Abstract
We 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.
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Cantone, D., Golińska-Pilarek, J., Nicolosi-Asmundo, M. (2014). A Relational Dual Tableau Decision Procedure for Multimodal and Description Logics. In: Polycarpou, M., de Carvalho, A.C.P.L.F., Pan, JS., Woźniak, M., Quintian, H., Corchado, E. (eds) Hybrid Artificial Intelligence Systems. HAIS 2014. Lecture Notes in Computer Science(), vol 8480. Springer, Cham. https://doi.org/10.1007/978-3-319-07617-1_41
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DOI: https://doi.org/10.1007/978-3-319-07617-1_41
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