Introduction to higher order categorical logic
Introduction to higher order categorical logic
Term rewriting and all that
Simplification by Cooperating Decision Procedures
ACM Transactions on Programming Languages and Systems (TOPLAS)
Resolution Methods for the Decision Problem
Resolution Methods for the Decision Problem
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Introduction to Mathematical Logic and Type Theory: To Truth through Proof
Journal of Logic, Language and Information
Cooperation of Background Reasoners in Theory Reasoning by Residue Sharing
Journal of Automated Reasoning
Invited Talk: Decision procedures for guarded logics
CADE-16 Proceedings of the 16th International Conference on Automated Deduction: Automated Deduction
Handbook of automated reasoning
Higher-order unification and matching
Handbook of automated reasoning
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
Information and Computation - Special issue: Combining logical systems
Fusions of description logics and abstract description systems
Journal of Artificial Intelligence Research
Connecting many-sorted structures and theories through adjoint functions
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
New results on rewrite-based satisfiability procedures
ACM Transactions on Computational Logic (TOCL)
Annals of Mathematics and Artificial Intelligence
Theory decision by decomposition
Journal of Symbolic Computation
An overview of AI research in Italy
Artificial intelligence
Satisfiability modulo theories: introduction and applications
Communications of the ACM
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We define a general notion of a fragment within higher order type theory; a procedure for constraint satisfiability in combined fragments is outlined, following Nelson-Oppen schema. The procedure is in general only sound, but it becomes terminating and complete when the shared fragment enjoys suitable noetherianity conditions and allows an abstract version of a ‘Keisler-Shelah like' isomorphism theorem. We show that this general decidability transfer result covers as special cases, besides applications which seem to be new, the recent extension of Nelson-Oppen procedure to non-disjoint signatures [16] and the fusion transfer of decidability of consistency of A-Boxes with respect to T-Boxes axioms in local abstract description systems [9]; in addition, it reduces decidability of modal and temporal monodic fragments [32] to their extensional and one-variable components.