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
axioms,
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.