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International Conference on Logic for Programming Artificial Intelligence and Reasoning

LPAR 2000: Logic for Programming and Automated Reasoning pp 436–450Cite as

The Boundary between Decidable and Undecidable Fragments of the Fluent Calculus

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Part of the book series: Lecture Notes in Artificial Intelligence ((LNAI,volume 1955))

Abstract

We consider entailment problems in the fluent calculus as they arise in reasoning about actions. Taking into account various fragments of the fluent calculus we formally show decidability results, establish their complexity, and prove undecidability results. Thus we draw a boundary between decidable and undecidable fragments of the fluent calculus.

new address: University of Leicester, Department of Mathematics and Computer Science, University Road, Leicester LE1 7RH, UK

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References

  1. W. Bibel. A deductive solution for plan generation. New Generation Computing, 4:115–132, 1986. 436

    MATH  Google Scholar 

  2. W. Bibel. Let’s plan it deductively! Artificial Intelligence, 103(1–2):183–208, 1998. 436

    Article  MATH  MathSciNet  Google Scholar 

  3. M. C. A. J. Bonner and M. Kifer. Transaction logic programming. Theoretical Computer Science, 133:205–265, 1994. 436

    Article  MATH  MathSciNet  Google Scholar 

  4. P. Doherty, J. Gustafsson, L. Karlsson, and J. Kvanström. Tal: Temporal action logics language specification and tutorial. Electronic Transactions on Artificial Intelligence, 2(3–4):273–306, 1998. 436

    MathSciNet  Google Scholar 

  5. S. Feferman and R. L. Vaught. The first order properties of algebraic systems. Fund. Math., 47:57–103, 1959. 444

    MATH  MathSciNet  Google Scholar 

  6. M. J. Fischer and M. O. Rabin. Super-exponential complexity of Presburger arithmetic. In Complexity of Computation, SIAM-AMS Proc. Vol. VII, pages 27–41. AMS, 1974. 442, 442

    MathSciNet  Google Scholar 

  7. M. Gelfond and V. Lifschitz. Action languages. Electronic Transactions on Artificial Intelligence, 2(3–4):193–210, 1998. 436

    MathSciNet  Google Scholar 

  8. J. Y. Girard. Linear logic. Journal of Theoretical Computer Science, 50(1):1–102, 1987. 436

    Article  MATH  MathSciNet  Google Scholar 

  9. S. Hölldobler. On deductive planning and the frame problem. In A. Voronkov, editor, Proceedings of the Conference on Logic Programming and Automated Reasoning, pages 13–29. Springer, LNCS, 1992. 437

    Google Scholar 

  10. S. Hölldobler. Descriptions in the fluent calculus. In Proceedings of the International Conference on Artificial Intelligence, volume III, pages 1311–1317, 2000. 436

    Google Scholar 

  11. S. Hölldobler and J. Schneeberger. A new deductive approach to planning. New Generation Computing, 8:225–244, 1990. 436

    Article  MATH  Google Scholar 

  12. S. Hölldobler and H.-P. Störr. Solving the entailment problem in the fluent calculus with binary decision diagrams. In Proceedings of the First International Conference on Computational Logic, pages 747–761, 2000. 448

    Google Scholar 

  13. R. A. Kowalski and M. Sergot. A logic-based calculus of events. New Generation Computing, 4:67–95, 1986. 436

    Google Scholar 

  14. J. Lambek. How to program an infinite abacus. Canad. Math. Bull., 4:295–302, 1961. 446, 448

    MathSciNet  Google Scholar 

  15. H. Lehmann and M. Leuschel. Decidability results for the propositional fluent calculus. In Proceedings of First International Conference on Computational Logic, pages 762–776, 2000. 448

    Google Scholar 

  16. H. Levesque, F. Pirri, and R. Reiter. Foundations for a calculus of situations. Electronic Transactions on Artificial Intelligence, 2(3–4):159–192, 1998. 436

    MathSciNet  Google Scholar 

  17. M. Masseron, C. Tollu, and J. Vauzielles. Generating plans in linear logic. In Foundations of Software Technology and Theoretical Computer Science, pages 63–75. Springer, LNCS 472, 1990. 436

    Google Scholar 

  18. J. McCarthy. Situations and actions and causal laws. Stanford Artificial Intelligence Project: Memo 2, 1963. 436

    Google Scholar 

  19. J. McCarthy and P. J. Hayes. Some philosophical problems from the standpoint of Artificial Intelligence. In B. Meltzer and D. Michie, editors, Machine Intelligence 4, pages 463–502. Edinburgh University Press, 1969. 436

    Google Scholar 

  20. A. R. Meyer. Weak monadic second order theory of one successor is not elementary recursive. In Proc. Logic Colloquium, volume 453 of Lecture Notes in Mathematics, pages 132–154. Springer, 1975. 444

    Google Scholar 

  21. M. L. Minsky. Recursive unsolvability of Post’s problem of “tag” and other topics in theory of Turing machines. The Annals of Mathematics, 74(3):437–455, 1961. 446, 448

    Article  MathSciNet  Google Scholar 

  22. D. C. Oppen. A 22 2 cn upper bound on the complexity of Presburger arithmetic. J. Comp. System Sci., 16:323–332, 1978. 442

    Article  MATH  MathSciNet  Google Scholar 

  23. M. Presburger. Über die Vollständigkeit eines gewissen Systems der Arithmetik ganzer Zahlen, in welchem die Addition als einzige Operation hervortritt. Sprawozdaniez 1 Kongresu Matematyków Krajow Slowiańskich, Ksiaznica Atlas, pages 92–10, 1930. 441

    Google Scholar 

  24. M. O. Rabin. Decidability of second-order theories and automata on infinite trees. Trans. Amer. Math. Soc., 141:1–35, 1969. 444

    Article  MATH  MathSciNet  Google Scholar 

  25. E. Sandewall. Features and Fluents. The Representation of Knowledge about Dynamical Systems. Oxford University Press, 1994. 436

    Google Scholar 

  26. M. Shanahan. Solving the Frame Problem: A Mathematical Investigation of the Common Sense Law of Inertia. MIT Press, 1997. 436

    Google Scholar 

  27. S. Shelah. The monadic theory of order. Annals of Mathematics, 102:379–419, 1975. 444

    Article  MathSciNet  Google Scholar 

  28. H.-P. Störr and M. Thielscher. A new equational foundation for the fluent calculus. In Proceedings of the First International Conference on Computational Logic, pages 733–746, 2000. 437

    Google Scholar 

  29. E. Ternovskaia. Automata theory for reasoning about actions. In Proceedings of the International Joint Conference on Artificial Intelligence, pages 153–158, 1999. 437, 437, 448, 448

    Google Scholar 

  30. M. Thielscher. Introduction to the fluent calculus. Electronic Transactions on Artificial Intelligence, 2(3–4):179–192, 1998. 436, 440

    MathSciNet  Google Scholar 

  31. Michael Thielscher. Nondeterministic actions in the fluent calculus: Disjunctive state update axioms. In S. Hölldobler, editor, Intellectics and Computational Logic. Kluwer Academic, 2000. 436

    Google Scholar 

  32. Michael Thielscher. Representing the knowledge of a robot. In Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR), pages 109–120, 2000. 436

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Künstliche Intelligenz, TU Dresden, D-01062, Dresden, Germany

    Steffen Hölldobler

  2. Institut für Algebra, TU Dresden, D-01062, Dresden, Germany

    Dietrich Kuske

Authors
  1. Steffen Hölldobler
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  2. Dietrich Kuske
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Editor information

Editors and Affiliations

  1. CNRS, Université de Paris 7, case 7012, 2 place Jussieu, 75251, Paris Cedex 05, France

    Michel Parigot

  2. Computer Science Department, University of Manchester, Oxford Rd, M13 9PL, Manchester, UK

    Andrei Voronkov

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© 2000 Springer-Verlag Berlin Heidelberg

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Hölldobler, S., Kuske, D. (2000). The Boundary between Decidable and Undecidable Fragments of the Fluent Calculus. In: Parigot, M., Voronkov, A. (eds) Logic for Programming and Automated Reasoning. LPAR 2000. Lecture Notes in Artificial Intelligence(), vol 1955. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44404-1_28

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  • DOI: https://doi.org/10.1007/3-540-44404-1_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41285-4

  • Online ISBN: 978-3-540-44404-6

  • eBook Packages: Springer Book Archive

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