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)


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.


Critical Pair Transitive Relation Proof Strategy Ground Atom Empty Clause 
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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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