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This paper describes a computer program which produces English discourse. The program is capable of describing in a sequence of English sentences any game of noughts-&-crosses (tic-tac-toe), whether given or actually played with the program. The object is to understand something of what a speaker is doing when he speaks, and the program therefore demonstrates the operation of rules for selecting information into sentences, for connecting sentences into a discourse, and for constructing clauses, groups, and words to convey the required information with the maximum possible economy. The program uses a systemic functional grammar to co-operate with semantic procedures in producing English. The grammar generates only a limited range of English, but one which is nonetheless sufficient to illustrate the advantages both theoretical and practical of such a grammar for a productive system. Many other computer programs have accepted more or less natural English input, usually in the form of questions requiring an answer, but few have been designed to produce natural English, particularly connected discourse. As a producing system the present model offers a view of language use from a viewpoint slightly different from that of its predecessors. However comprehension and production are dependent on each other, so that study of one may be expected to illuminate the other.

This work is concerned with the problem of constructing associative memory models which store and retrieve information in a distributed fashion - that is each store location can be involved in the storage of more than one piece of information. The models are to be logically simple in form and efficient in their use of store. It is hoped that those proposed may find a place in neurophysiological theories of memory. From the starting point of seeking a less complex representation of a holographic model of memory called the Holophone, several memory models have been proposed and their properties investigated by analytical and computer simulation methods. All the systems considered belong to a family of memory models which are described by a pair of matrix equations. It is found that the models which perform well are non-linear devices which have to store and retrieve highly redundant information. One of these, the Associative Net, is closely related to a recent theory of the cerebellum. Some of the contents of Chapters 3, 4 and 5 have already appeared in papers published in collaboration with H.C. Longuet-Higgins and O.P. Buneman. Otherwise this dissertation is believed to be original in content and in arrangement.

This work concerns a problem in modelling people's understanding of music. The problem is cast in the terms of discovering formal rules for transcribing melodies into musical notation, as this might be done by a student in a harmony class, taking musical dictation from a 'deadpan' performance on the keyboard. The score that results reflects important aspects of the structure and interpretation of the piece, which are only implicit in the performance. In Part I it is argued that this paradigm raises questions of general relevance to the study of our perception of music. In carrying out the task of notating a piece, two kinds of problem arise: what are the harmonic relations between the notes, and what are the metric units into which they are grouped? These two problems are considered in isolation from one another. In Part II, algorithms which embody two kinds of rule for the inference of metre are presented . In Part III the harmonic problem is considered. It arises from the fact that the number of keyboard semitones between two notes does not, by itself, identify their harmonic relation, which is what the notation has to express. Among other considerations, the key of the piece is an important characterisation of this identification - but the key is not explicit in the performance, and must itself be inferred. An earlier theory of harmonic relations is further developed into algorithms for assigning key-signatures and notation to melodies. By -the definition of the problem, we are committed to the concern of music belonging to the tradition of Western tonal music, to which the idea of key applies. Most of' the musical examples discussed will be taken from the work of one of its outstanding exponents, J.S. Bach, and in particular we shall be dealing with the fugue subjects of his “Well-Tempered Clavier". Some of the contents of Part II, Section § 2, and of Part III, Section § 3, have already appeared in a paper published in collaboration with H.C. Longuet-Higgins. Part III, Section § 2.1, describes his prior work in formulating the theory of harmonic relations, mentioned above, which forms the foundation of the work described in that section and has been published elsewhere by him.