Modal logic for modelling actions and agents

  • Helmut Prendinger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1085)


We present a modal logic approach to reasoning about actions and agents where propositional dynamic logic is used to describe plans and reasoning about belief is performed in a modal system as well. Eventually, the modal logic of belief is embedded within dynamic logic such that we may reason about changes of the agent's belief state as a result of executing actions. As a theory of actions, the proposed extension of standard dynamic logic has two distinguished features: it is monotonic and gives reasonable solutions to various ‘frame problems’ even when multiagent domains are considered. Moreover, updates are established as actions of a special kind within the same framework. Formal properties of the resulting system of belief and action can be proved by a methodology recently introduced by Finger and Gabbay.


theories of actions theories of agents combining reasoning formalisms formal models for reasoning 


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  1. 1.
    Craig Boutilier and Nir Friedman. Nondeterministic actions and the frame problem. Unpublished manuscript, 1995.Google Scholar
  2. 2.
    Philip R. Cohen and Hector J. Levesque. Intention is choice with commitment. Artificial Intelligence, 42:213–261, 1990.CrossRefGoogle Scholar
  3. 3.
    F. P. M. Dignum and J.-J. Ch. Meyer. Negations of transactions and their use in the specification of dynamic and deontic integrity constraints. In M. Z. Kwiatkowska, M. W. Shields, and R. M. Thomas, editors, Proceedings of the International BCS-FACS Workshop on Semantics for Concurrency, pages 61–80, University of Leicester, UK, 1990.Google Scholar
  4. 4.
    David W. Etherington, Sarit Kraus, and Donald Perlis. Nonmonotonicity and the scope of reasoning. Artificial Intelligence, 52:221–261, 1991.CrossRefGoogle Scholar
  5. 5.
    Kit Fine and Gerhard Schurz. Transfer theorems for stratified multimodal logics. In J. Copland, editor, Logic and Reality. Essays in Pure and Applied Logic. In Memory of Arthur Prior. Oxford University Press, 1995.Google Scholar
  6. 6.
    Marcelo Finger and Dov M. Gabbay. Adding a temporal dimension to a logic system. Journal of Logic, Language and Information, 1:203–233, 1992.Google Scholar
  7. 7.
    Nir Friedman and Joseph Y. Halpern. A knowledge-based framework for belief change, part II: Revision and update. In Proceedings Fourth International Conference on Principles of Knowledge Representation and Reasoning (KR-94), pages 190–201, 1994.Google Scholar
  8. 8.
    Michael P. Georgeff. Many agents are better than one. In F. M. Brown, editor, Proceedings of the 1987 Workshop on the Frame Problem in Artificial Intelligence, pages 59–75, Lawrence, Kansas, 1987.Google Scholar
  9. 9.
    Matthew L. Ginsberg. Computational considerations in reasoning about action. In James Allen, Richard Fikes, and Erik Sandevall, editors, Proceedings of the Second International Conference On Principles of Knowledge Representation and Reasoning, pages 250–261, Cambridge, Massachusetts, 1991.Google Scholar
  10. 10.
    R. Goldblatt. Logics of Time and Computation. Center for the Study of Language and Information Lecture Notes 7. Leland Stanford Junior University, Stanford, 1987.Google Scholar
  11. 11.
    Gösta Grahne. Updates and counterfactuals. In James Allen, Richard Fikes, and Erik Sandevall, editors, Proceedings of the Second International Conference On Principles of Knowledge Representation and Reasoning, pages 269–276, Cambridge, Massachusetts, 1991.Google Scholar
  12. 12.
    Joseph Y. Halpern and Yoram Moses. A guide to the modal logics of knowledge and belief: preliminary draft. In Proceedings of the Ninth International Joint Conference on Artificial Intelligence, pages 480–490, 1985.Google Scholar
  13. 13.
    Steve Hanks and Drew McDermott. Nonmonotonic logic and temporal projection. Artificial Intelligence, 33:379–412, 1987.CrossRefGoogle Scholar
  14. 14.
    David Harel, Dexter Kozen, and Rohit Parikh. Process logic: expressiveness, decidability, completeness. Journal of Computer and System Sciences, 25:144–170, 1982.CrossRefGoogle Scholar
  15. 15.
    Hirofumi Katsuno and Alberto O. Mendelzon. On the difference between updating a knowledge base and revising it. In James Allen, Richard Fikes, and Erik Sandevall, editors, Proceedings of the Second International Conference On Principles of Knowledge Representation and Reasoning, pages 387–394, Cambridge, Massachusetts, 1991.Google Scholar
  16. 16.
    Vladimir Lifschitz. Formal theories of action. In Matthew L. Ginsberg, editor, Readings in Nonmonotonic Reasoning, pages 410–432. Morgan Kaufmann Publishers, Inc., Los Altos, California, 1987.Google Scholar
  17. 17.
    Zohar Manna, Massimo Paltrinieri, and Richard Waldinger. Temporal planning. In Workshop on Reasoning about Action and Change at IJCAI-93, pages 37–41, Chambéry, France, 1993.Google Scholar
  18. 18.
    John McCarthy and Patrick J. Hayes. Some philosophical problems from the standpoint of Artificial Intelligence. In B. L. Webber and N.J. Nilsson, editors, Readings in Artificial Intelligence, pages 431–450. Morgan Kaufmann Publishers, Inc., Los Altos, California, 1981. Originally published in 1969.Google Scholar
  19. 19.
    Robert C. Moore. A formal theory of knowledge and action. In Jerry R. Hobbs and Robert C. Moore, editors, Formal Theories of the Commonsense World, pages 317–358. Ablex Publishing Corporation, Norwood, New Jersey, 1985.Google Scholar
  20. 20.
    Vaughan R. Pratt. Semantical considerations on Floyd-Hoare logic. In Proceedings of the 17th Annual IEEE Symposium on Foundations of Computer Science, 1976, pages 109–121, 1976.Google Scholar
  21. 21.
    Vaughan R. Pratt. A practical decision method for propositional dynamic logic. In Proceedings 10th Annual Association for Computing Machinery (ACM) Symposium on Theory of Computing, pages 326–337, 1978.Google Scholar
  22. 22.
    Helmut Prendinger and Gerhard Schurz. Reasoning about action and change: A dynamic logic approach. To appear in Journal of Logic, Language and Information.Google Scholar
  23. 23.
    Helmut Prendinger and Gerhard Schurz. Reasoning about action in dynamic logic. In Proceedings Second World Conference on the Fundamentals of Artificial Intelligence (WOCFAI 95), pages 355–366, Paris, France, 1995.Google Scholar
  24. 24.
    Krister Segerberg. A completeness theorem in the modal logic of programs. In Tadeusz Traczyk, editor, Universal Algebra and Applications, volume 9 of Banach Center Publications, pages 31–46, Warsaw, 1982.Google Scholar
  25. 25.
    Yoav Shoham. Agent-oriented programming. Artificial Intelligence, 60:51–92, 1993.CrossRefGoogle Scholar
  26. 26.
    Alvaro Del Val and Yoav Shoham. Deriving properties of belief update from theories of action. Journal of Logic, Language, and Information, 3:81–119, 1994.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Helmut Prendinger
    • 1
  1. 1.Int'l ForschungszentrumSalzburgAustria

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