Abstraction using generalization functions
We show how a generalization operator may be incorporated into resolution as a method of guiding the search for a proof. After each resolution, a “generalization operation” may be performed on the resulting caluse. This leads to a more general proof than the usual resolution proof. These general proofs may then be used as guides in the search for an ordinary resolution proof. This method overcomes some of the limitations of the abstraction strategies with which the author has experimented for several years. Some of the results of these previous experiments and comparisons of the two approaches are given.
KeywordsSelection Function Function Symbol Generalization Operator Automate Theorem Prove Generalization Function
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- Bibel, W., Automated Theorem Proving, Vieweg, 1982.Google Scholar
- Boyer, R., Locking, a restriction of resolution, Ph.D. thesis, University of Texas at Austin, TX (1971).Google Scholar
- Bundy, A., The Computer Modelling of Mathematical Reasoning (Academic Press, New York, 1983).Google Scholar
- Chang, C. and Lee, R., Symbolic Logic and Mechanical Theorem Proving (Academic Press, New York, 1973).Google Scholar
- Loveland, D., Automated theorem proving: a quarter century review, in Automated Theorem Proving: After 25 Years, W. Bledsoe and D. Loveland, eds., (American Mathematical Society, Providence, RI, 1984), pp. 1–45.Google Scholar
- Manna, Z., Mathematical Theory of Computation (McGraw-Hill, New York, 1974).Google Scholar
- Plaisted, D., and Greenbaum, S., Problem representations for back chaining and equality in resolution theorem proving, First Annual AI Applications Conference, Denver, Colorado, December, 1984.Google Scholar
- Stickel, M.E., A Prolog technology theorem prover, Proceedings of the 1984 International Symposium on Logic Programming, IEEE, Atlantic City, New Jersey, February, 1984, pp. 212–217.Google Scholar
- Winston, P.H., Artificial Intelligence (Addison-Wesley, Reading, Mass., 1977).Google Scholar
- Wos, L., Overbeek, R., Lusk, E., and Boyle, J., Automated Reasoning: Introduction and Applications (Prentice-Hall, Englewood Cliffs, NJ, 1984).Google Scholar