On global induction mechanisms in a $\mu $-calculus with explicit approximations

Sprenger, Christoph; Dam, Mads

doi:10.1051/ita:2003024

On global induction mechanisms in a

μ

-calculus with explicit approximations

Sprenger, Christoph ; Dam, Mads

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 4, pp. 365-391

Résumé

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.

MR Zbl

DOI : 10.1051/ita:2003024

Classification : 68Q60, 03F07, 03B35
Keywords: inductive reasoning, circular proofs, well-foundedness, global consistency condition, $\mu $-calculus, approximants

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     author = {Sprenger, Christoph and Dam, Mads},
     title = {On global induction mechanisms in a $\mu $-calculus with explicit approximations},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {365--391},
     year = {2003},
     publisher = {EDP Sciences},
     volume = {37},
     number = {4},
     doi = {10.1051/ita:2003024},
     mrnumber = {2053032},
     zbl = {1111.68518},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita:2003024/}
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Sprenger, Christoph; Dam, Mads. On global induction mechanisms in a $\mu $-calculus with explicit approximations. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 37 (2003) no. 4, pp. 365-391. doi: 10.1051/ita:2003024

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