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

Christoph Sprenger; Mads Dam

RAIRO - Theoretical Informatics and Applications (2010)

  • Volume: 37, Issue: 4, page 365-391
  • ISSN: 0988-3754

Abstract

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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.

How to cite

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Sprenger, Christoph, and Dam, Mads. "On global induction mechanisms in a μ-calculus with explicit approximations." RAIRO - Theoretical Informatics and Applications 37.4 (2010): 365-391. <http://eudml.org/doc/92728>.

@article{Sprenger2010,
abstract = { 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. },
author = {Sprenger, Christoph, Dam, Mads},
journal = {RAIRO - Theoretical Informatics and Applications},
keywords = {Inductive reasoning; circular proofs; well-foundedness; global consistency condition; μ-calculus; approximants.; inductive reasoning},
language = {eng},
month = {3},
number = {4},
pages = {365-391},
publisher = {EDP Sciences},
title = {On global induction mechanisms in a μ-calculus with explicit approximations},
url = {http://eudml.org/doc/92728},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Sprenger, Christoph
AU - Dam, Mads
TI - On global induction mechanisms in a μ-calculus with explicit approximations
JO - RAIRO - Theoretical Informatics and Applications
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 4
SP - 365
EP - 391
AB - 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.
LA - eng
KW - Inductive reasoning; circular proofs; well-foundedness; global consistency condition; μ-calculus; approximants.; inductive reasoning
UR - http://eudml.org/doc/92728
ER -

References

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  13. C. Sprenger and M. Dam, On the structure of inductive reasoning: Circular and tree-shaped proofs in the μ-calculus, Foundations of Software Science and Computational Structures (FoSSaCS 03), Warsaw, Poland, April 7-11 2003. A. Gordon, Springer, Lecture Notes in Comput. Sci.2620 (2003) 425-440.  Zbl1029.03016
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