“…We have played a key international role in the definition and development of mathematical fuzzy logic and we have obtained important results in the following topics: (1) General and deep results for completeness of fuzzy logics either propositional or first order with respect to different semantics (real, hyper‐real, rational, and finite) that cover and significantly extend previous results in the field. Our results have been possible as a consequence of a fruitful collaboration with researchers from different leading institutions on the topic; (2) Formalization of t‐normbased logics dealing with partial degrees of truth, with algebraic semantics, and axiomatization and completeness results, both for propositional and first‐order languages (Esteva, Godo, and Noguera 2009; Cintula et al 2009), which have high applicability in modeling graded notions (Casali, Godo, and Sierra 2011); (3) Development of different systems of fuzzy modal logic (Bou et al 2011), with applications to reasoning under different forms to uncertainty on non‐Boolean algebras of events (Flaminio, Godo, and Marchioni 2013); and (4) Development of a new hierarchy of fuzzy description logics, along with new complexity results based on results of mathematical fuzzy logic (Cerami, Garcia‐Cerdaña, and Esteva 2014).…”