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

A significant part of current research on ILP 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 class of languages are those that extend probabilistic models with elements of logic, such as in 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 that this mapping provides us with a learning algorithm for ICL. 1 Context: Probabilistic ILP and Statistical Relational Learning The fields of probabilistic inductive logic programming (probabilistic ILP) and statistical relational learning (SRL) have recently witnessed a large interest in probabilistic logical models and languages for representing such models [3]. Several popular languages deal with probabilistic extensions of logic programs. Syntactically one typically uses logic programs in which facts, clauses, or heads of clauses are annotated with probabilities. Semantically one often relies (explicitly or implicitly) on Sato’s distribution semantics (DS) [10]. We refer to languages that fit this description as DS languages. Examples are PRISM [3, Ch.4], the Independent Choice Logic [9], ProbLog [4] and even Logic Programs with Annotated Disjunctions [11]. Other popular languages deal with extensions of probabilistic graphical models to the relational case. For instance, Markov Logic [7, Ch.12] and Relational Markov Networks [7, Ch.6] are based on undirected models, while many other languages are based on directed models: Relational Bayesian Networks [3, Ch.13], Probabilistic Relational Models [7, Ch.5], Bayesian Logic Programs [7, Ch.10], BLOG [7, Ch.13], Logical Bayesian Networks (LBNs) [5, 6] and others. In this paper we focus on the language of LBNs, which is strongly related to other languages based on Bayesian networks, especially BLPs and PRMs [5]. 2 Problem Statement, Goal and Contributions The plethora of languages in SRL and probabilistic ILP is sometimes referred to as ‘alphabet soup’ (consisting of the acronyms of the many languages). There is currently a