A proof-theoretical investigation of global intuitionistic (fuzzy) logic
type: Item
instance of: scholarly article
title: A proof-theoretical investigation of global intuitionistic (fuzzy) logic
zbMATH Open document ID: 1071.03012
author: Agata Ciabattoni
published in: Archive for Mathematical Logic
publication date: 2005-05-26T00:00:00Z
review text: In this paper, hypersequent calculi for global intuitionistic logic and global intuitionistic fuzzy logic are introduced. Both logics are predicate logics extended by an additional logical symbol, \(\square\), called globalization (alternatively also Baaz delta), which keeps 1 and puts the rest to 0. Intuitionistic fuzzy logic has been originally introduced by Takeuti and Titani and later proved to coincide with Gödel logic based on the set of truth values \([0, 1]\). Some basic properties of the hypersequent calculi are presented and also versions of a cut-elimination theorem for both logics are proved. As a consequence, a Herbrand theorem for the prenex fragment of both logics is also proved.
reviewed by: Vilém Novák
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03F05
zbMATH DE Number: 2171986
zbMATH Keywords: fuzzy logic in narrow sense
zbMATH Keywords: hypersequent calculi, globalization
MaRDI profile type: Publication
full work available at URL: s00153-004-0265-8
OpenAlex ID: W2065076866
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DOI: 10.1007/S00153-004-0265-8
description: scientific article; zbMATH DE number 2171986