Towards a General Framework for Maximum Entropy Reasoning

A possible approach to extend classical logics to probabilistic logics is to consider a probability distribution over the classical interpretations that satisfies some constraints and maximizes entropy. Over the past years miscellaneous languages and semantics have been considered often based on similar ideas. In this paper a hierarchy of general probabilistic semantics is developed. It incorporates some interesting specific semantics and a family of standard semantics that can be used to extend arbitrary languages with finite interpretation sets to probabilistic languages. We use the hierarchy to generalize an approach reducing the complexity of the whole entailment process and sketch the importance for further theoretical and practical applications.