Logical Relations in a Statistical Problem

This paper presents the progicnet programme. It proposes a general framework for probabilistic logic that can guide inference based on both logical and probabilistic input, and it introduces a common calculus for making inferences in the framework. After an introduction to the programme as such, it is illustrated by means of a toy example from psychometrics. It is shown that the framework and calculus can accommodate a number of approaches to probabilistic reasoning: Bayesian statistical inference, evidential probability, probabilistic argumentation, and objective Bayesianism. The progicnet programme thus provides insight into the relations between these approaches, it illustrates how the results of different approaches can be combined, and it provides a basis for doing efficient inference in each