  The Bayesian Logic (BLOG) language was recently developed for defining
first-order probability models over worlds with unknown numbers of objects. It
handles important problems in AI, including data association and population
estimation. This paper extends BLOG by adopting generative processes over
function spaces - known as nonparametrics in the Bayesian literature. We
introduce syntax for reasoning about arbitrary collections of objects, and
their properties, in an intuitive manner. By exploiting exchangeability,
distributions over unknown objects and their attributes are cast as Dirichlet
processes, which resolve difficulties in model selection and inference caused
by varying numbers of objects. We demonstrate these concepts with application
to citation matching.
