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| In [[logic]], a '''logical constant''' of a [[formal language|language]] <math>\mathcal{L}</math> is a [[symbol (formal)|symbol]] that has the same [[Formal semantics (logic)|semantic value]] under every [[interpretation (logic)|interpretation]] of <math>\mathcal{L}</math>. Two important types of logical constants are [[logical connective]]s and [[quantifier]]s. The [[equality (mathematics)|equality]] predicate (usually written '=') is also treated as a logical constant in many [[formal system|systems of logic]].
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| Some symbols that are commonly treated as logical constants are:
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| <table border=1 class="wikitable">
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| <tr>
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| <th>Symbol</th>
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| <th>Meaning in English</th>
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| </tr>
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| <tr>
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| <td>T</td>
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| <td>"true"</td>
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| </tr>
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| <tr>
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| <td>F</td>
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| <td>"false"</td>
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| </tr>
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| <tr>
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| <td>¬</td>
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| <td>"not"</td>
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| </tr>
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| <tr>
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| <td>∧</td>
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| <td>"and"</td>
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| </tr>
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| <tr>
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| <td>∨</td>
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| <td>"or"</td>
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| </tr>
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| <tr>
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| <td>→</td>
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| <td>"implies", "if...then"</td>
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| </tr>
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| <tr>
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| <td>∀</td>
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| <td>"for all"</td>
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| </tr>
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| <tr>
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| <td>∃</td>
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| <td>"there exists", "for some"</td>
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| </tr>
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| <tr>
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| <td>=</td>
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| <td>"equals"</td>
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| </tr>
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| <tr>
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| <td><math>\Box</math></td>
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| <td>"necessarily"</td>
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| </tr>
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| <tr>
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| <td><math>\Diamond</math></td>
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| <td>"possibly"</td>
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| </tr>
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| </table>
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| For many logical constants also other symbols are commonly used to denote them, such as the symbol "&" for [[logical and]].
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| One of the fundamental questions in the [[philosophy of logic]] is "What is a logical constant?"; that is, what special feature of certain constants makes them ''logical'' in nature?<ref>Carnap</ref>{{full|date=November 2012}}
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| ==See also==
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| *[[Non-logical symbol]]
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| *[[Logical value]]
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| *[[Logical connective]]
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| ==References==
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| {{reflist}}
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| == External links ==
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| *[http://plato.stanford.edu/entries/logical-constants/ Stanford Encyclopedia of Philosophy entry on logical constants]
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| [[Category:Philosophical logic]]
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| [[Category:Concepts in logic]]
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| [[Category:Syntax (logic)]]
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| [[Category:Logical truth]]
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| [[Category:Logic symbols]]
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| {{logic-stub}}
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| {{philosophy-stub}}
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Latest revision as of 12:22, 5 May 2014
The title of the author is Figures but it's not the most masucline title out there. The favorite pastime for my kids and me is to play baseball but I haven't made a dime with it. Minnesota has usually been his house but his spouse wants them to move. For years I've been operating as a payroll clerk.
Feel free to visit my homepage - wmazowiecku.pl