CLP(BN): Constraint Logic Programming for Probabilistic Knowledge
  We present CLP(BN), a novel approach that aims at expressing Bayesian networks through the constraint logic programming framework. Arguably, an important limitation of traditional Bayesian networks is that they are propositional, and thus cannot represent relations between multiple similar objects in multiple contexts. Several researchers have thus proposed first-order languages to describe such networks. Namely, one very successful example of this approach are the Probabilistic Relational Models (PRMs), that combine Bayesian networks with relational database technology. The key difficulty that we had to address when designing CLP(cal{BN}) is that logic based representations use ground terms to denote objects. With probabilitic data, we need to be able to uniquely represent an object whose value we are not sure about. We use {sl Skolem functions} as unique new symbols that uniquely represent objects with unknown value. The semantics of CLP(cal{BN}) programs then naturally follow from the general framework of constraint logic programming, as applied to a specific domain where we have probabilistic data. This paper introduces and defines CLP(cal{BN}), and it describes an implementation and initial experiments. The paper also shows how CLP(cal{BN}) relates to Probabilistic Relational Models (PRMs), Ngo and Haddawys Probabilistic Logic Programs, AND Kersting AND De Raedts Bayesian Logic Programs. 
Vitor Santos Costa, David Page, Maleeha Qazi, James Cussens
cs.AI