Completion of a set of rules modulo a set of equations
SIAM Journal on Computing
Combination of unification algorithms
Proc. of the 8th international conference on Automated deduction
Unification in a combination of arbitrary disjoint equational theories
Journal of Symbolic Computation
Fundamentals of algebraic specification 2: module specifications and constraints
Fundamentals of algebraic specification 2: module specifications and constraints
Combining matching algorithms: The regular case
Journal of Symbolic Computation
A resolution principle for constrained logics
Artificial Intelligence
Combining unification algorithms
Journal of Symbolic Computation
Constraint solving by narrowing in combined algebraic domains
Proceedings of the eleventh international conference on Logic programming
Combining symbolic constraint solvers on algebraic domains
Journal of Symbolic Computation
Combination techniques and decision problems for disunification
RTA-93 Selected papers of the fifth international conference on Rewriting techniques and applications
Modular properties of composable term rewriting systems
Journal of Symbolic Computation
Combining decision algorithms for matching in the union of disjoint equational theories
Information and Computation
Unification in the union of disjoint equational theories: combining decision procedures
Journal of Symbolic Computation
ALP Proceedings of the fourth international conference on Algebraic and logic programming
Combination of constraint solvers for free and quasi-free structures
Theoretical Computer Science - Special issue: rewriting systems and applications
Term rewriting and all that
A Practical Decision Procedure for Arithmetic with Function Symbols
Journal of the ACM (JACM)
Deciding Combinations of Theories
Journal of the ACM (JACM)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Fundamentals of Algebraic Specification I
Fundamentals of Algebraic Specification I
LPAR '92 Proceedings of the International Conference on Logic Programming and Automated Reasoning
Why Combined Decision Problems Are Often Intractable
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Termination of Constraint Contextual Rewriting
FroCoS '00 Proceedings of the Third International Workshop on Frontiers of Combining Systems
Deciding the Word Problem in the Union of Equational Theories Sharing Constructors
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
Combination of Constraint Solving Techniques: An Algebraic POint of View
RTA '95 Proceedings of the 6th International Conference on Rewriting Techniques and Applications
On the Combination of Symbolic Constraints, Solution Domains, and Constraint Solvers
CP '95 Proceedings of the First International Conference on Principles and Practice of Constraint Programming
Combination Techniques for Non-Disjoint Equational Theories
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Combining word problems through rewriting in categories with products
Theoretical Computer Science - Category theory and computer science
Deciding the Word Problem in the Union of Equational Theories
Deciding the Word Problem in the Union of Equational Theories
Non-Disjoint Unions of Theories and Combinations of Satisfiability Procedures: First Results
Non-Disjoint Unions of Theories and Combinations of Satisfiability Procedures: First Results
Combining satisfiability procedures for automated deduction and constraint-based reasoning
Combining satisfiability procedures for automated deduction and constraint-based reasoning
Combining Decision Procedures for Positive Theories Sharing Constructors
RTA '02 Proceedings of the 13th International Conference on Rewriting Techniques and Applications
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
Journal of Automated Reasoning
Canonization for disjoint unions of theories
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Information and Computation - Special issue: Combining logical systems
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Decision procedures for term algebras with integer constraints
Information and Computation - Special issue: Combining logical systems
Hierarchical and Modular Reasoning in Complex Theories: The Case of Local Theory Extensions
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Annals of Mathematics and Artificial Intelligence
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Canonization for disjoint unions of theories
Information and Computation - Special issue: 19th international conference on automated deduction (CADE-19)
Combinations of theories for decidable fragments of first-order logic
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Combining theories with shared set operations
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Theory-specific automated reasoning
A 25-year perspective on logic programming
The reduced product of abstract domains and the combination of decision procedures
FOSSACS'11/ETAPS'11 Proceedings of the 14th international conference on Foundations of software science and computational structures: part of the joint European conferences on theory and practice of software
Combining theories: the Ackerman and guarded fragments
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
A Decidability Result for the Model Checking of Infinite-State Systems
Journal of Automated Reasoning
Nelson-Oppen, shostak and the extended canonizer: a family picture with a newborn
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
Connecting many-sorted structures and theories through adjoint functions
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Connecting many-sorted theories
CADE' 20 Proceedings of the 20th international conference on Automated Deduction
Extension of first-order theories into trees
AISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Symbolic Computation
On hierarchical reasoning in combinations of theories
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Combination of disjoint theories: beyond decidability
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
| Hi-index | 5.23 |
In this paper we outline a theoretical framework for the combination of decision procedures for constraint satisfiability. We describe a general combination method which, given a procedure that decides constraint satisfiability with respect to a constraint theory T1 and one that decides constraint satisfiability with respect to a constraint theory T2, produces a procedure that (semi-)decides constraint satisfiability with respect to the union of T1 and T2. We provide a number of model-theoretic conditions on the constraint language and the component constraint theories for the method to be sound and complete, with special emphasis on the case in which the signatures of the component theories are non-disjoint. We also describe some general classes of theories to which our combination results apply, and relate our approach to some of the existing combination methods in the field.