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On global induction mechanisms in a μ -calculus with explicit approximations

Christoph Sprenger;  Mads Dam — 2003

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

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...

On global induction mechanisms in a -calculus with explicit approximations

Christoph Sprenger;  Mads Dam — 2010

RAIRO - Theoretical Informatics and Applications

We investigate a Gentzen-style proof system for the first-order -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...

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