Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
Complete Instantiation for Quantified Formulas in Satisfiabiliby Modulo Theories
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
On Deciding Satisfiability by DPLL($\Gamma+{\mathcal T}$) and Unsound Theorem Proving
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Combining Non-stably Infinite, Non-first Order Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
Superposition modulo linear arithmetic SUP(LA)
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
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
Model evolution with equality modulo built-in theories
CADE'11 Proceedings of the 23rd international conference on Automated deduction
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
Superposition for bounded domains
Automated Reasoning and Mathematics
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Combination of theories underlies the design of satisfiability modulo theories (SMT) solvers. The Nelson-Oppen framework can be used to build a decision procedure for the combination of two disjoint decidable stably infinite theories. We here study combinations involving an arbitrary first-order theory. Decidability is lost, but refutational completeness is preserved. We consider two cases and provide complete (semi-)algorithms for them. First, we show that it is possible under minor technical conditions to combine a decidable (not necessarily stably infinite) theory and a disjoint finitely axiomatized theory, obtaining a refutationally complete procedure. Second, we provide a refutationally complete procedure for the union of two disjoint finitely axiomatized theories, that uses the assumed procedures for the underlying theories without modifying them.