For the past ten years we have been working on the problem of getting a computer to understand natural language.

Success of a knowledge-based program depends on both competence and acceptability. It must perform well for it to be worth using, but is must be acceptable to users for it to be used. There are many dimensions to developing competent and acceptable knowledge based systems which can serve as "intelligent assistants" for problem solvers in science (see Shortliffe and Davis, 1975). One of these is the old AI problem of representation of knowledge. Since most previous work on representation has stressed its importance for problem-solving (e.g.

A model for adaptive problem solving applied to natural language acquisition.

A program called "AM" is described which carries on simple mathematics research, defining and studying new concepts under the guidance of a large body of heuristic rules. The 250 heuristics communicate via an agenda mechanism, a global priority queue of small tasks for the program to perform, and reasons why each task is plausible (for example, "Find generalizations of'primes', because'primes' turned out to be so useful a concept"). Each concept is represented as an active, structured knowledge module. One hundred very incomplete modules are initially supplied, each one corresponding to an elementary set-theoretic concept (for example, union). This provides a definite but immense space which AM begins to explore.

J. Do RAN 433 22 Chromosome classification and segmentation as exercises in knowing what to expect.

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).

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).