A survey of first-order probabilistic models

There has been a long standing division in Artificial Intelligence between logical and probabilistic reasoning approaches. While probabilistic models can deal well with inherent uncertainty in many real-world domains, they operate on a mostly propositional level. Logic systems, on the other hand, can deal with much richer representations, especially first-order ones, but treat uncertainty only in limited ways. Therefore, an integration of these types of inference is highly desirable, and many approaches have been proposed, especially from the 1990s on. These solutions come from many different subfields and vary greatly in language, features and (when available at all) inference algorithms. Therefore their relation to each other is not always clear, as well as their semantics. In this survey, we present the main aspects of the solutions proposed and group them according to language, semantics and inference algorithm. In doing so, we draw relations between them and discuss particularly important choices and tradeoffs.