Deriving Focused Calculi for Transitive Relations

  • Georg Struth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2051)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Georg Struth
    • 1
  1. 1.Institut für InformatikAlbert-Ludwigs-Universität FreiburgFreiburg i. Br.Germany

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