Modular properties of composable term rewriting systems
Journal of Symbolic Computation
First-order logic and automated theorem proving (2nd ed.)
First-order logic and automated theorem proving (2nd ed.)
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Combining Decision Procedures for Positive Theories Sharing Constructors
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Uniform Derivation of Decision Procedures by Superposition
CSL '01 Proceedings of the 15th International Workshop on Computer Science Logic
Combination Techniques for Non-Disjoint Equational Theories
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Decision procedures in automated deduction
Decision procedures in automated deduction
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
Annals of Mathematics and Artificial Intelligence
Theory-specific automated reasoning
A 25-year perspective on logic programming
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The Nelson-Oppen combination method combines ground satisfiability checkers for first-order theories satisfying certain conditions into a single ground satisfiability checker for the union theory. The most significant restriction that the combined theories must satisfy, for the Nelson-Oppen combination method to be applicable, is that they must have disjoint signatures. Unfortunately, this is a very serious restriction since many combination problems concern theories over non-disjoint signatures.In this paper we present a tableau calculus for combining first-order theories over non-disjoint signatures. The calculus generalizes the Nelson-Oppen combination method to formulae with quantifiers and to the union of arbitrary theories over non necessarily disjoint signatures.