Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Why are modal logics so robustly decidable?
Current trends in theoretical computer science
Modal logic
Journal of Logic, Language and Information
Guarded fixed point logics and the monadic theory of countable trees
Theoretical Computer Science - Complexity and logic
Unions of non-disjoint theories and combinations of satisfiability procedures
Theoretical Computer Science
Invited Talk: Decision procedures for guarded logics
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
Combining Nonstably Infinite Theories
Journal of Automated Reasoning
Combining Non-stably Infinite, Non-first Order Theories
Electronic Notes in Theoretical Computer Science (ENTCS)
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
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Combination of decision procedures is at the heart of Satisfiability Modulo Theories (SMT) solvers. It provides ways to compose decision procedures for expressive languages which mix symbols from various decidable theories. Typical combinations include (linear) arithmetic, uninterpreted symbols, arrays operators, etc. In [7] we showed that any first-order theory from the Bernays-Schönfinkel-Ramsey fragment, the two variable fragment, or the monadic fragment can be combined with virtually any other decidable theory. Here, we complete the picture by considering the Ackermann fragment, and several guarded fragments. All theories in these fragments can be combined with other decidable (combinations of) theories, with only minor restrictions. In particular, it is not required for these other theories to be stably-infinite.