Local model checking in the modal mu-calculus
TAPSOFT '89 2nd international joint conference on Theory and practice of software development
A framework for defining logics
Journal of the ACM (JACM)
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TYPES '93 Proceedings of the international workshop on Types for proofs and programs
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TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Completeness of Kozen's Axiomatisation of the Propositional Mu-Calculus
LICS '95 Proceedings of the 10th Annual IEEE Symposium on Logic in Computer Science
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We present a Natural Deduction proof system for the propositional modal µ-calculus, and its formalization in the Calculus of Inductive Constructions. We address several problematic issues, such as the use of higher-order abstract syntax in inductive sets in presence of recursive constructors, the encoding of modal (sequent-style) rules and of context sensitive grammars. The formalization can be used in the system Coq, providing an experimental computer-aided proof environment for the interactive development of error-free proofs in the µ-calculus. The techniques we adopt can be readily ported to other languages and proof systems featuring similar problematic issues.