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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