First-order logic and automated theorem proving
First-order logic and automated theorem proving
Journal of the ACM (JACM)
Complete axiomatizations of some quotient term algebras
Theoretical Computer Science
Equational formulae with membership constraints
Information and Computation
On the duality of abduction and model generation in a framework for model generation with equality
FGCS'921 Selected papers of the conference on Fifth generation computer systems
The resolution calculus
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)
An Efficient Unification Algorithm
ACM Transactions on Programming Languages and Systems (TOPLAS)
Resolution Methods for the Decision Problem
Resolution Methods for the Decision Problem
Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
Journal of Automated Reasoning
Using Resolution for Testing Modal Satisfiability and Building Models
Journal of Automated Reasoning
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
A New Clausal Class Decidable by Hyperresolution
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
SATCHMO: A Theorem Prover Implemented in Prolog
Proceedings of the 9th International Conference on Automated Deduction
A Method for Building Models Automatically. Experiments with an Extension of OTTER
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
An Improved Lower Bound for the Elementary Theories of Trees
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Resolution decision procedures
Handbook of automated reasoning
Constructing decision procedures in equational clausal logic
Fundamenta Informaticae
Model building with ordered resolution: extracting models from saturated clause sets
Journal of Symbolic Computation - Special issue: First order theorem proving
A calculus combining resolution and enumeration for building finite models
Journal of Symbolic Computation - Special issue: First order theorem proving
Automated theorem proving: A logical basis (Fundamental studies in computer science)
Automated theorem proving: A logical basis (Fundamental studies in computer science)
LPAR'00 Proceedings of the 7th international conference on Logic for programming and automated reasoning
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We develop new techniques for the automated construction of models for subclasses of equational clausal logic. The models are represented by some specific class of rewrite rules. We show that the evaluation of arbitrary first-order formulae in these interpretations is a decidable problem. As an example of an application, we consider the class ${\mathcal{OCC}1\mathcal{N}}$ , a decidable subclass of first-order clausal logic without equality. In the equational case, ${\mathcal{OCC}1\mathcal{N}}$ is undecidable, but it is known to be decidable if all the equational literals are ground. We extend this result to a class of clause sets possibly containing nonground equational literals. The algorithms for extracting models from positively disconnected saturated sets proposed by Fermüller and Leitsch are extended in order to handle the full ordering restrictions of the resolution/paramodulation calculus.