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.

Work of the Soviet school (approximately half the book) in this explosively growing area of machine intelligence is thus made accessible for the first time to Western readers, in addition to the latest Western advances. The emergent theme of knowledge-representation is supported on the theoretical and experimental sides by recent work in inductive inference and theory-formation.

Intelligent Systems: Practice and Perspective Machine Intelligence, Editor-in-Chief: Donald Michie Volumes 1-7 are published by Edinburgh University Press and in the United States by Halsted Press (a subsidiary of John Wiley & Sons, Inc.) Volumes 8-10 are published by Ellis Horwood Ltd., Publishers, Chichester and in the United State by Halsted Press (a subsidiary of John Wiley & Sons, Inc.) ELLIS HORWOOD LIMITED Publishers - Chichester Halsted Press: a division of JOHN WILEY & SONS New York - Brisbane - Chichester - Toronto First published in 1982 by ELLIS HORWOOD LIMITED Market Cross House, Cooper Street, Chichester, West Sussex, P019 lEB, England The publisher's colophon is reproduced from James Gillison's drawing of the ancient Market Cross, Chichester. Q335 The Library of Congress cataloged this serial as follows -67-13648 ISBN 0-85312-431-0 (Ellis Horwood Limited) ISSN 0076-2032 ISBN 0-470-27323-2 (Halsted Press) Typeset in Press Roman by Ellis Horwood Limited. 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 permission of Ellis Horwood Limited, Market Cross House, Cooper Street, Chichester, West Sussex, England. The year of the first MI Workshop, 1965, was a milestone for more reasons than one, not least for the appearance of a paper entitled "A machine-oriented logic based on the resoluton principle". It was appropriate and a cause for pleasure that the author of that paper, J. A. Robinson, was the opening contributor to the scientific proceedings of MI-10, held in November 1981 at Case Western Reserve University, Cleveland, USA.

Motor control systems are complex systems that process information. Orientation behaviour, posture control, and the manipulation of objects are examples of motor control systems which involve one or more sensory modality and various central neural processes, as well as effector systems and their immediate neuronal control mechanisms. Like all complex information processing systems, they must be analysed and understood at several different levels (see, e.g., Marr & Poggio 1977). At the lowest level there is the analysis of basic components and circuits, the neurons, their synapses, etc. At the other extreme, there is the study of the computations performed by the system -- the problems it solves and the ways that it solves them -- and the analysis of its logical organization in terms of its primary modules. Each of these levels of description, and those in-between, has its place in the eventual understanding of motor control by the nervous system. None is sufficient, nor is there any simple translation from one to another. A purely biophysical investigation, however exhaustive, can say nothing by itself about the information processing performed by the system, nor, on the other hand, can an understanding of the computational problem which the system solves lead directly to an understanding of the properties of the hardware. Two examples of motor control theories belonging to different levels will illustrate this point.

We briefly describe the logic programming language PROLOG concentrating on those aspects of the language that make it suitable for implementing expert systems. We show how features of expert systems such as: (1) inference generated requests for data, (2) probabilistic reasoning, (3) explanation of behaviour can be easily programmed in PROLOG. We illustrate each of these features by showing how a fault finder expert could be programmed in PROLOG.

PROLOG is a simple and powerful progamming language based on first-order logic. This paper examines two possible extensions to the language which would generally be considered "higher-order".t The first extension introduces lambda expressions and predicate variables so that functions and relations can be treated as'first class' data objects. We argue that this extension does not add anything to the real power of the language. The other extension concerns the introduction of set expressions to denote the set of all (provable) solutions to some goal. We argue that this extension does indeed fill a real gap in the language, but must be defined with care.

Seven years or so after it was first proposed (Kowalski 1974), the technique of'logic programming' today has an enthusiastic band of users and an increasingly impressive record of applications. For most of these people, logic progamming means PROLOG, the system defined and originally implemented by the Marseille group (Roussel 1975). PROLOG has since been implemented in several other places, most notably at Edinburgh (Warren et al. 1977). Much of the rapid success of logic progamming is due to these implementations of PROLOG (as well as to the inspired missionary work of Kowalski, van Emden, Clark and others). The Edinburgh PROLOG system is in particular a superb piece of software engineering which allows the logic progammer to compile assertions into DEC-10 machine code and thus run logic programs with an efficiency which compares favourably with that of compiled LISP. All other implementations of logic programming (including our own, which we describe in this paper) are based on interpreters.

A programming language based on sets; motivation and examples.

A programming language based on sets; motivation and examples.