The eighth volume completes a ten-year span of the Machine Intelligence series. It is appropriate, therefore, to take stock of the main events, and to note certain solid steps and occasional forward leaps. Leaps are normally preceded by some preparatory back-tracking. The uniform procedures of heuristic search and resolution theorem-proving which dominated the scene in 1965 cannot of themselves, as we now see, be developed into "the answer" to automatic problem-solving. This realisation has paved the way for machine-aided forays into non-trivial mathematics, as indicated in Bledsoe and Tyson's contribution to this volume.

Names only appear which are in no sense bibliographic references; otherwise they are to be found in the author index.]

Machine intelligence problems are sometimes defined as those problems which (i) computers can't yet do, and (ii) humans can. We shall further consider how much "knowledge" about a finite mathematical function can, on certain assumptions, be credited to a computer program. Although our approach is quite general, we are really only interested in programs which evaluate "semi-hard" functions, believing that the evaluation of such functions constitutes the defining aspiration of machine intelligence work. If a function is less hard than "semi-hard," then we can evaluate it by pure algorithm (trading space for time) or by pure look-up (making the opposite trade), with no need to talk of knowledge, advice, machine intelligence, or any of those things. We call such problems "standard." If however the function is "semi-hard," then we will be driven to construct some form of artful compromise between the two representations: without such a compromise the function will not be evaluable within practical resource limits. If the function is harder than "semi-hard," i.e. is actually "hard," then no amount of compromise can ever make feasible its evaluation by any terrestrial device. "Hard" problems In a recent lecture Knuth (1976) called attention to the notion of a "hard" problem as one for which solutions are computable in the theoretical sense but 151 MEASUREMENT OF KNOWLEDGE For illustration he referred to the task, studied by Meyer and Stockmeyer, of determining the truth-values of statements about whole numbers expressed in a restricted logical symbolism, for example Vx Vy(y. But is the problem nevertheless in some important sense "hard?" Meyer and Stockmeyer showed that if we allow input expressions to be as long as only 617 symbols then the answer is "yes," reckoning "hardness" as follows: find an evaluation algorithm expressed as an electrical network of gates and registers such as to minimise the number of components; if this number exceeds the number of elementary particles in the observable Universe (say, 10125), then the problem is "hard."

Virginia Polytechnic Institute and State University Blacksburg, Virginia Philosophers and - "pseudognosticians" (the artificial intelligentsial) are coming more and more to recognize that they share common ground and that each can learn from the other. This has been generally recognized for many years as far as symbolic logic is concerned, but less so in relation to the foundations of probability. In this essay I hope to convince the pseudognostician that the philosophy of probability is relevant to his work. One aspect that I could have discussed would have been probabilistic causality (Good, 1961/62), in view of Hans Berliner's forthcoming paper "Inferring causality in tactical analysis", but my topic here will be mainly dynamic probability. The close relationship between philosophy and pseudognostics is easily understood, for philosophers often try to express as clearly as they can how people make judgments. To parody Wittgenstein, what can be said at all can be said clearly and it can be programmed A paradox might seem to arise. Formal systems, such as those used in mathematics, logic, and computer programming, can lead to deductions outside the system only when there is an input of assumptions. For example, no probability can be numerically inferred from the axioms of probability unless some probabilities are assumed without using the axioms: ex nihilo nihil fit.2 This leads to the main controversies in the foundations of statistics: the controversies of whether intuitive probability3 should be used in statistics and, if so, whether it should be logical probability (credibility) or subjective (personal).

Plan modification *The research reported herein was sponsored by the National Science Foundation under Grant GJ-36146.

The objects that ATRANS operates upon are abstract relationships and the physical instruments of ATRANS are rarely specified. The'trans' that was referred to in the beginning of this paper is what we call ATRANS. ATRANS takes as object the abstract relationship that holds between two real world objects.

To use language one must be able to make inferences about the information which language conveys. This is apparent in many ways. For one thing, many of the processes which we typically consider "linguistic" require inference making. For example, structural disambiguation: (1) Waiter, I would like spaghetti with meat sauce and wine. You would not expect to be served a bowl of spaghetti floating in meat sauce and wine. That is, you would expect the meal represented by structure (2) rather than that represented by (3).

The junction categories and link planting rules of SEE lyzed. That, however, is not the main point; it is merely typical of the way in which the program developed by a process of finding counter-examples that both invalidated old rules and hinted at new ones (Winston, 1973). The need to add and modify rules almost continuously to handle exceptions suggests that there is a basic flaw in the design. The flaw seems to be that Guzman used locally computed picture predicates as evidence for global scene-based properties. To avoid this one must ask what do the lines in the picture depict?

Many of the problems of recognition and interpretation encountered in archaeology have close parallels with classic artificial intelligence problems, notably those of scene analysis.

After an introduction to LOGO thinking and language, the benefits of children writing simple AI programs using the proper tools were described. Finally, the ways in which an Al system designed for education can interact with children were discussed. These ideas should be implemented and tested with children. Only then will the effects on education be known.