Cyclic proofs for the first-order µ-calculus

Abstract We introduce a path-based cyclic proof system for first-order $\mu $-calculus, the extension of first-order logic by second-order quantifiers for least and greatest fixed points of definable monotone functions. We prove soundness of the system and demonstrate it to be as expressive as the k...

Full description

Saved in:
Bibliographic Details
Published inLogic journal of the IGPL Vol. 32; no. 1; pp. 1 - 34
Main Authors Afshari, Bahareh, Enqvist, Sebastian, Leigh, Graham E
Format Journal Article
LanguageEnglish
Published Oxford University Press 25.01.2024
Subjects
sequent calculus
Cyclic proofs
completeness
modal µ-calculus
first-order µ-calculus
Online AccessGet full text
ISSN1367-0751
1368-9894
DOI10.1093/jigpal/jzac053

Cover

More Information
Summary:Abstract We introduce a path-based cyclic proof system for first-order $\mu $-calculus, the extension of first-order logic by second-order quantifiers for least and greatest fixed points of definable monotone functions. We prove soundness of the system and demonstrate it to be as expressive as the known trace-based cyclic systems of Dam and Sprenger. Furthermore, we establish cut-free completeness of our system for the fragment corresponding to the modal $\mu $-calculus.
ISSN:1367-0751
1368-9894
DOI:10.1093/jigpal/jzac053