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Description Logics (DLs) are knowledge representation languages, particularly suited to specify formal ontologies. DLs have been studied extensively over the last two decades. Fuzzy Description Logics (FDLs) incorporate vague concepts modeling them as fuzzy sets. Following ideas from Hájek, we propose the use of truth constants in the languages of description. In particular we introduce the languages [Ascr ][Lscr ][Cscr ]L*(S) and [Ascr ][Lscr ][Cscr ]L*~(S) as an adequate syntactical counterpart of some semantic calculi given in different works dealing with FDLs. In addition we give completeness results for some languages [Ascr ][Lscr ][Cscr ]-like.
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