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| In [[mathematical logic]], a '''literal''' is an [[atomic formula]] (atom) or its [[negation]].
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| The definition mostly appears in [[proof theory]] (of [[classical logic]]), e.g. in [[conjunctive normal form]] and the method of [[resolution (logic)|resolution]].
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| Literals can be divided into two types:
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| * A '''positive literal''' is just an atom.
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| * A '''negative literal''' is the negation of an atom.
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| For a literal <math>l</math>, the '''complementary literal''' is a literal corresponding to the negation of <math>l</math>,
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| we can write <math>\bar{l}</math> to denote the complementary literal of <math>l</math>. More precisely, if <math>l\equiv x</math> then <math>\bar{l}</math> is <math>\lnot x</math> and if <math>l\equiv \lnot x</math> then <math>\bar{l}</math> is <math>x</math>.
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| In the context of a formula in the [[conjunctive normal form]], a literal is '''pure''' if the literal's complement does not appear in the formula.
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| == Examples ==
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| In [[propositional calculus]] a literal is simply a [[propositional variable]] or its negation.
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| In [[predicate calculus]] a literal is an [[atomic formula]] or its negation, where an atomic formula is a [[Predicate (mathematical logic)|predicate]] symbol applied to some [[term (logic)|terms]], <math>P(t_1,\ldots,t_n)</math> with the terms [[recursive definition|recursively defined]] starting from constant symbols, variable symbols, and [[function (mathematics)|function]] symbols. For example, <math>\neg Q(f(g(x), y, 2), x)</math> is a negative literal with the constant symbol 2, the variable symbols ''x'', ''y'', the function symbols ''f'', ''g'', and the predicate symbol ''Q''.
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| ==References==
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| *{{cite book | author = Samuel R. Buss | chapter= An introduction to proof theory | editor = Samuel R. Buss | title=Handbook of proof theory | pages = 1–78 | url = http://math.ucsd.edu/~sbuss/ResearchWeb/handbookI/ | publisher = Elsevier | date = 1998 | id = ISBN 0-444-89840-9 }}
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| [[Category:Propositional calculus]]
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| [[Category:Logic symbols]]
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| {{logic-stub}}
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