Uncertainty in an unknown world

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 greatly 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 and in which several terms may refer
to the same object. The language has a simple syntax 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 full set of possible worlds for the
first-order language. Furthermore, complete inference algorithms exist
for a large fragment of the language. I will present several example
models and discuss interesting issues arising from the treatment of
evidence in such languages.
Professor Russell is the Director for the Center for Intelligent Systems.