Minsky introduced the terminology of'frames' to unify and denote a loose collection of related ideas on knowledge representation: a collection which, since the publication of his paper (Minsky, 1975) has become even looser. It is not at all clear now what frames are, or were ever intended to be. I will assume, below, that frames were put forward as a (set of ideas for the design of a) formal language for expressing knowledge, to be considered as an alternative to, for example, semantic networks or predicate calculus. At least one group have explicitly designed such a language, KRL (Bobrow/ Winograd, 1977a, 19776), based on the frames idea. But it is important to distinguish this from two other possible interpretations of what Minsky was urging, which one might call the metaphysical and the heuristic (following the terminology of (Mc Carthy/Hayes, 1968)). The "metaphysical" interpretation is, that to use frames is to make a certain kind of assumption about what entities shall be assumed to exist in the world being described.

Our purpose in studying natural language understanding in conjunction with problem solving is to bring together the constraints of what formal representation can actually be obtained with the question of what knowledge is required in order to solve a wide range of problems in a semantically rich domain. We believe that these issues cannot sensibly be tackled in isolation. In practical terms we have had the benefits of an increased awareness of common problems in both areas and a realisation that some of our techniques are applicable to both the control of inference and the control of parsing. Early work on solving mathematical problems stated in natural language was done by Bobrow (STUDENT - (i]) and Chamiak (CARPS - [5]). However the rudimentary parsing and simple semantic structures used by Bobrow and Charniak are inadequate for any but the easiest problems. Our intention has been to build on B/RG Chris This work was supported by SRC grant number 94493 and an SRC research studentship for Mellish.

We discuss the problem of incorporating into a heuristic theorem prover a decision procedure for a fragment of the logic. An obvious goal when incorporating such a procedure is to reduce the search space explored by the heuristic component of the system, as would be achieved by eliminating from the system's data base some explicitly stated axioms. For example, if a decision procedure for linear inequalities is added, one would hope to eliminate the explicit consideration of the transitivity axioms. However, the decision procedure must then be used in all the ways the eliminated axioms might have been. The difficulty of achieving this degree of integration is more dependent upon the complexity of the heuristic component than upon that of the decision procedure. The view of the decision procedure as a black box is frequently destroyed by the need pass large amounts of search strategic information back and forth between the two components.

Most resolution theorem provers convert a theorem into clause form before attempting to find a proof. The conventional translation of a first-order formula into clause form often obscures the structure of the formula, and may increase the length of the formula by an exponential amount in the worst case. We present a non-standard clause form translation that preserves more of the structure of the formula than the conventional translation. This new translation also avoids the exponential increase in size which may occur with the standard translation. We show how this idea may be combined with the idea of replacing predicates by their definitions before converting to clause form.

This paper presents a body of program synthesis knowledge dealing with array operations, space reutilization, the divide-and-conquer paradigm, conversion from recursive paradigms to iterative paradigms, and ordered set enumerations. Such knowledge can be used for the synthesis of efficient and in-place sorts including quicksort, mergesort, sinking sort, and bubble sort, as well as other ordered set operations such as set union, element removal, and element addition. The knowledge is explicated to a level of detail such that it is possible to codify this knowledge as a set of program synthesis rules for use by a computer-based synthesis system. The use and content of this set of programming rules is illustrated by the methodical synthesis of bubble sort, sinking sort, quicksort, and mergesort.

It is essentially a Horn clause theorem prover augmented with a special inference rule for'dealing with

"Computing can change our ways of thinking about many things, mathematics, biology, engineering, administrative procedures, and many more. But my main concern is that it can change our thinking about ourselves: giving us new models, metaphors, and other thinking tools to aid our efforts to fathom the mysteries of the human mind and heart. The new discipline of Artificial Intelligence is the branch of computing most directly concerned with this revolution. By giving us new, deeper, insights into some of our inner processes, it changes our thinking about ourselves. It therefore changes some of our inner processes, and so changes what we are, like all social, technological and intellectual revolutions." This book, published in 1978 by Harvester Press and Humanities Press, has been out of print for many years, and is now online, produced from a scanned in copy of the original, digitised by OCR software and made available in September 2001. Since then a number of notes and corrections have been added. Atlantic Highlands, NJ: Humanities Press.

Reprinted as Chapter 3 (pp.250-271) of Webber & Nilsson, Readings in Artificial IntelligenceElcock, E. W. and Michie, D. (Eds.), Machine Intelligence 8, pp. 94-€“138. Ellis Horwood.

Earlier work by Newell, Simon, Shaw, and Gelernter in the middle and late 1950s emphasized the heuristic approach, but the weight soon shifted to various syntactic methods culminating in a large effort on resolution type systems in the last half of the 1960s. It was about 1970 when considerable interest was revived in heuristic methods and the use of human supplied, domain dependent, knowledge. It is not my intention here to slight the great names in automatic theorem proving, and their contributions to all we do, but rather to show another side of it. For recent books on automatic theorem proving see Chang and Lee [19], Loveland [44], and Hayes [31]. Also see Nilsson's recent review article [61]. The word "resolution" has come to be associated with general purpose types of theorem provers which use very little domain dependent information and few if any special heuristics besides those of a syntactic nature. It has also connoted the use of clauses and refutation proofs. There was much hope in the late 60's that such systems, especially with various exciting improvements, such as set of support, model elimination, etc., would be powerful provers. But by the early 70's there was emerging a belief that resolution type systems could never really "hack" it, could not prove really hard mathematical theorems, without some extensive changes in philosophy.

EPISTEMOLOGICAL PROBLEMS OF ARTIFICIAL INTELLIGENCE John McCarthy Computer Science Department Stanford University Stanford, California 94305 Introduction In (McCarthy and Hayes 1969), we proposed dividing the artificial intelligence problem into two parts - an epistemological part and a heuristic part. This lecture further explains this division, explains some of the epistemological problems, and presents some new results and approaches. The epistemological part of Al studies what kinds of facts about the world are available to an observer with given Opportunities to observe, how these facts can be represented in the memory of a computer, and what rules permit legitimate conclusions to be drawn from these facts. It leaves aside the heuristic problems of how to search spaces of possibilities and how to match patterns. Considering epistemological problems separately has the following advantages: I. The same problems of what information is available to an observer and what conclusions can be drawn from information arise in connection with a variety of problem solving tasks. Recently we have found that introducing concepts as individuals makes possible a first order logic expression of facts usually expressed In modal logic but With important advantages over modal logic - and so far no disadvantages.