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Matching in a Class of Combined Non-disjoint Theories

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Automated Deduction – CADE-19 (CADE 2003)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 2741))

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Abstract

Solving equational problems is an ubiquitous process in automated deduction, where one needs for instance unification in completion procedures to compute critical pairs, and matching to apply rewrite rules. We present new equational matching and unification results in some combinations of non-disjoint equational theories. Some results are already known for theories sharing an appropriate notion of constructors. We investigate the idea of considering theories that are not explicitly based on the notion of constructors. In this direction, a new class of theories is presented, where a theory is defined as a union of two subtheories, one such that shared symbols do not affect the behavior of the theory, and another one given by a term rewrite system on shared symbols. Matching and unification problems are studied for this class of theories, and for unions of theories in this class. Results obtained for the matching problem are particularly relevant.

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Authors and Affiliations

  1. LORIA – INRIA, 615, rue du Jardin Botanique, BP 101, 54602, Villers-lès-Nancy Cedex, France

    Christophe Ringeissen

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  1. Christophe Ringeissen
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Editors and Affiliations

  1. Theoretical Computer Science, TU Dresden, Germany

    Franz Baader

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Ringeissen, C. (2003). Matching in a Class of Combined Non-disjoint Theories. In: Baader, F. (eds) Automated Deduction – CADE-19. CADE 2003. Lecture Notes in Computer Science(), vol 2741. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45085-6_17

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  • DOI: https://doi.org/10.1007/978-3-540-45085-6_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-40559-7

  • Online ISBN: 978-3-540-45085-6

  • eBook Packages: Springer Book Archive

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