David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
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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|
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References found in this work BETA
Kai Brünnler & Thomas Studer (2009). Syntactic Cut-Elimination for Common Knowledge. Annals of Pure and Applied Logic 160 (1):82-95.
Dexter Kozen (1988). A Finite Model Theorem for the Propositional Μ-Calculus. Studia Logica 47 (3):233 - 241.
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