A General Tableau Method for Deciding Description Logics, Modal Logics and Related First-Order Fragments

This paper presents a general method for proving termination of tableaux-based procedures for modal-type logics and related first-order fragments. The method is based on connections between filtration arguments and tableau blocking techniques. The method provides a general framework for developing tableau-based decision procedures for a large class of logics. In particular, the method can be applied to many well-known description and modal logics. The class includes traditional modal logics such as S4 and modal logics with the universal modality, as well as description logics such as $\mathcal{ALC}$ with nominals and general TBoxes. Also contained in the class are harder and less well-studied modal logics with complex modalities and description logics with complex role operators such as Boolean modal logic, and the description logic $\mathcal{ALBO}$. In addition, the techniques allow us to specify tableau-based decision procedures for related solvable fragments of first-order logic, including the two-variable fragment of first-order logic.

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