Adding modalities to MTL and its extensions

Abstract. Monoidal t-norm logic MTL and related fuzzy logics are extended with various modalities distinguished by the axiom (A ∨ B) → (A ∨ B). Such modalities include Linear logic-like exponentials, the globalization (or Delta) operator, and truth stressers like “very true”. Extensions of MTL with modal-ities are presented here via axiomatizations, hypersequent calculi, and algebraic semantics, and related to standard algebras based on t-norms. Embeddings of logics, decidability, and the finite embedding property are also investigated.