On the one hand, classical terminological knowledge representation excludes the possibility of handling uncertain concept descriptions involving, e.g., "usually true" concept properties, generalized quantifiers, or exceptions. On the other hand, purely numerical approaches for handling uncertainty in general are unable to consider terminological knowledge. This paper presents the language ALCP which is a probabilistic extension of terminological logics and aims at closing the gap between the two areas of research. We present the formal semantics underlying the language ALCP and introduce the probabilistic formalism that is based on classes of probabilities and is realized by means of probabilistic constraints. Besides infer-ing implicitly existent probabilistic relationships, the constraints guarantee terminological and probabilistic consistency. Altogether, the new language ALCP applies to domains where both term descriptions and uncertainty have to be handled.
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