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Reasoning and rewriting with set-relations I: Ground completeness

  • Valentinas Kriaučiukas
  • Michał Walicki
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 933)

Abstract

The paper investigates reasoning with set-relations: intersection, inclusion and identity of 1-element sets. A language is introduced which, interpreted in a multi-algebraic semantics, allows one to specify such relations. An inference system is given and shown sound and refutationally ground-complete for a particular proof strategy which selects only maximal literals from the premise clauses. Each of the introduced set-relations satisfies only two among the three properties of the equivalence relations — we study rewriting with such non-equivalence relations and point out differences from the equational case. As a corollary of the main ground-completeness theorem we obtain ground-completeness of the introduced rewriting technique.

Keywords

Critical Pair Transitive Relation Proof Strategy Ground Atom Empty Clause 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Valentinas Kriaučiukas
    • 1
  • Michał Walicki
    • 2
  1. 1.Department of Mathematical LogicInstitute of Mathematics and InformaticsVilniusLithuania
  2. 2.Deptartment of InformaticsUniversity of BergenNorway

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