We were led to this comparison by the observation that the computer model is weaker in three important ways: search depth is not unbounded, structures matching variables cannot be compared, and structures matching variables cannot be moved. Thus, every recursively enumerable language is generated by a transformational grammar with limited search depth, without equality comparisons of variables, and without moving structures corresponding to variables. On the other hand, both mathematical models allow unbounded depth of analysis; both allow equality comparisons of variables, although the Ginsburg-Partee model.compares
The Inductive Net is made up of a set of horizontal lines (input lines) crossing at right angles a set of vertical lines (output lines), binary switches being placed at the intersections so formed. Each possible feature value has one horizontal line and one vertical line identified with it. A pattern is stored in the Net by exciting the horizontal lines and the vertical lines identified with its feature values, and turning on each switch which receives excitation along both the lines on which it is placed. We do this by giving the Inductive Net additional horizontal lines, each of which has a mask placed on the front of it which causes the line to fire when a particular combination of feature values occur together in the input pattern.
Although it is convenient for experimental purposes to think of perception in stimulus-response terms, the immense contribution of stored data, required for prediction, makes us see perception as largely cognitive. Although there must be physiological mechanisms to carry out the cognitive logical processes, of generalising and selecting stored data, the concepts we need for understanding what the physiology is carrying out are not part of physiology. This makes parallel processing convenient for biological computing, and serial computing more convenient for man-made computers. If so, biological perception seems to demonstrate powers of parallel processing, while computers demonstrate very different powers of serial processing.
To illustrate how this may be done in very simple cases we give rules which translate certain declarative sentences and questions involving the quantifiers'some', 'every', 'any', and'no' into a modified first-order predicate calculus, and answer the questions by comparing their translated forms with those of the declaratives. John kissed Mary (1) Did John kiss Mary? (5) We begin by describing a method for translating a modest subset of English into a slightly modified first-order predicate calculus -- modified just enough to provide a representation for questions. We would like to have rules which transcribe such declarative sentences into predicate calculus formulae, such as VxMxj (7') 3x-- The matrix will be preceded by a string of quantifiers and negations -- and possibly a question mark; we have found that the transcription rules which appear below produce unique and acceptable orderings of these symbols from unambiguous sentences of the specified type.
We have attempted to discover formal rules for transcribing into musical notation the fugue subjects of the Well-Tempered Clavier, as this might be done by an amanuensis listening to a'deadpan' performance on the keyboard. What we have in fact done is to write two'parsing' programs, one for determining the metre and the other for explicating the harmonic relations between the notes of a Bach fugue subject. In writing these programs, which take account only of the note lengths and positions on the keyboard, we have attempted to make explicit our intuitive understanding of musical rhythm and harmony in general, and also to take account of one or two stylistic features which seem to distinguish Bach from some other classical masters. If our rules are to be able to decide the time signature and the key signature from the durations of the notes and their positions on the keyboard, some assumption must be made about how much of these data may safely be assumed congruent, and may therefore be used as evidence in reaching the required decision.