Propositional Probabilistic Reasoning at Maximum Entropy Modulo Theories

The principle of maximum entropy (MaxEnt principle) provides a valuable methodology for reasoning with probabilistic conditional knowledge bases realizing an idea of information economy in the sense of adding a minimal amount of assumed information. The conditional structure of such a knowledge base allows for classifying possible worlds regarding their influence on the MaxEnt distribution. In this paper, we present an algorithm that determines these equivalence classes and computes their cardinality by performing satisfiability tests of propositional formulas built upon the premises and conclusions of the conditionals. An example illustrates how the output of our algorithm can be used to simplify calculations when drawing nonmonotonic inferences under maximum entropy. For this, we use a characterization of the MaxEnt distribution in terms of conditional structure that completely abstracts from the propositional logic underlying the conditionals.