Probability Distributions Over Possible Worlds (1304.2341v1)

Abstract: 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.