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The global structure of various systems of logic connectives is investigated by looking at abstract group properties of the group of transformations of these. Such characterizations of fuzzy interval logics are examined in Sections 4–9. The paper starts by introducing readers to the Checklist Paradigm semantics of fuzzy interval logics (Sections 2 and 3). In the Appendix we present some basic notions of fuzzy logics, sets and many-valued logics in order to make the paper accessible to readers not familiar with fuzzy sets.