Superposition for Fixed Domains
Superposition is an established decision procedure for a variety of first-order logic theories represented by sets of clauses. A satisfiable theory, saturated by superposition, implicitly defines a perfect term-generated model for the theory. Proving universal properties with respect to a saturated theory directly leads to a modification of the perfect model’s term-generated domain, as new Skolem functions are introduced. For many applications, this is not desired. Therefore, we propose the first superposition calculus that can explicitly represent existentially quantified variables and can thus compute with respect to a given domain. This calculus is sound and complete for a first-order fixed domain semantics. For some classes of formulas and theories, we can even employ the calculus to prove properties of the perfect model itself, going beyond the scope of known superposition based approaches.
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- 7.Ganzinger, H., Nivelle, H.D.: A superposition decision procedure for the guarded fragment with equality. In: Proc. of LICS 1999, pp. 295–305. IEEE, Los Alamitos (1999)Google Scholar
- 8.Ganzinger, H., Stuber, J.: Inductive theorem proving by consistency for first-order clauses. In: Rusinowitch, M., Remy, J.-L. (eds.) CTRS 1992. LNCS, vol. 656, pp. 226–241. Springer, Heidelberg (1993)Google Scholar
- 12.Nieuwenhuis, R.: Basic paramodulation and decidable theories (extended abstract). In: Proc. of LICS 1996, pp. 473–482. IEEE Computer Society Press, Los Alamitos (1996)Google Scholar