A Relational Dual Tableau Decision Procedure for Multimodal and Description Logics

We present a dual tableau based decision procedure for a class of fragments of the classical relational logic of binary relations. The logics considered here share a common language with a restricted composition operator and infinitely many relational constants which may have the properties of reflexivity, transitivity, and heredity. The construction of the dual tableau is carried out by applying in a deterministic way axioms and inference rules of the system without resorting to external tools. The relational dual tableau presented in the paper can be used as a decision procedure for validity verification in the multimodal logic K, the description logic ALC, and several non-classical logics.