Recent Developments in Unifying Logic and Probability

PERHAPS THE MOST enduring idea from the early days of AI is that of a declarative system reasoning over explicitly represented knowledge with a general inference engine. Such systems require a formal language to describe the real world; and the real world has things in it. For this rea-son, classical AI adopted first-order logic-the mathe-matics of objects and relations-as its foundation. The key benefit of first-order logic is its expressive power, which leads to concise-and hence learnable-models. For example, the rules of chess occupy 10(0) pages in first-order logic, 10(5) pages in propositional logic, and 10(38) pages in the language of finite automata. The power comes from separating predicates from their arguments and quantifying over