This article is cited in 1 paper

Algebraic and logical methods in computer science and artificial intelligence

Admissible inference rules and semantic property of modal logics

V. V. Rimatskiy

Siberian Federal University, Krasnoyarsk, Russian Federation

Abstract: 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.

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

UDC: 510.643; 517.11

MSC: 03F25, 03B35

Received: 20.07.2021

DOI: 10.26516/1997-7670.2021.37.104

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