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  • 1. Sprenger, C.
    et al.
    Dam, Mads
    KTH, Superseded Departments, Microelectronics and Information Technology, IMIT.
    On global induction mechanisms in a mu-calculus with explicit approximations2003In: Informatique théorique et applications (En ligne), ISSN 0988-3754, E-ISSN 1290-385X, Vol. 37, no 4, p. 365-391Article in journal (Refereed)
    Abstract [en]

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