Abstract
This article addresses the problem of indexing and retrieving first-order predicate calculus terms in the context of automated deduction programs. The four retrieval operations of concern are to find variants, generalizations, instances, and terms that unify with a given term. Discrimination-tree indexing is reviewed, and several variations are presented. The path-indexing method is also reviewed. Experiments were conducted on large sets of terms to determine how the properties of the terms affect the performance of the two indexing methods. Results of the experiments are presented.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
References
R. Butler, E. Lusk, W. McCune, and R. Overbeek, ‘Paths to high-performance automated theorem proving’, in J. Siekmann (Editor), Proceedings of the 8th Conference on Automated Deduction, lecture Notes in Computer Science, Vol. 230, pp. 588–597, New York, 1986. Springer-Verlag. An early version appears as Argonne National Laboratory Tech. Memo ANL/MCS-TM-71.
R. Butler and R. Overbeek, ‘A tutorial on the construction of high-performance resolution/paramodulation systems’, Tech. report ANL-90/30, Argonne National Laboratory, Argonne IL, 1990.
E. Charniak, C. Reisbeck, and D. McDermott, Artificial Intelligence Programming, Lawrence Earlbaum Assoc., Hillside, NJ, 1980.
J. Christian, ‘Fast Knuth-Bendix completion: A summary’, In N. Dershowtiz (Editor), Proceedings of the 3rd International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science, Vol. 355, pp. 551–555, New York, 1989. Springer Verlag.
J. Christian, High-Performance Permutative Completion. PhD thesis, The University of Texas at Austin, 1989.
J. Christian, ‘Flatterms, discrimination nets, and fast term rewriting’. Preprint, 1990
J. M. Font, A. J. Rodriguez, and A. Torrens, ‘Wajsberg algebras’, Stochastica, 8(1): 5–31, 1984.
S. Greenbaum, Input Transformations and Resolution Implementation Techniques for Theorem Proving in First-Order Logic. PhD thesis, University of Illinois at Urbana-Champaign, 1986.
L. Henschen and S. Naqvi, ‘An improved filter for literal indexing in resolution systems’, In Proceedings of the Sixth International Joint Conference on Artificial Intelligence, pp. 528–530, 1981.
C. Hewitt, Description and Theoretical Analysis (Using Schemata) of Planner: A Language for Proving Theorems and Manipulating Models in a Robot. PhD thesis, Massachusetts Institute of Technology, Cambridge, MA, January 1971.
E. Lusk, W. McCune, and R. Overbeek, ‘Logic Machine Architecture: Kernel functions’. In D. Loveland (Editor), Proceedings of the 6th Conference on Automated Deduction, Lecture Notes in Computer Science, Vol. 138, pp. 70–84, New York, 1982. Springer-Verlag.
E. Lusk and R. Overbeek, ‘Data structures and control architecture for the implementation of theorem-proving programs’, in R. Kowalski and W. Bibel (Editors), Proceedings of the 5th Conference on Automated Deduction, lecture Notes in Computer Science, Vol. 87, pp. 232–249, New York, 1980. Springer-Verlag.
J. McCharen, R. Overbeek, and L. Wos, ‘Complexity and related enhancements for automated theorem-proving programs Computers and Mathematics with Applications, 2: 1–16, 1976.
W. McCune, ‘An indexing method for finding more general formulas’, Association for Automated Reasoning Newsletter, 1(9): 7–8, January, 1988.
W. McCune, ‘Discrimination tree indexing for large sets of formulas: Experiments and the structure of terms’. Notes on a talk given at the AAI symposium on High-performance theorem proving, Stanford, CA, March 1989.
W. McCune, ‘OTTER 2.0 Users Guide’. Tech. Report. ANL-90/9, Argonne National Laboratory, Argonne, IL, March 1990.
R. Overbeek A New Class of Automated Theorem-Proving Algorithms. PhD thesis, Pennsylvania State University, 1971.
K. Ramamohanarao and J. Shepard, ‘A superimposed codeword indexing scheme for very large Prolog databases’. In Third International Conference on Logic Programming, Lecture Notes in Computer Science, Vol. 225, pp. 569–576, New York, 1986. Springer-Verlag.
J. Slaney and E. Lusk, ‘Parallelizing the closure computation in automated deduction’, in M. Stickel (Editor), Proceedings of the 10th International Conference on Automated Deduction, Lecture Notes in Artificial Intelligence, Vol. 449, pp. 28–39, New York, July 1990. Springer-Verlag. Extended abstract.
M. Stickel, ‘The path-indexing method for indexing terms’, Technical Note 473, Artificial Intelligence Center, SRI International, Menlo Park, CA, October 1989.
S. Winkler, ‘Absorption and idempotency criteria for a problem in near-boolean algebras’. Preprint MCS-P177–0990, Argonne National Laboratory, Argonne, IL, August 1990.
M. Wise and D. Powers, ‘Indexing Prolog clauses via superimposed codewords and field encoded words’. In IEEE Conference on Logic Programming, pp. 203–210, Atlantic City, 1984.
Author information
Authors and Affiliations
Additional information
This was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, U.S. Department of Energy, under Contract W-31-109-Eng-38.
Rights and permissions
About this article
Cite this article
McCune, W. Experiments with discrimination-tree indexing and path indexing for term retrieval. J Autom Reasoning 9, 147–167 (1992). https://doi.org/10.1007/BF00245458
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00245458