A new method for establishing refutational completeness in theorem proving
Proc. of the 8th international conference on Automated deduction
First-order logic and automated theorem proving
First-order logic and automated theorem proving
Journal of the ACM (JACM)
A Machine-Oriented Logic Based on the Resolution Principle
Journal of the ACM (JACM)
Automatic Theorem Proving With Renamable and Semantic Resolution
Journal of the ACM (JACM)
Resolution Strategies as Decision Procedures
Journal of the ACM (JACM)
On the SUP-INF Method for Proving Presburger Formulas
Journal of the ACM (JACM)
An algorithm for reasoning about equality
Communications of the ACM
Resolution Methods for the Decision Problem
Resolution Methods for the Decision Problem
Using Resolution for Testing Modal Satisfiability and Building Models
Journal of Automated Reasoning
Superposition with Simplification as a Desision Procedure for the Monadic Class with Equality
KGC '93 Proceedings of the Third Kurt Gödel Colloquium on Computational Logic and Proof Theory
SATCHMO: A Theorem Prover Implemented in Prolog
Proceedings of the 9th International Conference on Automated Deduction
A Resolution Decision Procedure for the Guarded Fragment
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Resolution decision procedures
Handbook of automated reasoning
A Superposition Decision Procedure for the Guarded Fragment with Equality
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
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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A method is proposed to construct decision procedures for various subclasses of first-order logic with equality. We define a notion of complexity of first-order terms and equations, and we propose semantic and syntactic criteria ensuring that existing refinements of the paramodulation calculus terminate on the considered clause sets. These refinements use reduction orderings, selection functions and simplification rules. Since they are sound and refutationally complete, the corresponding classes of formulae are decidable. Moreover, the automatic extraction of models from saturated clause sets is also possible. A discussion and detailed comparisons with existing works in the field are provided, together with numerous examples and some undecidability results.