**First-order probabilistic inference**

*By Jacek Kisynski*

Probabilistic graphical models, such as belief networks, are a popular tool for
representing dependencies between random variables. However, such standard
representations are propositional, hence not well suited for describing
relations between individuals or quantifying over sets of individuals.
First-order logic has the capacity for representing relations and quantification
of variables, but it does not treat uncertainty. First representations that mix
probability and first-order logic (first-order probabilistic models) were
proposed nearly twenty years ago and many first-order probabilistic languages
have since emerged. The most common inference technique for such models consists
of dynamically grounding the portion of the first-order model that is relevant
to the query, then conducting probabilistic inference procedures at the
grounded, propositional level. The problem is that these grounded models may be
extremely large, rendering inference intractable even for very simple
first-order models.

In last five years there was a significant progress in solving difficult problem
of inference directly at first-order level (first-order probabilistic
inference). In my talk I will give an overview of work on exact first-order
probabilistic inference by various researchers.