Sentence examples for truth equivalent from inspiring English sources

Sentences ψ and χ are logically equivalent if they are both truth equivalent and falsity equivalent.[28] Due to the failure of bivalence, in IFL truth equivalence does not guarantee logical equivalence.

There are sentences φ of IFL such that ¬φ (which is a sentence of EIFL) is not truth equivalent to any sentence of IFL.

Hintikka (2004b) raises the question of the algebraic structure induced by these operators, when any two truth equivalent sentences are identified.

Hence the contradictory negation ¬φ is only expressible in IFL for those IFL sentences φ that are truth equivalent to an FO sentence.[42] Determined fragment.

If φ and ψ are sentences of IFL such that M ⊨ φ iff M ⊭ ψ, then each of φ and ψ is truth equivalent to a sentence of FO.

Sentences ψ and χ of IFL are truth equivalent if they are true in precisely the same models, and falsity equivalent if they are false in precisely the same models.

If φ is a sentence of IFL not truth equivalent to any FO sentence, the truth-condition of the sentence ¬φ of EIFL cannot be formulated without recourse to the set of all strategies of player 2: ¬φ is true in model M iff for all strategies of player 2 in game G φ, M), there is a sequence of moves by player 1 such that player 1 wins the resulting play.

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