Logic and Inference

Abstract

In the first half of this century, great strides were taken in the development of formal logic. Although largely motivated by puzzles in the philosophy of mathematics, the development of systems of formal logic in general, and of one such system in particular — the predicate calculus — revolutionized the study of inference. With its combination of expressive power and mathematical simplicity, the predicate calculus was unquestionably superior to the (basically) Aristotelian Logic which had gone before, and deduction in the predicate calculus came to be seen as a paradigm of rational inference. Moreover, where deduction seemed not to suffice as a model for inference — most notably, in the confirmation of scientific theories by empirical testing — the search began for an ‘inductive logic’ which was to be the equal of its deductive sibling in formality and rigour. (We shall have more to say about inductive logic in chapter 9.) Given the pre-eminence of the predicate calculus in providing a paradigm of rational inference, it was only to be expected that AI took the predicate calculus as its point of departure as a method for performing inference automatically. But, as we shall see, a surprise was lurking in the shadows.