Rank/activity: A canonical form for binary resolution
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.
KeywordsBinary Tree Internal Node Rank Function Binary Resolution Proof Procedure
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- 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
- 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
- 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