Abstract: This paper surveys first-order probabilistic languages (FOPLs), which combine the expressive power of first-order logic with a probabilistic treatment of uncertainty. We provide a taxonomy that helps make sense of the profusion of FOPLs that have been proposed over the past fifteen years. We also emphasize the importance of representing uncertainty not just about the attributes and relations of a fixed set of objects, but also about what objects exist. This leads us to Bayesian logic, or BLOG, a language for defining probabilistic models with unknown objects. We give a brief overview of BLOG syntax and semantics, and emphasize some of the design decisions that distinguish it from other languages. Finally, we consider the challenge of constructing FOPL models automatically from data.
Appeared in:Stephen Muggleton, Ramon Otero, and Alireza Tamaddoni-Nezhad, eds. Inductive Logic Programming: 16th International Conference (ILP-2006). Lecture Notes in AI 4455. Berlin: Springer, 2007. Pages 10-24. This is the written version of an invited talk that I (Brian) gave as a substitute for Stuart Russell.
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