How to Exploit Parametric Uniformity for Maximum Entropy Reasoning in a Relational Probabilistic Logic

The relational probabilistic conditional logic FO-PCL employs the principle of maximum entropy (ME). We show that parametric uniformity of an FO-PCL knowledge base $\mathcal R$ can be exploited for solving the optimization problem required for ME reasoning more efficiently. The original ME optimization problem containing a large number of linear constraints, one for each ground instance of a conditional, can be replaced by an optimization problem containing just one linear constraint for each conditional. We show that both optimization problems have the same ME distribution as solution. An implementation employing Generalized Iterative Scaling illustrates the benefits of our approach