Modal logics preserving admissible for S4 inference rules
The aim of the current paper is to provide a complete semantics description for modal logics with finite model property which preserve all admissible in S4 inference rules, with the intention of meeting some of the needs of computer science. It is shown a modal logic λ with fmp above S4 preserves all admissible for S4 inference rules iff λ has so-called co-cover property. In turned out there are continuously many logics of this kind. Using mentioned above semantics criterion we give some precise description of all tabular logics preserving admissible for S4 rules.
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