PP-2010-12: Complete Axiomatization of the Stutter-Invariant Fragment of the Linear-time mu-calculus

PP-2010-12: Gheerbrant, Amélie (2010) Complete Axiomatization of the Stutter-Invariant Fragment of the Linear-time mu-calculus. [Report]

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Abstract

The logic µ(U) is the fixpoint extension of the "Until"-only fragment of linear-time temporal logic. It also happens to be the stutter-invariant fragment of linear-time µ-calculus µ(◊). We provide complete axiomatizations of µ(U) on the class of finite words and on the class of ω-words. We introduce for this end another logic, which we call µ(◊_Γ), and which is a variation of µ(◊) where the Next time operator is replaced by the family of its stutter-invariant counterparts. This logic has exactly the same expressive power as µ(U). Using already known results for µ(◊), we first prove completeness for µ(◊_Γ), which finally allows us to obtain completeness for µ(U).

Item Type: Report
Report Nr: PP-2010-12
Series Name: Prepublication (PP) Series
Year: 2010
Uncontrolled Keywords: Complete axiomatization; Linear-time temporal logic; Linear-time mu-calculus; Stutter-invariancy
Subjects: Logic
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/391

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