RAIRO-Theor. Inf. Appl.
Volume 37, Number 4, October-December 2003Fixed Points in Computer Science (FICS'02)
|Page(s)||365 - 391|
|Published online||15 January 2004|
On global induction mechanisms in a μ-calculus with explicit approximations
INRIA Sophia Antipolis, 2004, route des Lucioles, BP 93, 06902 Sophia
Antipolis, France; firstname.lastname@example.org.
2 Dept. of Microelectronics and Information Technology, Royal Institute of Technology, KTH, Forum 105, 164 40 Kista, Sweden; email@example.com.
Accepted: 31 October 2003
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.
Mathematics Subject Classification: 68Q60 / 03F07 / 03B35
Key words: Inductive reasoning / circular proofs / well-foundedness / global consistency condition / μ-calculus / approximants.
© EDP Sciences, 2003
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.