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Fuzzy Description Logics (DLs) are a family of logics which allow therepresentation of (and the reasoning with) structured knowledge affected byvagueness. 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 intothe fuzzy case. In this paper we show that if we allow arbitrary knowledgebases, then the fuzzy DLs ALC under Lukasiewicz and Product fuzzy logics do notverify the FMP even if we restrict to witnessed models; in other words, finitesatisfiability and witnessed satisfiability are different for arbitraryknowledge bases. The aim of this paper is to point out the failure of FMPbecause it affects several algorithms published in the literature for reasoningunder fuzzy ALC.

On the Failure of the Finite Model Property in some Fuzzy Description Logics