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Unifying Logic and Probability

Recent Developments in Unifying Logic and Probability, illustration

Credit: Almagami

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 reason, classical AI adopted first-order logic—the mathematics of objects and relations—as its foundation.

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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 100 pages in first-order logic, 105 pages in propositional logic, and 1038 pages in the language of finite automata. The power comes from separating predicates from their arguments and quantifying over those arguments: so one can write rules about On(p, c, x, y, t) (piece p of color c is on square x, y at move t) without filling in each specific value for c, p, x, y, and t.


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Unifying Logic and Probability.