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.

Vitaliy Rimatskiy, Cand. Sci. (Phys.–Math.), Siberian Federal University, 79, Svobodniy Ave., Krasnoyarsk, 660041, Russian Federation, email: Gemmeny@rambler.ru

Rimatskiy V.V. Admissible Inference Rules and Semantic Property of Modal Logics. The Bulletin of Irkutsk State University. Series Mathematics, 2021, vol. 37, pp. 104-117. (in Russian) https://doi.org/10.26516/1997-7670.2021.37.104

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