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Unification and passive inference rules for modal logics. (English) Zbl 1040.03014
Summary: We study unification of formulas in modal logics and consider logics which are equivalent w.r.t. unification of formulas. A criterion is given for equivalence w.r.t. unification via existence or persistent formulas. A complete syntactic description of all formulas which are non-unifiable in wide classes of modal logics is given. Passive inference rules are considered, it is shown that in any modal logic over D4 there is a finite basis for passive rules.

MSC:
03B45 Modal logic (including the logic of norms)
03B55 Intermediate logics
03B35 Mechanization of proofs and logical operations
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