This paper describes the programming of a computer controlled arm. The programming is divided logically into planning and execution Communication between planning and execution is by a data fil e which specifies the arm trajectory with reapect to time, and actions that the arm should perform. The servo program which moves the arm along the trajectory is based on Legrangian mechanics and takes into account coupling between links, and the variation of inertial loading with change of arm configuration.In IJCAI-71: INTERNATIONAL JOINT CONFERENCE ON ARTIFICIAL INTELLIGENCE. British Computer Society, London.

Proc. Second Intern. Joint Conf. on Artificial Intelligence, 80-7. London: The British Computer Society

Ph.D. thesis, Edinburgh University. This thesis is concerned with algorithms for generating generalisations-from experience. These algorithms are viewed as examples of the general concept of a hypothesis discovery system which, in its turn, is placed in a framework in which it is seen as one component in a multi-stage process which includes stages of hypothesis criticism or justification, data gathering and analysis and prediction. Formal and informal criteria, which should be satisfied by the discovered hypotheses are given. In particular, they should explain experience and be simple. The formal work uses the first-order predicate calculus. These criteria are applied to the case of hypotheses which are generalisations from experience. A formal definition of generalisation from experience, relative to a body of knowledge is developed and several syntactical simplicity measures are defined. This work uses many concepts taken from resolution theory (Robinson, 1965). We develop a set of formal criteria that must be satisfied by any hypothesis generated by an algorithm for producing generalisation from experience. The mathematics of generalisation is developed. In particular, in the case when there is no body of knowledge, it is shown that there is always a least general generalisation of any two clauses, in the generalisation ordering. (In resolution theory, a clause is an abbreviation for a disjunction of literals.) This least general generalisation is effectively obtainable. Some lattices induced by the generalisation ordering, in the case where there is no body of knowledge, are investigated. The formal set of criteria is investigated. It is shown that for a certain simplicity measure, and under the assumption that there is no body of knowledge, there always exist hypotheses which satisfy them. Generally, however, there is no algorithm which, given the sentences describing experience, will produce as output a hypothesis satisfying the formal criteria. These results persist for a wide range of other simplicity measures. However several useful cases for which algorithms are available are described, as are some general properties of the set of hypotheses which satisfy the criteria. Some connections with philosophy are discussed. It is shown that, with sufficiently large experience, in some cases, any hypothesis which satisfies the formal criteria is acceptable in the sense of Hintikka and Hilpinen (1966). The role of simplicity is further discussed. Some practical difficulties which arise because of Goodman's (1965) "grue" paradox of confirmation theory are presented. A variant of the formal criteria suggested by the work of Meltzer (1970) is discussed. This allows an effective method to be developed when this was not possible before. However, the possibility is countenanced that inconsistent hypotheses might be proposed by the discovery algorithm. The positive results on the existence of hypotheses satisfying the formal criteria are extended to include some simple types of knowledge. It is shown that they cannot be extended much further without changing the underlying simplicity ordering. A program which implements one of the decidable cases is described. It is used to find definitions in the game of noughts and crosses and in family relationships. An abstract study is made of the progression of hypothesis discovery methods through time. Some possible and some impossible behaviours of such methods are demonstrated. This work is an extension of that of Gold (1967) and Feldman (1970). The results are applied to the case of machines that discover generalisations. They are found to be markedly sensitive to the underlying simplicity ordering employed.

Communications ACM 8:548-560

Machine Intelligence 6

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.(2) We can also define a language in which we describe the rules of a game. The program investigates the rules written with this language and finds some indications to improve its play. Artificial Intelligence and Heuristic Programming Edinburgh University Press

Machine Intelligence 6

Ph.D. thesis, Stanford University.

One of the central principles upon which intelligent devices seem to operate is that of maintaining internal models of their external environments. 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). 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. 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). 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. So that the law looks more like (Ci(s)& Ci(do(a, s))& & C„(do(a, s))&B(do(a, s)) for some very large n. This works for small problems (such as the familiar hungry anthropoid), but these are usually better formalized in the heuristic search paradigm anyway.

To every 3-dimensional scene there correspond as many 2-dimensional pictures as there are possible vantage points for the camera. It is, however, possible to construct pictures for which there is no corresponding scene containing physically -realizable objects. Pictures of such'impossible objects' can be useful in giving insight into the constraints or grammatical rules associated with the'language' of pictures, just as nonsense sentences can be useful in illustrating the rules of other languages. Impossible objects have been used by psychologists (Penrose and Penrose 1958) to create visual illusions which successfully challenge the ability of our perceptual systems to synthesize a 3-dimensional world from 2-dimensional information. The incompatibilities among the various portions of pictures of these objects are a novel way of testing our picture analysis procedures. The purpose of this paper is to demonstrate some possible decision procedures and to test them on pictures of both possible and impossible objects.