Partial Fuzzy Logic, Undefinedness, Generalized quantifier

We will recall three prominent families of quantifiers in first-order partial fuzzy logic and study their properties. The background fuzzy logic is the monoidal t-norm based logic MTL. First we will overview the semantics of partial fuzzy propositional logic, recall the basic notions, comment on axiomatization and present its first-order variant. Then we will present results on the properties of quantifiers from different families.