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