A Logic for Default Reasoning About Probabilities
This work addresses the challenge of default reasoning under uncertainty for AI and logic communities, offering a novel integration but with incremental theoretical development.
The paper tackles the problem of integrating statistical probabilities and subjective beliefs into a unified logical framework, achieving a semantics that models the influence of statistical information on belief formation through cross entropy minimization.
A logic is defined that allows to express information about statistical probabilities and about degrees of belief in specific propositions. By interpreting the two types of probabilities in one common probability space, the semantics given are well suited to model the influence of statistical information on the formation of subjective beliefs. Cross entropy minimization is a key element in these semantics, the use of which is justified by showing that the resulting logic exhibits some very reasonable properties.