Terminating Tableaux for Hybrid Logic with the Difference Modality and Converse

Authors:
Mark Kaminski;Gert Smolka
Affiliations:
Programming Systems Lab, Saarland University, Saarbrücken, Germany 66123;Programming Systems Lab, Saarland University, Saarbrücken, Germany 66123
Venue:
IJCAR '08 Proceedings of the 4th international joint conference on Automated Reasoning
Year:
2008

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Abstract

We present the first terminating tableau calculus for basic hybrid logic with the difference modality and converse modalities. The language under consideration is basic multi-modal logic extended with nominals, the satisfaction operator, converse, global and difference modalities. All of the constructs are handled natively.To obtain termination, we extend chain-based blocking for logics with converse by a complete treatment of difference.Completeness of our calculus is shown via a model existence theorem that refines previous constructions by distinguishing between modal and equational state equivalence.