C. COOPER 21 3 Data representation--the key to conceptualisation: D. B. VIGOR 33 MECHANISED MATHEMATICS 45 4 An approach to analytic integration using ordered algebraic expressions: L. I. HODGSON 47 5 Some theorem-proving strategies based on the resolution principle: J. L DARLINGTON 57 MACHINE LEARNING AND HEURISTIC PROGRAMMING 73 6 Automatic description and recognition of board patterns in Go-Moku: A. M. MURRAY and E. W. Etcomc

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and archives of the history of computing is encyclopedic, also provided additional information, some of which is still unpublished.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

OXFORD 1994 Oxford University Press, Walton Street, Oxford 0X2 6DP Oxford New York Athens Auckland Bangkok Bombay Calcutta Cape Town Dar es Salaam Delhi Florence Hong Kong Istanbul Karachi Kuala Lumpur Madras Madrid Melbourne Mexico City Nairobi Paris Singapore Taipei Tokyo Toronto and associated companies in Berlin lbadan Published in the United States by Oxford University Press Inc., New York 0 E. K. Furukawa, D. Michie, and S. Muggleton, 1994 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press. Enquiries concerning reproduction outside those terms and in other countries should be sent to the Rights Department, Oxford University Press, at the address above. This book is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, re-sold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cover other than that in which it is published and without a similar condition including this condition being imposed on the subsequent purchaser. The founder of modern computational logic, J.A. Robinson, opens this volume with a chapter on the field's great forefathers John von Neumann and Alan Turing.

Turing's best known work is concerned with whether universal machines can decide the truth value of arbitrary logic formulae. However, in this paper it is shown that there is a direct evolution in Turing's ideas from his earlier investigations of computability to his later interests in machine intelligence and machine learning. Turing realised that machines which could learn would be able to avoid some of the consequences of Godes and his results on incompleteness and undecidability. Machines which learned could continuously add new axioms to their repertoire. Inspired by a radio talk given by Turing in 1951, Christopher Strachey went on to implement the world's first machine learning program.

The aim of the Stat Log project is to compare the performance of statistical, machine learning, and neural network algorithms, on large real world problems. This paper describes the completed work on classification in the StatLog project. Classification is here defined to be the problem, given a set of multivariate data with assigned classes, of estimating the probability from a set of attributes describing a new example sampled from the same source that it has a pre-defined class. We gathered together a representative collection of algorithms from statistics (Naive Bayes, K-nearest Neighbour, Kernel density, Linear discriminant, Quadratic discriminant, Logistic regression, Projection pursuit, Bayesian networks), machine learning (CART, C4.5, NewID, AC2, CAL5, CN2, ITrule -- only propositional symbolic algorithms were considered), and neural networks (Backpropagation, Radial basis functions, Kohonen).

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.

Machine Intelligence 1 (1967) (eds N. Collins and D. Michie) Oliver & Boyd, Edinburgh Machine Intelligence 2 (1968) (eds E. Dale and D. Michie) Oliver & Boyd, Edinburgh (1 and 2 published as one volume in 1971 by Edinburgh University Press) (eds N. Collins, E. Dale, and D. Michie) Machine Intelligence 3 (1968) (ed. CLARENDON PRESS - OXFORD 1991 Oxford University Press, Walton Street, Oxford 0X2 6DP Oxford New York Toronto Delhi Bombay Calcutta Madras Karachi Petaling Jaya Singapore Hong Kong Tokyo Nairobi Dar es Salaam Cape Town Melbourne Auckland and associated companies in Berlin lbadan Oxford is a trade mark of Oxford University Press Published in the United States by Oxford University Press, New York C J. E. Hayes, D. Michie, and E. Tyugu, 1991 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press British Library Cataloguing in Publication Data Machine intelligence. ISBN 0-19-853823-5 Library of Congress Cataloging in Publication Data Machine intelligence 12: towards an automated logic of human thought /edited by J. E. Hayes, D. Michie, and It is a pleasure to contribute an introduction to this twelfth volume of the international Machine Intelligence series. My own work has, at times, cast me in the scientific roles of experimenter, instrumentation designer, and administrator.

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.

Machine Intelligence 1 (1967) (eds N. Collins and D. Michie) Oliver & Boyd, Edinburgh Machine Intelligence 2 (1968) (eds E. Dale and D. Michie) Oliver & Boyd, Edinburgh (1 and 2 published as one volume in 1971 by Edinburgh University Press) (eds N. Collins, E. Dale, and D. Michie). CLARENDON PRESS OXFORD 1988 Oxford University Press, Walton Street, Oxford 0X2 6DP Oxford New York Toronto Delhi Bombay Calcutta Madras Karachi Petaling Jaya Singapore Hong Kong Tokyo Nairobi Dar es Salaam Cape Town Melbourne Auckland and associated companies in Berlin lbadan Oxford is a trade mark of Oxford University Press Published in the United States by Oxford University Press, New York J. E. Hayes, D. Michie, and J. Richards 1988 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press British Library Cataloguing in Publication Data Machine Intelligence. Richard J. 006.3 ISBN 0-19-853718-2 Library of Congress Cataloging in Publication Data Data available Typeset and printed in Northern Ireland at The Universities Press (Belfast) Ltd. Held at intervals in Scotland, the first seven International Machine Intelligence Workshops spanning the period of 1965-71 were involved in developing the new subject internationally--in those early days mainly as a mid-Atlantic phenomenon.