Decision procedures and expressiveness in the temporal logic of branching time
Journal of Computer and System Sciences
A Machine-Checked Implementation of Buchberger's Algorithm
Journal of Automated Reasoning
A Mechanisation of Computability Theory in HOL
TPHOLs '96 Proceedings of the 9th International Conference on Theorem Proving in Higher Order Logics
Classical Propositional Decidability via Nuprl Proof Extraction
Proceedings of the 11th International Conference on Theorem Proving in Higher Order Logics
Handbook of Modal Logic, Volume 3 (Studies in Logic and Practical Reasoning)
Handbook of Modal Logic, Volume 3 (Studies in Logic and Practical Reasoning)
SFCS '79 Proceedings of the 20th Annual Symposium on Foundations of Computer Science
Packaging Mathematical Structures
TPHOLs '09 Proceedings of the 22nd International Conference on Theorem Proving in Higher Order Logics
A modular formalisation of finite group theory
TPHOLs'07 Proceedings of the 20th international conference on Theorem proving in higher order logics
Correctness and worst-case optimality of Pratt-style decision procedures for modal and hybrid logics
TABLEAUX'11 Proceedings of the 20th international conference on Automated reasoning with analytic tableaux and related methods
Mechanised computability theory
ITP'11 Proceedings of the Second international conference on Interactive theorem proving
Terminating tableaux for hybrid logic with eventualities
IJCAR'10 Proceedings of the 5th international conference on Automated Reasoning
Constructive completeness for modal logic with transitive closure
CPP'12 Proceedings of the Second international conference on Certified Programs and Proofs
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This paper reports on the formalization of classical hybrid logic with eventualities in the constructive type theory of the proof assistant Coq. We represent formulas and models and define satisfiability, validity, and equivalence of formulas. The representation yields the classical equivalences and does not require axioms. Our main results are an algorithmic proof of a small model theorem and the computational decidability of satisfiability, validity, and equivalence of formulas. We present our work in three steps: propositional logic, modal logic, and finally hybrid logic.