A Relational Dual Tableau Decision Procedure for Multimodal and Description Logics

  • Domenico Cantone
  • Joanna Golińska-Pilarek
  • Marianna Nicolosi-Asmundo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8480)


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.


Modal Logic Composition Operator Decision Procedure Description Logic Proof System 


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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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