Reasoning About Infinite Random Structures with Relational Bayesian Networks

Relational Bayesian networks extend standard Bayesian networks by integrating some of the expressive power of first-order logic into the Bayesian network paradigm. As in the case of the related technique of knowledge based model construction, so far, decidable semantics only have been provided for finite stochastic domains. In this paper we extend the semantics of relational Bayesian networks, so that they also define probability distributions over countably infinite structures. Using a technique remeniscent of quantifier elimination methods in model theory, we show that probabilistic queries about these distributions are decidable.