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

Pawlowski, Pawel and La Rosa, Elio (2021): Modular non-deterministic semantics for T, TB, S4, S5 and more. In: Journal of Logic and Computation, Vol. 32, No. 1: pp. 158-171

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 Shirt (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.

• Item Type: Journal article
• Faculties: Philosophy, Philosophy of Science and Religious Science
• Subjects: 100 Philosophy and Psychology > 100 Philosophy
• ISSN: 0955-792X
• Language: English