Solving Equational Problems Efficiently
Equational problems (i.e.: first-order formulae with quantifier prefix ∃* ∀*, whose only predicate symbol is syntactic equality) are an important tool in many areas of automated deduction, e.g.: restricting the set of ground instances of a clause via equational constraints allows the definition of stronger redundancy criteria and hence, in general, of more efficient theorem provers. Moreover, also the inference rules themselves can be restricted via constraints. In automated model building, equational problems play an important role both in the definition of an appropriate model representation and in the evaluation of clauses in such models. Also, many problems in the area of logic programming can be reduced to equational problem solving.
The goal of this work is a complexity analysis of the satisfiability problem of equational problems in CNF over an infinite Herbrand universe. The main result will be a proof of the NP-completeness (and, in particular, of the NP-membership) of this problem.
KeywordsLogic Programming Free Variable Transformation Rule Tree Representation Predicate Symbol
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- 1.F. Baader, J.H. Siekmann: Unification Theory, in Handbook of Logic in Artificial Intelligence and Logic Programming, D.M. Gabbay, C.J. Hogger, J.A. Robinson (eds.), Oxford University Press (1994).Google Scholar
- 4.R. Caferra, N. Peltier: Extending semantic Resolution via automated Model Building: applications, Proceedings of IJCAI’95, Morgan Kaufmann, (1995)Google Scholar
- 5.R. Caferra, N. Zabel: Extending Resolution for Model Construction, in Proceedings of Logics in AI-JELIA’90, LNAI 478, pp. 153–169, Springer (1991).Google Scholar
- 7.G. Gottlob, R. Pichler: Working with ARMs: Complexity Results on Atomic Representations of Herbrand Models, to appear in Proceedings of LICS’99, IEEE Computer Society Press, (1999).Google Scholar
- 9.J.-L. Lassez, M. Maher, K. Marriott: Elimination of Negation in Term Algebras, in Proceedings of MFCS’91, LNCS 520, pp. 1–16, Springer (1991).Google Scholar
- 10.D. Lugiez: A Deduction Procedure for First Order Programs, in Proceedings of ICLP’89, pp. 585–599, Lisbon (1989).Google Scholar
- 11.M. Maher: Complete Axiomatizations of the Algebras of Finite, Rational and Infinite Trees, in Proceedings of LICS’88, pp. 348–357, IEEE Computer Society Press, (1988).Google Scholar
- 13.R. Pichler: Algorithms on Atomic Representations of Herbrand Models, in Proceedings of Logics in AI-JELIA’98, LNAI 1489, pp. 199–215, Springer (1998).Google Scholar
- 15.T. Sato, F. Motoyoshi: A complete Top-down Interpreter for First Order Programs, in Proceedings of ILPS’91, pp. 35–53, (1991).Google Scholar
- 16.S. Vorobyov: An Improved Lower Bound for the Elementary Theories of Trees, in Proceedings of CADE-13, LNAI 1104, pp. 275–287, Springer (1996).Google Scholar