Open AccessAdmissible Inference Rules and Semantic Property of Modal Logics
Author(s) -
V.V. Rimatskiy
Publication year - 2021
Publication title -
izvestiâ irkutskogo gosudarstvennogo universiteta. seriâ "matematika"/izvestiâ irkutskogo gosudarstvennogo universiteta. seria matematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.411
H-Index - 3
eISSN - 2541-8785
pISSN - 1997-7670
DOI - 10.26516/1997-7670.2021.37.104
Subject(s) - rule of inference , property (philosophy) , inference , modal logic , normal modal logic , cover (algebra) , mathematics , accessibility relation , t norm fuzzy logics , modal , computer science , theoretical computer science , description logic , discrete mathematics , artificial intelligence , intermediate logic , multimodal logic , epistemology , philosophy , mechanical engineering , chemistry , membership function , fuzzy set , polymer chemistry , engineering , fuzzy logic
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 enjoys weak co-cover property iff all given rules are admissible for logic.