Probabilistic Reasoning in Terminological Logics

In this paper a probabilistic extensions for terminological knowledge representation languages is defined. 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 modelling of the way the two kinds of probabilistic knowledge are combined in commonsense inferences of probabilistic statements. Cross entropy minimization is a technique that turns out to be very well suited for achieving this end