We explore the proof theory of the modal µ -calculus with converse, aka the ‘fullµ -calculus’. Building on nested sequent calculi for tense logics and infinitary proof theory of fixed point logics, a cut-free sound and complete proof system for full µ -calculus is proposed. As a corollary of our framework, we also obtain a direct proof of the regular model property for the logic: every satisfiable formula has a tree model with finitely many distinct subtrees. To obtain the results we appeal to the basic theory of well-quasi-orderings in the spirit of Kozen’s proof of the finite model property for µ -calculus without converse.
CITATION STYLE
Afshari, B., Jäger, G., & Leigh, G. E. (2019). An Infinitary Treatment of Full Mu-Calculus. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 11541 LNCS, pp. 17–34). Springer Verlag. https://doi.org/10.1007/978-3-662-59533-6_2
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