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A Fibred Tableau Calculus for Modal Logics of Agents

  • Vineet Padmanabhan
  • Guido Governatori
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4327)

Abstract

In [15,19] we showed how to combine propositional multimodal logics using Gabbay’s fibring methodology. In this paper we extend the above mentioned works by providing a tableau-based proof technique for the combined/ fibred logics. To achieve this end we first make a comparison between two types of tableau proof systems, (graph & path), with the help of a scenario (The Friend’s Puzzle). Having done that we show how to uniformly construct a tableau calculus for the combined logic using Governatori’s labelled tableau system KEM. We conclude with a discussion on KEM’s features.

Keywords

Modal Logic Inference Rule Kripke Model Atomic Label Component Logic 
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.

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References

  1. 1.
    Artosi, A., Benassi, P., Governatori, G., Rotolo, A.: Shakespearian modal logic: A labelled treatment of modal identity. In: Advances in Modal Logic, CSLI, vol. 1 (1998)Google Scholar
  2. 2.
    Artosi, A., Governatori, G., Rotolo, A.: Labelled tableaux for non-monotonic reasoning: Cumulative consequence relations. Journal of Logic and Computation 12(6), 1027–1060 (2002)MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Baldoni, M.: Normal Multimodal Logics: Automatic Deduction and Logic Programming Extension. PhD thesis, Universita degli Studi di Torino, Italy (1998)Google Scholar
  4. 4.
    Blackburn, P., de Rijke, M.: Zooming in, zooming out. Journal of Logic, Language and Information (1996)Google Scholar
  5. 5.
    d’Avila Garcez, A.S., Gabbay, D.M.: Fibring neural networks. In: AAAI 2004, pp. 342–347. AAAI/MIT Press (2004) Google Scholar
  6. 6.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. The MIT Press, Cambridge (1995)MATHGoogle Scholar
  7. 7.
    Fitting, M.: Proof Methods for Modal and Intuitionistic Logics, Reidel, Dordrecht (1983)Google Scholar
  8. 8.
    Gabbay, D.M.: Fibring Logics. Oxford University Press, Oxford (1999)MATHGoogle Scholar
  9. 9.
    Gabbay, D.M., Governatori, G.: Dealing with label dependent deontic modalities. In: Norms, Logics and Information Systems. New Studies in Deontic Logic, IOS Press, Amsterdam (1998)Google Scholar
  10. 10.
    Gabbay, D.M., Governatori, G.: Fibred modal tableaux. In: Labelled Deduction. Kluwer academic Publishers, Dordrecht (2000)Google Scholar
  11. 11.
    Governatori, G.: Labelled tableau for multi-modal logics. In: Baumgartner, P., Posegga, J., Hähnle, R. (eds.) TABLEAUX 1995. LNCS, vol. 918, pp. 79–94. Springer, Heidelberg (1995)Google Scholar
  12. 12.
    Governatori, G.: Un modello formale per il ragionamento giuridico. PhD thesis, CIRSFID, University of Bologna (1997)Google Scholar
  13. 13.
    Governatori, G.: On the relative complexity of modal tableaux. Electronic Notes in Theoretical Computer Science 78, 36–53 (2003)CrossRefGoogle Scholar
  14. 14.
    Governatori, G., Luppi, A.: Labelled tableaux for non-normal modal logics. In: Lamma, E., Mello, P. (eds.) AI*IA 1999. LNCS (LNAI), vol. 1792, pp. 119–130. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  15. 15.
    Governatori, G., Padmanabhan, V., Sattar, A.: On Fibring Semantics for BDI Logics. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Kracht, M., Wolter, F.: Properties of independently axiomatizable bimodal logics. The Journal of Symbolic Logic 56(4), 1469–1485 (1991)MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    Llyod, J.W.: Modal higher-order logic for agents (2004), http://users.rsise.anu.edu.au/~jwl/beliefs.pdf
  18. 18.
    Lomuscio, A.: Information Sharing Among Ideal Agents. PhD thesis, School of Computer Science, University of Brimingham (1999)Google Scholar
  19. 19.
    Padmanabhan, V.: On Extending BDI Logics. PhD thesis, School of Information Technology, Griffith University, Brisbane, Australia (2003)Google Scholar
  20. 20.
    Rao, A.S., Georgeff, M.P.: Formal models and decision procedures for multi-agent systems. Technical note 61, Australian Artificial Intelligence Institute (1995)Google Scholar
  21. 21.
    Sernadas, A., Sernadas, C., Zanardo, A.: Fibring modal first-order logics: Completeness preservation. Logic Journal of the IGPL 10(4), 413–451 (2002)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    Wolter, F.: Fusions of modal logics revisited. In: Advances in Modal Logic. CSLI Lecture notes 87, vol. 1 (1997)Google Scholar
  23. 23.
    Wooldridge, M.: Reasoning about Rational Agents. The MIT Press, Cambridge (2000)MATHGoogle Scholar
  24. 24.
    Zanardo, A., Sernadas, A., Sernadas, C.: Fibring: Completeness preservation. Journal of Symbolic Logic 66(1), 414–439 (2001)MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Vineet Padmanabhan
    • 1
  • Guido Governatori
    • 1
  1. 1.School of Information Technology & Electrical EngineeringThe University of QueenslandQueenslandAustralia

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