Also to appear in Proceedings NIE--LRDC Conference on Thinking and Learning Skills, Lawrence Erlbaum Associates.

Where the accountants have fallen down, however, is in their reluctance and sometimes inability to make intensive studies of different equipment and to specify their requirements for equipment. As one authority in the field of electronic data processing has pointed out, "Accountants, unlike engineers, take the equipment as given without bothering to specify their own particular needs." But after all things are taken into consideration, it is of primary importance that the personnel who are handling the details of the investigation have a good knowledge of the particular application to be studied. Executives in many companies have been dissatisfied with the help received from outsiders who are expert programmers and who know a lot about equipment, but who are unfamiliar with business systems. In some companies executives have found that their own personnel, who know the firm's particular data processing system, after three or four months of experience in which to grasp the logics of the computer and the intricacies of programming, are much more valuable than such outside experts.

A. YONEZAWA and C. HEWITT 41 REPRESENTATIONS FOR ABSTRACT REASONING 4 A maximal method for set variables in automatic theorem-proving W. W. BLEDSOE

J. Do RAN 433 22 Chromosome classification and segmentation as exercises in knowing what to expect.

B.RANDELL 3 PROGRAM PROOF AND MANIPULATION 2 Some techniques for proving correctness of programs which alter data structures.

Among the many properties ascribed to the magical number seven is that of marking out the significant epochs of a human life-span -- seven years from birth to departure from the kindergarten, another seven to puberty, another seven to majority. The occasion of the Seventh International Machine Intelligence Workshop is perhaps an appropriate moment to take stock. Views differ as to exactly which of the successive thresholds is the one on which machine intelligence research is now poised. But there is no mistaking the sense of transition, felt both by its practitioners, who claim that their field is at last attaining maturity, and in a rather different way by its interested Spectators. The latter rightly point out that if maturation brings opportunity and new powers it also brings the obligation to earn a living.

The two outstanding figures in the history of computer science are Alan Turing and John von Neumann, and they shared the view that logic was the key to understanding and automating computation. In particular, it was Turing who gave us in the mid-1930s the fundamental analysis, and the logical definition, of the concept of'computability by machine' and who discovered the surprising and beautiful basic fact that there exist universal machines which by suitable programming can be made to t This essay is an expanded and revised version of one entitled The Role of Logic in Computer Science and Artificial Intelligence, which was completed in January 1992 (and was later published in the Proceedings of the Fifth Generation computer Systems 1992 Conference). Since completing that essay I have had the benefit of extremely helpful discussions on many of the details with Professor Donald Michie and Professor I. J. Good, both of whom knew Turing well during the war years at Bletchley Park. Professor J. A. N. Lee, whose knowledge of the literature and archives of the history of computing is encyclopedic, also provided additional information, some of which is still unpublished. Further light has very recently been shed on the von Neumann side of the story by Norman Macrae's excellent biography John von Neumann (Macrae 1992). Accordingly, it seemed appropriate to undertake a more complete and thorough version of the FGCS'92 essay, focussing somewhat more on the interesting historical and biographical issues. I am grateful to Donald Michie and Stephen Muggleton for inviting me to contribute such a'second edition' to the present volume, and I would also like to thank the Institute for New Computer Technology (ICOT) for kind permission to make use of the FGCS'92 essay in this way. 1 LOGIC, COMPUTERS, TURING, AND VON NEUMANN

They produce one set of rules from one set of data and have no memory which permits them to add to a knowledge base by further learning. Incremental learning systems remember the concepts which they have learned and can use them for further learning and problem solving. Some examples are, CONFUCIUS (Cohen 1978) and Marvin (Sammut 1981). These programs build a model of their task environment through successive learning experiences which require interaction with the environment. The task that we consider in this paper involves a program learning to control an agent in a reactive environment. This is an environment where changes occur in response to actions. Agents other than the learner may be present. As an agent accumulates experience, it constructs a world model or theory of behaviour which can be used to predict the outcome f Present address: Department of Computer Science, University of New South Wales, Sydney, Australia.

In this paper we will be concerned with such reasoning in its most general form, that is, in inferences that are defeasible: given more information, we may retract them. The purpose of this paper is to introduce a form of non-monotonic inference based on the notion of a partial model of the world. We take partial models to reflect our partial knowledge of the true state of affairs. We then define non-monotonic inference as the process of filling in unknown parts of the model with conjectures: statements that could turn out to be false, given more complete knowledge. To take a standard example from default reasoning: since most birds can fly, if Tweety is a bird it is reasonable to assume that she can fly, at least in the absence of any information to the contrary. We thus have some justification for filling in our partial picture of the world with this conjecture. If our knowledge includes the fact that Tweety is an ostrich, then no such justification exists, and the conjecture must be retracted.

This paper describes some work on automatically generating finite counterexamples in topology, and the use of counterexamples to speed up proof discovery in intermediate analysis, and gives some examples theorems where human provers are aided in proof discovery by the use of examples.