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On global induction mechanisms in a μ-calculus with explicitapproximations
Published online by Cambridge University Press: 15 January 2004
Abstract
We investigate a Gentzen-style proof system for the first-order μ-calculus based on cyclic proofs, produced by unfolding fixed point formulas and detecting repeated proof goals. Our system uses explicit ordinal variables and approximations to support a simple semantic induction discharge condition which ensures the well-foundedness of inductive reasoning. As the main result of this paper we propose a new syntactic discharge condition based on traces and establish its equivalence with the semantic condition. We give an automata-theoretic reformulation of this condition which is more suitable for practical proofs. For a detailed comparison with previous work we consider two simpler syntactic conditions and show that they are more restrictive than our new condition.
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- Type
- Research Article
- Information
- RAIRO - Theoretical Informatics and Applications , Volume 37 , Issue 4: Fixed Points in Computer Science (FICS'02) , October 2003 , pp. 365 - 391
- Copyright
- © EDP Sciences, 2003
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