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Deriving Focused Calculi for Transitive Relations

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Rewriting Techniques and Applications (RTA 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2051))

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Abstract

We propose a new method for deriving focused ordered resolution calculi, exemplified by chaining calculi for transitive relations. Previously, inference rules were postulated and a posteriori verified in semantic completeness proofs. We derive them from the theory axioms. Completeness of our calculi then follows from correctness of this synthesis. Our method clearly separates deductive and procedural aspects: relating ordered chaining to Knuth-Bendix completion for transitive relations provides the semantic background that drives the synthesis towards its goal. This yields a more restrictive and transparent chaining calculus. The method also supports the development of approximate focused calculi and a modular approach to theory hierarchies.

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Authors and Affiliations

  1. Institut für Informatik, Albert-Ludwigs-Universität Freiburg, Georges-Köhler-Allee, D-79110, Freiburg i. Br., Germany

    Georg Struth

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  1. Georg Struth
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Editor information

Editors and Affiliations

  1. Institute of Information Sciences and Electronics, University of Tsukuba, Tsukuba, 305-8573, Japan

    Aart Middeldorp

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© 2001 Springer-Verlag Berlin Heidelberg

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Struth, G. (2001). Deriving Focused Calculi for Transitive Relations. In: Middeldorp, A. (eds) Rewriting Techniques and Applications. RTA 2001. Lecture Notes in Computer Science, vol 2051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45127-7_22

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  • DOI: https://doi.org/10.1007/3-540-45127-7_22

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42117-7

  • Online ISBN: 978-3-540-45127-3

  • eBook Packages: Springer Book Archive

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