Probability Distributions Over Possible Worlds
This work addresses foundational issues in probabilistic logic for researchers in AI and logic, but it is incremental as it builds on Nilsson's framework to analyze limitations rather than introducing new methods.
The paper examines the probabilistic semantics of first-order languages using probability distributions over possible worlds, highlighting expressive limitations such as difficulty in representing statistical assertions and challenges in applying this approach to default reasoning.
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.