A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Efficiency and Completeness of the Set of Support Strategy in Theorem Proving
Journal of the ACM (JACM)
Automatic Theorem Proving With Renamable and Semantic Resolution
Journal of the ACM (JACM)
The use of theorem-proving techniques in question-answering systems
ACM '68 Proceedings of the 1968 23rd ACM national conference
A completeness theorem and a computer program for finding theorems derivable from given axioms
A completeness theorem and a computer program for finding theorems derivable from given axioms
Fuzzy Logic and the Resolution Principle
Journal of the ACM (JACM)
Automatic Theorem Proving with Built-in Theories Including Equality, Partial Ordering, and Sets
Journal of the ACM (JACM)
An Approach for Finding C-Linear Complete Inference Systems
Journal of the ACM (JACM)
Improving the Efficiency of Reasoning Through Structure-Based Reformulation
SARA '02 Proceedings of the 4th International Symposium on Abstraction, Reformulation, and Approximation
N-sorted logic for automatic theorem-proving in higher-order logic
ACM '72 Proceedings of the ACM annual conference - Volume 1
Partition-based logical reasoning for first-order and propositional theories
Artificial Intelligence - Special volume on reformulation
Fuzzy logic and the resolution principle
IJCAI'71 Proceedings of the 2nd international joint conference on Artificial intelligence
Application of automatic transformations to program verification
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
Theorem proving with structured theories
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Partition-based logical reasoning for first-order and propositional theories
Artificial Intelligence - Special volume on reformulation
Artificial Intelligence
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The resolution principle is an inference rule for quantifier-free first-order predicate calculus. In the past, the completeness theorems for resolution and its refinements have been stated and proved for finite sets of clauses. It is easy (by Gödel's Compactness Theorem) and of practical interest to extend them to countable sets, thus allowing schemata representing denumerably many axioms. In addition, some theorems similar to Craig's Interpolation Theorem are proved for deduction by resolution. In propositional calculus, the theorem proved is stronger, whereas in predicate calculus the theorems proved are in some ways stronger and in some ways weaker than Craig's theorem. These interpolation theorems suggest procedures which could be embodied in computer programs for automatic proof finding and consequence finding.