Statistical deducibility testing with stochastic parameters

The deducibility problem, i.e., the problem, how to test whether a formula of a formalized Iheory is or is not a theorem, is investigated from the statistical point of view. A model is proposed in which the corresponding statistical decision problem can be converted into a parametric test of a simple hypothesis against a simple alternative. Some results following from this possibility are formulated and proved, concerning the probabilities of both types of errors.