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And-or graphs and theorem-proving graphs determine the same kind of search space and differ only in the direction of search: from axioms to goals, in the case of theorem-proving graphs, and in the opposite direction, from goals to axioms, in the case of and-or graphs. Bidirectional search strategies combine both directions of search. We investigate the construction of a single general algorithm which covers unidirectional search both for and-or graphs and for theorem-proving graphs, bidirectional search for path-finding problems and search for a simplest solution as well as search for any solution. We obtain a general theory of completeness which applies to search spaces with infinite or-branching. In the case of search for any solution, we argue against the application of strategies designed for finding simplest solutions, but argue for assigning a major role in guiding the search to the use of symbol complexity (the number of symbol occurrences in a derivation).

This paper is concerned with two aspects of the'exact match' problem which is that of searching amongst a set of stored patterns to find those specified by a given partial description. We describe how to design simple contentaddressable memories, functioning in parallel, which can do this and which, in some sense, can generalise about the stored data. Secondly, we consider how certain graphical representations of data may be suitable for use in efficient serial search strategies. We indicate how such structures can be used in diagnosis when the availability or cost of tests to be applied cannot be determined in advance. The type of parallel system to be considered is to store descriptions of a set of patterns, and is then to be used to supplement an incomplete description of a newly presented pattern by matching it against those in store.

Cognitive Psychology 3:552-631.

In this paper we compare three models of transformational grammar: the mathematical model of Ginsburg and Partee (1969) as applied by Salomaa (1971), the mathematical model of Peters and Ritchie (1971 and forthcoming), and the computer model of Friedman et al. (1971). All of these are, of course, based on the work of Chomsky as presented in Aspects of the Theory of Syntax (1965). 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. All of these are important to the explanatory adequacy of transformational grammar. Both mathematical models allow the first, they each allow some form of the second, one of them allows the third. We were interested in the mathematical consequences of our restrictions. The comparison will be carried out by reformulating in the computer system the most interesting proofs to date of the ability of transformational grammars to generate any recursively enumerable set. These are Salomaa's proof that the Ginsburg-Partee model can generate any recursively enumerable (r.e.) set from a regular base, and the Peters-Ritchie proof that any r.e.

The phrase "technology and education" usually means inventing new gadgets to teach the same old stuff in a thinly disguised version of the same old way. Moreover, if the gadgets are computers, the same old teaching becomes incredibly more expensive and biased towards its dullest parts, namely the kind of rote learning in which measurable results can be obtained by treating the children like pigeons in a Skinner box. The purpose of this essay is to present a grander vision of an educational system in which technology is used not in the form of machines for processing children but as something the child himself will earn to manipulate, to extend, to apply to projects, thereby gaining a greater and more articulate mastery of the world, a sense of the power of applied knowledge and a self-confidently realistic image of himself as an intellectual agent. Stated more simply, I believe with Dewey, Montessori, and Piaget that children learn by doing and by thinking about what they do. And so the fundamental ingredients of educational innovation must be better things to do and better ways to think about oneself doing these things.

Selected quotes:"The Science Research Council has been receiving an increasing number of applications for research support in the rather broad field with mathematical engineering and biological aspects which often goes under the general description Articial Intelligence (Al). The research support applied for is sufficient in volume, and in variety of discipline involved, to demand that a general view of the field be taken by the Council itself.""To supplement the important mass of specialist and detailed information available to the Science Research Council its Chairman decided to commission an independent report by someone outside the Al field but with substantial general experience of research work in multidisciplinary fields including fields with mathematical, engineering and biological aspects."-----"Most workers in Al research and in related elds confess to a pro nounced feeling of disappointment in what has been achieved in the past twenty-five years. Workers entered the feld around 1950, and even around 1960, with high hopes that are very far from having been realised in 1972. In no part of the field have the discoveries made so far produced the major impact that was then promised.""In the meantime, claims and predictions regarding the potential results of Al research had been publicised which went even farther than the expectations of the majority of workers in the field whose embarrassments have been added to by the lamentable failure of such inflated predictions.""These general statements are expanded in a little more detail in the rest of section 3, which has been influenced by the views of large numbers of people listed in section 1 but which like the whole of this report represents in the last analysis only the personal view of the author. Before going into such detail he is inclined, as a mathematician, to single out one rather general cause for the disappointments that have been experienced: failure to recognise the implications of the 'combinatorial explosion'."See also: BBC TV - June 1973 - Lighthill Controversy Debate at the Royal Institution with Professor Sir James Lighthill, Professor Donald Michie, Professor Richard Gregory and Professor John McCarthy.Also in Lighthill, J., Sutherland, N. S., Needham, R. M., Longuet-Higgins, H. C., and Michie, D. (Eds.), Artificial Intelligence: A Paper Symposium. Science Research Council of Great Britain.

"In this paper we describe some major new additions to the STRIPS robot problem-solving system. The first addition is a process for generalizing a plan produced by STRIPS so that problem-specific constants appearing in the plan are replaced by problem-independent parameters.The generalized plan, stored in a convenient format called a triangle table, has two important functions. The more obvious function is as a single macro action that can be used by STRIPS—either in whole or in part—during the solution of a subsequent problem. Perhaps less obviously, the generalized plan also plays a central part in the process that monitors the real-world execution of a plan, and allows the robot to react "intelligently" to unexpected consequences of actions.We conclude with a discussion of experiments with the system on several example problems."Artificial Intelligence 3:251-288

The aim of this book is to advance our understanding of how humans think. It seeks to do so by putting forth a theory of human problem solving, along with a body of empirical evidence that permits assessment of the theory.

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