On the proof theory of the modal mu-calculus

Studia Logica 89 (3):343 - 363 (2008)
We study the proof-theoretic relationship between two deductive systems for the modal mu-calculus. First we recall an infinitary system which contains an omega rule allowing to derive the truth of a greatest fixed point from the truth of each of its (infinitely many) approximations. Then we recall a second infinitary calculus which is based on non-well-founded trees. In this system proofs are finitely branching but may contain infinite branches as long as some greatest fixed point is unfolded infinitely often along every branch. The main contribution of our paper is a translation from proofs in the first system to proofs in the second system. Completeness of the second system then follows from completeness of the first, and a new proof of the finite model property also follows as a corollary.
Keywords Philosophy   Computational Linguistics   Mathematical Logic and Foundations   Logic
Categories (categorize this paper)
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 23,217
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

Add more references

Citations of this work BETA

No citations found.

Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

37 ( #127,800 of 1,940,864 )

Recent downloads (6 months)

3 ( #272,622 of 1,940,864 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.