Tableau Systems for Some Ivlev-Like (Quantified) Modal Logics

Ivlev’s pioneering work started in the 1970s 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 S5m, the non-normal versions of T, S4 and S5, respectively, as well as for their corresponding first-order extensions Tm*, S4m* and S5m*. We also prove that the monadic fragments of Tm*, S4m* and S5m* are undecidable.