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 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.
second order probabilities probabilistic deduction conditional probabilities conditional events