Convergence results for relational Bayesian networks

Relational Bayesian networks are an extension of the method of probabilistic model construction by Bayesian networks. They define probability distributions on finite relational structures by conditioning the probability of a ground atom r(a₁, ..., a _n) on first-order properties of a₁, ..., a_n that have been established by previous random decisions. In this paper we investigate from a finite model theory perspective the convergence properties of the distributions defined in this manner. A subclass of relational Bayesian networks is identified that define distributions with convergence laws for first-order properties