Abstract
Recently Lee and Plaisted proposed a theorem-proving method, the hyperlinking proof procedure, to eliminate duplication of instances of clauses during the process of inference. A theorem prover, CLIN, which implements the procedure was also constructed. In this implementation, redundant work on literal unification checking, partial unification checking, and duplicate instance checking is performed repetitively, resulting in a large overhead when many rounds of hyperlinking are needed for an input problem. We propose a technique that maintains information across rounds in shared network structures, so that the redundant work in each hyperlinking round can be avoided. Empirical performance comparison has been done between CLIN and CLIN-net, which is the theorem prover with shared network structures, and some results are shown. Problems related to memory overhead and literal ordering are discussed.
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References
Bledsoe, W.W.: Non-resolution theorem proving,Artificial Intelligence 9 (1977), 1–35.
Butler, R. and Overbeek, R.: A tutorial on the construction of high-performance resolution/paramodulation systems, Technical Report ANL-90/30, Argonne National Laboratory, Argonne, Ill., 1990.
Chang, C. and Lee, R.:Symbolic Logic and Mechanical Theorem Proving, Academic Press, New York, 1973.
Charniak, E., Reisbeck C. and McDermott, D.:Artificial Intelligence Programming, Lawrence Earlbaum Assoc., Hillside, N.J., 1980.
Christian, J.: Fast knuth-Bendix completion: A summary, inProc. 3rd International Conference on Rewriting Techniques and Applications, Lecture Notes in Computer Science 355, New York, 1990, pp. 551–555.
Davis, M. and Putnam, H.: A computing procedure for quantification theory,J. Assoc. Comput. Machinery 7 (1960), 201–215.
Forgy, C. L.: Rete: A fast algorithm for the many pattern/many object pattern match problem,Artificial Intelligence 19 (1982), 17–37.
Freuder, E. C.: Synthesizing contraint expressions,Comm. Assoc. Comput. Machinery 21 (1978), 958–966.
Fujita, H. and Hasegawa, R.: A model generation theorem prover in KL1 using a ramified-stack algorithm, inProc. 8th International Conference on Logic Programming, 1991, pp. 535–548.
Giarratano, J. and Riley, G.:Expert Systems: Principles and Programming, PWS-KENT Publishing Company, Boston, 1989.
Greenbaum, S.:Input Transformations and Resolution Implementation Techniques for Theorem Proving in First-Order Logic, Ph.D. thesis, University of Illinois at Urbana-Champaign, 1986.
Lee, S.-J. and Plaisted, D.: New applications of a fast propositional calculus decision procedure, inProc. 8th Biennial Conference of Canadian Society for Computational Studies of Intelligence, Ottawa, Canada, 1990, pp. 204–211.
Lee, S.-J. and Plaisted, D.: Eliminating duplication with the hyperlinking strategy,J. Automated Reasoning 9(1) (1992), 25–42.
Lee, S.-J. and Plaisted, D.: Problem solving by searching for models with a theorem prover,Artificial Intelligence (to appear).
Loveland, D.:Automated Theorem Proving: A Logical Basis, North-Holland, New York, 1978.
Lusk, E. and Overbeek, R.: Non-Horn problems,J. Automated Reasoning 1 (1985), 103–114.
McCharen, J., Overbeek, R. and Wos, L.: Complexity and related enhancements for automated theoremproving programs,Computers and Mathematics with Applications 2 (1976), 1–16.
McCune, W.: Experiments with discrimination-Tree indexing and path indexing for term retrieval,J. Automatic Reasoning 9 (1992), 147–169.
Pelletier, F. J.: Seventy-five problems for testing automatic theorem provers,J. Automated Reasoning 2 (1986), 191–216.
Pereira, F.:C-Prolog User's Manual, SRI International, Menlo Park, California, 1984.
Plaisted, D.: A simplified problem reduction format,Artificial Intelligence 18 (1982), 227–261.
Plaisted, D. and Greenbaum, S.: A structure-preserving clause form translation.J. of Symbolic Computation 2 (1986), 293–304.
Robinson, J.: Theorem proving on the computer,J. Assoc. Comput. Machinery 10 (1963), 163–174.
Scales, D. J.: Efficient matching algorithm for the SOAR/OPS5 production system, Technical Report STAN-CS-86-1124, Departments of Computer Sciences, Stanford University, 1986.
Sterling, L. and Shapiro, E.:The Art of Prolog, MIT Press, Cambridge, Massachusetts, 1986.
Stickel, M. E.: The path-indexing method for indexing terms, Technical Note 473, Artificial Intelligence Center, SRI International, Menlo Park, California, 1989.
Stickel, M. E.: A Prolog technology theorem prover: Implementation by an extended Prolog compiler,J. Automated Reasoning 4 (1988), 353–380.
Sutcliffe, G.: The TPTP problem library, release v1.0.0, Technical Report, Department of Computer Sciences, James Cook University, 1993.
Ullman, J. D.:Database and Knowledge-Base Systems, Vol. 1: Classical Database Systems, Computer Science Press, 1988.
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Supported by National Science Council under grants NSC 81-0408-E-110-509 and NSC-82-0408-E-110-045. A preliminary version of this paper appeared in Proceedings of International Conference on Computing and Information (Sudbury, Ontario Canada, May 1993).
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Lee, SJ., Wu, CH. Improving the efficiency of a hyperlinking-based theorem prover by incremental evaluation with network structures. J Autom Reasoning 12, 359–388 (1994). https://doi.org/10.1007/BF00885766
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DOI: https://doi.org/10.1007/BF00885766