We present and analyze several examples of CEG taken from protocols. Based upon such examples, we present a model of the CEG process. We then briefly describe a computer implementation of the CEG model. This material is based upon wirk supported by the National Science Foundation under Grant No. IST-8017343.

Also to appear in Proceedings NIE--LRDC Conference on Thinking and Learning Skills, Lawrence Erlbaum Associates.

In mathematics, examples can be said to be as important to understanding as the traditionally exalted definitions, theorems, and proofs (Rissland 1978). In fact, some mathematical areas developed in response to troublesome counter-examples like modern real function theory which has been called'the branch of mathematics which deals with counter-examples" (Munroe 1953). In the law, examples -- that is, legal cases -- are the basis from which the law derives (at least in common law systems like those of the United States and England): the law is made through court decisions by consideration of specific problems in specific cases. The cases lead to rule-like decisions which are then refined (or perhaps refuted, i.e., overturned) in subsequent cases. In linguistics, for instance in the study of syntax, linguistic rules are derived from study of examples of actual language and are then subjected to testing on more examples. Some examples are taken from the infinite store of run of the mill sentences available to every natural speaker; others, like certain difficult garden path sentences, are fabricated and used as counter-examples are in mathematics.

Where the accountants have fallen down, however, is in their reluctance and sometimes inability to make intensive studies of different equipment and to specify their requirements for equipment. As one authority in the field of electronic data processing has pointed out, "Accountants, unlike engineers, take the equipment as given without bothering to specify their own particular needs." But after all things are taken into consideration, it is of primary importance that the personnel who are handling the details of the investigation have a good knowledge of the particular application to be studied. Executives in many companies have been dissatisfied with the help received from outsiders who are expert programmers and who know a lot about equipment, but who are unfamiliar with business systems. In some companies executives have found that their own personnel, who know the firm's particular data processing system, after three or four months of experience in which to grasp the logics of the computer and the intricacies of programming, are much more valuable than such outside experts.

A general game-playing program must know the rules of the particular playing game. These rules are: (1) an algorithm indicating the winning state; (2) an algorithm enumerating legal moves. A move gives a set of changes from the present situation. There are two means of giving these rules: (1) We can write a subroutine which recognizes if we have won and another which enumerates legal moves. Such a subroutine is a black box giving to the calling program the answer: 'you win' or'you do not win', or the list of legal moves. But it cannot know what is in that subroutine.

I] presented a systematic account of the facts of thought and of the methods to express them. But if we do not restrict the domain, there are too many things to be considered. Brunot accurately studied various ways to express surprise, prices, anteriority in the future, a question... But concepts used only in specific domains do not appear in his book. That is why I chose a technical domain -- annotations of chess games -- and I tried to fmd what was said in that domain.

It creates some plans and tries to execute them. It analyses the situations deeper in the tree only if the plan fails. In that case it generates new plans correcting what is wrong in the old one. So, the program considers only natural branches of the tree. It can find combinations for which it is necessary to look more than twenty ply ahead. The paper describes the methods used for analyzing a situation and for modifying unsuccessful plans. Then we examine some results found by the program.

Rote learning.We can keep all the situations already found. With each situation we store an indication on its interest or the move which has to be played. Samuell gives an example of such an application. This can be done if there are not too many possible situations. Even in games where there are many possible situations, this method can be useful for the beginning or the end of the games. We can improve this method: if the rulesare the same for all the players, we can standardize the situations: we assume that it is always the same player who has to play; for instance, at chess, white. We just keep half of the possible situations. At Go Moku where there are two axes of symetry, we just keep a quarter of the situations. But even with these improvements, there are many cases where this method is not useful because there are too many situations. It is doubtful that we can have good results in the middle game 398 at chess with such methods. We can try to generalize what has been done in a situation to another similar situation. For example in the second situation we play the same move than in the first one. Waterman2 has written an interesting progrpi playing poker. Let us describe it roughly. A situation is described by the value of seven variables: value of the program's hand, amount of money in the pot, measure of conservative style by the opponent... The program defines a partition of the set of possible values of these variables. For instance: If our hand is excellent, bet low if the opponent tends to be a conservative player and has just bet low. The problem is to define wisely these subsets. This can be done by the program which improves progressively the quality of the partition. This method is good for poker and it obtained very good results. But it is difficult to see how we can use it in a game like chess. How could we evaluate the similarity between situations, such as in similar situations we have to play the same move? A different position of a pawn can destroy a combination.

A. YONEZAWA and C. HEWITT 41 REPRESENTATIONS FOR ABSTRACT REASONING 4 A maximal method for set variables in automatic theorem-proving W. W. BLEDSOE

A. YONEZAWA and C. HEWITT 41 REPRESENTATIONS FOR ABSTRACT REASONING 4 A maximal method for set variables in automatic theorem-proving W. W. BLEDSOE