Probabilistic Reasoning

Although Mod- is a very sophisticated concept description language, the relationships among concepts that can be described are purely qualitative. Only inclusion, equality or disjointness relationships among concepts can be expressed. Jaeger [10] investigates an extension of terminological knowledge representation languages that incorporates probabilistic statements. The language based on allows the following two additional kinds of axioms. Probabilistic terminological axioms are expressions , where C and D are concept terms and . Probabilistic assertions are expressions , where a is an element of and . A knowledge base in consists of a set of terminological axiomsgif, a set of probabilistic terminological axioms and a set of probabilistic assertions for every object name a: .

It is important to realize that these two kinds of probabilistic statements are completely different from each other. The former codifies statistical information that, in general, is obtained by observing a large number of individual objects and checking their membership of the various concepts. The latter expresses a degree of uncertainty of our belief in a specific proposition. Its value is usually justified only by a subjective assessment of likelihood.

Both kinds of probabilistic statements are interpreted in one common probability space which essentially consists of the set of concept terms that can be formed in the language of the given knowledge base. Defining all the probability measures on the same probability space allows us to compare the measure assigned to an object a with the generic measure defined by the given statistical information. The most reasonable assignment of a probability measure to a, we choose then, among all the measures consistent with the constraints known for a is the one that most closely resembles the generic measure. The key question to be answered, therefore, is how resemblance of probability measures should be measured. We chose the method of minimizing the cross entropy of the two measures.

The language and the inferential services described above are not part of the MOTEL system.

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