A Relational Dual Tableau Decision Procedure for Multimodal and Description Logics

  • Domenico Cantone
  • Joanna Golińska-Pilarek
  • Marianna Nicolosi-Asmundo
Conference paper

DOI: 10.1007/978-3-319-07617-1_41

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8480)
Cite this paper as:
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

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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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Domenico Cantone
    • 1
  • Joanna Golińska-Pilarek
    • 2
  • Marianna Nicolosi-Asmundo
    • 1
  1. 1.Dept. of Mathematics and Computer ScienceUniversity of CataniaItaly
  2. 2.Institute of PhilosophyUniversity of WarsawPoland

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