%93%E8%AF%8D%E5%8F%98%E9%87%8F" title="谓词变量">谓词变量</a></li> <li><a href="/wiki/%E5%91%BD%E9%A2%98%E5%8F%98%E9%87%8F" title="命题变量">命题变量</a></li></ul></li> <li><a href="/wiki/%E9%87%8F%E5%8C%96_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)" title="量化 (数理逻辑)">量化</a> <ul><li><a href="/wiki/%E5%AD%98%E5%9C%A8%E9%87%8F%E5%8C%96" title="存在量化">∃</a></li> <li><a href="/wiki/%E5%94%AF%E4%B8%80%E9%87%8F%E5%8C%96" title="唯一量化">!</a></li> <li><a href="/wiki/%E5%85%A8%E7%A7%B0%E9%87%8F%E5%8C%96" title="全称量化">∀</a></li> <li><span class="ilh-all" data-orig-title="量词级别" data-lang-code="en" data-lang-name="英语" data-foreign-title="Quantifier rank"><span class="ilh-page"><a href="/w/index.php?title=%E9%87%8F%E8%AF%8D%E7%BA%A7%E5%88%AB&action=edit&redlink=1" class="new" title="量词级别（页面不存在）">级别</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Quantifier_rank" class="extiw" title="en:Quantifier rank"><span lang="en" dir="auto">Quantifier rank</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E5%8F%A5%E5%AD%90_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)" title="句子 (数理逻辑)">句子</a> <ul><li><a href="/wiki/%E5%8E%9F%E5%AD%90%E5%8F%A5%E5%AD%90" title="原子句子">原子句子</a></li></ul></li> <li><span class="ilh-all" data-orig-title="签名 (逻辑)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Signature (logic)"><span class="ilh-page"><a href="/w/index.php?title=%E7%AD%BE%E5%90%8D_(%E9%80%BB%E8%BE%91)&action=edit&redlink=1" class="new" title="签名 (逻辑)（页面不存在）">逻辑签名</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Signature_(logic)" class="extiw" title="en:Signature (logic)"><span lang="en" dir="auto">Signature (logic)</span></a></span>）</span></span></li> <li><a href="/wiki/%E5%AD%97%E7%AC%A6%E4%B8%B2" title="字符串">字符串</a></li> <li><span class="ilh-all" data-orig-title="替换法 (逻辑)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Substitution (logic)"><span class="ilh-page"><a href="/w/index.php?title=%E6%9B%BF%E6%8D%A2%E6%B3%95_(%E9%80%BB%E8%BE%91)&action=edit&redlink=1" class="new" title="替换法 (逻辑)（页面不存在）">替换法</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Substitution_(logic)" class="extiw" title="en:Substitution (logic)"><span lang="en" dir="auto">Substitution (logic)</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E7%AC%A6%E5%8F%B7%E8%A1%A8" title="逻辑符号表">逻辑符号</a> <ul><li><a href="/wiki/%E5%87%BD%E6%95%B0%E7%AC%A6%E5%8F%B7" class="mw-redirect" title="函数符号">函数符号</a></li> <li><span class="ilh-all" data-orig-title="逻辑常量" data-lang-code="en" data-lang-name="英语" data-foreign-title="Logical constant"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E5%B8%B8%E9%87%8F&action=edit&redlink=1" class="new" title="逻辑常量（页面不存在）">逻辑常量</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Logical_constant" class="extiw" title="en:Logical constant"><span lang="en" dir="auto">Logical constant</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="非逻辑符号" data-lang-code="en" data-lang-name="英语" data-foreign-title="Non-logical symbol"><span class="ilh-page"><a href="/w/index.php?title=%E9%9D%9E%E9%80%BB%E8%BE%91%E7%AC%A6%E5%8F%B7&action=edit&redlink=1" class="new" title="非逻辑符号（页面不存在）">非逻辑符号</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Non-logical_symbol" class="extiw" title="en:Non-logical symbol"><span lang="en" dir="auto">Non-logical symbol</span></a></span>）</span></span></li> <li><a href="/wiki/%E8%AE%8A%E6%95%B8" title="變數">變數</a></li></ul></li> <li><span class="ilh-all" data-orig-title="逻辑术语" data-lang-code="en" data-lang-name="英语" data-foreign-title="Term (logic)"><span class="ilh-page"><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E6%9C%AF%E8%AF%AD&action=edit&redlink=1" class="new" title="逻辑术语（页面不存在）">逻辑术语</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Term_(logic)" class="extiw" title="en:Term (logic)"><span lang="en" dir="auto">Term (logic)</span></a></span>）</span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F" title="公理系统">公理系统</a>示例<br /><span style="font-size:smaller;">（<span class="ilh-all" data-orig-title="一阶理论列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="List of first-order theories"><span class="ilh-page"><a href="/w/index.php?title=%E4%B8%80%E9%98%B6%E7%90%86%E8%AE%BA%E5%88%97%E8%A1%A8&action=edit&redlink=1" class="new" title="一阶理论列表（页面不存在）">列表</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/List_of_first-order_theories" class="extiw" title="en:List of first-order theories"><span lang="en" dir="auto">List of first-order theories</span></a></span>）</span></span>）</span></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="实算术" data-lang-code="en" data-lang-name="英语" data-foreign-title="True arithmetic"><span class="ilh-page"><a href="/w/index.php?title=%E5%AE%9E%E7%AE%97%E6%9C%AF&action=edit&redlink=1" class="new" title="实算术（页面不存在）">实算术</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/True_arithmetic" class="extiw" title="en:True arithmetic"><span lang="en" dir="auto">True arithmetic</span></a></span>）</span></span> <ul><li><a href="/wiki/%E7%9A%AE%E4%BA%9A%E8%AF%BA%E5%85%AC%E7%90%86" title="皮亚诺公理">皮亚诺公理</a></li> <li><span class="ilh-all" data-orig-title="二阶算术" data-lang-code="en" data-lang-name="英语" data-foreign-title="Second-order arithmetic"><span class="ilh-page"><a href="/w/index.php?title=%E4%BA%8C%E9%98%B6%E7%AE%97%E6%9C%AF&action=edit&redlink=1" class="new" title="二阶算术（页面不存在）">二阶</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Second-order_arithmetic" class="extiw" title="en:Second-order arithmetic"><span lang="en" dir="auto">Second-order arithmetic</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="初等函数算术" data-lang-code="en" data-lang-name="英语" data-foreign-title="Elementary function arithmetic"><span class="ilh-page"><a href="/w/index.php?title=%E5%88%9D%E7%AD%89%E5%87%BD%E6%95%B0%E7%AE%97%E6%9C%AF&action=edit&redlink=1" class="new" title="初等函数算术（页面不存在）">初等函数</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Elementary_function_arithmetic" class="extiw" title="en:Elementary function arithmetic"><span lang="en" dir="auto">Elementary function arithmetic</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="原始递归算术" data-lang-code="en" data-lang-name="英语" data-foreign-title="Primitive recursive arithmetic"><span class="ilh-page"><a href="/w/index.php?title=%E5%8E%9F%E5%A7%8B%E9%80%92%E5%BD%92%E7%AE%97%E6%9C%AF&action=edit&redlink=1" class="new" title="原始递归算术（页面不存在）">原始递归</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Primitive_recursive_arithmetic" class="extiw" title="en:Primitive recursive arithmetic"><span lang="en" dir="auto">Primitive recursive arithmetic</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="罗宾逊算术" data-lang-code="en" data-lang-name="英语" data-foreign-title="Robinson arithmetic"><span class="ilh-page"><a href="/w/index.php?title=%E7%BD%97%E5%AE%BE%E9%80%8A%E7%AE%97%E6%9C%AF&action=edit&redlink=1" class="new" title="罗宾逊算术（页面不存在）">罗宾逊算术</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Robinson_arithmetic" class="extiw" title="en:Robinson arithmetic"><span lang="en" dir="auto">Robinson arithmetic</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="斯科勒姆算术" data-lang-code="en" data-lang-name="英语" data-foreign-title="Skolem arithmetic"><span class="ilh-page"><a href="/w/index.php?title=%E6%96%AF%E7%A7%91%E5%8B%92%E5%A7%86%E7%AE%97%E6%9C%AF&action=edit&redlink=1" class="new" title="斯科勒姆算术（页面不存在）">斯科勒姆算术</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Skolem_arithmetic" class="extiw" title="en:Skolem arithmetic"><span lang="en" dir="auto">Skolem arithmetic</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E5%AF%A6%E6%95%B8%E7%9A%84%E6%A7%8B%E9%80%A0" title="實數的構造">實數的構造</a> <ul><li><span class="ilh-all" data-orig-title="塔尔斯基的实数公理化" data-lang-code="en" data-lang-name="英语" data-foreign-title="Tarski's axiomatization of the reals"><span class="ilh-page"><a href="/w/index.php?title=%E5%A1%94%E5%B0%94%E6%96%AF%E5%9F%BA%E7%9A%84%E5%AE%9E%E6%95%B0%E5%85%AC%E7%90%86%E5%8C%96&action=edit&redlink=1" class="new" title="塔尔斯基的实数公理化（页面不存在）">塔尔斯基公理化</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Tarski%27s_axiomatization_of_the_reals" class="extiw" title="en:Tarski's axiomatization of the reals"><span lang="en" dir="auto">Tarski's axiomatization of the reals</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E5%B8%83%E5%B0%94%E4%BB%A3%E6%95%B0" title="布尔代数">布尔代数</a> <ul><li><span class="ilh-all" data-orig-title="布尔代数的正则定义" data-lang-code="en" data-lang-name="英语" data-foreign-title="Boolean algebras canonically defined"><span class="ilh-page"><a href="/w/index.php?title=%E5%B8%83%E5%B0%94%E4%BB%A3%E6%95%B0%E7%9A%84%E6%AD%A3%E5%88%99%E5%AE%9A%E4%B9%89&action=edit&redlink=1" class="new" title="布尔代数的正则定义（页面不存在）">正则定义</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Boolean_algebras_canonically_defined" class="extiw" title="en:Boolean algebras canonically defined"><span lang="en" dir="auto">Boolean algebras canonically defined</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="布尔代数的最小公理" data-lang-code="en" data-lang-name="英语" data-foreign-title="Minimal axioms for Boolean algebra"><span class="ilh-page"><a href="/w/index.php?title=%E5%B8%83%E5%B0%94%E4%BB%A3%E6%95%B0%E7%9A%84%E6%9C%80%E5%B0%8F%E5%85%AC%E7%90%86&action=edit&redlink=1" class="new" title="布尔代数的最小公理（页面不存在）">最小公理</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Minimal_axioms_for_Boolean_algebra" class="extiw" title="en:Minimal axioms for Boolean algebra"><span lang="en" dir="auto">Minimal axioms for Boolean algebra</span></a></span>）</span></span></li></ul></li> <li><span class="ilh-all" data-orig-title="几何基础" data-lang-code="en" data-lang-name="英语" data-foreign-title="Foundations of geometry"><span class="ilh-page"><a href="/w/index.php?title=%E5%87%A0%E4%BD%95%E5%9F%BA%E7%A1%80&action=edit&redlink=1" class="new" title="几何基础（页面不存在）">几何</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Foundations_of_geometry" class="extiw" title="en:Foundations of geometry"><span lang="en" dir="auto">Foundations of geometry</span></a></span>）</span></span> <ul><li><a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="欧几里得几何">欧几里得几何</a></li> <li><a href="/wiki/%E5%87%A0%E4%BD%95%E5%8E%9F%E6%9C%AC" title="几何原本">《原本》</a></li> <li><a href="/wiki/%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E5%85%AC%E7%90%86" title="希尔伯特公理">希尔伯特公理</a></li> <li><a href="/wiki/%E9%9D%9E%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="非欧几里得几何">非欧几里得几何</a></li> <li><span class="ilh-all" data-orig-title="塔尔斯基公理" data-lang-code="en" data-lang-name="英语" data-foreign-title="Tarski's axioms"><span class="ilh-page"><a href="/w/index.php?title=%E5%A1%94%E5%B0%94%E6%96%AF%E5%9F%BA%E5%85%AC%E7%90%86&action=edit&redlink=1" class="new" title="塔尔斯基公理（页面不存在）">塔尔斯基公理</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Tarski%27s_axioms" class="extiw" title="en:Tarski's axioms"><span lang="en" dir="auto">Tarski's axioms</span></a></span>）</span></span></li></ul></li> <li>《<a href="/wiki/%E6%95%B0%E5%AD%A6%E5%8E%9F%E7%90%86" title="数学原理">数学原理</a>》</li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%AF%81%E6%98%8E%E8%AE%BA" title="证明论">证明论</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F" title="公理系统">形式证明</a></li> <li><a href="/wiki/%E8%87%AA%E7%84%B6%E6%BC%94%E7%BB%8E" title="自然演绎">自然演绎</a></li> <li><a href="/wiki/%E8%95%B4%E6%B6%B5" title="蕴涵">蕴涵</a></li> <li><a href="/wiki/%E6%8E%A8%E7%90%86%E8%A7%84%E5%88%99" title="推理规则">推理规则</a></li> <li><a href="/wiki/%E7%9B%B8%E7%BB%A7%E5%BC%8F%E6%BC%94%E7%AE%97" title="相继式演算">相继式演算</a></li> <li><a href="/wiki/%E5%AE%9A%E7%90%86" title="定理">定理</a></li> <li>系统 <ul><li><a href="/wiki/%E5%BD%A2%E5%BC%8F%E7%B3%BB%E7%B5%B1" title="形式系統">形式</a></li> <li><a href="/wiki/%E5%85%AC%E7%90%86%E7%B3%BB%E7%BB%9F" title="公理系统">公理</a></li> <li><a href="/wiki/%E5%BD%A2%E5%BC%8F%E7%B3%BB%E7%B5%B1" title="形式系統">演绎</a></li> <li><a href="/wiki/%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E6%BC%94%E7%BB%8E%E7%B3%BB%E7%BB%9F" title="希尔伯特演绎系统">希尔伯特演绎系统</a> <ul><li><span class="ilh-all" data-orig-title="希尔伯特系统列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="List of Hilbert systems"><span class="ilh-page"><a href="/w/index.php?title=%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9%E7%B3%BB%E7%BB%9F%E5%88%97%E8%A1%A8&action=edit&redlink=1" class="new" title="希尔伯特系统列表（页面不存在）">列表</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/List_of_Hilbert_systems" class="extiw" title="en:List of Hilbert systems"><span lang="en" dir="auto">List of Hilbert systems</span></a></span>）</span></span></li></ul></li></ul></li> <li><span class="ilh-all" data-orig-title="完备理论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Complete theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%AE%8C%E5%A4%87%E7%90%86%E8%AE%BA&action=edit&redlink=1" class="new" title="完备理论（页面不存在）">完备理论</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Complete_theory" class="extiw" title="en:Complete theory"><span lang="en" dir="auto">Complete theory</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%AD%96%E6%A2%85%E6%B4%9B-%E5%BC%97%E5%85%B0%E5%85%8B%E5%B0%94%E9%9B%86%E5%90%88%E8%AE%BA" title="策梅洛-弗兰克尔集合论">ZFC</a>系统的<span class="ilh-all" data-orig-title="独立性 (数理逻辑)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Independence (mathematical logic)"><span class="ilh-page"><a href="/wiki/%E7%8D%A8%E7%AB%8B%E6%80%A7_(%E6%95%B8%E7%90%86%E9%82%8F%E8%BC%AF)" title="獨立性 (數理邏輯)">独立性</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Independence_(mathematical_logic)" class="extiw" title="en:Independence (mathematical logic)"><span lang="en" dir="auto">Independence (mathematical logic)</span></a></span>）</span></span> <ul><li><a href="/wiki/ZFC%E7%B3%BB%E7%B5%B1%E7%84%A1%E6%B3%95%E7%A2%BA%E5%AE%9A%E7%9A%84%E5%91%BD%E9%A1%8C%E5%88%97%E8%A1%A8" title="ZFC系統無法確定的命題列表">列表</a></li></ul></li> <li><span class="ilh-all" data-orig-title="不可能证明" data-lang-code="en" data-lang-name="英语" data-foreign-title="Proof of impossibility"><span class="ilh-page"><a href="/w/index.php?title=%E4%B8%8D%E5%8F%AF%E8%83%BD%E8%AF%81%E6%98%8E&action=edit&redlink=1" class="new" title="不可能证明（页面不存在）">不可能证明</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Proof_of_impossibility" class="extiw" title="en:Proof of impossibility"><span lang="en" dir="auto">Proof of impossibility</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="序数分析" data-lang-code="en" data-lang-name="英语" data-foreign-title="Ordinal analysis"><span class="ilh-page"><a href="/w/index.php?title=%E5%BA%8F%E6%95%B0%E5%88%86%E6%9E%90&action=edit&redlink=1" class="new" title="序数分析（页面不存在）">序数分析</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Ordinal_analysis" class="extiw" title="en:Ordinal analysis"><span lang="en" dir="auto">Ordinal analysis</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%80%86%E6%95%B0%E5%AD%A6" title="逆数学">逆数学</a></li> <li><span class="ilh-all" data-orig-title="自恰理论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Self-verifying theories"><span class="ilh-page"><a href="/w/index.php?title=%E8%87%AA%E6%81%B0%E7%90%86%E8%AE%BA&action=edit&redlink=1" class="new" title="自恰理论（页面不存在）">自恰理论</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Self-verifying_theories" class="extiw" title="en:Self-verifying theories"><span lang="en" dir="auto">Self-verifying theories</span></a></span>）</span></span></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%A8%A1%E5%9E%8B%E8%AE%BA" title="模型论">模型论</a></th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%A7%A3%E9%87%8B_(%E9%82%8F%E8%BC%AF)" title="解釋 (邏輯)">解释</a></li> <li><a href="/wiki/%E7%BB%93%E6%9E%84_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)" title="结构 (数理逻辑)">结构</a> <ul><li><a href="/wiki/%E5%88%9D%E7%AD%89%E7%AD%89%E4%BB%B7" title="初等等价">初等等价</a></li> <li><span class="ilh-all" data-orig-title="有限模型理论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Finite model theory"><span class="ilh-page"><a href="/w/index.php?title=%E6%9C%89%E9%99%90%E6%A8%A1%E5%9E%8B%E7%90%86%E8%AE%BA&action=edit&redlink=1" class="new" title="有限模型理论（页面不存在）">有限模型</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Finite_model_theory" class="extiw" title="en:Finite model theory"><span lang="en" dir="auto">Finite model theory</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%A3%BD%E5%92%8C%E6%A8%A1%E5%9E%8B" title="飽和模型">飽和模型</a></li> <li><a href="/wiki/%E5%AD%90%E7%BB%93%E6%9E%84" title="子结构">子结构</a></li></ul></li> <li><a href="/wiki/%E9%9D%9E%E6%A0%87%E5%87%86%E6%A8%A1%E5%9E%8B" title="非标准模型">非标准模型</a> <ul><li><span class="ilh-all" data-orig-title="非标准的算术模型" data-lang-code="en" data-lang-name="英语" data-foreign-title="Non-standard model of arithmetic"><span class="ilh-page"><a href="/w/index.php?title=%E9%9D%9E%E6%A0%87%E5%87%86%E7%9A%84%E7%AE%97%E6%9C%AF%E6%A8%A1%E5%9E%8B&action=edit&redlink=1" class="new" title="非标准的算术模型（页面不存在）">算术</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Non-standard_model_of_arithmetic" class="extiw" title="en:Non-standard model of arithmetic"><span lang="en" dir="auto">Non-standard model of arithmetic</span></a></span>）</span></span></li></ul></li> <li><span class="ilh-all" data-orig-title="结构图 (数理逻辑)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Diagram (mathematical logic)"><span class="ilh-page"><a href="/w/index.php?title=%E7%BB%93%E6%9E%84%E5%9B%BE_(%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91)&action=edit&redlink=1" class="new" title="结构图 (数理逻辑)（页面不存在）">结构图</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Diagram_(mathematical_logic)" class="extiw" title="en:Diagram (mathematical logic)"><span lang="en" dir="auto">Diagram (mathematical logic)</span></a></span>）</span></span> <ul><li><span class="ilh-all" data-orig-title="基本结构图" data-lang-code="en" data-lang-name="英语" data-foreign-title="Elementary diagram"><span class="ilh-page"><a href="/w/index.php?title=%E5%9F%BA%E6%9C%AC%E7%BB%93%E6%9E%84%E5%9B%BE&action=edit&redlink=1" class="new" title="基本结构图（页面不存在）">基本图</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Elementary_diagram" class="extiw" title="en:Elementary diagram"><span lang="en" dir="auto">Elementary diagram</span></a></span>）</span></span></li></ul></li> <li><span class="ilh-all" data-orig-title="分类理论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Categorical theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%88%86%E7%B1%BB%E7%90%86%E8%AE%BA&action=edit&redlink=1" class="new" title="分类理论（页面不存在）">分类理论</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Categorical_theory" class="extiw" title="en:Categorical theory"><span lang="en" dir="auto">Categorical theory</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="完备模型论" data-lang-code="en" data-lang-name="英语" data-foreign-title="Model complete theory"><span class="ilh-page"><a href="/w/index.php?title=%E5%AE%8C%E5%A4%87%E6%A8%A1%E5%9E%8B%E8%AE%BA&action=edit&redlink=1" class="new" title="完备模型论（页面不存在）">完备模型论</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Model_complete_theory" class="extiw" title="en:Model complete theory"><span lang="en" dir="auto">Model complete theory</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="可满足性" data-lang-code="en" data-lang-name="英语" data-foreign-title="Satisfiability"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%AF%E6%BB%A1%E8%B6%B3%E6%80%A7&action=edit&redlink=1" class="new" title="可满足性（页面不存在）">可满足性</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Satisfiability" class="extiw" title="en:Satisfiability"><span lang="en" dir="auto">Satisfiability</span></a></span>）</span></span></li> <li><a href="/wiki/%E9%82%8F%E8%BC%AF%E8%AA%9E%E7%BE%A9%E5%AD%B8" title="邏輯語義學">邏輯語義學</a></li> <li><span class="ilh-all" data-orig-title="强度 (模型论)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Strength (mathematical logic)"><span class="ilh-page"><a href="/w/index.php?title=%E5%BC%BA%E5%BA%A6_(%E6%A8%A1%E5%9E%8B%E8%AE%BA)&action=edit&redlink=1" class="new" title="强度 (模型论)（页面不存在）">强度</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Strength_(mathematical_logic)" class="extiw" title="en:Strength (mathematical logic)"><span lang="en" dir="auto">Strength (mathematical logic)</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%9C%9F%E7%90%86" title="真理">真理</a> <ul><li><a href="/wiki/%E7%9C%9F%E7%90%86%E7%9A%84%E8%AF%AD%E4%B9%89%E7%90%86%E8%AE%BA" title="真理的语义理论">语义理论</a></li> <li><a href="/wiki/%E7%9C%9F%E7%90%86%E7%9A%84%E8%AF%AD%E4%B9%89%E7%90%86%E8%AE%BA" title="真理的语义理论">塔尔斯基</a></li> <li><a href="/wiki/%E7%9C%9F%E7%90%86%E7%9A%84%E8%AF%AD%E4%B9%89%E7%90%86%E8%AE%BA" title="真理的语义理论">克里普克</a></li></ul></li> <li><a href="/wiki/T-%E6%A8%A1%E5%BC%8F" title="T-模式">T-模式</a></li> <li><span class="ilh-all" data-orig-title="转移原则" data-lang-code="en" data-lang-name="英语" data-foreign-title="Transfer principle"><span class="ilh-page"><a href="/w/index.php?title=%E8%BD%AC%E7%A7%BB%E5%8E%9F%E5%88%99&action=edit&redlink=1" class="new" title="转移原则（页面不存在）">转移原则</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Transfer_principle" class="extiw" title="en:Transfer principle"><span lang="en" dir="auto">Transfer principle</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="真理谓词" data-lang-code="en" data-lang-name="英语" data-foreign-title="Truth predicate"><span class="ilh-page"><a href="/w/index.php?title=%E7%9C%9F%E7%90%86%E8%B0%93%E8%AF%8D&action=edit&redlink=1" class="new" title="真理谓词（页面不存在）">真理谓词</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Truth_predicate" class="extiw" title="en:Truth predicate"><span lang="en" dir="auto">Truth predicate</span></a></span>）</span></span></li> <li><a href="/wiki/%E7%9C%9F%E5%80%BC" title="真值">真值</a></li> <li><a href="/wiki/%E5%9E%8B_(%E6%A8%A1%E5%9E%8B%E8%AE%BA)" title="型 (模型论)">型</a></li> <li><a href="/wiki/%E8%B6%85%E7%A9%8D" title="超積">超積</a></li> <li><a href="/wiki/%E6%9C%89%E6%95%88%E6%80%A7" title="有效性">有效性</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%8F%AF%E8%AE%A1%E7%AE%97%E6%80%A7%E7%90%86%E8%AE%BA" title="可计算性理论">可计算性理论</a></th><td class="navbox-list-with-group navbox-list navbox-even hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%82%B1%E5%A5%87%E6%95%B0" title="邱奇数">邱奇数</a></li> <li><a href="/wiki/%E9%82%B1%E5%A5%87-%E5%9B%BE%E7%81%B5%E8%AE%BA%E9%A2%98" title="邱奇-图灵论题">邱奇-图灵论题</a></li> <li><a href="/wiki/%E9%80%92%E5%BD%92%E5%8F%AF%E6%9E%9A%E4%B8%BE%E9%9B%86%E5%90%88" title="递归可枚举集合">递归可枚举集合</a></li> <li><a href="/wiki/%E5%8F%AF%E8%AE%A1%E7%AE%97%E5%87%BD%E6%95%B0" title="可计算函数">可计算函数</a></li> <li><a href="/wiki/%E9%80%92%E5%BD%92%E9%9B%86%E5%90%88" title="递归集合">递归集合</a></li> <li><a href="/wiki/%E6%B1%BA%E5%AE%9A%E6%80%A7%E5%95%8F%E9%A1%8C" title="決定性問題">決定性問題</a> <ul><li><span class="ilh-all" data-orig-title="可决定性 (逻辑)" data-lang-code="en" data-lang-name="英语" data-foreign-title="Decidability (logic)"><span class="ilh-page"><a href="/w/index.php?title=%E5%8F%AF%E5%86%B3%E5%AE%9A%E6%80%A7_(%E9%80%BB%E8%BE%91)&action=edit&redlink=1" class="new" title="可决定性 (逻辑)（页面不存在）">可决定性</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Decidability_(logic)" class="extiw" title="en:Decidability (logic)"><span lang="en" dir="auto">Decidability (logic)</span></a></span>）</span></span></li> <li><a href="/wiki/%E4%B8%8D%E5%8F%AF%E5%88%A4%E5%AE%9A%E9%97%AE%E9%A2%98" title="不可判定问题">不可决定性</a></li> <li><a href="/wiki/P_(%E8%A4%87%E9%9B%9C%E5%BA%A6)" title="P (複雜度)">P</a></li> <li><a href="/wiki/NP_(%E8%A4%87%E9%9B%9C%E5%BA%A6)" title="NP (複雜度)">NP</a></li> <li><a href="/wiki/P/NP%E9%97%AE%E9%A2%98" title="P/NP问题">P/NP问题</a></li></ul></li> <li><a href="/wiki/%E6%9F%AF%E6%B0%8F%E5%A4%8D%E6%9D%82%E6%80%A7" title="柯氏复杂性">柯氏复杂性</a></li> <li><a href="/wiki/%CE%9B%E6%BC%94%E7%AE%97" title="Λ演算">Λ演算</a></li> <li><a href="/wiki/%E5%8E%9F%E5%A7%8B%E9%80%92%E5%BD%92%E5%87%BD%E6%95%B0" title="原始递归函数">原始递归函数</a></li> <li><a href="/wiki/%E9%80%92%E5%BD%92" title="递归">递归</a></li> <li><a href="/wiki/%E9%80%92%E5%BD%92%E9%9B%86%E5%90%88" title="递归集合">递归集合</a></li> <li><a href="/wiki/%E5%9B%BE%E7%81%B5%E6%9C%BA" title="图灵机">图灵机</a></li> <li><a href="/wiki/%E7%B1%BB%E5%9E%8B%E8%AE%BA" title="类型论">类型论</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">其他相关</th><td class="navbox-list-with-group navbox-list navbox-odd hlist" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><span class="ilh-all" data-orig-title="抽象逻辑" data-lang-code="en" data-lang-name="英语" data-foreign-title="Abstract logic"><span class="ilh-page"><a href="/w/index.php?title=%E6%8A%BD%E8%B1%A1%E9%80%BB%E8%BE%91&action=edit&redlink=1" class="new" title="抽象逻辑（页面不存在）">抽象逻辑</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Abstract_logic" class="extiw" title="en:Abstract logic"><span lang="en" dir="auto">Abstract logic</span></a></span>）</span></span></li> <li><a href="/wiki/%E8%8C%83%E7%95%B4%E8%AE%BA" title="范畴论">范畴论</a></li> <li><a href="/wiki/%E5%85%B7%E9%AB%94%E7%AF%84%E7%96%87" title="具體範疇">具象范畴</a>、<a href="/wiki/%E7%AF%84%E7%96%87_(%E6%95%B8%E5%AD%B8)" title="範疇 (數學)">抽象范畴</a></li> <li><a href="/wiki/%E9%9B%86%E5%90%88%E8%8C%83%E7%95%B4" title="集合范畴">集合范畴</a></li> <li><a href="/wiki/%E9%80%BB%E8%BE%91%E5%8F%B2" title="逻辑史">逻辑史</a></li> <li><a href="/wiki/%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91" title="数理逻辑">数理逻辑</a> <ul><li><span class="ilh-all" data-orig-title="数理逻辑年表" data-lang-code="en" data-lang-name="英语" data-foreign-title="Timeline of mathematical logic"><span class="ilh-page"><a href="/w/index.php?title=%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91%E5%B9%B4%E8%A1%A8&action=edit&redlink=1" class="new" title="数理逻辑年表（页面不存在）">历史年表</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Timeline_of_mathematical_logic" class="extiw" title="en:Timeline of mathematical logic"><span lang="en" dir="auto">Timeline of mathematical logic</span></a></span>）</span></span></li></ul></li> <li><a href="/wiki/%E9%82%8F%E8%BC%AF%E4%B8%BB%E7%BE%A9" title="邏輯主義">邏輯主義</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%AF%B9%E8%B1%A1" title="数学对象">数学对象</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%93%B2%E5%AD%A6" title="数学哲学">数学哲学</a></li> <li><span class="ilh-all" data-orig-title="超任务" data-lang-code="en" data-lang-name="英语" data-foreign-title="Supertask"><span class="ilh-page"><a href="/w/index.php?title=%E8%B6%85%E4%BB%BB%E5%8A%A1&action=edit&redlink=1" class="new" title="超任务（页面不存在）">超任务</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Supertask" class="extiw" title="en:Supertask"><span lang="en" dir="auto">Supertask</span></a></span>）</span></span></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/16px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/24px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/32px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <a href="/wiki/Portal:%E6%95%B0%E5%AD%A6" title="Portal:数学">数学主题</a></b></div></td></tr></tbody></table></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">检索自“<a dir="ltr" href="https://zh.wikipedia.org/w/index.php?title=逻辑运算符&oldid=74670111">https://zh.wikipedia.org/w/index.php?title=逻辑运算符&oldid=74670111</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Special:%E9%A1%B5%E9%9D%A2%E5%88%86%E7%B1%BB" title="Special:页面分类">分类</a>：<ul><li><a href="/wiki/Category:%E5%B8%83%E5%B0%94%E4%BB%A3%E6%95%B0" title="Category:布尔代数">布尔代数</a></li><li><a href="/wiki/Category:%E9%82%8F%E8%BC%AF%E8%81%AF%E7%B5%90%E8%A9%9E" title="Category:邏輯聯結詞">邏輯聯結詞</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">隐藏分类：<ul><li><a href="/wiki/Category:%E8%87%AA2018%E5%B9%B412%E6%9C%88%E7%BC%BA%E5%B0%91%E6%9D%A5%E6%BA%90%E7%9A%84%E6%9D%A1%E7%9B%AE" title="Category:自2018年12月缺少来源的条目">自2018年12月缺少来源的条目</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> 本页面最后修订于2022年11月18日 (星期五) 13:52。</li> <li id="footer-info-copyright">本站的全部文字在<a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.zh">知识共享署名-相同方式共享 4.0协议</a>之条款下提供，附加条款亦可能应用。（请参阅<a class="external text" href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Terms_of_Use">使用条款</a>）<br /> Wikipedia®和维基百科标志是<a rel="nofollow" class="external text" href="https://wikimediafoundation.org/zh">维基媒体基金会</a>的注册商标；维基™是维基媒体基金会的商标。<br /> 维基媒体基金会是按美国国內稅收法501(c)(3)登记的<a class="external text" href="https://donate.wikimedia.org/wiki/Special:MyLanguage/Tax_deductibility">非营利慈善机构</a>。<br /></li> </ul> <ul id="footer-places"> <li id="footer-places-privacy"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Privacy_policy">隐私政策</a></li> <li id="footer-places-about"><a href="/wiki/Wikipedia:%E5%85%B3%E4%BA%8E">关于维基百科</a></li> <li id="footer-places-disclaimers"><a href="/wiki/Wikipedia:%E5%85%8D%E8%B4%A3%E5%A3%B0%E6%98%8E">免责声明</a></li> <li id="footer-places-wm-codeofconduct"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Universal_Code_of_Conduct">行为准则</a></li> <li id="footer-places-developers"><a href="https://developer.wikimedia.org">开发者</a></li> <li id="footer-places-statslink"><a href="https://stats.wikimedia.org/#/zh.wikipedia.org">统计</a></li> <li id="footer-places-cookiestatement"><a href="https://foundation.wikimedia.org/wiki/Special:MyLanguage/Policy:Cookie_statement">Cookie声明</a></li> <li id="footer-places-mobileview"><a href="//zh.m.wikipedia.org/w/index.php?title=%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6&mobileaction=toggle_view_mobile" class="noprint stopMobileRedirectToggle">手机版视图</a></li> </ul> <ul id="footer-icons" class="noprint"> <li id="footer-copyrightico"><a href="https://wikimediafoundation.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/static/images/footer/wikimedia-button.svg" width="84" height="29" alt="Wikimedia Foundation" loading="lazy"></a></li> <li id="footer-poweredbyico"><a href="https://www.mediawiki.org/" class="cdx-button cdx-button--fake-button cdx-button--size-large cdx-button--fake-button--enabled"><img src="/w/resources/assets/poweredby_mediawiki.svg" alt="Powered by MediaWiki" width="88" height="31" loading="lazy"></a></li> </ul> </footer> </div> </div> </div> <div class="vector-settings" id="p-dock-bottom"> <ul></ul> </div><script>(RLQ=window.RLQ||[]).push(function(){mw.config.set({"wgHostname":"mw-web.codfw.main-5c59558b9d-zjw24","wgBackendResponseTime":187,"wgPageParseReport":{"limitreport":{"cputime":"0.563","walltime":"0.743","ppvisitednodes":{"value":3435,"limit":1000000},"postexpandincludesize":{"value":512055,"limit":2097152},"templateargumentsize":{"value":8567,"limit":2097152},"expansiondepth":{"value":15,"limit":100},"expensivefunctioncount":{"value":66,"limit":500},"unstrip-depth":{"value":0,"limit":20},"unstrip-size":{"value":26124,"limit":5000000},"entityaccesscount":{"value":0,"limit":400},"timingprofile":["100.00% 401.728 1 -total"," 83.18% 334.173 5 Template:Navbox"," 44.18% 177.466 1 Template:数理逻辑"," 27.13% 109.002 57 Template:Tsl"," 17.89% 71.870 1 Template:逻辑联结词"," 16.96% 68.129 1 Template:Unreferenced"," 15.46% 62.099 1 Template:Ambox"," 14.20% 57.050 1 Template:NoteTA"," 6.75% 27.136 7 Template:Le"," 1.78% 7.162 1 Template:Portal-inline"]},"scribunto":{"limitreport-timeusage":{"value":"0.212","limit":"10.000"},"limitreport-memusage":{"value":6600884,"limit":52428800}},"cachereport":{"origin":"mw-web.eqiad.main-5bcbddc6db-lxhbf","timestamp":"20241127104309","ttl":2592000,"transientcontent":false}}});});</script> <script type="application/ld+json">{"@context":"https:\/\/schema.org","@type":"Article","name":"\u903b\u8f91\u8fd0\u7b97\u7b26","url":"https:\/\/zh.wikipedia.org\/wiki\/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6","sameAs":"http:\/\/www.wikidata.org\/entity\/Q211790","mainEntity":"http:\/\/www.wikidata.org\/entity\/Q211790","author":{"@type":"Organization","name":"\u7ef4\u57fa\u5a92\u4f53\u9879\u76ee\u8d21\u732e\u8005"},"publisher":{"@type":"Organization","name":"Wikimedia Foundation, Inc.","logo":{"@type":"ImageObject","url":"https:\/\/www.wikimedia.org\/static\/images\/wmf-hor-googpub.png"}},"datePublished":"2004-03-20T12:00:45Z","dateModified":"2022-11-18T13:52:52Z"}</script> </body> </html>