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.
