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2009-02-13T17:03:41Z

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'''Equivalence''' is a 1. (material equivalence) the combination of two formulas with the [[connective]] <-> (''if and only if'', ''iff''), which is only true if both formulas have the same [[truth value]]. phi <-> psi can also be defined as the conjunction of two implications: phi -> psi and psi -> phi. For this reason, the connective of material equivalence is sometimes called the biconditional. The [[truth table]] for material equivalence is as follows:

(i) phi psi phi <-> psi
1 1 1
1 0 0
0 1 0
0 0 1

See [[Connective]]. 2. (logical equivalence) a relation obtaining between two formulas phi and psi if their material equivalence phi <-> Psi is a [[tautology]]. In other words, two formulas which are logically equivalent have the same truth value for every possible [[model]].

=== Example ===

phi -> psi is logically equivalent with Neg [ phi & Neg psi ] in [[propositional logic]] and ThereIs(x) [ P(x) ] is equivalent with Neg All(x) [ Neg P(x) ] in [[predicate logic]]. When two expressions are logically equivalent, it is possible to substitute them for each other, without changing the truth values of the proposition they are contained in.

=== Link ===

[http://www2.let.uu.nl/UiL-OTS/Lexicon/zoek.pl?lemma=Equivalence&lemmacode=783 Utrecht Lexicon of Linguistics]

=== References ===

* Gamut, L.T.F. 1991. ''Logic, language, and meaning,'' Univ. of Chicago Press, Chicago.

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[[Category:Semantics]]

Equivalence - Revision history

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