  Fuzzy Description Logics (DLs) are a family of logics which allow the
representation of (and the reasoning with) structured knowledge affected by
vagueness. Although most of the not very expressive crisp DLs, such as ALC,
enjoy the Finite Model Property (FMP), this is not the case once we move into
the fuzzy case. In this paper we show that if we allow arbitrary knowledge
bases, then the fuzzy DLs ALC under Lukasiewicz and Product fuzzy logics do not
verify the FMP even if we restrict to witnessed models; in other words, finite
satisfiability and witnessed satisfiability are different for arbitrary
knowledge bases. The aim of this paper is to point out the failure of FMP
because it affects several algorithms published in the literature for reasoning
under fuzzy ALC.
