On the Relationship between Logical Bayesian Networks and Probabilistic Logic Programming Based on the Distribution Semantics

A significant part of current research on (inductive) logic programming deals with probabilistic logical models. Over the last decade many logics or languages for representing such models have been introduced. There is currently a great need for insight into the relationships between all these languages. One kind of languages are those that extend probabilistic models with elements of logic, such as the language of Logical Bayesian Networks (LBNs). Some other languages follow the converse strategy of extending logic programs with a probabilistic semantics, often in a way similar to that of Sato's distribution semantics. In this paper we study the relationship between the language of LBNs and languages based on the distribution semantics. Concretely, we define a mapping from LBNs to theories in the Independent Choice Logic (ICL). We also show how this mapping can be used to learn ICL theories from data.