Representing Statistical Information and Degrees of Belief in First-Order Probabilistic Conditional Logic

Employing maximum entropy methods on probabilistic conditional logic has proven to be a useful approach for commonsense reasoning. Yet, the expressive power of this logic and similar formalisms is limited due to their foundations on propositional logic and in the past few years a lot of proposals have been made for probabilistic reasoning in relational settings. Most of these proposals rely on extensions of traditional graph-based probabilistic models like Bayes nets or Markov nets whereas probabilistic conditional logic does not presuppose any graphical structure underlying the model to be represented. In this paper we take an approach of lifting maximum entropy methods to the relational case by using a first-order version of probabilistic conditional logic. Furthermore, we take a specific focus on representing relational probabilistic knowledge by differentiating between different intuitions on relational probabilistic conditionals, namely between statistical interpretations and interpretations on degrees of belief. We develop a list of desirable properties on an inference procedure that supports these different interpretations and propose a specific inference procedure that fulfills these properties. We furthermore discuss related work and give some hints on future research.