0 Angel García-Cerdaña Eva Armengol Francesc Esteva 2010 International Journal of Approximate reasoning Elsevier 51 6 632 -- 655 July/2010 Description Logics, Fuzzy Description Logics, Many-valued Logics, Propositional and Predicate t-norm based Fuzzy Logics, Truth-constantsReceived 22 May 2009 Description Logics (DLs) are knowledge representation languages built on the basis of classical logic. DLs allow the creation of knowledge bases and provide ways to reason on the contents of these bases. Fuzzy Description Logics (FDLs) are natural extensions of DLs for dealing with vague concepts, commonly present in real applications. Ha?jek proposed to deal with FDLs taking as basis t-norm based fuzzy logics with the aim of enriching the expressive possibilities in FDLs and to capitalize on recent developments in the field of Mathematical Fuzzy Logic. From this perspective we define a family of description lan- guages, denoted by ALC