Decision procedures and expressiveness in the temporal logic of branching time
Journal of Computer and System Sciences
Basic proof theory (2nd ed.)
Dynamic Logic
On the temporal analysis of fairness
POPL '80 Proceedings of the 7th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
TPHOLs '08 Proceedings of the 21st International Conference on Theorem Proving in Higher Order Logics
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
Constructive formalization of hybrid logic with eventualities
CPP'11 Proceedings of the First international conference on Certified Programs and Proofs
| Hi-index | 0.00 |
Classical modal logic with transitive closure appears as a subsystem of logics used for program verification. The logic can be axiomatized with a Hilbert system. In this paper we develop a constructive completeness proof for the axiomatization using Coq with Ssreflect. The proof is based on a novel analytic Gentzen system, which yields a certifying decision procedure that for a formula constructs either a derivation or a finite countermodel. Completeness of the axiomatization then follows by translating Gentzen derivations to Hilbert derivations. The main difficulty throughout the development is the treatment of transitive closure.