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On global induction mechanisms in a μ-calculus with explicitapproximations

Published online by Cambridge University Press:  15 January 2004

Christoph Sprenger  and
Mads Dam
Christoph Sprenger
Affiliation:
INRIA Sophia Antipolis, 2004, route des Lucioles, BP 93, 06902 Sophia Antipolis, France; [email protected].
Mads Dam
Affiliation:
Dept. of Microelectronics and Information Technology, Royal Institute of Technology, KTH, Forum 105, 164 40 Kista, Sweden; [email protected].
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Abstract

We investigate a Gentzen-style proof system for the first-order μ-calculusbased on cyclic proofs, produced by unfolding fixed point formulasand detecting repeated proof goals. Our system uses explicit ordinalvariables and approximations to support a simple semantic inductiondischarge condition which ensures the well-foundedness of inductivereasoning. As the main result of this paper we propose a new syntacticdischarge condition based on traces and establish its equivalencewith the semantic condition. We give an automata-theoretic reformulationof this condition which is more suitable for practical proofs. Fora detailed comparison with previous work we consider two simpler syntacticconditions and show that they are more restrictive than our new condition.

Keywords

Inductive reasoningcircular proofswell-foundednessglobal consistency conditionμ-calculusapproximants.
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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