Achieving parametric uniformity for knowledge bases in a relational probabilistic conditional logic with maximum entropy semantics

Abstract

When extending probabilistic logic to a relational setting, it is desirable to still be able to use efficient computation mechanisms developed for the propositional case. In this paper, we investigate the relational probabilistic conditional logic FO-PCL whose semantics employs the principle of maximum entropy. While in general, this semantics is defined via the ground instances of the rules in an FO-PCL knowledge base ${\cal R}$ , the maximum entropy model can be computed on the level of rules rather than on the level of instances of the rules if ${\cal R}$ is parametrically uniform. We elaborate in detail the reasons that cause ${\cal R}$ to be not parametrically uniform. Based on this investigation, we derive a new syntactic criterion for parametric uniformity and develop an algorithm that transforms any FO-PCL knowledge base ${\cal R}$ into an equivalent knowledge base ${\cal R}^{\prime}$ that is parametrically uniform. This provides a basis for a simplified maximum entropy model computation since for this computation, ${\cal R}^{\prime}$ can be used instead of ${\cal R}$ .