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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/?utm_source=donate&utm_medium=sidebar&utm_campaign=spontaneous&uselang=zh-hans"><span>资助维基百科</span></a></li><li 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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-例子" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#例子"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>例子</span> </div> </a> <ul id="toc-例子-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参见" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参见"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>参见</span> </div> </a> <ul id="toc-参见-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-引用" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#引用"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>引用</span> </div> </a> <ul id="toc-引用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-参考" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#参考"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>参考</span> </div> </a> <ul id="toc-参考-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部链接" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部链接"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>外部链接</span> </div> </a> <ul id="toc-外部链接-sublist" class="vector-toc-list"> </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">有效性</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。25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-25" 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">25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%B5%D8%AD%D8%A9_(%D8%A7%D9%84%D9%85%D9%86%D8%B7%D9%82)" title="صحة (المنطق) – 阿拉伯语" lang="ar" hreflang="ar" data-title="صحة (المنطق)" 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-bew mw-list-item"><a href="https://bew.wikipedia.org/wiki/Keacian_(mant%C3%A8k)" title="Keacian (mantèk) – 貝塔維文" lang="bew" hreflang="bew" data-title="Keacian (mantèk)" data-language-autonym="Betawi" data-language-local-name="貝塔維文" class="interlanguage-link-target"><span>Betawi</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%92%D0%B0%D0%BB%D0%B8%D0%B4%D0%BD%D0%BE%D1%81%D1%82" title="Валидност – 保加利亚语" lang="bg" hreflang="bg" data-title="Валидност" 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/Validesa_l%C3%B2gica" title="Validesa lògica – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Validesa 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-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%A8%DA%95%D8%B3%D8%AA_(%D9%84%DB%86%DA%98%DB%8C%DA%A9)" title="بڕست (لۆژیک) – 中库尔德语" lang="ckb" hreflang="ckb" data-title="بڕست (لۆژیک)" data-language-autonym="کوردی" data-language-local-name="中库尔德语" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Allgemeing%C3%BCltigkeit" title="Allgemeingültigkeit – 德语" lang="de" hreflang="de" data-title="Allgemeingültigkeit" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Validity_(logic)" title="Validity (logic) – 英语" lang="en" hreflang="en" data-title="Validity (logic)" 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/Validez_(l%C3%B3gica)" title="Validez (lógica) – 西班牙语" lang="es" hreflang="es" data-title="Validez (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/Kehtivus" title="Kehtivus – 爱沙尼亚语" lang="et" hreflang="et" data-title="Kehtivus" 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-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A7%D8%B9%D8%AA%D8%A8%D8%A7%D8%B1_(%D9%85%D9%86%D8%B7%D9%82)" title="اعتبار (منطق) – 波斯语" lang="fa" hreflang="fa" data-title="اعتبار (منطق)" 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/Validit%C3%A9_(logique)" title="Validité (logique) – 法语" lang="fr" hreflang="fr" data-title="Validité (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%AA%D7%A7%D7%A4%D7%95%D7%AA_(%D7%9C%D7%95%D7%92%D7%99%D7%A7%D7%94)" title="תקפות (לוגיקה) – 希伯来语" lang="he" hreflang="he" data-title="תקפות (לוגיקה)" 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-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Gild_r%C3%B6ksemdaf%C3%A6rsla" title="Gild röksemdafærsla – 冰岛语" lang="is" hreflang="is" data-title="Gild röksemdafærsla" 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/Validit%C3%A0_(logica)" title="Validità (logica) – 意大利语" lang="it" hreflang="it" data-title="Validità (logica)" 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/%E5%A6%A5%E5%BD%93%E6%80%A7" title="妥当性 – 日语" lang="ja" hreflang="ja" data-title="妥当性" 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-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%ED%83%80%EB%8B%B9%EC%84%B1" title="타당성 – 韩语" lang="ko" hreflang="ko" data-title="타당성" 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%92%D0%B0%D0%BB%D0%B8%D0%B4%D0%BD%D0%BE%D1%81%D1%82_(%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0)" title="Валидност (логика) – 马其顿语" lang="mk" hreflang="mk" data-title="Валидност (логика)" 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-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Validade" title="Validade – 葡萄牙语" lang="pt" hreflang="pt" data-title="Validade" 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/Validitate" title="Validitate – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Validitate" 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%9E%D0%B1%D1%89%D0%B5%D0%B7%D0%BD%D0%B0%D1%87%D0%B8%D0%BC%D0%BE%D1%81%D1%82%D1%8C" title="Общезначимость – 俄语" lang="ru" hreflang="ru" data-title="Общезначимость" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Validity" title="Validity – Simple English" lang="en-simple" hreflang="en-simple" data-title="Validity" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%92%D0%B0%D1%99%D0%B0%D0%BD%D0%BE%D1%81%D1%82_(%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0)" title="Ваљаност (логика) – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Ваљаност (логика)" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Giltig_(logik)" title="Giltig (logik) – 瑞典语" lang="sv" hreflang="sv" data-title="Giltig (logik)" 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-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A7%D0%B8%D0%BD%D0%BD%D1%96%D1%81%D1%82%D1%8C" title="Чинність – 乌克兰语" lang="uk" hreflang="uk" data-title="Чинність" 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-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E9%82%8F%E8%BC%AF%E6%95%88%E5%BA%A6" title="邏輯效度 – 粤语" lang="yue" hreflang="yue" data-title="邏輯效度" 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/Q1047000#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/%E6%9C%89%E6%95%88%E6%80%A7" 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:%E6%9C%89%E6%95%88%E6%80%A7" 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</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> <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"><span class="mw-redirectedfrom">（重定向自<a href="/w/index.php?title=%E6%9C%89%E6%95%88%E7%9A%84&redirect=no" class="mw-redirect" title="有效的">有效的</a>）</span></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:r85099211">.mw-parser-output .hatnote{font-size:small}.mw-parser-output div.hatnote{padding-left:2em;margin-bottom:0.8em;margin-top:0.8em}.mw-parser-output .hatnote-notice-img::after{content:"\202f \202f \202f \202f "}.mw-parser-output .hatnote-notice-img-small::after{content:"\202f \202f "}.mw-parser-output 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.ifmobile>.mobile{display:none}body.skin-minerva .mw-parser-output .ifmobile>.nomobile{display:inherit;display:initial}</style><span class="ifmobile"><span class="nomobile">  </span><span class="mobile"></span></span><b>提示</b>：此条目页的主题不是<b><a href="/wiki/%E6%95%88%E5%BA%A6" title="效度">效度</a></b>。</div> <p><a href="/wiki/%E9%80%BB%E8%BE%91%E5%AD%A6" class="mw-redirect" title="逻辑学">逻辑学</a>中，一个演绎<a href="/wiki/%E8%AE%BA%E8%AF%81" class="mw-redirect" title="论证">论证</a>或论据（argument）是「<b>有效的</b>（valid）」，当且仅当它没有所有<a href="/wiki/%E5%89%8D%E6%8F%90" title="前提">前提</a>为真同时结论为假，并且它的结论跟随前提的逻辑，否则它是<b>无效的</b>。<sup id="cite_ref-FOOTNOTEcopi201926_1-0" class="reference"><a href="#cite_note-FOOTNOTEcopi201926-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>一个有效的演绎论证并不必需要它的部分前提或结论为<a href="/wiki/%E7%9C%9F%E5%80%BC" title="真值">真</a>，但是如果它所有的前提为真，那么它的结论必为真。 </p><p>我們可以引入內在矛盾（internally contradictory）的概念來定義「<b>有效性</b>（validity）」：「對於任何論證而言(假設它的所有前提所組成的集合不是內在矛盾的)，如果由它的所有前提以及對於結論的否定所共同組成的語句集合是內在矛盾的，則該論證是有效的。」在定義中之所以有「假設所有的前提所組成的集合不是內在矛盾的」這樣的一個但書，是因為從矛盾的前提可以推導出任何的結論，這一性質在自然演繹法（natural deduction）中是顯然的。 </p><p>一个论证的<b>有效性</b>可以被检验、证明或反驳，并取决于它的逻辑形式<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup>。 </p><p>在形式演繹系統中，一个逻辑<a href="/wiki/WFF" class="mw-redirect" title="WFF">公式</a>被称为是有效的，如果它在所有释义（interpretation）下都是真的。更一般的說，給定一個形式語言 <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span>，當我們說公式 <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 \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> 是有效的，即表示該形式語言 <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> 中的所有釋義 <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> 都是 <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 \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> 的模型(Model)，用符號表示即為：<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 \models _{L}\Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mo>⊨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \models _{L}\Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e0036fd7d59368a986fb21badbed7d105cbb7a6a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.69ex; height:2.843ex;" alt="{\displaystyle \models _{L}\Phi }"></span>。另外，在邏輯學中我們已經約定：對於形式語言 <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> 的所有釋義 <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 I}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>I</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle I}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/535ea7fc4134a31cbe2251d9d3511374bc41be9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.172ex; height:2.176ex;" alt="{\displaystyle I}"></span> 都是空集合 <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> 的模型，所以形式語言 <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span> 中的每一個有效公式 <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 \Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/aed80a2011a3912b028ba32a52dfa57165455f24" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \Phi }"></span> 都是空集合 <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 \phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72b1f30316670aee6270a28334bdf4f5072cdde4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.385ex; height:2.509ex;" alt="{\displaystyle \phi }"></span> 的語意結論（semantic consequence），用符號來表示即為： <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 \phi \models _{L}\Phi }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ϕ</mi> <msub> <mo>⊨</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>L</mi> </mrow> </msub> <mi mathvariant="normal">Φ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \phi \models _{L}\Phi }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a86469d6e18879d231ab0a51cb9c1e22ca2137d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.72ex; height:2.843ex;" alt="{\displaystyle \phi \models _{L}\Phi }"></span>。在某些中文邏輯教科書中，也將「model」翻譯成「釋模」。参见<a href="/wiki/%E6%A8%A1%E5%9E%8B%E8%AE%BA" title="模型论">模型论</a>或<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>。 </p><p>一个<a href="/wiki/%E9%87%8D%E8%A8%80%E5%BC%8F" class="mw-redirect mw-disambig" title="重言式">重言式</a>，或重言公式，是真值泛函有效的。不是所有量化逻辑的有效的公式都是重言式。参见<a href="/wiki/%E7%9C%9F%E5%80%BC%E8%A1%A8" title="真值表">真值表</a>。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="例子"><span id=".E4.BE.8B.E5.AD.90"></span>例子</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%9C%89%E6%95%88%E6%80%A7&action=edit&section=1" title="编辑章节：例子"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>以下的演绎论证是有效的，且前提与结论皆为真。 </p> <dl><dd>人必有一死。</dd> <dd>苏格拉底是人。</dd> <dd>因此，苏格拉底必有一死。</dd></dl> <p>以下的演绎论证也是有效的，但是前提不全是真的。 </p> <dl><dd>猫有九条命。</dd> <dd>苏格拉底是猫。</dd> <dd>因此，苏格拉底有九条命。</dd></dl> <p>形式逻辑中，有效的论证可以表示如下，其中P、Q和A表示未分析的或未解释的句子。 </p> <dl><dd>所有P是Q，</dd> <dd>A是P，</dd> <dd>所以A是Q。</dd></dl> <p>实际论证的有效性可以通过把它转换到一个论证形式中，并接着分析这个论证形式的有效性来确定。（上述论证形式是有效的，参见<a href="/wiki/%E4%B8%89%E6%AE%B5%E8%AE%BA" class="mw-redirect" title="三段论">三段论</a>。） </p> <dl><dd>如果所有P是Q，并且A是P，那么A是Q。</dd></dl> <div class="mw-heading mw-heading2"><h2 id="参见"><span id=".E5.8F.82.E8.A7.81"></span>参见</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%9C%89%E6%95%88%E6%80%A7&action=edit&section=2" title="编辑章节：参见"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%E9%80%BB%E8%BE%91%E6%8E%A8%E8%AE%BA&action=edit&redlink=1" class="new" title="逻辑推论（页面不存在）">逻辑推论</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="引用"><span id=".E5.BC.95.E7.94.A8"></span>引用</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%9C%89%E6%95%88%E6%80%A7&action=edit&section=3" title="编辑章节：引用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist" style="list-style-type: decimal;"> <ol class="references"> <li id="cite_note-FOOTNOTEcopi201926-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEcopi201926_1-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFcopi2019">copi 2019</a>，第26頁.<span class="error harv-error" style="display: none; font-size:100%"> sfn模板錯誤: 無指向目標: CITEREFcopi2019 (<a href="/wiki/Category:%E5%90%AB%E6%9C%89%E5%93%88%E4%BD%9B%E5%8F%82%E8%80%83%E6%96%87%E7%8C%AE%E6%A0%BC%E5%BC%8F%E7%B3%BB%E5%88%97%E6%A8%A1%E6%9D%BF%E9%93%BE%E6%8E%A5%E6%8C%87%E5%90%91%E9%94%99%E8%AF%AF%E7%9A%84%E9%A1%B5%E9%9D%A2" title="Category:含有哈佛参考文献格式系列模板链接指向错误的页面">幫助</a>)</span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><cite class="citation book">Gensler, Harry J., 1945-. Introduction to logic Third. New York. January 6, 2017. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-138-91058-4" title="Special:网络书源/978-1-138-91058-4"><span title="国际标准书号">ISBN</span> 978-1-138-91058-4</a>. <a rel="nofollow" class="external text" href="//www.worldcat.org/oclc/957680480"><span title="OCLC">OCLC 957680480</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%9C%89%E6%95%88%E6%80%A7&rft.au=Gensler%2C+Harry+J.%2C+1945-&rft.btitle=Introduction+to+logic&rft.date=2017-01-06&rft.edition=Third&rft.genre=book&rft.isbn=978-1-138-91058-4&rft.place=New+York&rft_id=info%3Aoclcnum%2F957680480&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="参考"><span id=".E5.8F.82.E8.80.83"></span>参考</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%9C%89%E6%95%88%E6%80%A7&action=edit&section=4" title="编辑章节：参考"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation book">Copi, Irving M.; Cohen, Carl; Rodych, Victor. Introduction to Logic. New York. 2019. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-1-138-50086-0" title="Special:网络书源/978-1-138-50086-0"><span title="国际标准书号">ISBN</span> 978-1-138-50086-0</a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%9C%89%E6%95%88%E6%80%A7&rft.au=Cohen%2C+Carl&rft.au=Rodych%2C+Victor&rft.aufirst=Irving+M.&rft.aulast=Copi&rft.btitle=Introduction+to+Logic&rft.date=2019&rft.genre=book&rft.isbn=978-1-138-50086-0&rft.place=New+York&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="外部链接"><span id=".E5.A4.96.E9.83.A8.E9.93.BE.E6.8E.A5"></span>外部链接</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%9C%89%E6%95%88%E6%80%A7&action=edit&section=5" title="编辑章节：外部链接"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r82655521">.mw-parser-output .side-box{margin:4px 0;box-sizing:border-box;border:1px solid #aaa;font-size:88%;line-height:1.25em;background-color:#f9f9f9;display:flow-root}.mw-parser-output .side-box-abovebelow,.mw-parser-output .side-box-text{padding:0.25em 0.9em}.mw-parser-output .side-box-image{padding:2px 0 2px 0.9em;text-align:center}.mw-parser-output .side-box-imageright{padding:2px 0.9em 2px 0;text-align:center}@media(min-width:500px){.mw-parser-output .side-box-flex{display:flex;align-items:center}.mw-parser-output .side-box-text{flex:1}}@media(min-width:720px){.mw-parser-output .side-box{width:238px}.mw-parser-output .side-box-right{clear:right;float:right;margin-left:1em}.mw-parser-output .side-box-left{margin-right:1em}}</style><div class="side-box side-box-right plainlinks sistersitebox" style="font-size:small;"><style data-mw-deduplicate="TemplateStyles:r82655520">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style> <div class="side-box-flex"> <div class="side-box-image"><span class="noviewer" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/40px-Wiktionary-logo.svg.png" decoding="async" width="40" height="38" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/60px-Wiktionary-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ec/Wiktionary-logo.svg/80px-Wiktionary-logo.svg.png 2x" data-file-width="370" data-file-height="350" /></span></span></div> <div class="side-box-text plainlist">查看<a href="/wiki/%E7%BB%B4%E5%9F%BA%E8%AF%8D%E5%85%B8" title="维基词典">维基词典</a>中的词条「<b><a href="https://zh.wiktionary.org/wiki/Special:Search/%E6%9C%89%E6%95%88%E6%80%A7" class="extiw" title="wikt:Special:Search/有效性">有效性</a></b>」。</div></div> </div> <ul><li><a href="/w/index.php?title=Jon_Barwise&action=edit&redlink=1" class="new" title="Jon Barwise（页面不存在）">Barwise, Jon</a>; <a href="/w/index.php?title=John_Etchemendy&action=edit&redlink=1" class="new" title="John Etchemendy（页面不存在）">Etchemendy, John</a>. <i>Language, Proof and Logic</i> (1999): 42.</li> <li>Beer, Francis A. "<a rel="nofollow" class="external text" href="https://www.tandfonline.com/doi/abs/10.1080/02691729308578683">Validities: A Political Science Perspective</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20221009145842/https://www.tandfonline.com/doi/abs/10.1080/02691729308578683">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）", <i>Social Epistemology</i> 7, 1 (1993): 85-105.</li></ul> <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 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.navbox{display:none!important}}</style></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"><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:%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 class="mw-selflink selflink">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 href="/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="逻辑运算符">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 href="/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="逻辑运算符">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 class="mw-selflink selflink">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 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