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What you always wanted to know about clause graph resolution

  • Graph Based Deduction
  • Conference paper
  • First Online:
8th International Conference on Automated Deduction (CADE 1986)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 230))

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Abstract

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.

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Authors and Affiliations

  1. Fachbereich Informatik, Universität Kaiserslautern, D-6750, Kaiserslautern, F.R.Germany

    Norbert Eisinger

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  1. Norbert Eisinger
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Jörg H. Siekmann

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© 1986 Springer-Verlag Berlin Heidelberg

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Eisinger, N. (1986). What you always wanted to know about clause graph resolution. In: Siekmann, J.H. (eds) 8th International Conference on Automated Deduction. CADE 1986. Lecture Notes in Computer Science, vol 230. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16780-3_100

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  • DOI: https://doi.org/10.1007/3-540-16780-3_100

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16780-8

  • Online ISBN: 978-3-540-39861-5

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