A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Model Finding Strategies in Semantically Guided Instance-based Theorem Proving
ISMIS '93 Proceedings of the 7th International Symposium on Methodologies for Intelligent Systems
Single Axioms in the Implicational Propositional Calculus
Proceedings of the 9th International Conference on Automated Deduction
The Central Variable Strategy of Str+ve
CADE-11 Proceedings of the 11th International Conference on Automated Deduction: Automated Deduction
Conditional Term Rewriting and First-Order Theorem Proving
CTRS '92 Proceedings of the Third International Workshop on Conditional Term Rewriting Systems
Using examples to generate instantiations of set variables
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
Model Finding In Semantically Guided Instance-Based Theorem Proving
Fundamenta Informaticae
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Semantic hyper-linking [Plaisted et al., 1992, Chu and Plaisted, 1993, Chu and Plaisted, 1992] has been proposed recently to use semantics with hyper-linking [Lee and Plaisted, 1992], an instance-based theorem proving technique. Ground instances are generated until an unsatisfiable ground set is obtained; semantics is used to greatly reduce the search space. One disadvantage of semantic hyper-linking is that large ground literals, if needed in the proofs, sometimes are hard to generate. In this paper we propose rough resolution, a refinement of resolution [Robinson, 1965], to only resolve upon maximum literals, that are potentially large in ground instances, and obtain rough resolvents. Rough resolvents can be used by semantic hyper-linking to avoid generating large ground literals since maximum literals have been deleted. As an example, we will show how rough resolution helps to prove LIM3 [Bledsoe, 1990], which cannot be proved using semantic hyper-linking only. We will also show other results in which rough resolution helps to find the proofs faster. Though incomplete, rough resolution can be used with other complete methods that prefer small clauses.