In addition to the various edited collections and single-author volumes that concentrate on the philosophical foundations of AI, there is a recent collected volume that is devoted to the formal foundations of AI (Genesereth and Nilsson, 1987). The existence of this specific work relieves us of the necessity of devoting a large number of pages in the present collection to this important foundational aspect of AI. Nevertheless, for the sake of completeness and in order to provide a natural focus for the papers that do consider formal foundational issues, we decided to include the current chapter.

In the previous section Chandrasekaran introduced and discussed the role and flavour of logical abstraction theories in AI. Logical formalisms have always been favored as the best candidates with which to construct a science of AI, and notable successes can be found: McCarthy's LISP, the basic language of AI, based on the lambda calculus, and PROLOG, a language now inextricably intertwined with expert systems' technology. The latter became a practical possibility with the discovery of linear-time algorithms based on Robinson's resolution principle for mechanical proof. Another AI sub-area in which formal results have been obtained is heuristic and non-heuristic search: efficient searching of a large space of possibilities is seen by many to be a paradigm with general applicability in AI, and definite progress has been made with the formal characterization of the problem.