Recent advances in knowledge representation for probability models have allowed for uncertainty about the properties of objects and the relations that might hold among them. Such models, however, typically assume exact knowledge of which objects exist and of which object is which---that is, they assume *domain closure* and *unique names*. These assumptions simplify the sample space for probability models, but are inappropriate for many real-world situations. This talk presents a formal language, BLOG, for defining probability models over worlds with unknown objects in which several terms may refer to the same object. BLOG syntax is based on first-order logic combined with local probability functions for quantifying conditional dependencies. A key additional element is the "number statement", which specifies a conditional distribution over the number of objects that satisfy a given property. Subject to certain acyclicity constraints, every BLOG model specifies a unique probability distribution over the set of possible worlds for the first-order language. Furthermore, complete inference algorithms exist for a useful fragment of the language. I will present several example models and discuss interesting issues arising from the treatment of evidence in such languages.

[Joint work with Brian Milch, Bhaskara Marthi, Hanna Pasula, David Sontag, Andrey Kolobov, and Daniel Ong]