A Linear Format for Resolution With Merging and a New Technique for Establishing Completeness
Journal of the ACM (JACM)
Two Results on Ordering for Resolution with Merging and Linear Format
Journal of the ACM (JACM)
An Implementation of the Model Elimination Proof Procedure
Journal of the ACM (JACM)
A Proof Procedure Using Connection Graphs
Journal of the ACM (JACM)
Extensions and comparisons of refinement strategies for theorem proving and applications in a parallel environment
Formal languages and their relation to automata
Formal languages and their relation to automata
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
IEEE Transactions on Computers
Using active connection graphs for reasoning with recursive rules
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
Subsumption and connection graphs
IJCAI'81 Proceedings of the 7th international joint conference on Artificial intelligence - Volume 1
IJCAI'83 Proceedings of the Eighth international joint conference on Artificial intelligence - Volume 2
A predicate connection graph based logic with flexible control
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 2
Deductive methods for large data bases
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
Predicate logic: a calculus for deriving programs
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
Formal grammars as models of logic derivations
IJCAI'77 Proceedings of the 5th international joint conference on Artificial intelligence - Volume 1
Resolution plans in theorem proving
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
Conditional answers in question-answering systems
IJCAI'79 Proceedings of the 6th international joint conference on Artificial intelligence - Volume 1
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This paper presents a new representation and technique for proving theorems automatically that is both computationally more effective than resolution and permits a clear and concise formal description. A problem in automatic theorem proving can be specified by a set of clauses, containing literals, that represents a set of axioms and the negation of a theorem to be proved. The set of clauses can be replaced by a graph in which the nodes represent literals and the edges link unifiable complements. The nodes are partitioned by clause membership, and the edges are labeled with a most general unifying substitution. Given this representation, theorem proving becomes a graph-searching problem. The search technique presented here, in effect, unrolls the graph into sets of solution trees. The trees grow in a well-defined breadth-first way that defines a measure of proof complexity.