On probabilistic inference in relational conditional logics

The principle of maximum entropy has proven to be a powerful approach for commonsense reasoning in probabilistic conditional logics on propositional languages. Due to this principle, reasoning is performed based on the unique model of a knowledge base that has maximum entropy. This kind of model-based inference fulfills many desirable properties for inductive inference mechanisms and is usually the best choice for reasoning from an information theoretical point of view. However, the expressive power of propositional formalisms for probabilistic reasoning is limited and in the past few years many proposals have been given for probabilistic reasoning in relational settings. It seems to be a common view that in order to interpret probabilistic first-order sentences, either a statistical approach that counts (tuples of) individuals has to be used, or the knowledge base has to be grounded to make a possible worlds semantics applicable, for a subjective interpretation of probabilities. Most of these proposals of the second type rely on extensions of traditional probabilistic models like Bayes nets or Markov networks whereas there are only few works on first-order extensions of probabilistic conditional logic. Here, we take an approach of lifting maximum entropy methods to the relational case by employing a relational version of probabilistic conditional logic. First, we propose two different semantics and model theories for interpreting first-order probabilistic conditional logic. We address the problems of ambiguity that are raised by the difference between subjective and statistical views, and develop a comprehensive list of desirable properties for inductive model-based probabilistic inference in relational frameworks. Finally, by applying the principle of maximum entropy in the two different semantical frameworks, we obtain inference operators that fulfill these properties and turn out to be reasonable choices for reasoning in first-order probabilistic conditional logic.