Refutation in first order logic
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05-11-2019 - |
Question
Consider the following statement
In FOL, we can reduce entailment checking to satisfiability checking:
$S \models S' \iff S \land \neg S'$ is satisfiable (This proof strategy is called refutation).
Is the above statement true? If yes, then I got confusion because of the following steps
$ S \models S' \iff S\implies S'$ is true
$S \models S' \iff \neg S \lor S'$ is satisfiable
$S \models S' \iff \neg( S \land \neg S') $ is satisfiable
$S \models S' \iff S \land \neg S' $ is unsatisfiable
Which one is true?
No correct solution
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