PP-2023-03:
Afshari, Bahareh and Enqvist, Sebastian and Leigh, Graham E. and Marti, Johannes and Venema, Yde
(2023)
*Proof Systems for Two-way Modal mu-Calculus.*
[Pre-print]
(Submitted)

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## Abstract

We present sound and complete sequent calculi for the modal mu-calculus with converse modalities, aka two-way modal mu-calculus. Notably, we introduce a cyclic proof system wherein proofs can be represented as finite trees with back-edges, i.e., finite graphs. The sequent calculi incorporate ordinal annotations and structural rules for managing them. Soundness is proved with relative ease as is the case for the modal mu-calculus with explicit ordinals. The main ingredients in the proof of completeness are isolating a class of non-well-founded proofs with sequents of bounded size, called slim proofs, and a counter-model construction that shows slimness suffices to capture all validities. Slim proofs are further transformed into cyclic proofs by means of re-assigning ordinal annotations.

Item Type: | Pre-print |
---|---|

Report Nr: | PP-2023-03 |

Series Name: | Prepublication (PP) Series |

Year: | 2023 |

Uncontrolled Keywords: | Sequent Calculus, Full Modal mu-Calculus, Cyclic Proofs, Two-way Modal mu-Calculus, Temporal Logic, Fixed Point Logic |

Subjects: | Computation Logic Mathematics |

Depositing User: | dr Bahareh Afshari |

Date Deposited: | 04 Apr 2023 07:50 |

Last Modified: | 04 Apr 2023 07:50 |

URI: | https://eprints.illc.uva.nl/id/eprint/2241 |

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