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id="toc-Tipologie" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Tipologie"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Tipologie</span> </div> </a> <ul id="toc-Tipologie-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Bibliografia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Bibliografia"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Bibliografia</span> </div> </a> <ul id="toc-Bibliografia-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Voci_correlate" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Voci_correlate"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Voci correlate</span> </div> </a> <ul id="toc-Voci_correlate-sublist" class="vector-toc-list"> </ul> </li> <li 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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="Mostra/Nascondi l'indice" > <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">Mostra/Nascondi l'indice</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">Connettivo logico</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="Vai a una voce in un'altra lingua. Disponibile in 39 lingue" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-39" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">39 lingue</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D8%A7%D8%A8%D8%B7%D8%A9_%D9%85%D9%86%D8%B7%D9%82%D9%8A%D8%A9" title="رابطة منطقية - arabo" lang="ar" hreflang="ar" data-title="رابطة منطقية" data-language-autonym="العربية" data-language-local-name="arabo" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/M%C9%99ntiqi_%C9%99m%C9%99liyyat" title="Məntiqi əməliyyat - azerbaigiano" lang="az" hreflang="az" data-title="Məntiqi əməliyyat" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaigiano" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Логическа операция - bulgaro" lang="bg" hreflang="bg" data-title="Логическа операция" data-language-autonym="Български" data-language-local-name="bulgaro" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Connectiva_l%C3%B2gica" title="Connectiva lògica - catalano" lang="ca" hreflang="ca" data-title="Connectiva lògica" data-language-autonym="Català" data-language-local-name="catalano" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Logisk_operator" title="Logisk operator - danese" lang="da" hreflang="da" data-title="Logisk operator" data-language-autonym="Dansk" data-language-local-name="danese" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Logische_Verkn%C3%BCpfung" title="Logische Verknüpfung - tedesco" lang="de" hreflang="de" data-title="Logische Verknüpfung" data-language-autonym="Deutsch" data-language-local-name="tedesco" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9B%CE%BF%CE%B3%CE%B9%CE%BA%CE%AD%CF%82_%CF%83%CF%85%CE%BD%CE%B1%CF%81%CF%84%CE%AE%CF%83%CE%B5%CE%B9%CF%82" title="Λογικές συναρτήσεις - greco" lang="el" hreflang="el" data-title="Λογικές συναρτήσεις" data-language-autonym="Ελληνικά" data-language-local-name="greco" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Conet%C3%AEv_l%C3%B2gic" title="Conetîv lògic - Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Conetîv lògic" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Logical_connective" title="Logical connective - inglese" lang="en" hreflang="en" data-title="Logical connective" data-language-autonym="English" data-language-local-name="inglese" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Conectiva_l%C3%B3gica" title="Conectiva lógica - spagnolo" lang="es" hreflang="es" data-title="Conectiva lógica" data-language-autonym="Español" data-language-local-name="spagnolo" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Konnektor_(keeleteadus)" title="Konnektor (keeleteadus) - estone" lang="et" hreflang="et" data-title="Konnektor (keeleteadus)" data-language-autonym="Eesti" data-language-local-name="estone" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Lokailu_logiko" title="Lokailu logiko - basco" lang="eu" hreflang="eu" data-title="Lokailu logiko" data-language-autonym="Euskara" data-language-local-name="basco" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%D8%A7%D8%A8%D8%B7_%D9%85%D9%86%D8%B7%D9%82%DB%8C" title="رابط منطقی - persiano" lang="fa" hreflang="fa" data-title="رابط منطقی" data-language-autonym="فارسی" data-language-local-name="persiano" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Connecteur_logique" title="Connecteur logique - francese" lang="fr" hreflang="fr" data-title="Connecteur logique" data-language-autonym="Français" data-language-local-name="francese" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A7%D7%A9%D7%A8_%D7%9C%D7%95%D7%92%D7%99" title="קשר לוגי - ebraico" lang="he" hreflang="he" data-title="קשר לוגי" data-language-autonym="עברית" data-language-local-name="ebraico" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Logikai_m%C5%B1velet" title="Logikai művelet - ungherese" lang="hu" hreflang="hu" data-title="Logikai művelet" data-language-autonym="Magyar" data-language-local-name="ungherese" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%8F%D6%80%D5%A1%D5%B4%D5%A1%D5%A2%D5%A1%D5%B6%D5%A1%D5%AF%D5%A1%D5%B6_%D5%A3%D5%B8%D6%80%D5%AE%D5%B8%D5%B2%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Տրամաբանական գործողություն - armeno" lang="hy" hreflang="hy" data-title="Տրամաբանական գործողություն" data-language-autonym="Հայերեն" data-language-local-name="armeno" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Operator_logika" title="Operator logika - indonesiano" lang="id" hreflang="id" data-title="Operator logika" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiano" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/R%C3%B6ka%C3%B0ger%C3%B0" title="Rökaðgerð - islandese" lang="is" hreflang="is" data-title="Rökaðgerð" data-language-autonym="Íslenska" data-language-local-name="islandese" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E8%AB%96%E7%90%86%E6%BC%94%E7%AE%97" title="論理演算 - giapponese" lang="ja" hreflang="ja" data-title="論理演算" data-language-autonym="日本語" data-language-local-name="giapponese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9F%D1%80%D0%BE%D0%BF%D0%BE%D0%B7%D0%B8%D1%86%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D3%A9%D0%B7%D0%B0%D1%80%D0%B0_%D2%9B%D0%B0%D1%82%D1%8B%D0%BD%D0%B0%D1%81" title="Пропозициялық өзара қатынас - kazako" lang="kk" hreflang="kk" data-title="Пропозициялық өзара қатынас" data-language-autonym="Қазақша" data-language-local-name="kazako" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EB%85%BC%EB%A6%AC_%EC%97%B0%EC%82%B0" title="논리 연산 - coreano" lang="ko" hreflang="ko" data-title="논리 연산" data-language-autonym="한국어" data-language-local-name="coreano" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%BA%D0%B0_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Логичка операција - macedone" lang="mk" hreflang="mk" data-title="Логичка операција" data-language-autonym="Македонски" data-language-local-name="macedone" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pengoperasi_logik" title="Pengoperasi logik - malese" lang="ms" hreflang="ms" data-title="Pengoperasi logik" data-language-autonym="Bahasa Melayu" data-language-local-name="malese" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Logisk_konstant" title="Logisk konstant - norvegese nynorsk" lang="nn" hreflang="nn" data-title="Logisk konstant" data-language-autonym="Norsk nynorsk" data-language-local-name="norvegese nynorsk" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Funktor_zdaniotw%C3%B3rczy" title="Funktor zdaniotwórczy - polacco" lang="pl" hreflang="pl" data-title="Funktor zdaniotwórczy" data-language-autonym="Polski" data-language-local-name="polacco" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Conectivo_l%C3%B3gico" title="Conectivo lógico - portoghese" lang="pt" hreflang="pt" data-title="Conectivo lógico" data-language-autonym="Português" data-language-local-name="portoghese" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Conector_logic" title="Conector logic - rumeno" lang="ro" hreflang="ro" data-title="Conector logic" data-language-autonym="Română" data-language-local-name="rumeno" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0%D1%8F_%D0%BE%D0%BF%D0%B5%D1%80%D0%B0%D1%86%D0%B8%D1%8F" title="Логическая операция - russo" lang="ru" hreflang="ru" data-title="Логическая операция" data-language-autonym="Русский" data-language-local-name="russo" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/V%C3%BDrokov%C3%A1_spojka" title="Výroková spojka - slovacco" lang="sk" hreflang="sk" data-title="Výroková spojka" data-language-autonym="Slovenčina" data-language-local-name="slovacco" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Logisk_operator" title="Logisk operator - svedese" lang="sv" hreflang="sv" data-title="Logisk operator" data-language-autonym="Svenska" data-language-local-name="svedese" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8F%E0%AE%B0%E0%AE%A3_%E0%AE%87%E0%AE%A3%E0%AF%88%E0%AE%AA%E0%AF%8D%E0%AE%AA%E0%AE%BF" title="ஏரண இணைப்பி - tamil" lang="ta" hreflang="ta" data-title="ஏரண இணைப்பி" data-language-autonym="தமிழ்" data-language-local-name="tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%90%D0%BC%D0%B0%D0%BB%D2%B3%D0%BE%D0%B8_%D0%BC%D0%B0%D0%BD%D1%82%D0%B8%D2%9B%D3%A3" title="Амалҳои мантиқӣ - tagico" lang="tg" hreflang="tg" data-title="Амалҳои мантиқӣ" data-language-autonym="Тоҷикӣ" data-language-local-name="tagico" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%95%E0%B8%B1%E0%B8%A7%E0%B8%94%E0%B8%B3%E0%B9%80%E0%B8%99%E0%B8%B4%E0%B8%99%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%95%E0%B8%A3%E0%B8%A3%E0%B8%81%E0%B8%B0" title="ตัวดำเนินการตรรกะ - thailandese" lang="th" hreflang="th" data-title="ตัวดำเนินการตรรกะ" data-language-autonym="ไทย" data-language-local-name="thailandese" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Mant%C4%B1k_ba%C4%9Flac%C4%B1" title="Mantık bağlacı - turco" lang="tr" hreflang="tr" data-title="Mantık bağlacı" data-language-autonym="Türkçe" data-language-local-name="turco" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9B%D0%BE%D0%B3%D1%96%D1%87%D0%BD%D0%B8%D0%B9_%D1%81%D0%BF%D0%BE%D0%BB%D1%83%D1%87%D0%BD%D0%B8%D0%BA" title="Логічний сполучник - ucraino" lang="uk" hreflang="uk" data-title="Логічний сполучник" data-language-autonym="Українська" data-language-local-name="ucraino" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%85%D9%86%D8%B7%D9%82%DB%8C_%D8%B9%D8%A7%D9%85%D9%84" title="منطقی عامل - urdu" lang="ur" hreflang="ur" data-title="منطقی عامل" data-language-autonym="اردو" data-language-local-name="urdu" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E9%80%BB%E8%BE%91%E8%BF%90%E7%AE%97%E7%AC%A6" title="逻辑运算符 - cinese" lang="zh" hreflang="zh" data-title="逻辑运算符" data-language-autonym="中文" data-language-local-name="cinese" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a 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id="contentSub"><div id="mw-content-subtitle"><span class="mw-redirectedfrom">(Reindirizzamento da <strong><a href="/w/index.php?title=Operatori_booleani&redirect=no" class="mw-redirect" title="Operatori booleani">Operatori booleani</a></strong>)</span></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="it" dir="ltr"><p>Un <b>connettivo logico</b> o <b>operatore logico</b> (nel contesto dell'<a href="/wiki/Algebra_di_Boole" title="Algebra di Boole">algebra di Boole</a>, i connettivi logici sono detti anche <b>operatori booleani</b>), è un elemento grammaticale di collegamento che instaura fra due <a href="/wiki/Proposizione_(logica)" title="Proposizione (logica)">proposizioni</a> <i>A</i> e <i>B</i> una qualche relazione che dia origine ad una terza proposizione <i>C</i> con un valore vero o falso, in base ai valori delle due proposizioni fattori ed al carattere del connettivo utilizzato. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Descrizione">Descrizione</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connettivo_logico&veaction=edit&section=1" title="Modifica la sezione Descrizione" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connettivo_logico&action=edit&section=1" title="Edit section's source code: Descrizione"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I connettivi logici possono essere separati da parentesi tonde. Esistono regole di precedenza fra i connettivi logici (dimostrabili col semplice calcolo algebrico), analoghe a quelle esistenti fra le quattro operazioni elementari (secondo le quali la coppia di moltiplicazione e divisione, precedono somma e sottrazione): la negazione precede tutti gli altri connettivi, congiunzione e disgiunzione precedono sia l'implicazione che la doppia implicazione. Le regole di precedenza rendono in molti casi superfluo l'uso delle parentesi tonde, che possono tranquillamente essere omesse. </p> <dl><dd><table class="wikitable" style="text-align:center"> <tbody><tr> <th><i>Operatore</i></th> <th><i>Precedenza</i> </th></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa78fd02085d39aa58c9e47a6d4033ce41e02fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.204ex; margin-bottom: -0.376ex; width:1.55ex; height:1.176ex;" alt="{\displaystyle \neg }"></span></td> <td>1 </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \wedge }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \wedge }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1caa4004cb216ef2930bb12fe805a76870caed94" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \wedge }"></span></td> <td>2 </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \vee }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \vee }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b76220c6805c9b465d6efbc7686c624f49f3023" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \vee }"></span></td> <td>3 </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e574cc3aa5b4bf5f3f5906caf121a378eef08b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightarrow }"></span></td> <td>4 </td></tr> <tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"></span></td> <td>5 </td></tr></tbody></table></dd></dl> <p>Ognuna delle operazioni logiche suddette è efficacemente esplicata nella propria <a href="/wiki/Tabella_della_verit%C3%A0" title="Tabella della verità">tabella della verità</a>, la quale evidenzia i valori risultanti da tutte le possibili combinazioni esistenti fra le due proposizioni di partenza A e B, siano esse vere o false, utilizzando il connettivo dato. Le tavole di verità degli operatori logici sono state formalizzate per la prima volta nel <i><a href="/wiki/Tractatus_logico-philosophicus" title="Tractatus logico-philosophicus">Tractatus logico-philosophicus</a></i> di <a href="/wiki/Ludwig_Wittgenstein" title="Ludwig Wittgenstein">Ludwig Wittgenstein</a>. </p><p>Assunti di base della tavola di verità sono il <a href="/w/index.php?title=Principio_di_determinatezza&action=edit&redlink=1" class="new" title="Principio di determinatezza (la pagina non esiste)">principio di determinatezza</a> e il <a href="/wiki/Principio_di_bivalenza" title="Principio di bivalenza">principio di bivalenza</a>, degli enunciati dichiarativi secondo il quale una proposizione può trovarsi in uno e un solo Stato di verità, e gli Stati di verità possibili che un enunciato può assumere sono soltanto due, "vero" oppure "falso". Entrambi i due principi citati non sono dimostrati né in via deduttiva (dal generale al particolare) né in via induttiva (dal caso particolare a quello generale), e nello stesso tempo non sono negati da nessuna delle logiche matematiche note; si applicano al singolo enunciato elementare atomico, non ulteriormente scomponibile, e non sono da confondere con principi equivalenti ma "binari", cioè che si applicano invece all'insieme di due o più enunciati legati da un connettivo logico: <a href="/wiki/Principio_di_non-contraddizione" class="mw-redirect" title="Principio di non-contraddizione">principio di non-contraddizione</a> (più propriamente <b><a href="/wiki/Antinomia" title="Antinomia">antinomia</a> del mentitore</b>) e <a href="/wiki/Principio_del_terzo_escluso" class="mw-redirect" title="Principio del terzo escluso">principio del terzo escluso</a>. </p><p>Non tutti gli enunciati sono di tipo dichiarativo ovvero atti ad assumere un valore di verità "vero" oppure "falso": già Aristotele affermava che la preghiera è un discorso né vero né falso, quindi irrilevante per la logica. Altro esempio di enunciati non dichiarativi sono quelli modali, caratterizzati dalle parole logiche: "può essere..", "deve necessariamente...", "credo che...", "so che..."; oppure il <a href="/wiki/Paradosso_del_mentitore" title="Paradosso del mentitore">paradosso del mentitore</a>: "il cretese Epimènide dice che tutti i cretesi sono bugiardi", "questa frase è falsa". </p> <figure class="mw-halign-left noresize mw-ext-imagemap-desc-bottom-left" typeof="mw:File"><span title="Tabella connettivi logici"><img alt="Tabella connettivi logici" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/380px-Logical_connectives_table.svg.png" decoding="async" width="380" height="493" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/570px-Logical_connectives_table.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Logical_connectives_table.svg/760px-Logical_connectives_table.svg.png 2x" data-file-width="547" data-file-height="710" usemap="#ImageMap_14166f75052c61ff" resource="/wiki/File:Logical_connectives_table.svg" /></span><map name="ImageMap_14166f75052c61ff"><area href="/wiki/Tabella_della_verit%C3%A0" shape="rect" coords="277,1,376,27" alt="input A" title="input A" /><area href="/wiki/Tabella_della_verit%C3%A0" shape="rect" coords="278,27,375,51" alt="input B" title="input B" /><area href="/wiki/Tabella_della_verit%C3%A0" shape="rect" coords="278,89,376,490" alt="output f(A,B)" title="output f(A,B)" /><area href="/wiki/Contraddizione" shape="rect" coords="2,89,276,113" alt="X and ¬X" title="X and ¬X" /><area href="/wiki/Congiunzione_logica" shape="rect" coords="2,113,276,138" alt="A and B" title="A and B" /><area href="/wiki/Non-implicazione_inversa" shape="rect" coords="2,138,276,163" alt="¬A and B" title="¬A and B" /><area href="/wiki/Proposizione_(logica)" shape="rect" coords="3,163,277,190" alt="B" title="B" /><area href="/wiki/Non-implicazione_materiale" shape="rect" coords="2,190,276,215" alt="A and ¬B" title="A and ¬B" /><area href="/wiki/Proposizione_(logica)" shape="rect" coords="1,214,276,239" alt="A" title="A" /><area href="/wiki/Disgiunzione_esclusiva" shape="rect" coords="1,239,275,263" alt="A xor B" title="A xor B" /><area href="/wiki/Disgiunzione_logica" shape="rect" coords="1,263,276,288" alt="A or B" title="A or B" /><area href="/wiki/NOR_logico" shape="rect" coords="2,291,275,315" alt="¬A and ¬B" title="¬A and ¬B" /><area href="/wiki/Bicondizionale_logica" shape="rect" coords="2,315,274,340" alt="A xnor B" title="A xnor B" /><area href="/wiki/Negazione_(matematica)" shape="rect" coords="2,340,275,365" alt="¬A" title="¬A" /><area href="/wiki/Implicazione_materiale" shape="rect" coords="2,365,275,389" alt="¬A or B" title="¬A or B" /><area href="/wiki/Negazione_(matematica)" shape="rect" coords="2,391,276,417" alt="¬B" title="¬B" /><area href="/wiki/A_or_%C2%ACB" shape="rect" coords="1,417,274,442" alt="A or ¬B" title="A or ¬B" /><area href="/wiki/%C2%ACA_or_%C2%ACB" shape="rect" coords="1,440,276,466" alt="¬A or ¬B" title="¬A or ¬B" /><area href="/wiki/Tautologia" shape="rect" coords="2,465,276,490" alt="X or ¬X" title="X or ¬X" /></map><figcaption>Tabella connettivi logici</figcaption></figure> <figure class="mw-halign-right noresize mw-ext-imagemap-desc-bottom-right" typeof="mw:File"><span title="Diagramma di Hasse"><img alt="Diagramma di Hasse" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/350px-Logical_connectives_Hasse_diagram.svg.png" decoding="async" width="350" height="495" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/525px-Logical_connectives_Hasse_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/700px-Logical_connectives_Hasse_diagram.svg.png 2x" data-file-width="744" data-file-height="1052" usemap="#ImageMap_2425541f41a5b1ee" resource="/wiki/File:Logical_connectives_Hasse_diagram.svg" /></span><map name="ImageMap_2425541f41a5b1ee"><area href="/wiki/Tautologia" shape="rect" coords="153,13,196,94" alt="X or ¬X" title="X or ¬X" /><area href="/wiki/%C2%ACA_or_%C2%ACB" shape="rect" coords="38,110,78,192" alt="¬A or ¬B" title="¬A or ¬B" /><area href="/wiki/A_or_%C2%ACB" shape="rect" coords="122,109,164,192" alt="A or ¬B" title="A or ¬B" /><area href="/wiki/%C2%ACA_or_B" shape="rect" coords="185,108,226,192" alt="¬A or B" title="¬A or B" /><area href="/wiki/Disgiunzione_logica" shape="rect" coords="270,109,312,192" alt="A or B" title="A or B" /><area href="/wiki/Negazione_(matematica)" shape="rect" coords="6,205,48,290" alt="¬B" title="¬B" /><area href="/wiki/Negazione_(matematica)" shape="rect" coords="69,206,111,290" alt="¬A" title="¬A" /><area href="/wiki/Disgiunzione_esclusiva" shape="rect" coords="131,207,173,290" alt="A xor B" title="A xor B" /><area href="/wiki/A_xnor_B" shape="rect" coords="176,207,218,290" alt="A xnor B" title="A xnor B" /><area href="/wiki/Proposizione_(logica)" shape="rect" coords="239,207,280,290" alt="A" title="A" /><area href="/wiki/Proposizione_(logica)" shape="rect" coords="301,206,344,290" alt="B" title="B" /><area href="/wiki/%C2%ACA_and_%C2%ACB" shape="rect" coords="37,304,79,389" alt="¬A and ¬B" title="¬A and ¬B" /><area href="/wiki/A_and_%C2%ACB" shape="rect" coords="122,304,164,389" alt="A and ¬B" title="A and ¬B" /><area href="/wiki/%C2%ACA_and_B" shape="rect" coords="184,304,227,389" alt="¬A and B" title="¬A and B" /><area href="/wiki/Congiunzione_logica" shape="rect" coords="270,304,312,389" alt="A and B" title="A and B" /><area href="/wiki/Contraddizione" shape="rect" coords="154,401,196,487" alt="X and ¬X" title="X and ¬X" /></map><figcaption>Diagramma di Hasse</figcaption></figure> <div style="clear:both;"></div> <div class="mw-heading mw-heading2"><h2 id="Tipologie">Tipologie</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connettivo_logico&veaction=edit&section=2" title="Modifica la sezione Tipologie" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connettivo_logico&action=edit&section=2" title="Edit section's source code: Tipologie"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>I principali connettivi logici <a href="/wiki/Operazione_binaria" title="Operazione binaria">binari</a> sono: </p> <ul><li>la <a href="/wiki/Congiunzione_logica" title="Congiunzione logica">congiunzione logica</a> <i>e</i>, in latino <i>et</i>, in logica <a href="/wiki/Algebra_di_Boole" title="Algebra di Boole">booleana</a> <i>AND</i>, indicata con il simbolo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \land }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∧</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \land }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d6823e5a222eb3ca49672818ac3d13ec607052c4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \land }"></span></li> <li>la <a href="/wiki/Disgiunzione_inclusiva" class="mw-redirect" title="Disgiunzione inclusiva">disgiunzione inclusiva</a> <i>o</i> (talvolta indicato come <i>e/o</i>), in latino <i>vel</i>, in logica <a href="/wiki/Algebra_di_Boole" title="Algebra di Boole">booleana</a> <i>OR</i>, indicata con il simbolo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span></li> <li>la <a href="/wiki/Disgiunzione_esclusiva" title="Disgiunzione esclusiva">disgiunzione esclusiva</a> <i>o</i> o <i>o... o...</i>, in latino <i>aut</i>, in logica booleana <i>XOR</i>, indicata dal simbolo <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 {\dot {\lor }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>∨</mo> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\lor }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dabfe21c610b4dcebabbe36e8c9be20f2ae2dcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.509ex;" alt="{\displaystyle {\dot {\lor }}}"></span> oppure <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \not \equiv }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≢</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \not \equiv }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7d130bfc3eff6deb5c732a636f866cd9e373c197" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.809ex; height:2.676ex;" alt="{\displaystyle \not \equiv }"></span></li> <li>l'<a href="/wiki/Implicazione_logica" title="Implicazione logica">implicazione logica</a> <i>se ... allora ...</i> indicata col simbolo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/469b737d167b9b28a74e27c7f5e35b5ea9256100" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Rightarrow }"></span> oppure <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \supset }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>⊃</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \supset }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/27bfe0828a2ed4c9c6b70987a85c02a1f005843c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:1.843ex;" alt="{\displaystyle \supset }"></span></li> <li>la <a href="/wiki/Implicazione_logica#Coimplicazione" title="Implicazione logica">coimplicazione</a> o doppia implicazione <i><a href="/wiki/Se_e_solo_se" title="Se e solo se">se e solo se</a></i> indicata col simbolo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64812e13399c20cf3ce94e049d3bb2d85f26abcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \Leftrightarrow }"></span> oppure <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 \equiv }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>≡</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \equiv }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c5c34250859b6f6d2a77b4e8a2ceaa90638076d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.081ex; margin-bottom: -0.253ex; width:1.808ex; height:1.509ex;" alt="{\displaystyle \equiv }"></span></li></ul> <p>Spesso si annovera inoltre fra i connettivi logici la <a href="/wiki/Negazione_(matematica)" title="Negazione (matematica)">negazione logica</a> "non", indicata con il simbolo <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa78fd02085d39aa58c9e47a6d4033ce41e02fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.204ex; margin-bottom: -0.376ex; width:1.55ex; height:1.176ex;" alt="{\displaystyle \neg }"></span> la quale agisce però su un'<a href="/wiki/Operazione_unaria" title="Operazione unaria">unica</a> proposizione, mentre gli altri connettivi logici si dicono appunto binari perché operano su almeno due proposizioni. </p> <div class="mw-heading mw-heading2"><h2 id="Bibliografia">Bibliografia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connettivo_logico&veaction=edit&section=3" title="Modifica la sezione Bibliografia" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connettivo_logico&action=edit&section=3" title="Edit section's source code: Bibliografia"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><cite class="citation libro" style="font-style:normal"> Lloyd Humberstone, <span style="font-style:italic;">The Connectives</span>, Cambridge (MA), The MIT Press, 2011, <a href="/wiki/ISBN" title="ISBN">ISBN</a> <a href="/wiki/Speciale:RicercaISBN/978-0-262-01654-4" title="Speciale:RicercaISBN/978-0-262-01654-4">978-0-262-01654-4</a>.</cite></li></ul> <div class="mw-heading mw-heading2"><h2 id="Voci_correlate">Voci correlate</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connettivo_logico&veaction=edit&section=4" title="Modifica la sezione Voci correlate" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connettivo_logico&action=edit&section=4" title="Edit section's source code: Voci correlate"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Algebra_di_Boole" title="Algebra di Boole">Algebra di Boole</a></li> <li><a href="/wiki/Congiunzione_logica" title="Congiunzione logica">Congiunzione logica</a></li> <li><a href="/wiki/Mappa_di_Karnaugh" title="Mappa di Karnaugh">Mappa di Karnaugh</a></li> <li><a href="/wiki/Operazioni_booleane_sui_poligoni" title="Operazioni booleane sui poligoni">Operazioni booleane sui poligoni</a></li> <li><a href="/wiki/Operazione_bit_a_bit" title="Operazione bit a bit">Operazione bit a bit</a></li> <li><a href="/wiki/Porta_logica" title="Porta logica">Porta logica</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Altri_progetti">Altri progetti</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connettivo_logico&veaction=edit&section=5" title="Modifica la sezione Altri progetti" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connettivo_logico&action=edit&section=5" title="Edit section's source code: Altri progetti"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="interProject" class="toccolours" style="display: none; clear: both; margin-top: 2em"><p id="sisterProjects" style="background-color: #efefef; color: black; font-weight: bold; margin: 0"><span>Altri progetti</span></p><ul title="Collegamenti verso gli altri progetti Wikimedia"> <li class="" title=""><a href="https://it.wiktionary.org/wiki/connettivo_logico" class="extiw" title="wikt:connettivo logico">Wikizionario</a></li></ul></div> <ul><li><span typeof="mw:File"><a href="https://it.wiktionary.org/wiki/" title="Collabora a Wikizionario"><img alt="Collabora a Wikizionario" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/18px-Wiktionary_small.svg.png" decoding="async" width="18" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/27px-Wiktionary_small.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f9/Wiktionary_small.svg/36px-Wiktionary_small.svg.png 2x" data-file-width="350" data-file-height="350" /></a></span> <a href="https://it.wiktionary.org/wiki/" class="extiw" title="wikt:">Wikizionario</a> contiene il lemma di dizionario «<b><a href="https://it.wiktionary.org/wiki/connettivo_logico" class="extiw" title="wikt:connettivo logico">connettivo logico</a></b>»</li></ul> <div class="mw-heading mw-heading2"><h2 id="Collegamenti_esterni">Collegamenti esterni</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Connettivo_logico&veaction=edit&section=6" title="Modifica la sezione Collegamenti esterni" class="mw-editsection-visualeditor"><span>modifica</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Connettivo_logico&action=edit&section=6" title="Edit section's source code: Collegamenti esterni"><span>modifica wikitesto</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li class="mw-empty-elt"></li> <li><cite id="CITEREFMathWorld" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Eric W. Weisstein, <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Connective.html"><span style="font-style:italic;">Connettivo logico</span></a>, su <span style="font-style:italic;"><a href="/wiki/MathWorld" title="MathWorld">MathWorld</a></span>, Wolfram Research.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q211790#P2812" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFSpringerEOM" class="citation web" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) <a rel="nofollow" class="external text" href="https://encyclopediaofmath.org/wiki/Propositional_connective"><span style="font-style:italic;">Connettivo logico</span></a>, su <span style="font-style:italic;"><a href="/wiki/Encyclopaedia_of_Mathematics" title="Encyclopaedia of Mathematics">Encyclopaedia of Mathematics</a></span>, Springer e European Mathematical Society.</cite> <span class="mw-valign-text-top noprint" typeof="mw:File/Frameless"><a href="https://www.wikidata.org/wiki/Q211790#P7554" title="Modifica su Wikidata"><img alt="Modifica su Wikidata" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/10px-Blue_pencil.svg.png" decoding="async" width="10" height="10" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/15px-Blue_pencil.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/73/Blue_pencil.svg/20px-Blue_pencil.svg.png 2x" data-file-width="600" data-file-height="600" /></a></span></li> <li><cite id="CITEREFSEP-connectives-logic" class="citation testo" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) Lloyd Humberstone, <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/connectives-logic/"><span style="font-style:italic;">Sentence Connectives in Formal Logic</span></a>, in Edward N. Zalta (a cura di), <span style="font-style:italic;"><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></span>, Center for the Study of Language and Information (CSLI), <a href="/wiki/Universit%C3%A0_di_Stanford" title="Università di Stanford">Università di Stanford</a>.</cite></li> <li><cite id="CITEREFSEP-david-lewis" class="citation testo" style="font-style:normal">(<span style="font-weight:bolder; font-size:80%"><abbr title="inglese">EN</abbr></span>) John MacFarlane, <a rel="nofollow" class="external text" href="http://plato.stanford.edu/entries/david-lewis/"><span style="font-style:italic;">Logical constants</span></a>, in Edward N. Zalta (a cura di), <span style="font-style:italic;"><a href="/wiki/Stanford_Encyclopedia_of_Philosophy" title="Stanford Encyclopedia of Philosophy">Stanford Encyclopedia of Philosophy</a></span>, Center for the Study of Language and Information (CSLI), <a href="/wiki/Universit%C3%A0_di_Stanford" title="Università di Stanford">Università di Stanford</a>.</cite></li></ul> <style data-mw-deduplicate="TemplateStyles:r141815314">.mw-parser-output .navbox{border:1px solid #aaa;clear:both;margin:auto;padding:2px;width:100%}.mw-parser-output .navbox th{padding-left:1em;padding-right:1em;text-align:center}.mw-parser-output .navbox>tbody>tr:first-child>th{background:#ccf;font-size:90%;width:100%;color:var(--color-base,black)}.mw-parser-output .navbox_navbar{float:left;margin:0;padding:0 10px 0 0;text-align:left;width:6em}.mw-parser-output .navbox_title{font-size:110%}.mw-parser-output .navbox_abovebelow{background:#ddf;font-size:90%;font-weight:normal}.mw-parser-output .navbox_group{background:#ddf;font-size:90%;padding:0 10px;white-space:nowrap}.mw-parser-output .navbox_list{font-size:90%;width:100%}.mw-parser-output .navbox_list a{white-space:nowrap}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_odd{background:#fdfdfd;color:var(--color-base,black)}html:not(.vector-feature-night-mode-enabled) .mw-parser-output .navbox_even{background:#f7f7f7;color:var(--color-base,black)}.mw-parser-output .navbox a.mw-selflink{color:var(--color-base,black)}.mw-parser-output .navbox_center{text-align:center}.mw-parser-output .navbox .navbox_image{padding-left:7px;vertical-align:middle;width:0}.mw-parser-output .navbox+.navbox{margin-top:-1px}.mw-parser-output .navbox .mw-collapsible-toggle{font-weight:normal;text-align:right;width:7em}body.skin--responsive .mw-parser-output .navbox_image img{max-width:none!important}.mw-parser-output .subnavbox{margin:-3px;width:100%}.mw-parser-output .subnavbox_group{background:#e6e6ff;padding:0 10px}@media screen{html.skin-theme-clientpref-night .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-night .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-night .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-night .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbox>tbody>tr:first-child>th{background:var(--background-color-interactive)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox th{color:var(--color-base)!important}html.skin-theme-clientpref-os .mw-parser-output .navbox_abovebelow,html.skin-theme-clientpref-os .mw-parser-output .navbox_group{background:var(--background-color-interactive-subtle)!important}html.skin-theme-clientpref-os .mw-parser-output .subnavbox_group{background:var(--background-color-neutral-subtle)!important}}</style><table class="navbox mw-collapsible mw-collapsed noprint metadata" id="navbox-Connettivi_logici"><tbody><tr><th colspan="3"><div class="navbox_navbar"><div class="noprint plainlinks" style="background-color:transparent; padding:0; font-size:xx-small; color:var(--color-base, #000000); white-space:nowrap;"><a href="/wiki/Template:Connettivi_logici" title="Template:Connettivi logici"><span title="Vai alla pagina del template">V</span></a> · <a href="/wiki/Discussioni_template:Connettivi_logici" title="Discussioni template:Connettivi logici"><span title="Discuti del template">D</span></a> · <a class="external text" href="https://it.wikipedia.org/w/index.php?title=Template:Connettivi_logici&action=edit"><span title="Modifica il template. Usa l'anteprima prima di salvare">M</span></a></div></div><span class="navbox_title"><a class="mw-selflink selflink">Connettivi logici</a></span></th></tr><tr><td colspan="2" class="navbox_list navbox_center navbox_odd"><a href="/wiki/Tautologia" title="Tautologia">Tautologia ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \top }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">⊤</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \top }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf12e436fef2365e76fcb1034a51179d8328bb33" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.808ex; height:2.176ex;" alt="{\displaystyle \top }"></span> )</a></td><td rowspan="5" class="navbox_image"><span typeof="mw:File"><a href="/wiki/File:Logical_connectives_Hasse_diagram.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/100px-Logical_connectives_Hasse_diagram.svg.png" decoding="async" width="100" height="141" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/150px-Logical_connectives_Hasse_diagram.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Logical_connectives_Hasse_diagram.svg/200px-Logical_connectives_Hasse_diagram.svg.png 2x" data-file-width="744" data-file-height="1052" /></a></span></td></tr><tr><td colspan="2" class="navbox_list navbox_center navbox_even"><a href="/wiki/NAND" class="mw-redirect" title="NAND">Non-congiunzione ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \uparrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↑</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \uparrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ddb20b28c74cdaa09e1f101d426441da1996072f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \uparrow }"></span> )</a><b> ·</b> <a href="/wiki/Implicazione_inversa" title="Implicazione inversa">Implicazione inversa ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">←</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c0fb4bce772117bbaf55b7ca1539ceff9ae218c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftarrow }"></span> )</a><b> ·</b> <a href="/wiki/Implicazione_logica" title="Implicazione logica">Implicazione ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">→</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53e574cc3aa5b4bf5f3f5906caf121a378eef08b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \rightarrow }"></span> )</a><b> ·</b> <a href="/wiki/Disgiunzione_logica" title="Disgiunzione logica">Disgiunzione inclusiva ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \lor }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∨</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lor }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab47f6b1f589aedcf14638df1d63049d233d851a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.009ex;" alt="{\displaystyle \lor }"></span> )</a></td></tr><tr><td colspan="2" class="navbox_list navbox_center navbox_odd"><a href="/wiki/Negazione_(matematica)" title="Negazione (matematica)">Negazione ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \neg }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">¬</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \neg }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fa78fd02085d39aa58c9e47a6d4033ce41e02fad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.204ex; margin-bottom: -0.376ex; width:1.55ex; height:1.176ex;" alt="{\displaystyle \neg }"></span> )</a><b> ·</b> <a href="/wiki/Disgiunzione_esclusiva" title="Disgiunzione esclusiva">Disgiunzione esclusiva ( <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 {\dot {\lor }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mo>∨</mo> <mo>˙</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\dot {\lor }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4dabfe21c610b4dcebabbe36e8c9be20f2ae2dcb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.509ex;" alt="{\displaystyle {\dot {\lor }}}"></span> )</a><b> ·</b> <a href="/wiki/Implicazione_logica#Coimplicazione" title="Implicazione logica">Doppia implicazione ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \leftrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↔</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \leftrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/046b918c43e05caf6624fe9b676c69ec9cd6b892" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.324ex; height:1.843ex;" alt="{\displaystyle \leftrightarrow }"></span> )</a><b> ·</b> <a href="/wiki/Proposizione_(logica)" title="Proposizione (logica)">Proposizione</a></td></tr><tr><td colspan="2" class="navbox_list navbox_center navbox_even"><a href="/wiki/Non-disgiunzione_inclusiva" title="Non-disgiunzione inclusiva">Non-disgiunzione inclusiva ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \downarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">↓</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \downarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4618f22b0f780805eb94bb407578d9bc9487947a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.162ex; height:2.509ex;" alt="{\displaystyle \downarrow }"></span> )</a><b> ·</b> <a href="/wiki/Non-implicazione" title="Non-implicazione">Non-implicazione ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nrightarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↛</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nrightarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c458d67617e028ed10948d2dbcfef80e9e060a2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; margin-bottom: -0.308ex; width:2.324ex; height:1.509ex;" alt="{\displaystyle \nrightarrow }"></span> )</a><b> ·</b> <a href="/wiki/Non-implicazione_inversa" title="Non-implicazione inversa">Non-implicazione inversa ( <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \nleftarrow }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>↚</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nleftarrow }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7694c9fc8eebe8a57c8156dd3c2caf022a619439" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: 0.137ex; 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