Sergey Babenyshev

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Rules that are admissible can be used in any derivations in any axiomatic system of a logic. In this paper we introduce a method for checking the admissibility of rules in the modal logic S4. Our method is based on a standard semantic ground tableau approach. In particular, we reduce rule admissibility in S4 to satisfiability of a formula in a logic that(More)
The object of our study is the propositional linear temporal logic LTL with operations Until and Next. We deal with inference rules admissible in LTL. Earlier the decidability of LTL w.r.t. to admissibility was shown. That, in particular, allowed to suggest a recursive infinite basis for admissible rules. However, that result gives no information about the(More)
We prove that a propositional Linear Temporal Logic with Until and Next (LTL) has unitary unification. Moreover, for every unifiable in LTL formula A there is amost general projective unifier, corresponding to some projective formula B, such that A is derivable from B in LTL. On the other hand, it can be shown that not every open and unifiable in LTL(More)