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Symposium on Automatic Demonstration pp 163–190Cite as

Refinement theorems in resolution theory

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Part of the book series: Lecture Notes in Mathematics ((LNM,volume 125))

Abstract

The paper discusses some basic refinements of the Resolution Principle which are intended to improve the speed and efficiency of theorem-proving programs based on this rule of inference. It is proved that two of the refinements preserve the logical completeness of the proof procedure when used separately, but not when used in conjunction. The results of some preliminary experiments with the refinements are given.

The research reported here was supported in part by the Advanced Research Projects Agency of the Office of the Secretary of Defense (SD-183).

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References

  1. Andrews, P. B., "Resolution with Merging", JACM, 15, No. 3, pp. 367–381, July 1968.

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  2. Luckham, D., "The Resolution Principle in Theorem-Proving", Machine Intelligence 1, Collins and Michie (Eds), American Elsevier Inc., New York, 1967.

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  3. Luckham, D., "Some Tree-Paring Strategies for Theorem-Proving", Machine Intelligence 3, D. Michie (Ed), Edinburgh University Press, pp. 95–112, 1968.

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  4. Robinson, J. A., "A Machine-Oriented Logic Based on the Resolution Principle", JACM, 12, No. 1, pp. 23–41, January 1965.

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  5. Robinson, J. A., "Automatic Deduction with Hyper-Resolution", International Journal of Computer Mathematics, Vol. 1, pp. 227–234, 1965.

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  6. Slagle, J. R., "Automatic Theorem-Proving with Renamable and Semantic Resolution", JACM, 14, pp. 687–697, October 1967.

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  7. Wos, L., Robinson, G., Carson, D., "Efficiency and Completeness of the Set of Support Strategy in Theorem Proving", JACM, 12, No. 4, pp. 536–541, October 1965.

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  8. Wos, L., Robinson, G., Carson, D., Shalla, L., "The Concept of Demodulation in Theorem-Proving", JACM, 14, No. 4, pp. 698–704.

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  9. Wos, L., and Robinson, G., "The Maximal Model Theorem", Abstract, Spring 1968 meeting of Association for Symbolic Logic, to appear in J. Symb. Logic.

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Authors
  1. David Luckham
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Editor information

M. Laudet D. Lacombe L. Nolin M. Schützenberger

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© 1970 Springer-Verlag

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Luckham, D. (1970). Refinement theorems in resolution theory. In: Laudet, M., Lacombe, D., Nolin, L., Schützenberger, M. (eds) Symposium on Automatic Demonstration. Lecture Notes in Mathematics, vol 125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060631

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  • DOI: https://doi.org/10.1007/BFb0060631

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-04914-2

  • Online ISBN: 978-3-540-36262-3

  • eBook Packages: Springer Book Archive

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