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Reasoning with preorders and dynamic sorts using free variable tableaux

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Artificial Intelligence and Symbolic Mathematical Computation (AISMC 1996)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1138))

Abstract

In this paper we present a three valued many sorted logic for dealing with preorders, incorporating subsort relations into the syntax of the language, and where formulas taking the third boolean value as interpretation contain a term or a predicate which is not well-sorted w.r.t. the signature. For this logic a ground tableau-based deduction method and a free variable extension version are proposed, proving their completeness.

This paper has been supported by Proyecto Precompetitivo PR 219/94 5564.

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References

  1. L. Bachmair, H. Ganzinger, Ordered Chaining Calculi for First-Order Theories of Binary Relations. MPI-I-95-2-009, 1995.

    Google Scholar 

  2. B. Beckert, R. Hähnle. An Improved Method for Adding Equality to Free Variable Semantic Tableaux. Proc. CADE'10. LNAI 607, 507–521, 1992.

    Google Scholar 

  3. W. W. Bledsoe, K. Kunen, R. Shostak. Completeness Results for Inequality Provers. Artificial Intelligence 27, 255–288, 1985.

    Article  Google Scholar 

  4. M. Fitting. First-Order modal tableaux. J. of Automated Reasoning 4, 191–213, 1988.

    Google Scholar 

  5. M. Fitting. First-Order Logic and Automated Theorem Proving. Second edition. Springer, 1996.

    Google Scholar 

  6. A. Gavilanes-Franco, F. Lucio-Carrasco. A first order logic for partial functions. TCS 74, 37–69, 1990.

    Google Scholar 

  7. A. Gavilanes, J. Leach, S. Nieva. Free Variable Tableaux for a Many Sorted Logic with Preorders. To appear in Proc. AMAST'96, Springer, 1996.

    Google Scholar 

  8. A. Gavilanes, J. Leach, P. J. Martín, S. Nieva. Reasoning with Preorders and Dynamic Sorts using Free Variable Tableaux. Technical Report DIA 34/96, Univ. Complutense de Madrid, 1996.

    Google Scholar 

  9. J. A. Goguen, J. Meseguer. Order-sorted algebra I: Eguational deduction for multiple inheritance, overloading, exceptions and partial operations. TCS 105, 217–273, 1992.

    Article  Google Scholar 

  10. R. Hähnle, P. H. Schmitt. The liberalized δ-rule in free variable semantic tableaux. J. of Automated Reasoning 13, 211–221, 1994.

    Google Scholar 

  11. J. Jaffar, M. J. Maher. Constraint logic programming: A survey. J. of Logic Programming 19/20, 503–582, 1994.

    Article  Google Scholar 

  12. J. Levy, J. Agustí. Bi-rewriting, a term rewriting technique for monotonie order relations. Proc. RTA'93. LNCS 690, 17–31, 1993.

    Google Scholar 

  13. J. Leach, S. Nieva. Foundations of a Theorem Prover for Functional and Mathematical Uses. J. of Applied Non-Classical Logics 3(1), 7–38, 1993.

    Google Scholar 

  14. F. Oppacher, E. Suen. HARP: A Tableau-Based Theorem Prover. J. of Automated Reasoning 4, 69–100, 1988.

    Google Scholar 

  15. M. Schmidt-Schauss. Computational aspects of an order sorted logic with term declarations. LNAI 395. Springer,1989.

    Google Scholar 

  16. P.H. Schmitt, W. Wernecke. Tableau Calculus for Order Sorted Logic. Proc. Workshop on Sorts and Types in Artificial Intelligence (1989). LNAI 418, 49–60, 1990.

    Google Scholar 

  17. C. Walther. A Many-sorted Calculus based on Resolution and Paramodulation. Research Notes in Artificial Intelligence. Pitman, 1987.

    Google Scholar 

  18. C. Walther. Many Sorted Inferences in Automated Theorem Proving. Proc. Workshop on Sorts and Types in Artificial Intelligence (1989). LNAI 418, 18–48, 1990.

    Google Scholar 

  19. C. Weidenbach. A sorted logic using dynamic sorts. MPI-I-91-218, 1991.

    Google Scholar 

  20. C. Weidenbach. First-Order Tableaux with Sorts. J. of the Interest Group in Pure and Applied Logics 3(6), 887–907, 1995.

    Google Scholar 

  21. C. Weidenbach. Unification in Sort Theories and its Applications. Annals of Mathematics and Artificial Intelligence. To appear.

    Google Scholar 

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Authors and Affiliations

  1. Dep. de Informática y Automática, Universidad Complutense de Madrid, Spain

    A. Gavilanes, J. Leach, P. J. Martín & S. Nieva

Authors
  1. A. Gavilanes
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  2. J. Leach
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  3. P. J. Martín
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  4. S. Nieva
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Editor information

Jacques Calmet John A. Campbell Jochen Pfalzgraf

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© 1996 Springer-Verlag Berlin Heidelberg

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Gavilanes, A., Leach, J., Martín, P.J., Nieva, S. (1996). Reasoning with preorders and dynamic sorts using free variable tableaux. In: Calmet, J., Campbell, J.A., Pfalzgraf, J. (eds) Artificial Intelligence and Symbolic Mathematical Computation. AISMC 1996. Lecture Notes in Computer Science, vol 1138. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61732-9_69

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  • DOI: https://doi.org/10.1007/3-540-61732-9_69

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-61732-7

  • Online ISBN: 978-3-540-70740-0

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