Studia Logica

, Volume 89, Issue 3, pp 343–363 | Cite as

On the Proof Theory of the Modal mu-Calculus

Article

Abstract

We study the proof-theoretic relationship between two deductive systems for the modal mu-calculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a second infinitary calculus which is based on non-well-founded trees. In this system proofs are finitely branching but may contain infinite branches as long as some greatest fixed point is unfolded infinitely often along every branch. The main contribution of our paper is a translation from proofs in the first system to proofs in the second system. Completeness of the second system then follows from completeness of the first, and a new proof of the finite model property also follows as a corollary.

Keywords

Infinitary proof theory μ-calculus 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  1. 1.Institut für Informatik und angewandte MathematikUniversität BernBernSwitzerland

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