Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
Journal of Automated Reasoning
Modular proof systems for partial functions with Evans equality
Information and Computation - Special issue: Combining logical systems
A comprehensive combination framework
ACM Transactions on Computational Logic (TOCL)
Ground Interpolation for the Theory of Equality
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,
Differential dynamic logics: automated theorem proving for hybrid systems
Differential dynamic logics: automated theorem proving for hybrid systems
Invited contribution: a comprehensive framework for combined decision procedures
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
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We propose a general way of combining background reasoners in theory reasoning. Using a restricted version of the Craig interpolation lemma, we show that background reasoner cooperation can be achieved as a form of constraint propagation, much in the spirit of existing combination methods for decision procedures. In this case, constraint information is propagated across reasoners eexchanging residues that are, in essence, disjunctions of ground literals over a common signature. As an application of our approach, we describe a multitheory version of the semantic tableau calculus, and we prove it sound and complete.