Towards a foundation of completion procedures as semidecision procedures
Theoretical Computer Science
Term rewriting and all that
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
ICS: Integrated Canonizer and Solver
CAV '01 Proceedings of the 13th International Conference on Computer Aided Verification
A SAT Based Approach for Solving Formulas over Boolean and Linear Mathematical Propositions
CADE-18 Proceedings of the 18th International Conference on Automated Deduction
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Combining superposition, sorts and splitting
Handbook of automated reasoning
Decision Problems in Ordered Rewriting
LICS '98 Proceedings of the 13th Annual IEEE Symposium on Logic in Computer Science
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
ACM Transactions on Computational Logic (TOCL)
AI Communications - CASC
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
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Decision procedures for extensions of the theory of arrays
Annals of Mathematics and Artificial Intelligence
A comprehensive combination framework
ACM Transactions on Computational Logic (TOCL)
Automatic Decidability and Combinability Revisited
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Combination Methods for Satisfiability and Model-Checking of Infinite-State Systems
CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
Architecting Solvers for SAT Modulo Theories: Nelson-Oppen with DPLL
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
Noetherianity and Combination Problems
FroCoS '07 Proceedings of the 6th international symposium on Frontiers of Combining Systems
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
On Deciding Satisfiability by DPLL($\Gamma+{\mathcal T}$) and Unsound Theorem Proving
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Combinable Extensions of Abelian Groups
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Annals of Mathematics and Artificial Intelligence
Theory decision by decomposition
Journal of Symbolic Computation
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
On theorem proving for program checking: historical perspective and recent developments
Proceedings of the 12th international ACM SIGPLAN symposium on Principles and practice of declarative programming
Automatic decidability and combinability
Information and Computation
On Deciding Satisfiability by Theorem Proving with Speculative Inferences
Journal of Automated Reasoning
A Decidability Result for the Model Checking of Infinite-State Systems
Journal of Automated Reasoning
Automatic combinability of rewriting-based satisfiability procedures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
An Instantiation Scheme for Satisfiability Modulo Theories
Journal of Automated Reasoning
Combination of disjoint theories: beyond decidability
IJCAR'12 Proceedings of the 6th international joint conference on Automated Reasoning
Superposition for bounded domains
Automated Reasoning and Mathematics
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In the context of combinations of theories with disjoint signatures, we classify the component theories according to the decidability of constraint satisfiability problems in arbitrary and in infinite models, respectively. We exhibit a theory T1 such that satisfiability is decidable, but satisfiability in infinite models is undecidable. It follows that satisfiability in T1∪T2 is undecidable, whenever T2 has only infinite models, even if signatures are disjoint and satisfiability in T2 is decidable. In the second part of the paper we strengthen the Nelson-Oppen decidability transfer result, by showing that it applies to theories over disjoint signatures, whose satisfiability problem, in either arbitrary or infinite models, is decidable. We show that this result covers decision procedures based on rewriting, complementing recent work on combination of theories in the rewrite-based approach to satisfiability.