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PDL-based framework for reasoning about actions

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 992))

Abstract

Prepositional Dynamic Logics (PDL's) provide a suitable formal framework for modeling actions and reasoning about them. However, the basic language of PDL's lack several features that are important for a sophisticated treatment of actions. In this paper, we present a new logic that is obtained by enriching the basic PDL with powerful modeling constructs that allow us to represent determinism and non-determinisms, concurrency, hierarchies, mutual exclusion, backward execution, and non-execution of actions. We demonstrate, by means of examples, the expressive power of the formalism. In particular, we show that although nonmonotonicity is not generally captured by PDL's, our logic is perfectly suited for exploiting monotonic solutions to the frame problem. Finally, we establish that the proposed formalism is decidable, and that the basic reasoning problems are EXPTIME-complete.

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References

  1. P. Blackburn and E. Spaan. A modal perspective on computational complexity of attribute value grammar. Journal of Logic, Language and Computation, 2:129–169, 1993.

    Google Scholar 

  2. C. Boutilier and N. Friedman. Nondeterministic actions and the frame problem. In [3], 39–44, 1995.

    Google Scholar 

  3. C. Boutilier, M. Goldszmidt, T. Dean, S. Hanks, D. Heckerman, and R. Reiter, editors. Working notes of the AAAI 1995 Spring Symposium on Extending Theories of Action: Formal and Practical Applications, Stanford, CA, USA, 1995.

    Google Scholar 

  4. P. Cohen and H. Levesque. Intention is choice with communication. Artificial Intelligence, 42:213–261, 1990.

    Google Scholar 

  5. G. De Giacomo. Decidability of Class-Based Knowledge Representation Formalisms and their Application to Medical Terminology Servers. PhD thesis, Dipartimento di Informatica e Sistemistica, Università di Roma ”La Sapienza”, 1995.

    Google Scholar 

  6. G. De Giacomo and M. Lenzerini. Boosting the correspondence between description logics and propositional dynamic logics. In Proceedings of the 12th National Conference on Artificial Intelligence, pages 205–212, 1994.

    Google Scholar 

  7. G. De Giacomo and M. Lenzerini. Description logics with inverse roles, functional restrictions, and n-ary relations. In Proceedings of the 4th European Workshop on Logics in Artificial Intelligence, LNAI 838, pages 332–346. Springer-Verlag, 1994.

    Google Scholar 

  8. G. De Giacomo and M. Lenzerini. Enhanced propositional dynamic logic for reasoning about concurrent actions (extended abstract). In [3], pages 62–67, 1995.

    Google Scholar 

  9. N. J. Fisher and R. E. Ladner. Propositional dynamic logic of regular programs. Journal of Computer and System Sciences, 18:194–211, 1979.

    Google Scholar 

  10. N. Friedman and J. Halpern. On the complexity of conditional logics. In Proc. of the 4th Int. Conf. on Principles of Knowledge Representation and Reasoning, 1994.

    Google Scholar 

  11. C. Green. Theorem proving by resolution as basis for question-answering systems. In Machine Intelligence, volume 4, pages 183–205. American Elsevier, 1969.

    Google Scholar 

  12. G. Grosse. Propositional state event logic. In Proceedings of the 4th European Workshop on Logics in Artificial Intelligence, LNAI 838, pages 316–331. Springer-Verlag, 1994.

    Google Scholar 

  13. A. Haas. The case for domain-specific frame axioms. In Proc. of the Workshop on the Frame Problem, pages 343–348. Morgan Kaufmann Publishers, 1987.

    Google Scholar 

  14. J. Halpern and Y. Moses. A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54:319–379, 1992.

    Google Scholar 

  15. D. Harel. Dynamic logic. In D. M. Gabbay and F. Guenthner, editors, Handbook of Philosophical Logic, pages 497–603. D. Reidel Publishing Company, Oxford, 1984.

    Google Scholar 

  16. M. Hennessy and R. Milner. Algebraic laws for nondetrminism and concurrency. Journal of Association for Computing Machinery, 32:137–162, 1985.

    Google Scholar 

  17. H. Kautz. A first order dynamic logic for planning. Master's thesis, Department of Computer Science, University of Toronto, Toronto, Ontario, Canada, 1980.

    Google Scholar 

  18. D. Kozen. Results on the propositional mu-calculus. Theoretical Computer Science, 27:333–355, 1983.

    Google Scholar 

  19. D. Kozen and J. Tiuryn. Logics of programs. In J. van Leeuwen, editor, Handbook of Theoretical Computer Science, pages 790–840. Elsevier Science Publishers, 1990.

    Google Scholar 

  20. K. J. Larsen. Proof systems for satisfiability in Hennessy-Milner logic with recursion. Theoretical Computer Science, 72:265–288, 1990.

    Google Scholar 

  21. F. Lin and R. Reiter. State constraints revisited. Journal of Logic and Computation, Special Issue on Action and Processes, 4(5):655–678, 1994.

    Google Scholar 

  22. M. Milner. Communication and Concurrency. Prentice-Hall, 1989.

    Google Scholar 

  23. R. Parikh. Propositional dynamic logic of programs: A survey. In Proceedings of the 1st Workshop on Logic of Programs, LNCS 125, pages 102–144. Springer-Verlag, 1981.

    Google Scholar 

  24. R. Reiter. The frame problem in the situation calculus: A simple solution (sometimes) and a completeness result for goal regression. In Artificial Intelligence and Mathematical Theory of Computation: Papers in Honor of John McCarthy, pages 359–380. Academic Press, 1991.

    Google Scholar 

  25. R. Reiter. Formalizing database evolution in the situation calculus. In Proc. Int. Conf. on Fifth Generation Computer Systems, pages 600–609, 1992.

    Google Scholar 

  26. R. Reiter. The projection problem in the situation calculus: a soundness and completeness result, with an application to database updates. In Proc. First Int. Conf. on AI Planning Systems, pages 198–203, 1992.

    Google Scholar 

  27. R. Reiter. Proving properties of states in the situation calculus. Artificial Intelligence, 64:337–351, 1993.

    Google Scholar 

  28. S. Rosenschein. Plan synthesis: a logical approach. In Proc. of the 8th Int. Joint Conf. on Artificial Intelligence, 1981.

    Google Scholar 

  29. K. Schild. A correspondence theory for terminological logics: Preliminary report. In Proc. of the 12th Int. Joint Conf. on Artificial Intelligence, 1991.

    Google Scholar 

  30. L. Schubert. Monotonie solution of the frame problem in the situation calculus: an efficient method for worlds with fully specified actions. In Knowledge representation and Defeasible Reasoning, pages 23–67. Kluwer Academic Press, 1990.

    Google Scholar 

  31. C. Stirling. Modal and temporal logic. In S. Abramsky, D. M. Gabbay, and T. S. E. Maibaum, editors, Handbook of Logic in Computer Science, pages 477–563. Clarendon Press, Oxford, 1992.

    Google Scholar 

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Marco Gori Giovanni Soda

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© 1995 Springer-Verlag Berlin Heidelberg

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De Giacomo, G., Lenzerini, M. (1995). PDL-based framework for reasoning about actions. In: Gori, M., Soda, G. (eds) Topics in Artificial Intelligence. AI*IA 1995. Lecture Notes in Computer Science, vol 992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60437-5_10

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  • DOI: https://doi.org/10.1007/3-540-60437-5_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60437-2

  • Online ISBN: 978-3-540-47468-5

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