Studia Logica

, Volume 91, Issue 2, pp 145–169 | Cite as

On Modal μ-Calculus and Gödel-Löb Logic

Article

Abstract

We show that the modal μ-calculus over GL collapses to the modal fragment by showing that the fixpoint formula is reached after two iterations and answer to a question posed by van Benthem in [4]. Further, we introduce the modal μ~-calculus by allowing fixpoint constructors for any formula where the fixpoint variable appears guarded but not necessarily positive and show that this calculus over GL collapses to the modal fragment, too. The latter result allows us a new proof of the de Jongh, Sambin Theorem and provides a simple algorithm to construct the fixpoint formula.

Keywords

Fixpoint Modal μ-Calculus Gödel-Löb Logic 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.IAM, University of BernBernSwitzerland
  2. 2.ISI - HEC, University of LausanneLausanneSwitzerland
  3. 3.LaBRI, University of Bordeaux 1Talence cedexFrance

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