Prefixed Tableaux Systems for Modal Logics with Enriched Languages

Abstract

We present sound and complete prefixed tableaux systems for various modal logics with enriched languages including the "difference" modal operator [6=] and the "only if" modal operator [\\GammaR]. These logics are of special interest in Artificial Intelligence since their expressive power is higher than the standard modal logics and for most of them the satisfiability problem remains decidable. We also include in the paper decision procedures based on these systems. In the conclusion, we relate our work with similar ones from the literature and we propose extensions to other logics. 1 Introduction The definition of logical formalisms that model cognitive and reasoning processes has been always confronted to two issues: how to decrease the expressive power of existing untractable logics in order to obtain tractable fragments and how to increase the expressive power of decidable logics while preserving decidability - this includes for instance the extension of known decidable fragments ...