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Equisatisfiability : ウィキペディア英語版 | Equisatisfiability
In logic, two formulae are equisatisfiable if the first formula is satisfiable whenever the second is and vice versa; in other words, either both formulae are satisfiable or both are not. Two equisatisfiable formulae may have different models, provided they both have some or both have none. As a result, equisatisfiability is different from logical equivalence, as two equivalent formulae always have the same models. Equisatisfiability is generally used in the context of translating formulae, so that one can define a translation to be correct if the original and resulting formulae are equisatisfiable. Examples of translations involving this concept are Skolemization and some translations into conjunctive normal form. ==Examples==
A translation from propositional logic into propositional logic in which every binary disjunction is replaced by , where is a new variable (one for each replaced disjunction) is a transformation in which satisfiability is preserved: the original and resulting formulae are equisatisfiable. Note that these two formulae are not equivalent: the first formula has the model in which is true while and are false, and this is not a model of the second formula, in which has to be true in this case.
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Equisatisfiability」の詳細全文を読む
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