  The First-Order Variable Elimination (FOVE) algorithm allows exact inference
to be applied directly to probabilistic relational models, and has proven to be
vastly superior to the application of standard inference methods on a grounded
propositional model. Still, FOVE operators can be applied under restricted
conditions, often forcing one to resort to propositional inference. This paper
aims to extend the applicability of FOVE by providing two new model conversion
operators: the first and the primary is joint formula conversion and the second
is just-different counting conversion. These new operations allow efficient
inference methods to be applied directly on relational models, where no
existing efficient method could be applied hitherto. In addition, aided by
these capabilities, we show how to adapt FOVE to provide exact solutions to
Maximum Expected Utility (MEU) queries over relational models for decision
under uncertainty. Experimental evaluations show our algorithms to provide
significant speedup over the alternatives.
