Some additional axioms for t-normal logics. Defining K45, KB4, KD45 and S5 without using modal rules

Andrzej Pietruszczak

doi:10.18778/0138-0680.2024.12

Authors

Andrzej Pietruszczak Department of Logic, Nicolaus Copernicus University in Toruń https://orcid.org/0000-0001-9133-5081

DOI:

https://doi.org/10.18778/0138-0680.2024.12

Keywords:

modal logic, t-normal logics, Kripke-style semantics

Abstract

The paper will study extensions of t-normal logics S0.5^o and S0.5 using some axioms of normal logics. We will prove determination theorems for these extensions by appropriate Kripke-style models. It will allow us to obtain the determinations of the logics K45, KB4 (= KB5), KD45 and S5 without using modal rules.

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