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Combining Decision Procedures for Positive Theories Sharing Constructors

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Rewriting Techniques and Applications (RTA 2002)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2378))

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Abstract

This paper addresses the following combination problem: given two equational theories E 1 and E 2 whose positive theories are decidable, how can one obtain a decision procedure for the positive theory of E 1∪E 2? For theories over disjoint signatures, this problem was solved by Baader and Schulz in 1995. This paper is a first step towards extending this result to the case of theories sharing constructors. Since there is a close connection between positive theories and unification problems, this also extends to the non-disjoint case the work on combining decision procedures for unification modulo equational theories.

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References

  1. F. Baader and K.U. Schulz. Unification in the union of disjoint equational theories: Combining decision procedures. In Proc. CADE-11, Springer LNCS 607, 1992.

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  2. F. Baader and K.U. Schulz. Combination of constraint solving techniques: An algebraic point of view. In Proc. RTA’95, Springer LNCS 914, 1995.

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  3. F. Baader and K.U. Schulz. Unification in the union of disjoint equational theories: Combining decision procedures. J. Symbolic Computation 21, 1996.

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  4. F. Baader and C. Tinelli. Combining decision procedures for positive theories sharing constructors. Technical report no. 02-02, Dept. of Computer Science, University of Iowa, 2002 (available at http://cs.uiowa.edu/~tinelli/papers.html).

  5. F. Baader and C. Tinelli. Deciding the word problem in the union of equational theories. Information and Computation, 2002. To appear (preprint available at http://cs.uiowa.edu/~tinelli/papers.html).

  6. E. Domenjoud, F. Klay, and Ch. Ringeissen. Combination techniques for non-disjoint equational theories. In Proc. CADE-12, Springer LNCS 814, 1994.

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  7. W. Hodges. Model Theory, Cambridge University Press, 1993.

    Google Scholar 

  8. G. Nelson and D.C. Oppen. Simplification by cooperating decision procedures. ACM Trans. on Programming Languages and Systems 1, 1979.

    Google Scholar 

  9. D. Pigozzi. The join of equational theories. Colloquium Mathematicum 30, 1974.

    Google Scholar 

  10. Ch. Ringeissen. Personal communication, 2001.

    Google Scholar 

  11. M. Schmidt-Schauß. Unification in a combination of arbitrary disjoint equational theories. J. Symbolic Computation 8, 1989.

    Google Scholar 

  12. M. E. Stickel. A unification algorithm for associative commutative functions. J. ACM 28, 1981.

    Google Scholar 

  13. C. Tinelli and Ch. Ringeissen. Unions of non-disjoint theories and combinations of satisfiability procedures. Theoretical Computer Science, 2002. To appear (preprint available at http://cs.uiowa.edu/~tinelli/papers.html).

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Author information

Authors and Affiliations

  1. TU Dresden, Germany

    Franz Baader

  2. University of Iowa, USA

    Cesare Tinelli

Authors
  1. Franz Baader
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  2. Cesare Tinelli
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Editor information

Editors and Affiliations

  1. LIFL Bâtiment M3, Université de Lille 1, Cité Scientifique, 59655, Villeneuve d’Ascq cedex, France

    Sophie Tison

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© 2002 Springer-Verlag Berlin Heidelberg

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Baader, F., Tinelli, C. (2002). Combining Decision Procedures for Positive Theories Sharing Constructors. In: Tison, S. (eds) Rewriting Techniques and Applications. RTA 2002. Lecture Notes in Computer Science, vol 2378. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45610-4_25

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  • DOI: https://doi.org/10.1007/3-540-45610-4_25

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43916-5

  • Online ISBN: 978-3-540-45610-0

  • eBook Packages: Springer Book Archive

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