A Probabilistic Extension of Terminological Logics

In this report we define a probabilistic extension for a basic terminological knowledge representation languages. Two kinds of probabilistic statements are introduced: statements about conditional probabilities between concepts and statements expressing uncertain knowledge about a specific object. The usual model-theoretic semantics for terminological logics are extended to define interpretations for the resulting probabilistic language. It is our main objective to find an adequate modeling of the way the two kinds of probabilistic knowledge are combined in what we call default reasoning about probabilities. Cross entropy minimization is a technique that turns out to be a very promising tool towards achieving this end