Focus-Style Proofs for the Two-Way Alternation-Free $$\mu $$-Calculus

Rooduijn, Jan; Venema, Yde

doi:10.1007/978-3-031-39784-4_20

Lecture Notes in Computer Science

2023

DOI: 10.1007/978-3-031-39784-4_20

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Focus-Style Proofs for the Two-Way Alternation-Free $$\mu $$-Calculus

Jan Rooduijn,

Yde Venema

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Proof Systems for Two-Way Modal Mu-Calculus

AFSHARI,

ENQVIST,

LEIGH

et al. 2023

J. symb. log.

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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-wellfounded 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.

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Proof Systems for Two-Way Modal Mu-Calculus

AFSHARI,

ENQVIST,

LEIGH

et al. 2023

J. symb. log.

View full text Add to dashboard Cite

show abstract

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Focus-Style Proofs for the Two-Way Alternation-Free $$\mu $$-Calculus

Cited by 1 publication

References 14 publications

Proof Systems for Two-Way Modal Mu-Calculus

Proof Systems for Two-Way Modal Mu-Calculus

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