Communications of the ACM
Journal of the ACM (JACM)
Principles of artificial intelligence
Principles of artificial intelligence
Many hard examples for resolution
Journal of the ACM (JACM)
Methods and calculi for deduction
Handbook of logic in artificial intelligence and logic programming (vol. 1)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness
Journal of the ACM (JACM)
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
Journal of the ACM (JACM)
Symbolic Logic and Mechanical Theorem Proving
Symbolic Logic and Mechanical Theorem Proving
On the Completeness of Connection Graph Resolution
GWAI '81 Proceedings of the German Workshop on Artificial Intelligence
Origins of Software Performance Engineering: Highlights and Outstanding Problems
Performance Engineering, State of the Art and Current Trends
Algorithmic Proof with Diminishing Resources, Part 1
CSL '90 Proceedings of the 4th Workshop on Computer Science Logic
Semantic Tableaux with Ordering Restrictions
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
The intractability of resolution (complexity)
The intractability of resolution (complexity)
An Open Research Problem: Strong Completeness of R. Kowalski's Connection Graph Proof Procedure
Computational Logic: Logic Programming and Beyond, Essays in Honour of Robert A. Kowalski, Part II
Some Remarks on Completeness, Connection Graph Resolution and Link Deletion
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Ordered Resolution vs. Connection Graph Resolution
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Early History and Perspectives of Automated Deduction
KI '07 Proceedings of the 30th annual German conference on Advances in Artificial Intelligence
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This paper addresses and answers a fundamental question about resolution. Informally, what is gained with respect to the search for a proof by performing a single resolution step? It is first shown that any unsatisfiable formula may be decomposed into regular formulas provable in linear time (by resolution). A relevant resolution step strictly reduces at least one of the formulas in the decomposition while an irrelevant one does not contribute to the proof in any way. the relevance of this insight into the nature of resolution and of the unsatisfiability problem for the development of proof strategies and for complexity considerations are briefly discussed.The decomposition also provides a technique for establishing completeness proofs for refinements of resolution. As a first application, connection-graph resolution is shown to be strongly complete. This settles a problem that remained open for two decades despite many proff attempts. The result is relevant for theorem proving because without strong completeness a connection graph resolution prover might run into an infinite loop even on the ground level.