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A linear format for resolution

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

Abstract

The Resolution procedure of J. A. Robinson is shown to remain a complete proof procedure when the refutations permitted are restricted so that clauses C and D and resolvent R of clauses C and D meet the following conditions: (1) C is the resolvent immediately preceding R in the refutation if any resolvent precedes R, (2) either D is a member of the given set S of clauses or D precedes C in the refutation and R subsumes an instance of C or R is the empty clause, and (3) R is not a tautology.

Keywords

  • Initial Segment
  • Primary Branch
  • Primary Node
  • Ground Instance
  • Final Segment

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported by the Advanced Research Projects Agency of the Office of the Secretary of Defense (F44620-67-C-0058) and is monitored by the Air Force Office of Scientific Research. This document has been approved for public release and sale; its distribution is unlimited.

This research was also partially supported by NSF Grant GP-7064.

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Bibliography

  1. Andrews, P. B. "Resolution with merging", J.ACM, 15, 3 (July 1968), 367–381.

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  2. Robinson, J. A. "A machine-oriented logic based on the resolution principle," J.ACM, 12, 1 (Jan. 1965), 23–41.

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  3. Robinson, J. A. "Automatic deduction with hyper-resolution", Int. J. Computer Math. 1 (1965), 227–234.

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  4. Wos, L., G. A. Robinson and D. F. Carson. "Efficiency and completeness of the set of support strategy in theorem proving", J.ACM 12, 4 (Oct. 1965), 536–541.

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© 1970 Springer-Verlag

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Loveland, D.W. (1970). A linear format for resolution. 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/BFb0060630

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  • DOI: https://doi.org/10.1007/BFb0060630

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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