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
A DPLL-Based Calculus for Ground Satisfiability Modulo Theories
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Combining word problems through rewriting in categories with products
Theoretical Computer Science - Category theory and computer science
Handbook of automated reasoning
Higher-order unification and matching
Handbook of automated reasoning
A Superposition Decision Procedure for the Guarded Fragment with Equality
LICS '99 Proceedings of the 14th Annual IEEE Symposium on Logic in Computer Science
ε-connections of abstract description systems
Artificial Intelligence
Model-Theoretic Methods in Combined Constraint Satisfiability
Journal of Automated Reasoning
Information and Computation - Special issue: Combining logical systems
Efficient theory combination via boolean search
Information and Computation - Special issue: Combining logical systems
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
The Description Logic Handbook
The Description Logic Handbook
Fusions of description logics and abstract description systems
Journal of Artificial Intelligence Research
Decidability and undecidability results for nelson-oppen and rewrite-based decision procedures
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
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
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
Combination of convex theories: Modularity, deduction completeness, and explanation
Journal of Symbolic Computation
Combined satisfiability modulo parametric theories
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Data structures with arithmetic constraints: a non-disjoint combination
FroCoS'09 Proceedings of the 7th international conference on Frontiers of combining systems
Modular termination and combinability for superposition modulo counter arithmetic
FroCoS'11 Proceedings of the 8th international conference on Frontiers of combining systems
A Decidability Result for the Model Checking of Infinite-State Systems
Journal of Automated Reasoning
Studia Logica
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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 admits an abstract version of a “Keisler-Shelah-like” isomorphism theorem. We show that this general decidability transfer result covers recent work on combination in first-order theories as well as in various intensional logics such as description, modal, and temporal logics.