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and archives of the history of computing is encyclopedic, also provided additional information, some of which is still unpublished.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

When you lose a game of chess to a computer then don't pretend that you didn't think at the game.

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.

Such methods can effectively and efficiently induce good descriptions from a given set of examples and, optionally, induce counter-examples (for example Michalski, 1975, 1980a; Quinlan, 1979; Langley et al., 1983). These methods cannot modify concept descriptions which are contradicted by new examples, but must re-learn the descriptions from scratch. In contrast, incremental learning methods modify concept descriptions to accommodate new learning events (Winston, 1975; Michalski and Larson, 1978). When we observe human learning we clearly see that it is incremental.

It is a rich source of difficult and challenging problems which involve issues of knowledge representation, the analysis of natural language, and the automation of practical and common-sense reasoning.

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.

The notion of an ethical machine can be interpreted in more than one way. Perhaps the most important interpretation is a machine that can generalize from existing literature to infer one or more consistent ethical systems and can work out their consequences. An ultra-intelligent machine should be able to do this, and that is one reason for not fearing it. INTRODUCTION There is fear that'the machine will become the master', especially compounded by the possibility that the machine will go wrong. There is, for example, a play by E. M. Foster based on this theme.

We are interested in constructing a computer agent whose behaviour will be intelligent enough to perform cooperative tasks involving other agents like itself. The construction of such agents has been a major goal of artificial intelligence research. One of the key tasks such an agent must perform is to form plans to carry out its intentions in a complex world in which other planning agents also exist. To construct such agents, it will be necessary to address a number of issues that concern the interaction of knowledge, actions, and planning. Briefly stated, an agent at planning time must take into account what his future states of knowledge will be if he is to form plans that he can execute; and if he must incorporate the plans of other agents into his own, then he must also be able to reason about the knowledge and plans of other agents in an appropriate way.

A programming language based on sets; motivation and examples.

K.A.PATON 411 24 Centromere finding: some shape descriptors for small chromosome outlines.