PP-2023-03: Proof Systems for Two-way Modal mu-Calculus

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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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
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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