Admissible inference rules and semantic property of modal logics

V. V. Rimatskiy

The Bulletin of Irkutsk State University. Series Mathematics, Tome 37 (2021), pp. 104-117

Résumé

Firstly semantic property of nonstandart logics were described by formulas which are peculiar to studied a models in general, and do not take to consideration a variable conditions and a changing assumptions. Evidently the notion of inference rule generalizes the notion of formulas and brings us more flexibility and more expressive power to model human reasoning and computing. In 2000-2010 a few results on describing of explicit bases for admissible inference rules for nonstandard logics (S4, K4, H etc.) appeared. The key property of these logics was weak co-cover property. Beside the improvement of deductive power in logic, an admissible rule are able to describe some semantic property of given logic. We describe a semantic property of modal logics in term of admissibility of given set of inference rules. We prove that modal logic over logic $GL$ enjoys weak co-cover property iff all given rules are admissible for logic.

Détail

Keywords: modal logic, frame and model Kripke, admissible inference rule, weak co-cover property.

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