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Strict Basic Superposition

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons44055

Bachmair,  Leo
Programming Logics, MPI for Informatics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons44474

Ganzinger,  Harald
Programming Logics, MPI for Informatics, Max Planck Society;

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Zitation

Bachmair, L., & Ganzinger, H. (1998). Strict Basic Superposition. In C. Kirchner, & H. Kirchner (Eds.), Proceedings of the 15th International Conference on Automated Deduction (CADE-98) (pp. 160-174). Berlin, Germany: Springer.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-000F-3891-1
Zusammenfassung
In this paper we solve a long-standing open problem by showing that strict superposition---that is, superposition without equality factoring---is refutationally complete. The difficulty of the problem arises from the fact that the strict calculus, in contrast to the standard calculus with equality factoring, is not compatible with arbitrary removal of tautologies, so that the usual techniques for proving the (refutational) completeness of paramodulation calculi are not directly applicable. We deal with the problem by introducing a suitable notion of {\em direct rewrite proof\/} and modifying proof techniques based on candidate models and counterexamples in that we define these concepts, not in terms of semantic truth, but in terms of direct provability. We introduce a corresponding concept of redundancy with which strict superposition is compatible and that covers most simplification techniques.