A proof-theoretical investigation of global intuitionistic (fuzzy) logic

Archive for Mathematical Logic 44 (4):435-457 (2005)
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Abstract

We perform a proof-theoretical investigation of two modal predicate logics: global intuitionistic logic GI and global intuitionistic fuzzy logic GIF. These logics were introduced by Takeuti and Titani to formulate an intuitionistic set theory and an intuitionistic fuzzy set theory together with their metatheories. Here we define analytic Gentzen style calculi for GI and GIF. Among other things, these calculi allows one to prove Herbrand’s theorem for suitable fragments of GI and GIF.

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10.1007/s00153-004-0265-8

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Citations of this work

First-order Gödel logics.Richard Zach, Matthias Baaz & Norbert Preining - 2007 - Annals of Pure and Applied Logic 147 (1):23-47.
Hypersequent calculi for intuitionistic logic with classical atoms.Hidenori Kurokawa - 2010 - Annals of Pure and Applied Logic 161 (3):427-446.

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References found in this work

The method of hypersequents in the proof theory of propositional non-classical logics.Arnon Avron - 1996 - In Wilfrid Hodges (ed.), Logic: Foundations to Applications. Oxford: pp. 1-32.
Globalization of intui tionistic set theory.Gaisi Takeuti & Satoko Titani - 1987 - Annals of Pure and Applied Logic 33 (C):195-211.
Completeness of global intuitionistic set theory.Satoko Titani - 1997 - Journal of Symbolic Logic 62 (2):506-528.

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