Library translation 1122, Royal Aircraft Establishment.

AIAA Journal, 3 (8), 1445-1450.

Republished as The Mathematical Foundations of Learning Machines, San Francisco: Morgan Kaufmann Publishers, 1990McGraw-Hill. Republished in 1990.

"Meaning" may be assigned to a string in a context-free language by defining "attributes" of the symbols in a derivation tree for that string. The attributes can be defined by functions associated with each production in the grammar. This paper examines the implications of this process when some of the attributes are "synthesized", i.e., defined solely in terms of attributes of thedescendants of the corresponding nonterminal symbol, while other attributes are "inherited", i.e., defined in terms of attributes of theancestors of the nonterminal symbol. An algorithm is given which detects when such semantic rules could possibly lead to circular definition of some attributes. An example is given of a simple programming language defined with both inherited and synthesized attributes, and the method of definition is compared to other techniques for formal specification of semantics which have appeared in the literature.

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One of the fundamental concepts in mathematics is that of transformation. The study of the unfolding over time of a physical process leads naturally to investigations of the effects of the repetition of a transformation, which is to say to the study of multistage processes. Much of classical and contemporary analysis stems from this source: iteration, ergodic theory, the theory of semigroups [1], the theory of branching processes [2], random transformations at fixed times and deterministic transformations at stochastic times [3, 4]. We wish to indicate still another direction of research, that of multistage decision processes. What happens when we allow a choice of the transformation to be employed at each time?

W. W. Bledsoe is a major figure in the evolution of the new scientific field artificial intelligence and one of the founding fathers of the related scientific field automated reasoning. At the time we write, Bledsoe is an active contributor to science and education at the University of Texas at Austin. We hope that our fondness for Bledsoe, whom we have known well for twenty-three years, has not clouded our assessment of his many achievements. We are certain that we have failed to treat adequately many aspects of Bledsoe's life prior to our first meeting him in 1966, and sadly fear that lack of space and lack of investigative effort cause us to omit quite a few interesting aspects of his career since then. We hope, however, that this short sketch of Bledsoe will please his friends and perhaps provide some useful information for a future biographer or historian of science.

Consider the sentence "I am very unhappy these days". Suppose a foreigner with only a limited knowledge of English but with a very good ear heard that sentence spoken but understood only the first two words "I am". Wishing to appear interested, perhaps even sympathetic, he may reply "How long have you been very unhappy these days?" What he must have done is to apply a kind of template to the original sentence, one part of which matched the two words "I am" and the remainder isolated the words "very unhappy these days". He must also have a reassembly kit specifically associated with that template, one that specifies that any sentence of the form "I am BLAH" can be transformed to "How long have you been BLAH", independently of the meaning of BLAH.

In J. A. Fodor and J. J. Katz, The structure of language. Englewood Cliffs, N.J.: Prentice- Hall, 137-151.