A Relational Dual Tableau Decision Procedure for Multimodal and Description Logics

Abstract

AbstractWe present a dual tableau based decision procedure for a class of fragments of the classical relational logic of binary relations. The logics considered share a common language involving 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. An important feature of the dual tableau procedure is a rule to handle the relational composition operator, that permits to decompose in a single step compositional formulae and negative compositional formulae with the same left object variable.Our relational dual tableau can be used as a decision procedure for validity verification in the multimodal logic K, the description logic \(\mathcal{ALC}\), and several non-classical logics for reasoning in various AI systems.KeywordsModal LogicComposition OperatorDecision ProcedureDescription LogicProof SystemThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.