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International Conference on Automated Deduction

CADE 2015: Automated Deduction - CADE-25 pp 311–325Cite as

Quantifier-Free Equational Logic and Prime Implicate Generation

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

Abstract

An algorithm for generating prime implicates of sets of equational ground clauses is presented. It consists in extending the standard Superposition Calculus with rules that allow attaching hypotheses to clauses to perform additional inferences. The hypotheses that lead to a refutation represent implicates of the original set of clauses. The set of prime implicates of a clausal set can thus be obtained by saturation of this set. Data structures and algorithms are also devised to represent sets of constrained clauses in an efficient and concise way.

Our method is proven to be correct and complete. Practical experimentations show the relevance of our method in comparison to existing approaches for propositional or first-order logic.

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Notes

  1. 1.

    Using logical entailment makes the calculus incomplete due to the deletion of clauses whose constraint is not in normal form.

  2. 2.

    Many thanks to Prof. L. Simon for providing the executable file.

  3. 3.

    Many thanks to Prof. H. Nabeshima for providing the executable file.

  4. 4.

    Personal communication of Prof. Nabeshima.

  5. 5.

    http://users.cecs.anu.edu.au/~baumgart/systems/smttotptp/.

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Author information

Authors and Affiliations

  1. Grenoble Informatics Laboratory, Grenoble, France

    Mnacho Echenim, Nicolas Peltier & Sophie Tourret

  2. Grenoble INP - Ensimag, Saint-martin-d’hères, France

    Mnacho Echenim

  3. Université Grenoble 1, Grenoble, France

    Sophie Tourret

  4. CNRS, Toulouse, France

    Nicolas Peltier

Authors
  1. Mnacho Echenim
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  2. Nicolas Peltier
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  3. Sophie Tourret
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Corresponding author

Correspondence to Nicolas Peltier .

Editor information

Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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Echenim, M., Peltier, N., Tourret, S. (2015). Quantifier-Free Equational Logic and Prime Implicate Generation. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_21

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21400-9

  • Online ISBN: 978-3-319-21401-6

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