Description Logics (DLs) are knowledge representation languages particularly suited to specify
formal ontologies. DLs allow the creation of knowledge bases and provide ways to reason on the
contents of these bases. Fuzzy Description Logics (FDLs) is a natural extension of DL for dealing
with vague concepts, commonly present in real applications. Hájek proposed to deal with FDL taking
as basis t-norm based fuzzy logics  with the aim of enriching the expressive possibilities in FDL and
to take profit of the recent developments in mathematical fuzzy logics. Now we introduce a new family
of description languages, denoted by ALC*(S), that includes truth constants for representing truth
degrees. Having truth constants in the language allow us to have a syntactical counterpart in FDLs of
the axioms of the knowledge bases in a similar way as in classical DL. On the other hand  truth
constants also allow to define graded notions of validity, satisfiability and subsumption from a syntactic
perspective.