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A first order resolution calculus with symmetries

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Logic Programming and Automated Reasoning (LPAR 1993)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 698))

Abstract

In this paper, we present a resolution calculus extended by the notion of symmetries. A new deduction rule named symmetry extension is introduced. Combining resolution deduction and symmetry extension yields a new extended resolution deduction concept called SR-deduction (resolution deduction with symmetries). By extending the given clause set by a clause derived by symmetry extension, exponentially shorter refutations may be obtained than by applying resolution to the given clause set.

This research was supported by the Federal Ministry for Research and Technology within the project TASSO under grant no. ITW 8900 C2.

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References

  1. M. Baaz and A. Leitsch. Complexity of Resolution Proofs and Function Introduction. Annals of Pure and Applied Logic, 57:181–215, 1992.

    Article  Google Scholar 

  2. B. Benhamou and L. Sais. Theoretical Study of Symmetries in Propositional Calculus and Applications. In D. Kapur, editor, Proceedings of the Conference on Automated Deduction, pages 281–294, Berlin, 1992. Lecture Notes in Artificial Intelligence, Springer.

    Google Scholar 

  3. W. Bibel. Automated Theorem Proving. Vieweg, Braunschweig, second edition, 1987.

    Google Scholar 

  4. W. Bibel. Short Proofs of the Pigeonhole Formulas Based on the Connection Method. Journal of Automated Reasoning, 6:287–297, 1990.

    Article  Google Scholar 

  5. W. W. Bledsoe. Splitting and Reduction Heuristics in Automatic Theorem Proving. Artificial Intelligence, 2:57–78, 1971.

    Article  Google Scholar 

  6. C. L. Chang and R. C. Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York, 1973.

    Google Scholar 

  7. U. Egly. A Simple Proof for the Pigeonhole Formulae. In B. Neumann, editor, Proceedings of the European Conference on Artificial Intelligence, pages 70–1. John Wiley & Sons, 1992.

    Google Scholar 

  8. U. Egly. Shortening Proofs by Quantifier Introduction. In A. Voronkov, editor, Proceedings of the International Conference on Logic Programming and Automated Reasoning, pages 148–159. Springer Verlag, 1992.

    Google Scholar 

  9. T. W. Hungerford. Algebra. Springer Verlag, 1974.

    Google Scholar 

  10. B. Krishnamurthy. Short Proofs for Tricky Formulas. Acta Informatica, 22(3):253–275, Aug. 1985.

    Article  Google Scholar 

  11. A. Leitsch. On Different Concepts of Resolution. Zeitschrift f. math. Logik und Grundlagen d. Mathematik, 35:71–77, 1989.

    Google Scholar 

  12. D. W. Loveland. Automated Theorem Proving: A Logical Basis, volume 6 of Fundamental Studies in Computer Science. North-Holland Publishing Company, Amsterdem, New York, Oxford, 1978.

    Google Scholar 

  13. N. V. Murray and E. Rosenthal. Short Proofs of the Pigeonhole Formulas Using Path Dissolution. Technical report, Dept. of Computer Science, State Univ. of N.Y. at Albany, Albany N.Y. 12222, 1988.

    Google Scholar 

  14. U. Schöning. Graph Isomorphism is in the Low Hierarchy. In STACS, 1987.

    Google Scholar 

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Andrei Voronkov

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© 1993 Springer-Verlag Berlin Heidelberg

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Egly, U. (1993). A first order resolution calculus with symmetries. In: Voronkov, A. (eds) Logic Programming and Automated Reasoning. LPAR 1993. Lecture Notes in Computer Science, vol 698. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56944-8_46

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  • DOI: https://doi.org/10.1007/3-540-56944-8_46

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-56944-2

  • Online ISBN: 978-3-540-47830-0

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