Volume II: Parallel Languages on PARLE: Parallel Architectures and Languages Europe
First-order logic and automated theorem proving
First-order logic and automated theorem proving
Relative complexities of first order calculi
Relative complexities of first order calculi
The resolution calculus
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Algorithms and Data Structures in VLSI Design
Algorithms and Data Structures in VLSI Design
A Compressed Breadth-First Search for Satisfiability
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
On Different Concepts of Function Introduction
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
Paramodulation without Duplication
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
Space Complexity of Random Formulae in Resolution
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
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We present a resolution calculus for first-order logic using a more concise formalism for representing sets of clauses. The idea is to represent the clause set at hand as a Directed Acyclic Graph, which allows one to share common literals instead of duplicating them, thus yielding a much more compact representation of the search space. We define inference rules operating on this language and we prove their soundness and refutational completeness. We also design simplification rules for pruning the search space. Finally we compare our technique with the usual resolution calculus and we prove (using the pigeonhole example) that our method can reduce the length of the proof by an exponential factor (in propositional logic).