On three implication-less fragments of t-norm based fuzzy logics

This paper concerns the study of the fragments without implication of the logic of residuated lattices (or monoidal logic, or intuitionistic logic without contraction). We obtain that these fragments are exactly the same fragments as those found in classical logic. As a corollary of this result we obtain that the implication-less fragments of every t-norm based fuzzy logic are exactly the same fragments as those found in classical logic.