Abstract
This paper describes a number of heuristics that have been implemented in a program that proves theorems by constructing closed semantic trees. The program is called HERBY. We studied the effectiveness of these heuristics on the Stickel Test Set and found that when HERBY was given two hours to prove each theorem, it was able to prove 78 of the 84 theorems in the set. Constructing semantic trees has been used as a theoretical tool for confirming the unsatisfiability of a set of clauses in first-order predicate calculus; this paper shows that this approach has some practicality as well.
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References
M. Almulla, Analysis of the use of semantic trees in automated theorem proving, Ph.D. thesis, School of Computer Science, McGill University, Montreal, Canada (1995).
C.L. Chang and R.C.T. Lee, Symbolic Logic and Mechanical Theorem Proving(Academic Press, New York, 1973).
C.L. Chang, Theorem Proving by Generation of Pseudo-Semantic Trees(Division of Computer Research and Technology, NIT, Bethesda, MD, 1971).
J. Hsiang and M. Rusinowitch, Proving refutational completeness of theorem-proving strategies: the transfinite semantic tree method, Journal of ACM 38(3) (1991) 559–587.
R. Kowalski and J.P. Hayes, Semantic trees in automatic theorem proving, Machine Intelligence 4 (1969) 87–101.
R. Letz, S. Bayerl and W. Bibel, SETHEO, a high performance theorem prover, Journal of Automated Reasoning 8(2) (1992) 183–213.
D.W. Loveland, Automated Theorem Proving: A Logical Basis(North-Holland, Amsterdam, 1978).
Z. Manna, Mathematical Theory of Computation, Computer Science Series (McGraw-Hill, 1974).
M. Newborn, The Great Theorem Prover, Version 2(Newborn Software, Montreal, 1994).
N.J. Nilsson and M.R. Genesereth, Logical Foundations of Artificial Intelligence(Morgan Kaufmann, San Mateo, CA, 1987).
J. Robinson, A machine-oriented logic based on the resolution principle, Journal of ACM 12(1) (1965) 601–607.
J.R. Slagle, Automatic theorem-proving with renameable and semantic resolution, Journal of ACM 14(4) (1967) 687–697.
M.E. Stickel, A Prolog technology theorem prover: implementation by an extended Prolog compiler, Journal of Automated Reasoning 4(4) (1988) 353–380.
R. Stoll, Set Theory and Logic(W.H. Freeman, New York, 1963).
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Yu, Q., Almulla, M. & Newborn, M. Heuristics used by HERBY for semantic tree theorem proving. Annals of Mathematics and Artificial Intelligence 23, 247–266 (1998). https://doi.org/10.1023/A:1018976510663
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DOI: https://doi.org/10.1023/A:1018976510663