Relational Probabilistic Conditional Reasoning at Maximum Entropy

This paper presents and compares approaches for reasoning with relational probabilistic conditionals, i. e. probabilistic conditionals in a restricted first-order environment. It is well-known that conditionals play a crucial role for default reasoning, however, most formalisms are based on propositional conditionals, which restricts their expressivity. The formalisms discussed in this paper are relational extensions of a propositional conditional logic based on the principle of maximum entropy. We show how this powerful principle can be used in different ways to realize model-based inference relations for first-order probabilistic knowledge bases. We illustrate and compare the different approaches by applying them to several benchmark examples, and we evaluate each approach with respect to properties adopted from default reasoning. We also compare our approach to Bayesian logic programs (BLPs) from the field of statistical relational learning which focuses on the combination of probabilistic reasoning and relational knowledge representation as well.