#### Distinguished Lecture

# Uncertainty in an unknown world

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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.