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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abraham, A.: Special issue: Hybrid approaches for approximate reasoning. J. Intell. Fuzzy Syst. 23(2,3), 41–42 (2012)MathSciNetGoogle Scholar
  2. 2.
    Baader, F., Calvanese, D., McGuinness, D.L., Nardi, D., Patel-Schneider, P.F. (eds.): The Description Logic Handbook: Theory, Implementation, and Applications. Cambridge University Press, New York (2003)Google Scholar
  3. 3.
    Cantone, D., Nicolosi-Asmundo, M., Orlowska, E.: Dual tableau-based decision procedures for some relational logics. In: Proceedings of the 25th Italian Conference on Computational Logic. CEUR Workshop Proceedings, vol. 598, pp. 1–16 (2010)Google Scholar
  4. 4.
    Cantone, D., Nicolosi-Asmundo, M., Orlowska, E.: Dual tableau-based decision procedures for relational logics with restricted composition operator. Journal of Applied Non-Classical Logics 21(2), 177–200 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Corchado, E., Wozniak, M., Abraham, A., de Carvalho, A.C.P.L.F., Snásel, V.: Recent trends in intelligent data analysis. Neurocomputing 126, 1–2 (2014)CrossRefGoogle Scholar
  6. 6.
    Formisano, A., Nicolosi-Asmundo, M.: An efficient relational deductive system for propositional non-classical logics. Journal of Applied Non-Classical Logics 16(3,4), 367–408 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  7. 7.
    Golinska-Pilarek, J., Huuskonen, T., Muñoz-Velasco, E.: Relational dual tableau decision procedures and their applications to modal and intuitionistic logics. Ann. Pure Appl. Logic 165(2), 409–427 (2014)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Golinska-Pilarek, J., Muñoz-Velasco, E., Mora, A.: A new deduction system for deciding validity in modal logic k. Logic Journal of the IGPL 19(2), 425–434 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Medsker, L.R.: Hybrid intelligent systems. Kluwer (1995)Google Scholar
  10. 10.
    Mora, A., Muñoz-Velasco, E., Golinska-Pilarek, J.: Implementing a relational theorem prover for modal logic. Int. J. Comput. Math. 88(9), 1869–1884 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    Orłowska, E., Golińska-Pilarek, J.: Dual Tableaux: Foundations, Methodology, Case Studies. Trends in Logic, vol. 36. Springer (2011)Google Scholar
  12. 12.
    Orłowska, E.: Relational interpretation of modal logics. In: Andreka, H., Monk, D., Nemeti, I. (eds.) Algebraic Logic. Colloquia Mathematica Societatis Janos Bolyai, vol. 54, pp. 443–471. North Holland (1988)Google Scholar
  13. 13.
    Sattler, U.: A concept language extended with different kinds of transitive roles. In: Görz, G., Hölldobler, S. (eds.) KI 1996. LNCS, vol. 1137, pp. 333–345. Springer, Heidelberg (1996)CrossRefGoogle Scholar

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

Personalised recommendations