Abstract
We show that two Boolean terms which are unifiable have a most general unifier, which can be described using the terms themselves and a single unifier. Techniques for finding a single unifier are given.
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References
Boole, G., The Mathematical Analysis of Logic, Macmillan 1847. Reprinted B. Blackwell (1948).
Büttner, W., Simonis, H., ‘Embedding Boolean expressions into Logic Programming’, preprint, to appear in Journal of Symbolic Computation (1987).
Hailpern, T., Boole's Logic and Probability, North-Holland (1986).
Herbrand, J., ‘Investigations in Proof Theory’, [Herbrand's thesis] in Jacques Herbrand Logical Writings, ed. W. Goldfarb, pp. 44–202. D. Reidel (1971).
Herstein, I. N., ‘Non-commutative rings’, Carus Mathematical Monograph, Wiley (1968).
Herold, A., ‘Combination of Unification Algorithms’, in 8th International Conference on Automated Deduction, Lecture Notes in Computer Science 230, pp. 450–469. Springer (1986).
Hsiang, J., ‘Rewrite rules for clausal and non-clausal theorem proving’, in Proc. 10th ICALP, LNCS 154 (1983).
Hsiang, J., ‘Refutational Theorem Proving using Term-Rewriting Systems’, Artificial Intelligence 25 (1985).
Kapur, D., Narendran, P., ‘An equational approach to theorem proving in the first order predicate calculus’, Proc. IJCAI 85, Los Angeles (1985).
Löwenheim, L., Über das Auflösungproblem im logischen Klassenkalkül’, Sitzungber. Berl. Math. Gesell. 7, 89–94 (1908).
Martin, U., Nipkow, T., ‘Unification in Boolean Rings’, in 8th International Conference on Automated Deduction, Lecture Notes in Computer Science 230, pp. 506–513. Springer (1986).
Martin, U., Nipkow, T., ‘Boolean Unification — A Survey’, to appear in Journal of Symbolic Computation.
Monk, J. D., Mathematical Logic, Springer (1976).
Robinson, J. A., ‘A machine oriented logic based on the resolution principle’, J.ACM 12, 23–41 (1974).
Rudeanu, S., Boolean functions and equations, North Holland (1974).
Siekmann, J. H., ‘Universal Unification’, in Proceedings of European Conference on Artificial Intelligence, Brighton (1986).
Schröder, E., ‘Vorlesungen über die Algebra der Logic, (Leipzig, Vol. 1, 1890; Vol. 2, 1891, 1905; Vol. 3, 1895). Reprint Chelsea, Bronx, NY. (1966).
Vitter, J. S., Simons, R. A., ‘New Classes for Parallel Complexity: A Study of Unification and Other Complete Problems for P’, IEEE Transactions on Computers, 403–418 (1986).
Watts, D. E., Cohen, J. K., ‘Computer-Implemented Set Theory’, Amer. Math. Month. 87 (1980).
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Martin, U., Nipkow, T. Unification in Boolean rings. J Autom Reasoning 4, 381–396 (1988). https://doi.org/10.1007/BF00297246
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DOI: https://doi.org/10.1007/BF00297246