Prefixed Tableaux Systems for Modal Logics with Enriched Languages

We present sound and complete prefixed tableaux systems for various modal logics with enriched languages including the "difference" modal operator ] and the "only if" modal operator [—R]. These logics are of special interest in Art i f icial 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 exten­ sions to other logics.