Commentary on McDermott

Logic provides an important framework for talking about knowledge and reasoning. Logical languages seem useful for representing the knowledge needed by intelligent systems, and logical operations appear useful for manipulating that knowledge. Thus, logic plays the same role in the design and analysis of intelligent systems that differential equations play in the design and analysis of control systems. Many successful AI systems can be clearly understood using the vocabulary of logic even though the designers of these systems might not have used that vocabulary. Logic provides the most powerful theoretical apparatus yet proposed for understanding the operation of intelligent programs. Thus, it is troubling indeed when an eminent and influential A1 scientist becomes disillusioned with logic. In my opinion, most of McDermott’s misgivings arise from an overly simplified view about what people who subscribe to the “logical approach” are trying to do with logic. In what follows, I discuss a number of points in the order they arise in McDermott’s article. McDermott bases much of his argument against logic on the assumption that “logicists” (as he calls us) tacitly assume “ . . . that a lot of reasoning can be analyzed as deductive or approximately deductive . . . ” Actually, few logicists make this assumption in the way McDermott thinks they do. We understand, of course, that we cannot obtain (Vx)P(x) from the single premise P ( A ) A P ( B ) A P ( C ) using only sound inferences, and that inductive generalization is sometimes an appropriate reasoning step. The point is that any program that does inductive generalization makes the equivalent of a statement about when it is appropriate to do so. Such a statement might go something like this: 1 (3x) P ( x ) and (3x1, . . . , x,,)[P(x,) A * . A P(x,,)] and (xI f x2 f * * f X,,) implies (Vx)P(x) . This statement can, in tum, be encoded as a formula of first-order logic, which together with the original premise, would permit the desired deduction. (Alternatively, the statement might be encoded as a special inference rule). We might have no guarantee that the meta-theoretic formula encoding the reasoning step is satisfied by the actual world we are intending to model by such a statement. But any synthetic statement about the world we are intending to model might not be satisfied by that world. Such is the property of all scientific statements-they are inherently falsified. Similarly, if a special inference rule is used to encode an inductive generalization step, it won’t necessarily be a sound rule of inference-but committing oneself to a logical approach does not oblige one to use sound rules of inference. Indeed, logicians consider it special and interesting when an inference rule is sound. McDermott’s statement (about the inadequacy of deductive processes) falsely identifies the logical approach with an overriding concern for deducrion. Just as important as deduction is the use of logical languages (such as the first-order predicate calculus) to express knowledge. If there is a unifying theme among A1 researchers that separates them from the rest of computer science, it is their commitment to express knowledge declaratively as statements in a language of some sort. While