What you always wanted to know about clause graph resolution

  • Norbert Eisinger
Graph Based Deduction
Part of the Lecture Notes in Computer Science book series (LNCS, volume 230)


Clause graph (or connection graph) resolution was invented by Robert Kowalski in 1975. Its behaviour differs significantly from that of traditional resolution in clause sets. Standard notions like completeness do not adequately cover the new phenomena introduced by clause graph resolution and standard proof techniques do not work for clause graphs, which are the major reasons why important questions have been open for years. This paper defines a series of relevant properties in precise terms and answers several of the open questions. The clause graph inference system is refutation complete and refutation confluent. Compared to clause set resolution, clause graph resolution does not increase the complexity of simplest refutations. Many well-known restriction strategies are refutation complete, but most are not refutation confluent for clause graph resolution, which renders them useless. Exhaustive ordering strategies do not exist and contrary to a wide-spread conjecture the plausible approximations of exhaustiveness do not ensure the detection of a refutation.

Key words

Clause Graphs Connection Graphs Resolution Strategies Completeness Confluence 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Norbert Eisinger
    • 1
  1. 1.Fachbereich InformatikUniversität KaiserslauternKaiserslauternF.R.Germany

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