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.

A programming language based on sets; motivation and examples.

The equivalence problem for program schemes, or for programs, is reduced to the proving of a theorem in second-order logic. This work extends Manna's first-order logic reductions. Some examples of the technique are given together with a suggested method for obtaining proofs in special cases by firstorder methods. INTRODUCTION Several workers in recent years have considered using techniques and ideas of various mathematical theories of computation for proving interesting results about computer programs. This paper is concerned with two of these approaches.

Two types of expression of empirical interest have been studied: sentences in English and other'natural' languages, and programs written in some high-level procedural language like ALGOL. Expressions in these languages consist of sets of elements (words and characters) co-ordinated with one another according to the sensorily manifest relationship'alongside', more commonly termed'followed by'.

R.M.BURSTALL 373 23 Assertions: programs written without specifying unnecessary order.

J. P. Thorne Department of English Language P. Bratley and H. Dewar Department of Computer Science University of Edinburgh 1. INTRODUCTION In this paper we describe a program which will assign deep and surface structure analyses to an infinite number of English sentences.1 The design of this program differs in several respects from that of other automatic parsers presently in existence. All these differences are a consequence of the particular aim we have pursued in writing the program, which represents an attempt to construct a device that will not only assign a syntactic analysis to any English sentence-that is, a record of the syntactic structure that the native speaker Perceives in any English sentence-but which also, to some extent, simulates the way in which he perceives this structure. This is not to say that the analyzer differs from others because we have based its design upon the findings of psycholinguistic experiments. For one thing very few experiments on the perception of syntactic structure have been carried out and for the most part the results have been fairly inconclusive. But it is the case that we have, as far as possible, treated the task of constructing an automatic parser as being itself a psycholinguistic experiment. That is to say, any proposal regarding the possible operation of the program has been judged (mainly as the result of introspection) according to whether or not it seemed to be consistent with human behaviour. And this has led to our incorporating certain features which are absent from other automatic parsing systems. Among the most notable of these features is the program's ability to assign syntactic labels to an infinite number of words while operating with a finite dictionary. As far as we know, all other automatic parsers of English (or 1 This work was supported by the Office for Scientific and Technical Information Grant No. ID/102/2/06 to Professor Angus McIntosh.

Networks as models of word storage: G. R. Kiss

RELATION TO PHYSIOLOGY It is possible to compare the organisation of this system with the organisation of the visual system, as revealed by microelectrode studies in the cat (Hubel & Wiesel 1962, 1965) and the frog (Lettvin, Maturana, McCulloch & Pitts 1959). Briefly the following points emerge: (1) Cells in the visual cortex only respond to local properties of the visual scene, e.g., edges, line segments. This mirrors the immediate constituent constraint imposed for economic reasons in the picture grammar.

Psychological theory attempts to explain how thinking--the subject matter of psychology--is possible by a brain composed of single mechanistic elements--the basic assumption of psychology. The problem of programming digital computers to behave in complex fashions is equivalent to this aspect of the psychological problem. Today automata theorists agree that no fundamental barrier blocks the development of machines which can think, by any reasonable definition of the term. However, the precise techniques for implementing general thinking proceGseE-J have been only partially developed. An example of a high-level, general thinking process is comprehension: the understanding of passages of a natural language.

This report presents BAOBAB-2, a computer program built upon MYCIN [Shortliffe, 1974] that Is used for understanding medical summaries describing the status of patients. Due both to the conventional way physicians present medical problems In these summaries and the constrained nature of medical jargon, these texts have a very strong structure. BAOBAB-2 takes advantage of this structure by using a model of this organization as a set of related schemes that facilitate the Interpretation of these texts. Structures of the schemes and their relation to the surface structure are described. Issues relating to selection and use of these schemes by the program during interpretation of the summaries are discussed.