Rashmi Pandya and Antony Galton
In D. L. Lowe, K. B. Korb, J. J. Oliver (editors), ISIS: Information, Statistics and Induction in Science Melbourne, Australia, August 1996, pages 141-151. World Scientific, 1996. ISBN 981-02-2824-4.
Abstract
In this paper we develop a highly general perspective from which to view the use of possible worlds, propositions, and predicates in theories of probabilistic reasoning, such as have been advocated within artificial intelligence. We set up a layered structure of domains of increasing generality, and characterise key concepts of probabilistic reasoning in terms of their various functionalities within this structure. This leads to an elucidation of issues relating to the probabilities of logical combinations, higher-order probabilities, Miller's principle, and reasoning with statistical knowledge.