Communications of the ACM
Technical Perspective: Combining Logic and Probability
A goal of research in artificial intelligence and machine learning since the early days of expert systems has been to develop automated reasoning methods that combine logic and probability. Probabilistic theorem proving (PTP) unifies three areas of research in computer science: reasoning under uncertainty, theorem-proving in first-order logic, and satisfiability testing for propositional logic.
Why is there a need to combine logic and probability? Probability theory allows one to quantify uncertainty over a set of propositions—ground facts about the world—and a probabilistic reasoning system allows one to infer the probability of unknown (hidden) propositions conditioned on the knowledge of other propositions. However, probability theory alone has nothing to say about how propositions are constructed from relationships over entities or tuples of entities, and how general knowledge at the level of relationships is to be represented and applied.
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