Perhaps the most promising and yet most difficult application of machine learning is in the area of scientific discovery: 'the most technically gripping challenge,... will be how to spread the computer wave from the front end of the scientific process, the telescopes, microscopes,... spark chambers, and the like, back to recognition and reasoning processes by which the chaos of data is finally consolidated into orderly discovery' (Michie 1982). For scientific discovery, machine learning is viewed as a tool to aid working scientists in forming theories from data.

In this paper we will be concerned with such reasoning in its most general form, that is, in inferences that are defeasible: given more information, we may retract them. The purpose of this paper is to introduce a form of non-monotonic inference based on the notion of a partial model of the world. We take partial models to reflect our partial knowledge of the true state of affairs. We then define non-monotonic inference as the process of filling in unknown parts of the model with conjectures: statements that could turn out to be false, given more complete knowledge. To take a standard example from default reasoning: since most birds can fly, if Tweety is a bird it is reasonable to assume that she can fly, at least in the absence of any information to the contrary. We thus have some justification for filling in our partial picture of the world with this conjecture. If our knowledge includes the fact that Tweety is an ostrich, then no such justification exists, and the conjecture must be retracted.

Recognition of three-dimensional objects, puzzle solving, electronic circuit analysis and truth-maintenance systems are examples of such problems, and these are normally solved by various versions of backtrack search. In this work we show how advice can be automatically generated to guide the order in which the search algorithm assigns values to the variables, so as to reduce the amount of backtracking. The advice is generated by consulting relaxed models of the subproblems created by each value-assignment candidate. The relaxed problems are chosen to yield backtrack-free solutions, and the information retrieved from these models induces a preference order among the choices pending in the original problem.

It is assumed that Si are sorted in increasing order of s(Si). Non-linearities of four trees are shown in Figure 6. Ti is absolutely linear; thus its non-linearity measure is zero. T2 is very close to being a balanced tree: non-linearity one. T3 is preferred to T4, i.e. this function is sensitive to the location of non-linearity within a tree (the lower a non-linearity occurs in a tree the lower (better) its measure).

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.

AL3 (Advice Language 3) is a problem-solving system whose structure facilitates the implementation of knowledge for a chosen problem-domain in terms of plans for solving problems, pieces-of-advice', patterns, motifs, etc. AL3 is a successor of ALI and AL 1.5 (Michie 1976, Bratko & Michie 1980a, I980b, Mozetic 1979). Experiments in which AU was applied to chess endgames established that it is a powerful tool for representing search heuristics and problem-solving strategies. The power of ALI lies mainly in the use of a fundamental concept of AU: piece-of-advice. A piece-of-advice suggests what goal should be achieved next while preserving some other condition. If this goal can be achieved in a given problem-situation (e.g. a given chess position) then we say that the piece-ofadvice is'satisfiable' in that position.

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.

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.