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10px; -webkit-border-radius: 10px; border-radius: 10px;"> <tbody><tr style="padding:3px; border-collapse:collapse;"> <td colspan="2"><figure class="mw-halign-left" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_miscellaneous.svg" class="mw-file-description" title="lezione"><img alt="lezione" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Nuvola_apps_edu_miscellaneous.svg/30px-Nuvola_apps_edu_miscellaneous.svg.png" decoding="async" width="30" height="30" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Nuvola_apps_edu_miscellaneous.svg/45px-Nuvola_apps_edu_miscellaneous.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Nuvola_apps_edu_miscellaneous.svg/60px-Nuvola_apps_edu_miscellaneous.svg.png 2x" data-file-width="128" data-file-height="128" /></a><figcaption>lezione</figcaption></figure> <div style="background-color:#CADFF5; border-bottom:1px solid #5090B0; font-weight:bold;">Calcolo proposizionale</div> </td></tr> <tr style="padding:2px; border-collapse:collapse'"> <td><span typeof="mw:File"><a href="/wiki/File:Fileshare.png" class="mw-file-description" title="Tipo di risorsa"><img alt="Tipo di risorsa" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Fileshare.png/35px-Fileshare.png" decoding="async" width="35" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Fileshare.png/53px-Fileshare.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Fileshare.png/70px-Fileshare.png 2x" data-file-width="256" data-file-height="256" /></a></span> </td> <td><b><a href="/wiki/Wikiversit%C3%A0:Risorsa#Tipi_di_risorsa" title="Wikiversità:Risorsa">Tipo</a></b>: lezione </td></tr> <tr style="padding:2px; border-collapse:collapse;"> <td style="border-top:1px solid #5090B0;border-collapse:collapse;"><span typeof="mw:File"><a href="/wiki/File:Gnome-applications-office.svg" class="mw-file-description" title="Materia di appartenenza"><img alt="Materia di appartenenza" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Gnome-applications-office.svg/35px-Gnome-applications-office.svg.png" decoding="async" width="35" height="35" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Gnome-applications-office.svg/53px-Gnome-applications-office.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Gnome-applications-office.svg/70px-Gnome-applications-office.svg.png 2x" data-file-width="48" data-file-height="48" /></a></span> </td> <td style="border-top:1px solid #5090B0;width:100%; border-collapse:collapse;"><b><a href="/wiki/Wikiversit%C3%A0:Materia" title="Wikiversità:Materia">Materia</a></b>: <a href="/wiki/Materia:Logica_e_filosofia_della_scienza" title="Materia:Logica e filosofia della scienza">Logica e filosofia della scienza</a> </td></tr> </tbody></table> <p>Un <b>calcolo proposizionale</b> è un calcolo dei valori di verità delle proposizioni in esse contenute. </p><p>Se per esempio abbiamo da calcolare il valore di verità di una <i>congiunzione</i> "ET" e sappiamo che "P" è vera e "Q" è vera, possiamo calcolare il valore di verità di "P et Q" come vero. Infatti la tabella dei valori di verità di "Et" dice che la proposizione complessa è vera se e solo se sono vere entrambe le proposizioni contenute e congiunte. </p><p>Nel caso della <i>negazione</i> invece l'operatore <i>negazione</i> modifica il valore di verità della proposizione a cui è applicato. Quindi se "P" è vero, "Non P" è falso. Viceversa se "P" è falso, "non P" è vero. </p><p>Nel caso della <i>disgiunzione</i> abbiamo due casi. </p> <ul><li>Il <b>Vel</b> (<i>disgiunzione debole</i>). Essa è vera se almeno una proposizione è vera. Ad esempio se "P" è vera e "Q" è falsa: "P vel Q" è vera.</li> <li>L' <b>Aut</b> (<i>disgiunzione forte</i>). Essa è vera se e solo se una sua proposizione è vera. Se "P" è vera e "Q" è falsa: "P aut Q" è vera.</li></ul> <p>L'<i>implicazione</i> è vera se e solo se da premesse vere consegue una proposizione altrettanto vera. </p> <div class="mw-heading mw-heading2"><h2 id="Casi_notevoli">Casi notevoli</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Calcolo_proposizionale&action=edit&section=1" title="Modifica la sezione Casi notevoli"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Due casi sono notevoli nel calcolo proposizionale: la <i>tautologia</i>, nella quale i valori calcolati sono sempre veri, e la <i>contraddizione</i>, nella quale i valori di verità sono sempre falsi. </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=Calcolo_proposizionale&action=edit&section=2" title="Modifica la sezione Bibliografia"><span>modifica</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Rigamonti, Corso di logica, Bollati Boringhieri </p>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Estratto da "<a dir="ltr" href="https://it.wikiversity.org/w/index.php?title=Calcolo_proposizionale&oldid=201548">https://it.wikiversity.org/w/index.php?title=Calcolo_proposizionale&oldid=201548</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Speciale:Categorie" title="Speciale:Categorie">Categorie</a>: <ul><li><a href="/wiki/Categoria:Lezioni_di_Logica_e_filosofia_della_scienza" title="Categoria:Lezioni di Logica e filosofia della scienza">Lezioni di Logica e filosofia della scienza</a></li><li><a href="/wiki/Categoria:Risorse_con_il_parametro_avanzamento_non_compilato_o_errato" title="Categoria:Risorse con il parametro avanzamento non compilato o errato">Risorse con il parametro avanzamento non compilato o errato</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Questa pagina è stata modificata per l'ultima volta l'11 apr 2019 alle 11:18.</li> <li id="footer-info-copyright">Il testo è disponibile secondo la <a rel="nofollow" class="external text" href="//creativecommons.org/licenses/by-sa/4.0/deed.it">licenza Creative Commons Attribuzione-Condividi allo stesso modo</a>; possono applicarsi condizioni ulteriori. 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