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Modal tableaux for reasoning about actions and plans

  • Marcos A. Castilho
  • Olivier Gasquet
  • Andreas Herzig
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1348)

Abstract

In this paper we investigate tableau proof procedures for reasoning about actions and plans. Our framework is a multimodal language close to that of propositional dynamic logic, wherein we solve the frame problem by introducing the notion of dependence as a weak causal connection between actions and atoms. The tableau procedure is sound and complete for an important fragment of our language, within which all standard problems of reasoning about actions can be expressed, in particular planning tasks. Moreover, our tableaux are analytic and provide thus a decision procedure.

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References

  1. [Bak91]
    A.B. Baker. Nonmonotonic reasoning in the framework of situation calculus. Artificial Intelligence (AI), 49(1-3):5–23, may 1991.Google Scholar
  2. [Byl94]
    T. Bylander. The computational complexity of propositional STRIPS planning. Artificial Intelligence (AI), 69(1-2):165–204, 1994.Google Scholar
  3. [Cat89]
    L. Catach. Les logiques multi-modales. PhD thesis, Université Paris VI, France, 1989.Google Scholar
  4. [CGH96]
    M.A. Castilho, O. Gasquet, and A. Herzig. Modal tableaux for reasoning about actions and plans. IRIT internal report, nov 1996.Google Scholar
  5. [DGL95]
    G. De Giacomo and M. Lenzerini. PDL-based framework for reasoning about actions. In Proc. 4th Congresss of the Italian Association for Artificial Intelligence (IA * AI'95), number 992 in LNAI, pages 103–114. Springer-Verlag, 1995.Google Scholar
  6. [FdCH96]
    L. Farinas del Cerro and A. Herzig. Belief change and dependence. In Yoav Shoham, editor, Proc. 6th Conf. on Theoretical Aspects of Rationality and Knowledge (TARK'96), pages 147–162. Morgan Kaufmann Publishers, 1996.Google Scholar
  7. [GKL95]
    E. Giunchiglia, G. N. Kartha, and V. Lifschitz. Actions with indirect effects (extended abstract). In Working notes of the AAAI-Spring Sysposium on Extending Theories of Actions, 1995.Google Scholar
  8. [GL93]
    M. Gelfond and V. Lifschitz. Representing action and change by logic programs. Journal of Logic Programming, pages 301–321, 1993.Google Scholar
  9. [Gor92]
    R.P. Goré. Cut-free sequent and tableau systems for propositional normal modal logics. PhD thesis, University of Cambridge, England, 1992.Google Scholar
  10. [GS96]
    F. Giunchiglia and R Sebastiani. A SAT-based decision procedure for ALC. In Proc. Int. Conf. on Knowledge Representation and Reasoning (KR'96), pages 302–314, Cambridge, Massachussetts, 1996.Google Scholar
  11. [Har84]
    D. Harel. Dynamic logic. In D. Gabbay and F. Günthner, editors, Handbook of Philosophical Logic, volume II, pages 497–604. D. Reidel, Dordrecht, 1984.Google Scholar
  12. [Her97]
    A. Herzig. How to change factual beliefs using laws and independence information. In Dov M. Gabbay and Rudolf Kruse, editors, Proc. Int. Joint Conf. on Qualitative and Quantitative Practical Reasoning (ECSQARU/FAPR97), LNCS. Springer-Verlag, jun 1997.Google Scholar
  13. [HM86]
    S. Hanks and D. McDermott. Default reasoning, nonmonotonic logics, and the frame problem. In Proc. Nat. (US) Conf. on Artificial Intelligence (AAAI'86), pages 328–333, Philadelphia, PA, 1986.Google Scholar
  14. [HSZ96]
    A. Heuerding, M. Seyfried, and H. Zimmermann. Efficient loop-check for backward proof search in some non-classical propositional logics. In P. Miglioli, U. Moscato, D. Mundici, and M. Ornaghi, editors, Proceedings of the 5th International Workshop TABLEAUX'96: Theorem Proving with Analytic Tableaux and Related Methods, number 1071 in LNAI, pages 210–225. Springer-Verlag, 1996.Google Scholar
  15. [KL94]
    G. N. Kartha and V. Lifschitz. Actions with indirect effects (preliminary report). In Proc. Int. Conf. on Knowledge Representation and Reasoning (KR'94), pages 341–350, 1994.Google Scholar
  16. [Lin95]
    F. Lin. Embracing causality in specifying the indirect effects of actions. In Proc. of the 14th International Joint Conference on Artificial Intelligence (IJCAI'95), pages 1985–1991, Montreal, Canada, 1995.Google Scholar
  17. [Mas97]
    F. Massacci. Personal communication, may 1997.Google Scholar
  18. [Mat93]
    C. Mathieu. A resolution method for a non-monotonic multimodal logic. In S. Moral, editor, Proc. ECSQ UAR U'93, LNCS, pages 257–264. Springer-Verlag, 1993.Google Scholar
  19. [MT95]
    N. McCain and H. Turner. A causal theory of ramifications and qualifications. In Proc. of the 14th International Joint Conference on Artificial Intelligence (IJCAI'95), pages 1978–1984, 1995.Google Scholar
  20. [Rei91]
    R. Reiter. The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression. Artificial Intelligence and Mathematical Theory of Computation, Papers in Honor of John McCarthy:359–380, 1991.Google Scholar
  21. [Ros81]
    S. Rosenschein. Plan synthesis: a logical approach. In Proc. of the 8th International Joint Conference on Artificial Intelligence (IJCAI'81), pages 359–380, Academic Press, 1981.Google Scholar
  22. [San95]
    E. Sandewall. Features and Fluents. Oxford University Press, 1995.Google Scholar
  23. [SB93]
    W. Stephan and S. Biundo. A new logical framework for deductive planning. In Proc. of the 13th International Joint Conference on Artificial Intelligence (IJCAI'93), pages 32–38, 1993.Google Scholar
  24. [Sie87]
    P. Siegel. Représentation et utilisation de la connaissance en calcul propositionnel. PhD thesis, Université d'Aix-Marseille II, Aix-Marseille, France, jul 1987.Google Scholar
  25. [Thi95]
    M. Thielscher. The logic of dynamic systems. In Proc, of the 14th International Joint Conference on Artificial Intelligence (IJCAI'95), pages 1956–1962, Montreal, Canada, 1995.Google Scholar
  26. [Thi97]
    M. Thielscher. Ramification and causality. Artificial Intelligence (AI), 89:317–364, 1997.Google Scholar
  27. [Tse83]
    G.S. Tseitin. On the complexity of derivations in propositional calculus. In Siekmann Wrightson, editor, Automated Reasoning 2: Classical papers on computational logic, pages 466–483, 1983.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Marcos A. Castilho
    • 1
  • Olivier Gasquet
    • 1
  • Andreas Herzig
    • 1
  1. 1.Université Paul Sabatier - IRIT - Applied Logic GroupToulouse Cedex 4France

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