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.

Electrical and Computer Engineering will give you the power to change the world. From providing clean, efficient energy to controlling digital data, from global communication to nanotechnologies, from robotics to entertainment, the future is being created by our graduates today. If you want to make a difference, study Electrical and Electronic Engineering or Computer Engineering at UC - the future is in your hands.

Reprinted in Marvin Minsky (ed), Semantic Information Processing, pp. 354-402, Cambridge, MA: MIT Press, 1968.

In Part I, four ostensibly different theoretical models of induction are presented, in which the problem dealt with is the extrapolation of a very long sequence of symbols—presumably containing all of the information to be used in the induction. Almost all, if not all problems in induction can be put in this form. Some strong heuristic arguments have been obtained for the equivalence of the last three models. One of these models is equivalent to a Bayes formulation, in which a priori probabilities are assigned to sequences of symbols on the basis of the lengths of inputs to a universal Turing machine that are required to produce the sequence of interest as output. Though it seems likely, it is not certain whether the first of the four models is equivalent to the other three.

This article presents a design principle of a neural network using Gaussian activation functions, referred to as a Gaussian Potential Function Network (GPFN), and explores the capability of a GPFN in learning a continuous input-output mapping from a given set of teaching patterns. The design principle is highlighted by a Hierarchically Self-Organizing Learning (HSOL) algorithm featuring the automatic recruitment of hidden units under the paradigm of hierarchical learning. A GPFN generates an arbitrary shape of a potential field over the domain of the input space, as an input-output mapping, by synthesizing a number of Gaussian potential functions provided by individual hidden units referred to as Gaussian Potential Function Units (GPFUs). The construction of a GPFN is carried out by the HSOL algorithm which incrementally recruits the minimum necessary number of GPFUs based on the control of the effective radii of individual GPFUs, and trains the locations (mean vectors) and shapes (variances) of individual Gaussian potential functions, as well as their summation weights, based on the Backpropagation algorithm. Simulations were conducted for the demonstration and evaluation of the GPFNs constructed based on the HSOL algorithm for several sets of teaching patterns.

"Among the new languages for instructing computers is a remarkable one called LISP. The name comes from the first three letters of LIST and the first letter of PROCESSING. Not only is LISP a language for instructing computers but it is also a formal mathematical language, in the same way as elëmentary algebra when rigorously defined and used is a formal mathematical language.The LISP language and its implementation on the IBM 7090 computer were worked out by a group including John McCarthy, Stephen B. Russell , Daniel J. Edwards, Paul W. Abrahams, Timothy P. Hart, Michael I. Levin, Marvin L. Minsky, and others.LISP is designed primarily for processing data consisting of lists of symbols. It has been used for symbolic calculations in differential and integral calculus, electrical circuit theory, mathematical logic , game playing, and other fields of intelligent handling of symbols."Information International, Inc, Cambridge, Mass.

"It is well known to be impossible to tile with dominoes a checkerboard with two opposite corners deleted. This fact is readily stated in the first order predicate calculus, but the usual proof which involves a parity and counting argument does not readily translate into predicate calculus. We conjecture that this problem will be very difficult for programmed proof procedures."Stanford Artificial Intelligence Project Memo No. 16