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Execution and Proof in a Horn-Clause Temporal Logic

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Advances in Temporal Logic

Part of the book series: Applied Logic Series ((APLS,volume 16))

Abstract

Both proof, via clausal resolution, and execution, via the imperative future approach, depend on the use of a normal form for temporal formulae. While the systems developed have centred around the use of an unrestricted normal form, we here consider a Horn clause-like version of the normal form and its effect on both execution and resolution. This refined normal form is as expressive as the original, and represents a natural way to describe systems, yet allows both execution and resolution to be implemented more efficiently in practice.

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References

  • M. Abadi. Temporal-Logic Theorem Proving. PhD thesis, Department of Computer Science, Stanford University, March 1987.

    Google Scholar 

  • H. Barringer, M. Fisher, D. Gabbay, and A. Hunter. Meta-Reasoning in Executable Temporal Logic. In Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning (KR), April 1991.

    Google Scholar 

  • H. Barringer, M. Fisher, D. Gabbay, G. Gough, and R. Owens. METATEM: An Introduction. Formal Aspects of Computing, 7 (5): 533–549, 1995.

    Article  Google Scholar 

  • H. Barringer, M. Fisher, D. Gabbay, R. Owens, and M. Reynolds, editors. The Imperative Future: Principles of Executable Temporal Logics. Research Studies Press, Chichester, United Kingdom, 1996.

    Google Scholar 

  • C. L. Chang. The Unit Proof and the Input Proof in Theorem Proving. ACM Journal, 17: 698–707, 1970.

    Article  Google Scholar 

  • C. Dixon. Search Strategies for Resolution in Temporal Logics. In Proceedings of the Thirteenth International Conference on Automated Deduction (CADE), volume 1104 of Lecture Notes in Computer Science, New Brunswick, New Jersey, July/August 1996.

    Google Scholar 

  • E. A. Emerson and A. P. Sistla. Deciding full branching time logic. Information and Control, 61: 175–201, 1984.

    Article  Google Scholar 

  • L. Fariñas del Cerro and M. Penttonen, editors. Intensional Logics for Programming. Oxford University Press, 1992.

    Google Scholar 

  • M. Finger, P. McBrien, and R. Owens. Databases and Executable Temporal Logic. In Proceedings of the ESPRIT Conference, November 1991.

    Google Scholar 

  • M. Finger, M. Fisher, and R. Owens. METATEM at Work: Modelling Reactive Systems Using Executable Temporal Logic. In Sixth International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems (IEA/AIE),Edinburgh, U.K., June 1993. Gordon and Breach Publishers.

    Google Scholar 

  • M. Fisher. A Resolution Method for Temporal Logic. In Proceedings of the Twelfth International Joint Conference on Artificial Intelligence, Sydney, Australia, 1991.

    Google Scholar 

  • M. Fisher. A Survey of Concurrent METATEM — The Language and its Applications. In First International Conference on Temporal Logic (ICTL), Bonn, Germany, July 1994.

    Google Scholar 

  • M. Fisher. A Normal Form for Temporal Logic and its Application in TheoremProving and Execution. Journal of Logic and Computation, 7 (4), August 1997.

    Google Scholar 

  • M. Fisher and R. Owens, editors. Executable Modal and Temporal Logics, volume 897 of Lecture Notes in Artificial Intelligence. Springer-Verlag, February 1995.

    Google Scholar 

  • D. Gabbay, A. Pnueli, S. Shelah, and J. Stavi. The Temporal Analysis of Fairness. In Proceedings of the Seventh Symposium on the Principles of Programming Languages, 1980.

    Google Scholar 

  • N. D. Jones and W. T. Lasser. Complete problems for deterministic polynomial time. Theoretical Computer Science, 3: 107–117, 1977.

    Google Scholar 

  • R. McNaughton. Testing and Generating Infinite Sequences by a Finite Automaton. Information and Control, 9: 521–530, 1966.

    Article  Google Scholar 

  • B. Moszkowski. Executing Temporal Logic Programs. Cambridge University Press, Cambridge, U.K., 1986.

    Google Scholar 

  • M. Peim. Propositional Temporal Resolution Over Labelled Transition Systems. Unpublished Technical Note, Department of Computer Science, University of Manchester, 1994.

    Google Scholar 

  • J. A. Robinson. A Machine—Oriented Logic Based on the Resolution Principle. ACM Journal, 12 (1): 23–41, January 1965.

    Article  Google Scholar 

  • S. Safra and M. Y. Vardi. On w-Automata and Temporal Logic. In STOC,pages 127–137, Seattle, Washington, May 1989. ACM.

    Google Scholar 

  • A. P. Sistla and E. M. Clarke. Complexity of propositional linear temporal logics. ACM Journal, 32 (3): 733–749, July 1985.

    Article  Google Scholar 

  • M. Y. Vardi and P. Wolper. Automata-theoretic Techniques for Modal Logics of Programs. Journal of Computer and System Sciences, 32 (2): 183–219, April 1986.

    Article  Google Scholar 

  • P. Wolper. The Tableau Method for Temporal Logic: An overview. Logique et Analyse, 110–111:119–136, June-Sept 1985.

    Google Scholar 

  • L. Wos, D. Carson, and G. Robinson. The Unit Preference Strategy in Theorem Proving. In Proceedings of AFIPS Fall Joint Computer Conference. Thompson Book Co., 1964.

    Google Scholar 

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© 2000 Springer Science+Business Media Dordrecht

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Dixon, C., Fisher, M., Reynolds, M. (2000). Execution and Proof in a Horn-Clause Temporal Logic. In: Barringer, H., Fisher, M., Gabbay, D., Gough, G. (eds) Advances in Temporal Logic. Applied Logic Series, vol 16. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9586-5_21

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  • DOI: https://doi.org/10.1007/978-94-015-9586-5_21

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-5389-3

  • Online ISBN: 978-94-015-9586-5

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