Schubert's steamroller problem: formulations and solutions
Journal of Automated Reasoning
Automated deduction by theory resolution
Journal of Automated Reasoning
On equational theories, unification and decidability
on Rewriting techniques and applications
Automated reasoning: 33 BASIC research problems
Automated reasoning: 33 BASIC research problems
The Concept of Demodulation in Theorem Proving
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
Subsumption and Connectionsgraphs
GWAI '81 Proceedings of the German Workshop on Artificial Intelligence
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
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This paper addresses two problems concerning the issue of redundant information in resolution based reasoning systems. The first one deals with the question, how the derivation of redundant clauses can be substantially reduced a priori. The second one asks for a criterion to decide, which clauses need not be tested for reduncancy. In this paper we consider a particular kind of reduncancy, which we call ancestor subsumption, that is the subsumption of a resolvent by one of its ancestors. We give a complete syntactic characterization of clause sets producing ancestor subsumed clauses. Given this characterization, a solution to the problem with generating redundant clauses is proposed. Moreover, a suitable restriction of the (usually very expensive) subsumption test is derived from this result. SAM's lemma will serve as an example for demonstrating various possibilities how to avoid the derivation of redundant clauses.