Encoding the Consistency of Relational Bayesian Networks

Given an input structure, a relational Bayesian network returns a Bayesian network over ground atoms. In this paper, we analyze the problem of checking the consistency of a relational Bayesian network for a given class of input structures. This consistency is defined as the acyclicity of the output Bayesian network. We employ first-order logic to encode both the input structure and the structure of the corresponding output Bayesian network. Then we use a transitive closure operator to express the acyclicity of the resulting Bayesian network, translating the consistency of a relational Bayesian network for a given input class into the validity of a logical formula.