Probability Distributions Over Possible Worlds

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 concen­ trated on inference and associated computational issues. This paper, on the other hand, exam­ ines 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 proba­ bilities 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 us­ ing probabilities assigned to logical sentences.