Such methods can effectively and efficiently induce good descriptions from a given set of examples and, optionally, induce counter-examples (for example Michalski, 1975, 1980a; Quinlan, 1979; Langley et al., 1983). These methods cannot modify concept descriptions which are contradicted by new examples, but must re-learn the descriptions from scratch. In contrast, incremental learning methods modify concept descriptions to accommodate new learning events (Winston, 1975; Michalski and Larson, 1978). When we observe human learning we clearly see that it is incremental.

This paper describes some work on automatically generating finite counterexamples in topology, and the use of counterexamples to speed up proof discovery in intermediate analysis, and gives some examples theorems where human provers are aided in proof discovery by the use of examples.

Work of the Soviet school (approximately half the book) in this explosively growing area of machine intelligence is thus made accessible for the first time to Western readers, in addition to the latest Western advances. The emergent theme of knowledge-representation is supported on the theoretical and experimental sides by recent work in inductive inference and theory-formation.

A programming language based on sets; motivation and examples.

A technique that has proved useful in shortest path and other discrete optimization computations has been bi-directional search. The method has been well tested in the two-node shortest-path problem providing substantial computational savings. A natural impulse is to extend its benefits to heuristic search. In the uni-directional algorithms, the search proceeds from an initial node forward until the goal node is encountered. Problems for which the goal node is explicitly known can be searched backward from the goal node. An algorithm combining both search directions is bi-directional. This method has not seen much use because book-keeping problems were thought to outweigh the possible search reduction. The use of hashing functions to partition the search space provides a solution to some of these implementation problems.

THE FRAME PROBLEM One of the central principles upon which intelligent devices seem to operate is that of maintaining internal models of their external environments. In artificial systems which have been constructed to date various representations for this internal model have been used; but in every nontrivial case the need arises to consider the effect, upon the structure of the model, of the performance by the system of actions in the external world, so that their potential consequences may be reckoned. How difficult this is, depends upon both the complexity of the model and its method of representation. In particular, it is usually easy when the problem is posed in the classical heuristic search paradigm, and the data structures used to represent static configurations of the puzzle are relatively unproblematic (arrays, lists, and so on). For in this case [see, for instance, Manna (1970) and Pikes (1970) for examples] one can use the ordinary device of assignment to model the changes in the world.which The lack of side-effects reflects the simplicity of the physics which such models embody. This limitation to elementary forms of interaction is not, of course, intrinsic to the heuristic search method; but when more complex models are constructed it becomes less trivial to pursue the consequences of performing an action. The use of assignment to portray the doing of actions does seem to presuppose a trivial physics. Another method of constructing microcosms is to use a logical language to describe the real world (McCarthy 1959, McCarthy and Hayes 1969). This approach is more general than the heuristic search method (but the latter -- when it has sufficient expressive power -- wins at present by its computational advantage). The key idea is to use expressions denoting situations to separate out assertions according to which (static) state of the world they purport to describe. Assertions mentioning several different situations can then be used to describe dynamical laws which move us from one situation to another. But in some ways the resulting sharp separations between states of affairs are an embarrassment. For if we distinguish two situations s1 and s2, then from the fact, if such it be, that a predicate p is true of Si, nothing whatever follows concerning s2. And this is true even when s2 is directly associated with sl. Say s2 results from s1 by the performance of some action: s2 do (a, si) then no matter how remote -- speaking intuitively -- the connection between the property p and the action a, it still does not follow that p is true of s2. If we want it to so follow we must state this explicitly. Now, unfortunately, there are innumerable facts which might remain unchanged when actions are performed. So instead of writing a law of motion' in the form A(s) B(do(a, s)) where A and B are fairly short expressions, we are apparently obliged to list systematically all conceivable facts which are not changed.

In particular, we consider situations where functional properties of a computer program are given in the form of explicit input-output correspondences, and the problem is to synthesize (to form) a program, in a given programming language, that satisfies the given correspondences. The motivation behind the work is twofold: (1) to explore and elucidate schemes for solving formation problems by machine, and (2) to gain further insight into questions of representation in problem solving, to examine their nature and significance in the context of formation procedures, and to clarify the role of models in the solution of formation problems. The present approach to program formation derives from work done several years ago (Amarel 1962a, 1962b), in which we found it conceptually fruitful to view the automatic formation of computer programs that is based on computational examples as a case of automatic theory formation. A theory in an empirical science emerges from a body of observed correspondences and has the function of an intellectual mechanism for explanation and prediction. The theory evolves from a succession of hypotheses that are tested against experience, and attains a degree of stability once it explains with reasonable consistency the given body of observations. The form of a hypothesis capable of emerging in a scientific culture depends on the language, the basic concepts, and the schemas that are available in the culture.

We have written a program which will recognize a range of objects including a cup, a wedge, a hammer, a pencil, and a pair of spectacles. A visual image, represented by a 64.x 64 array of light levels, is first partitioned into connected regions. These regions are chosen to have welldefined edges. Having chosen the regions, the program then computes properties of and relations between regions. Properties include shape as defined by Fourier analysis of the s--tfr equation of the bounding curve. A typical relation between regions is the degree of adjacency. Finally, the program matches the actual relational structure of the regions of the picture with ideal relational structures representing various objects, using a heuristic search procedure, and selects that object whose relational structure best matches the actual picture. INTRODUCTION In November 1969, a Mark i robot device (Barrow and Salter 1970) was connected on-line to the ICI, 4130 computer of the Department of Machine Intelligence and Perception, University of Edinburgh.

The Genetics Counselor is a computer program, written in LISP, designed to handle problems of medical genetics counseling. It is an attempt to apply the methods of artificial intelligence research to medical diagnostic problems. The program attempts to map the data space of a family-tree structure into the hypothesis space of classical Mendelian genetics by use of a heuristic search. The input data are the family members along with their children (or parents), and phenotype. The program generates a family tree and searches for consanguinity.

Yet the attention given to the program as an application of artificial intelligence research has tended to obscure the more general concerns of the project investigators.