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. 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 .
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.