Extension of the concept of propositional deduction from classical logic to probability: an overview of probability-selection approaches

Establishing a rigorous framework for propositional deduction which also ag rees with what is termed "commonsense reasoning" poses a difficult challeng e. This paper is the first of a two-part effort in considering the issue an d proposing (in future Part 2) a particular approach via the use of "second order" probabilities, i.e., distributions of probability measures, as oppo sed to probability-selection approaches, especially that of maximum entropy and Adams' high probability schemes. In the second order probability appro ach, usually all probability distributions are assumed a priori to be eithe r equally likely, or more generally, to be distributed via the Dirichlet fa mily, up to the constraints involved in the premise set of the potential de duction considered. Published by Elsevier Science Inc.