Handbook of theoretical computer science (vol. B)
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Journal of Automated Reasoning
LICS '02 Proceedings of the 17th Annual IEEE Symposium on Logic in Computer Science
A rewriting approach to satisfiability procedures
Information and Computation - RTA 2001
Automatic combinability of rewriting-based satisfiability procedures
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
FroCoS'05 Proceedings of the 5th international conference on Frontiers of Combining Systems
Satisfiability Procedures for Combination of Theories Sharing Integer Offsets
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
Combinable Extensions of Abelian Groups
CADE-22 Proceedings of the 22nd International Conference on Automated Deduction
Automatic decidability and combinability
Information and Computation
An Instantiation Scheme for Satisfiability Modulo Theories
Journal of Automated Reasoning
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We present an inference system for clauses with ordering constraints, called Schematic Paramodulation. Then we show how to use Schematic Paramodulation to reason about decidability and stable infiniteness of finitely presented theories. We establish a close connection between the two properties: if Schematic Paramodulation for a theory halts then the theory is decidable; and if, in addition, Schematic Paramodulation does not derive the trivial equality X= Ythen the theory is stably infinite. Decidability and stable infiniteness of component theories are conditions required for the Nelson-Oppen combination method. Schematic Paramodulation is loosely based on Lynch-Morawska's meta-saturation but it differs in several ways. First, it uses ordering constraints instead of constant constraints. Second, inferences into constrained variables are possible in Schematic Paramodulation. Finally, Schematic Paramodulation uses a special deletion rule to deal with theories for which Lynch-Morawska's meta-saturation does not halt.