PP-2009-41: Complete Axiomatization of the Stutter-Invariant Fragment of the Linear-time mu-calculus

PP-2009-41: Gheerbrant, Amélie (2009) Complete Axiomatization of the Stutter-Invariant Fragment of the Linear-time mu-calculus. [Report]

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Abstract

The logic \mu(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 \mu-calculus \mu(\diamond). We provide complete axiomatizations of \mu(U) on the class of finite words and on the class of \omega-words. We introduce for this end another logic, which we call \mu(\diamond\Gamma), and which is a variation of \mu(\diamond) where the Next time operator is replaced by the family of its stutter-invariant counterparts. This logic has exactly the same expressive power as \mu(U). Using already known results for \mu(\diamond), we first prove completeness for \mu(\diamond\Gamma), which finally allows us to obtain completeness for \mu(U).

Item Type: Report
Report Nr: PP-2009-41
Series Name: Prepublication (PP) Series
Year: 2009
Uncontrolled Keywords: Specification languages; Linear-time temporal logic; Linear-time mu-calculus; Stutter-invariancy; Complete axiomatization
Subjects: Language
Date Deposited: 12 Oct 2016 14:37
Last Modified: 12 Oct 2016 14:37
URI: https://eprints.illc.uva.nl/id/eprint/371

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