Tableau systems for some Ivlev-like (quantified) modal logics

TL;DR

This paper develops tableau proof systems for non-normal modal logics derived from Ivlev's many-valued modal logic framework, including their first-order extensions, advancing the proof-theoretic tools for these logics.

Contribution

It introduces tableau systems for Ivlev-like non-normal modal logics Tm, S4m, S5m and their first-order counterparts, expanding the proof methods available for these logics.

Findings

Tableau systems for Tm, S4m, S5m established

First-order extensions Tm*, S4m*, S5m* developed

Provides a proof-theoretic foundation for Ivlev-like modal logics

Abstract

Ivlev's pioneering work started in the 1970's showed a new and promissory way in the study of modal logic from the perspective of many-valued logics. Continuing our previous work on Ivlev-like non-normal modal logics with non-deterministic semantics, we present in this paper tableau systems for Tm, S4m and S5m, the non-normal versions of T, S4 and S5, respectively, as well as for their corresponding first-order extensions Tm*, S4m* and S5m*.