Deriving Focused Calculi for Transitive Relations

Authors:
Georg Struth
Affiliations:
-
Venue:
RTA '01 Proceedings of the 12th International Conference on Rewriting Techniques and Applications
Year:
2001

Citing 11
Cited 2

Completeness results for inequality provers

Artificial Intelligence
Completeness of a prover for dense linear orders

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Bi-rewrite systems

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Ordered chaining calculi for first-order theories of transitive relations

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Automatic Theorem Proving with Built-in Theories Including Equality, Partial Ordering, and Sets

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Abstract

We propose a new method for deriving focused ordered resolution calculi, exemplified by chaining calculi for transitive relations. Previously, inference rules were postulated and a posteriori verified in semantic completeness proofs. We derive them from the theory axioms. Completeness of our calculi then follows from correctness of this synthesis. Our method clearly separates deductive and procedural aspects: relating ordered chaining to Knuth-Bendix completion for transitive relations provides the semantic background that drives the synthesis towards its goal. This yields a more restrictive and transparent chaining calculus. The method also supports the development of approximate focused calculi and a modular approach to theory hierarchies.