A proof-theoretical investigation of global intuitionistic (fuzzy) logic
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.
scientific article; zbMATH DE number 2171986
scientific article