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Rank/activity: A canonical form for binary resolution

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Automated Deduction — CADE-15 (CADE 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1421))

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Abstract

The rank/activity restriction on binary resolution is introduced. It accepts only a single derivation tree from a large equivalence class of such trees. The equivalence classes capture all trees that are the same size and differ only by reordering the resolution steps. A proof procedure that combines this restriction with the authors' minimal restriction of binary resolution computes each minimal binary resolution tree exactly once.

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References

  1. G. M. Adelson-Velskii and E. M. Landis. An algorithm for the organizaton of information. Soviet Math. Doklady, 3:1259–1263, 1962.

    Google Scholar 

  2. Chin-Liang Chang and Richard Char-Tung Lee. Symbolic Logic and Mechanical Theorem Proving. Academic Press, New York and London, 1973.

    Google Scholar 

  3. Hans de Nivelle. Resolution games and non-liftable resolution orderings. Collegium Logicum, Annals of the Kurt Gödel Society, 2:1–20, 1996.

    MATH  Google Scholar 

  4. J. D. Horton and Bruce Spencer. Bottom up procedures to construct each minimal clause tree once. Technical Report TR97-115, Faculty of Computer Science, University of New Brunwsick, PO Box 4400, Fredericton, New Brunswick, Canada, 1997.

    Google Scholar 

  5. J. D. Horton and Bruce Spencer. Clause trees: a tool for understanding and implementing resolution in automated reasoning. Artificial Intelligence, 92:25–89, 1997.

    Article  MathSciNet  Google Scholar 

  6. J. A. Robinson. A machine-oriented logic based on the resolution principle. J. ACM, 12:23–41, 1965.

    Article  MATH  Google Scholar 

  7. Bruce Spencer and J.D. Horton. Extending the regular restriction of resolution to non-linear subdeductions. In Proceedings of the Fourteenth National Conference on Artificial Intelligence, pages 478–483. AAAI Press/MIT Press, 1997.

    Google Scholar 

  8. Bruce Spencer and J.D. Horton. Efficient procedures to detect and restore minimality, an extension of the regular restriction of resolution. Journal of Automated Reasoning, 1998. accepted for publication.

    Google Scholar 

  9. G. S. Tseitin. On the complexity of derivation in propositional calculus. In Studies in Constructive Mathematics, Seminars in Mathematics: Mathematicheskii Institute, pages 115–125. Consultants Bureau, 1969.

    Google Scholar 

  10. L. Wos. Automated Reasoning: 33 Basic Research Problems. Prentice-Hall, Englewood Cliffs, New Jersey, 1988.

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Computer Science, University of New Brunswick, P.O. Box 4400, E3B 5A3, Fredericton, New Brunswick, Canada

    J. D. Horton & Bruce Spencer

Authors
  1. J. D. Horton
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  2. Bruce Spencer
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Editor information

Claude Kirchner Hélène Kirchner

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© 1998 Springer-Verlag Berlin Heidelberg

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Horton, J.D., Spencer, B. (1998). Rank/activity: A canonical form for binary resolution. In: Kirchner, C., Kirchner, H. (eds) Automated Deduction — CADE-15. CADE 1998. Lecture Notes in Computer Science, vol 1421. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054275

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  • DOI: https://doi.org/10.1007/BFb0054275

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64675-4

  • Online ISBN: 978-3-540-69110-5

  • eBook Packages: Springer Book Archive

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