  In Probabilistic Logic Nilsson uses the device of a probability distribution
over a set of possible worlds to assign probabilities to the sentences of a
logical language. In his paper Nilsson concentrated on inference and associated
computational issues. This paper, on the other hand, examines the probabilistic
semantics in more detail, particularly for the case of first-order languages,
and attempts to explain some of the features and limitations of this form of
probability logic. It is pointed out that the device of assigning probabilities
to logical sentences has certain expressive limitations. In particular,
statistical assertions are not easily expressed by such a device. This leads to
certain difficulties with attempts to give probabilistic semantics to default
reasoning using probabilities assigned to logical sentences.

Artificial Intelligence