First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
Unification of infinite sets of terms schematized by primal grammars
Theoretical Computer Science
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
The Unification of Infinite Sets of Terms and Its Applications
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
The Disconnection Method - A Confluent Integration of Unification in the Analytic Framework
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
FINDER: Finite Domain Enumerator - System Description
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
FDPLL - A First Order Davis-Putnam-Longeman-Loveland Procedure
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
DCTP - A Disconnection Calculus Theorem Prover - System Abstract
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
Integration of Equality Reasoning into the Disconnection Calculus
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
TABLEAUX '02 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
The model evolution calculus as a first-order DPLL method
Artificial Intelligence
A Bottom-Up Approach to Clausal Tableaux
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Logical Engineering with Instance-Based Methods
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Instantiation-Based Automated Reasoning: From Theory to Practice
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Comparing instance generation methods for automated reasoning
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Proof output and transformation for disconnection tableaux
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Unit propagation in a tableau framework
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Hyper tableaux — the third version
KSEM'06 Proceedings of the First international conference on Knowledge Science, Engineering and Management
Model representation via contexts and implicit generalizations
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
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We present the disconnection tableau calculus, which is a free-variable clausal tableau calculus where variables are treatedin a nonrigidmanner. The calculus essentially consists of a single inference rule, the so-calledlinking rule, which strongly restricts the possible clauses in a tableau. The methodcan also be viewedas an integration of the linking rule as usedin Plaisted's linking approach into a tableau format. The calculus has the proof-theoretic advantage that, in the case of a satisfiable formula, one can characterise a model of the formula, a property which most of the free-variable tableau calculi lack. In the paper, we present a rigorous completeness proof and give a procedure for extracting a model from a finitely failed branch.