Modular non-deterministic semantics for T, TB, S4, S5 and more

Abstract

Abstract In this paper, a modular approach for non-deterministic semantics for (non-normal) modal logics is developed. In particular, our aim is to improve and reinterpret some results from Omori and Skurt (2016, IfCoLog J. Logics Appl., 3, 815–845) and Coniglio et al. (2015, J. Appl. Non-Class. Log., 25, 20–45) regarding modal systems T, TB, S4 and S5. More economical axiomatizations make the rule of necessitation modular, thus providing non-deterministic semantics for (NEC)-free fragments for all the investigated systems. Moreover, by fixing the interpretation of all connectives but the modal ones, a combinatorial outlook at their matrices is provided to the effect that a new modal system and simplification of those for T and S4 are achieved.