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

Abstract

Abstract Establishing a rigorous framework for propositional deduction which also agrees with what is termed “commonsense reasoning” poses a difficult challenge. This paper is the first of a two-part effort in considering the issue and proposing (in future Part 2) a particular approach via the use of “second order” probabilities, i.e., distributions of probability measures, as opposed to probability-selection approaches, especially that of maximum entropy and Adams' high probability schemes. In the second order probability approach, usually all probability distributions are assumed a priori to be either equally likely, or more generally, to be distributed via the Dirichlet family, up to the constraints involved in the premise set of the potential deduction considered.