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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