a teachable machine in the real world

Int. J. Man-Machine Studies (1978) I0, 301-312

A teachable machine in the real worldt

PETER M. ANDREAE AND JOHN H. ANDREAE

Department of Electrical Engineering, University of Canterbury, Christchurch, New Zealand

(Received 24 October 1977)

The design of learning machines which can be taught how to solve problems in the real world is of importance in industrial automation and in other fields. This paper outlines a new approach to this problem and describes PURR-PUSS, a working system embodying this approach. The two key features of the system are "multiple context" and "novelty". We discuss the way in which these two features contribute to the teachability of PURR-PUSS.

1. I n t r o d u c t i o n Industrial automation progresses by making jobs mechanical. That is, a task is made suitable for a machine and a machine is built to do the now mechanical job. Before a job is mechanized, it has to be done by humans because there are no machines that can adapt to new tasks as well as humans can.

One of the aims of Artificial Intelligence (AI) research is to design machines that can adapt to new tasks as humans do. This does not mean that AI is attempting to simulate humans on machines, or even just to copy human behaviour, but, since humans are the most intelligent and adaptable systems known, human behaviour is a source of ideas and suggestions as to how an intelligent machine should be able to behave.

This paper describes a machine called PURR-PUSS (Andreae, 1977). PURR-PUSS is a learning machine which uses its past experience to modify its actions. This, in itself, is not new but the approach to learning machines, which PURR-PUSS represents, is new. In particular, PURR-PUSS is (1) teachable, (2) able to act in the real world (i.e. not restricted to artificial environments), (3) can be given a body and is, in fact, designed to have a body, and (4) starts from scratch with nothing in its memory; it does not have any knowledge or procedures programmed into it when it starts and all knowledge it obtains is learned. (It does not have an innate universal grammar, as proposed by Chomsky, 1971.)

Section 2 explains why these characteristics are considered desirable, if not essential, for a machine that can learn to perform new tasks and adapt as humans do. Section 3 describes how PURR-PUSS works and how the interaction between PURR-PUSS, the teacher and the rest of the environment is organized and carried out. In section 4, we summarize those aspects of PURR-PUSS that we consider to be significant.

2. Characteristics 2.1. TEACHABILITY The ability to learn is a prominent feature of human behaviour, particularly in the first

tOriginal presented at the International Conference on Applied Systems Research, Binghamton New York, August 1977.

301 0020-7373/78/030301 + 12 $02.00/0 (c) 1978 Academic Press Inc. (London) Limited

302 P.M. ANDREAEANDJ. H. ANDREAE

15 years or so of life. Although some of this learning is done when the child is by himself, most of it involves active interaction with other people, especially with parents, friends and teachers. Sometimes the other person instructs the child in a relatively formal manner, but more often informally guides the child's learning. This guiding (formal or informal) of the learning process is what is meant by teaching. Without teaching, a child would learn very much less than he does with teaching because he would have to dis- cover everything for himself. He could not learn a language or most of the many skills that the child normally learns from other people. If a learning machine cannot interact with a teacher in this way, it will have to learn everything for itself and the process will be slow and unsatisfactory.

An alternative approach, favoured by mainline workers in AI, is to program a machine with the knowledge that it would otherwise have to learn (Jackson, 1974). We doubt that this approach will succeed because of the enormous amount of knowledge that a child learns in 15 years, and also because of the great difficulty in determining what this knowledge is.

I f a learning machine is able to interact with an environment which includes a teacher, then, as long as the machine behaves in a manner relatively similar to a human, the human teacher will be able to guide the way in which the machine learns. Teaching will be easier for the teacher if the interaction is natural.

2.2. REAL WORLD ACTING

If a learning machine is to be teachable by humans, then it must be able to act in the same world as humans, on the same sort of tasks, and in the same conditions of noise, lack of specification and open-endedness. Similarly, if people are to be convinced that the machine can adapt and learn as humans can, then it will have to be able to work at real world tasks, not just tasks in an artificially restricted or formalized environment.

Another reason why a machine should be able to act in the real world is to do with the restriction on formal machines expressed by G~del's theorem. In the words of Lucas (1964), "G~del 's theorem states that in any consistent system which is strong enough to produce simple arithmetic there are formulae which cannot be proved-in-the-system, but which we can see to be t r u e . . . It follows that no machine can be a complete or adequate model of the mind, that minds are essentially different from machines." However, if a learning machine is strongly connected to the "open system" of the real world, then it will cease to be a formal system and G~del's theorem will cease to apply to it.

2.3. CAN BE GIVEN A BODY

Piaget (1972) and others have shown that the learning process of children is not a passive one in which the child just accepts and processes experience, but rather an active process of assimilation and accommodation, in which both the actions of the child on the environment and his observations of the results of those actions are integrated in experience. Children act on their environment with their bodies, as do adults. If a machine is to act on its environment in the same way, it also will need a "body", that is, some part of the environment which is directly under control of the machine. The more versatile the body, the more effectively the machine will be able to act and learn in the world. This body is also the means by which the formal machine is connected to the informal, open, real world. It has the added advantage for a machine that learns from scratch that at the start of the learning process, there will be a very regular and consistent part of the

A TEACHABLE MACHINE 303

ENVIRONMENT

REAL WORLD

Teacher Robot

MEDEATOR

!

SIMULATED

Abacus Hand

Drawin@ Board

Maze

Broom

PURR-PUSS

FIG. 1. PURR-PUSS and her environment.

environment which will be easier to learn about than the less controllable parts of the environment.

2.4. STARTS FROM SCRATCH

There are many advantages in designing a machine to learn from scratch. Having decided to design a machine that learns, it is easier not to prime it. We do not know how to prime it or what to prime it with. If we try to prime it with an "adult" intelligence, then we are faced with an enormous task. If we try to prime it with the instincts and reflexes of a baby, we find that these are quite obscure: anything from a sucking reflex to an innate universal grammar has to be considered ! Finally, if the machine learns from scratch, then we know that its behaviour has been learned and is not the result of priming.

3. PURR-PUSS and her environment 3.1. ORGANIZATION

The details of the way in which we have set up PURR-PUSS in "her" environment are not important here, since these are being improved continually, but the overall organization of PURR-PUSS and her environment will help the reader to understand the mechanisms of PURR-PUSS and to appreciate the interaction between PURR-PUSS and her teacher.

Figure 1 shows PURR-PUSS and her environment schematically. PURR-PUSS, the learning machine, remembers past experience and chooses actions on the basis of that experience. MEDEATOR is a switchboard program which routes PURR-PUSS's actions to the appropriate part of the environment, returns the responses from the environment to PURR-PUSS, and accepts teacher's commands.

The environment comprises several sections: the "real world" section includes teacher, different robots and a "voice"; the simulated section includes an abacus, a hand, a drawing board, and a broom to balance. In both the real and simulated sections, some

304 P. M. ANDREAE AND J. H. ANDREAE

parts are more or less under PURR-PUSS's control and constitute the "body". Teacher is part of the real world environment, but has special powers, like disapproval, which will be explained later.

3.2. THE INTERACTION

The interaction between PURR-PUSS and her environment is a sequence of patterns, or stimuli, from the environment alternating with actions, or responses, from PURR-PUSS. Both patterns and actions may be null. Of the infinity of patterns and actions allowed-- any string of characters terminated by a space--there are several special classes of pattern and action identified by their first characters. In the present organization of PURR-PUSS, there are "speech" (beginning with a letter), "physical" (beginning with a [), "'drawing board" (beginning with a ~o), and different patterns and actions for the robots.

Teacher is always given the option ofproviding a pattern if the rest of the environment does not respond (i.e. when an action is chosen that does not elicit a response from some part of the environment). Also, if PURR-PUSS cannot choose an action other than the null action (a pause), teacher is given the option of providing PURR-PUSS with an action. Teacher is also able, if he desires, to change any action or pattern produced by PURR- PUSS or by the environment. This corresponds to "shouting down" patterns or forcing actions. Sometimes this seems reasonable to do, but at other times it does not. The more realistic PURR-PUSS's body and world become, the easier it will be to judge what is reasonable for teacher to do.

Teacher may also "disapprove" any action of PURR-PUSS. The effect of this is discussed below, but PURR-PUSS tends to avoid actions that have been disapproved.

At present, teacher communicates via a teletype-writer and all actions and patterns, including those to and from the robots, are represented as character strings and are printed on the teletype so that teacher can see the entire interaction.

Speech actions--those starting with an alphabetic character--have the special property that the following pattern is just an echo of the action. This corresponds to hearing what you say. This "echo speech" turns out to be particularly powerful, since even a very simple form of PURR-PUSS can be taught to be any finite automaton if echo speech is used.

Figure 2 gives an example of an interaction with PURR-PUSS in which PURR-PUSS was taught to draw as many poles as teacher told her to. At the beginning of the interaction, the memory was completely blank. The figure shows the sequence of patterns and actions. The underlined actions were provided by teacher when PURR-PUSS did not choose any action. All other actions, except pauses, were chosen by PURR-PUSS. The indented speech patterns were automatic echoes of PURR-PUSS's speech actions. The actions beginning with ~o affected the drawing board environment, and the ~o patterns were returned automatically by that environment. All other patterns were provided by teacher. Null actions and patterns (pauses) are shown as hyphens. Notice how, after being taught to draw four poles, PURR-PUSS can draw just three poles straight off, and can draw five poles after being shown how to count down from five to four.

3.3. THE PUSS MECHANISM

There are two main parts to PURR-PUSS. One is the modeller/predictor consisting of a number of PUSSes, and the other is the action decision strategy called PURR. The


Pattern Action

DRAW

S OME

VERTICAL -

POLES

Puss Is

. . . l l . . . I - HOW MANY oo FOUR

FOUR

MORE - POLES

TO DRAW ;ME

.P move I

east I

Pattern Action

IN IMN

lIP I

ILS TWO

TWO

MORE

POLES

TO DRAW ;ME

I I I ' P I

. . . 41 . . . I lOS

I t l r ] I N I M N

l J i P I

ILS ONE

... 21 ... - -

l ~DS ONE - draJi MORE

POL E TO IP south I DRAW ~ME

fN ~m

I P I I P III I

... 51 ...

ILS - 1 IDS THREE -

L 1 THREE - I I l i P MORE POLES - IN IMN • o [

P DRAW tME I I 1 1

1 ' 1 ] I L S -

NO

. . . 31 . . . MORE - 1 IDS POLES -

Pattern Action Pattern Action

DRAW - 1 IS

... 61 ... I 1S SOME - I HOW

VERTICAL - HOW MANY

POLES - MANY ?? PUSS IS ... 121 ...

I rg FIVE - I Is - - 1 HOW FIVE -

HOW MANY MORE -

MANY ?? POLES -

THREE - TO - ... 71 ... DRAW ZME

- - 1 /DS THREE - IN IMN

MORE - ILS - POLES - ... 131 ... TO - FOUR -

DRAW IME - - f IDS FOUR -

IN INN MORE - ILS TWO POLES -

TWO - TO ... 81 ... DRAW IME - TWO l IDS TWO MORE IN IMN MORE POLES ILS THREE

POLES TO ... 141 ... DRAW IME THREE -

I IDS - THREE

IN tMN THREE MORE ILS ONE MORE POLES

ONE - POLES TO

... 91 ... TO DRAW - ONE DRAW IME

ore MORE l IDS MORE POLE IN IMN POLE TO ILS TWO

TO DRAW ... 151 .,.

DRAW IME TWO - I Ims - TWO

IN IMN TWO MORE ILS NO MORE POLES

NO MORE POLES TO

... I01 ,.. TO DRAW

MORE POLES DRAW IME

POLES - I IDS - - ZN IMN - - ILS ONE

WELL - ... 161 ... DONE - ONE - - - - ONE

-- - ONE MORE - - MORE POLE

NOW - POLE TO

... iii ... TO DRAW

DRAW - DRAW XME

SOME - I IDS

VERTICAL - IN IMN POLES - ILS NO PUSS XS NO MORE

MORE _ POLES etc,

FIG. 2. The drawing poles task.


PUSSes model the interaction and provide predictions of how the environment is likely to respond and what actions are appropriate. PURR, described in the next section, uses the predictions of the PUSSes to choose an action.

A single PUSS is a simple mechanism for predicting the next event in a sequence of events. In an interaction of PURR-PUSS, an event for a PUSS may be a pattern, or an action, or a pattern-action pair, or an action-pattern pair. The most recent n events in the sequence of events are held in a short-term memory called the "window" of the PUSS. The window may be of any fixed length and this length, n, characterizes the particular PUSS. The events in the window form a "context" which determines the prediction and the storing of the next event. Each event, as it occurs, is stored at an address found by "hashing" (Knuth, 1973) the context in the window. The window is then updated with the latest event, and the predictions of the next event are the contents of the addresses obtained by hashing the new context in the window. If the window holds the context C, the PUSS's predictions of the next event will be all events that in the past have occurred immediately after the context C.

It should be noted that a PUSS never has to rub anything out of memory--i t is purely additive. Also, the speed of both storage and prediction is almost independent of memory size, thereby allowing very large memories without loss of speed.

A single PUSS will never be 100~o successful at predicting events in a sequence, except for a few trivial sequences, but as long as some sections of the sequence are repeated later in the sequence, the PUSS will be able to make some correct predictions. The biggest problem with a single PUSS is that the predictions are always determined by the n event context. If the choice between several predictions of the next event depends upon an event more than n events ago, then PUSS cannot resolve the ambiguity and will predict all the possibilities.

In PURR-PUSS, these difficulties are overcome by using a modeller/predictor consisting of several PUSSes each modelling the sequence of patterns and actions in a different way. There are three PUSSes--main-PUSS, pattern-PUSS and action-PUSS-- which receive events consisting of all pattern-action pairs, all patterns, and all actions, respectively. There are also the "threading" PUSSes, each of which receives events consisting of action-pattern pairs of one type. For example, physical-PUSS receives all physical actions (beginning with [) and the following patterns.

Predictions of the next pattern and action are based on the combined predictions from the "multiple context" of the windows of all the different PUSSes, which may all have different length windows. Since the window of a threading PUSS only holds action- pattern pairs of one type, it may be holding events which occurred an indefinite time before the events in the windows of the non-threading PUSSes; and, therefore, the predictions of the multiple context predictor are not bound by a finite time span.

Figure 3 shows the contents of the windows, and the predictions of all the PUSSes at the 79th step of the Drawing Poles task shown in Fig. 2. It illustrates the "elastic" memory of the threading PUSS windows and the effect of predicting from a multiple context. Main-PUSS is predicting the pattern-action pair "7oLS, - " . Action-PUSS is predicting actions "ONE", "TWO", " T H R E E " and "FOUR" . It cannot say which is the correct one because its window is not long enough to include the last number. The window of speech-PUSS, although the same length as the action-PUSS window, does include the last number ( "THREE") and so speech-PUSS unambiguously predicts the action-pattern pair "TWO, TWO". Pattern-PUSS is predicting the pattern "TWO",


pattern-PUSS

main-PUSS

action-PUSS

speech-PUSS

drawing-PUSS

window length event

pattern

pattern-action

action

action-pattern

action-pattern

~attern-PUSS

pat. I - THREE MORE A

main-PUSS

pat. act.

action-PUSS

act.

speech-PUSS

act. I THREE MORE A

pat. I THREE MORE

drawing-PUSS

act. pat.

~indows

POLES TO DRAW I IN ILS

predictions

l l ~ TWO

DRAW I IN i ~ ILS IME IDS IMN r -

ONE

I TO" DRAW IME IDS XMN TWO l THREE

FOUR

POLES TO DRAW ~ TWO POLES TO DRAW r TWO

IME IDS IMN i ~ IME I IN ILS I r t

I£ a speech pattern £ollows a null action, speech-PUSS and action-PUSS receive the speech action which would have produced the pattern instead o£ the null action.

FxG. 3. Multiple context: the contents of the windows at step 79.

• ' ~ O O ' , which supports the speech-PUSS prediction. The prediction of drawing-PUSS ( ~ ME,~ ) is not used until step 86. The way PURR uses these predictions to choose the action "TWO" is described in the next section.

3.4. THE PURR MECHANISM

If the predictions of the PUSSes suggest that several different actions would all be appropriate at a given time, the decision mechanism of PURR-PUSS must have some way of choosing sensibly between the alternatives. In other words, it must have some goal such that an action can be chosen to attain that goal. The simplest form of goal is a reward provided by the teacher, but this proves to be very teacher-dependent and not conducive to the exploration of new environments. A new sort of goal, called "novelty", has been found to be very successful. A pattern is defined as being "novel" if it occurs


window o£ pattern-PUSS at step 149

THREE - THREE MORE POLES TO DRAW 2' ~N I==> ~LS ==> TWO ==> - t I

==> TWO ==> MORE ==> POLES ==> TO ==> DRAW ==> I ==> IN ==>

ILS ==> ONE ==> - ==> ONE ==> MORE ==> POLE ==> TO ==> DRAW

==> I ==> IN ==> ILS ==> NO ==> MORE ==> POLES ==> - ==> WELL

novel even t

==> represents a prediction from the previous 9 patterns.

FIG. 4. Hypothesis constructed at step 149 of the Drawing Poles task.

without first being predicted by pattern-PUSS. That is, a pattern is novel if it occurs after a context after which it has not occurred previously. Any such pattern becomes a goal pattern for PURR-PUSS until it occurs again after the same context or until it is predicted in the formation of an "hypothesis".

To enable PURR-PUSS to choose actions which will lead her to a goal pattern, a forward series of predictions from the present window of pattern-PUSS is constructed until some novel pattern is reached. This sequence of patterns ending in a novel pattern is called an hypothesis and PURR-PUSS will attempt to choose actions to follow this hypothesis. I n forming an hypothesis, PURR-PUSS tends to choose the more recent patterns with a higher probability than the less recent patterns. PURR-PUSS will not attempt to form a new hypothesis until either the novel pattern at the end of the old hypothesis is reached, or a pattern is received that does not agree with the hypothesis. In the latter case, the old hypothesis is retained unless pattern-PUSS is making some prediction of the next pattern. Figure 4 shows the hypothesis that was formed at step 149 of the Drawing Poles task listed in Fig. 2.

To choose an action, the decision mechanism PURR may have the hypothesis which it is trying to follow and/or predictions from main-PUSS, action-PUSS and the threading PUSSes. The prediction of an action by just one PUSS is not taken as sufficient evidence for choosing the action; the more PUSSes agree on a certain action, the better choice that action is considered to be. There are several different priority levels at which actions can be chosen. PURR will choose at random one of the actions on the highest non-empty priority level. Figure 5 shows the scheme for determining the priority level of a predicted action. It can be seen that priority levels above 5 all take the hypothesis into account.

There is one other factor which influences the choice of action. No action will be chosen while teacher is applying disapproval. Also, any action or pattern stored while teacher is


Pattern P1 has just occurred.

Each action in a prediction by Main-PUSS and/or by a Threading-PUSS is put in the priority level corresponding to its value. The value of each action is found by the following precedure:

IF there is an action A such that:

Main-PUSS is predicting the pattern-action A further prediction by Main-PUSS assuming P1 A to occur is

THEN ~%

Action-PUSS predicting a~ion A adds 1

Any Threading-PUSS predictihg an adds 2 action-pattern A P

The next pattern on the hypothe- adds 4 sis being P2

P1 A And

P2 A'

to the value o f A

to the value of A

to the value o£ A

IF there is an action A such that:

A Threading-PUSS is predicting the action-pattern AP 2

And Main-PUSS is not predicting the pattern-action P1 A

THEN

Action-PUSS predicting action A adds 2 to the value of A

The next pattern on the hypothe- adds 4 to the value of A sis being P2

I Priority Level: 1 2 3 4 5 6

Action Value: 7 6 5 4 3 2

Note. I£ the highest priority level o£ any action is below 4, then there is a small probability that no action will be chosen. This small probability is reduced by the occurrence o£ novel events in any o£ the PUSSes, but gradually rises in the absence of novelty.

FIG. 5. Determining the priority levels of actions.

applying disapproval is marked as disapproved. PURR-PUSS will not do any predicted action that has the disapproval mark; nor will she form an hypothesis through a disapproved pattern. Disapproval is removed if the pattern or action occurs again in the same context without disapproval being applied. Disapproval is a useful way of correcting PURR-PUSS and, like novelty, it is not permanently attached to patterns and actions. It appears that the permanence of either reward or punishment is bad for teachability.

4. Conclusion There are three desirable qualities for any teachable system, whether a human or a


Teachable

Potential Aptitude Resilience

.//I /I \ / \ ~eech elastic open to cumul- correc- self- noise additive consol-

power memory world ative tible acting resis- storage idation o£ o£ for trans- by and rant of of finite thread- Turing £er o£ disap- explor- mf exper- learned state ing machine learn- proval atory / ience behaviour

\ / no stora@e no searching of contexts o£ memory

\ / Context- hashing

f a s t implementation with unlimited memory

FIG. 6. Potential, aptitude and resilience.

machine: "potential", "aptitude" and "resilience". Potential refers to the highest level of competence to which the system could attain--the maximum difficulty of the tasks it can learn. Aptitude relates to the ease and speed of learning, while resilience refers to the robustness of the system's acquired knowledge when exposed to new knowledge or "noisy" information.

The particular organization of PURR-PUSS that we have developed so far is unlikely to be near optimal. Many improvements can be expected in the way the environment is organized, in the way PUSSes are chosen, and in the way the predictions of the PUSSes are used for the choice of action by PURR. However, there are two key ideas in PURR- PUSS which are, in our opinion, significant for both AI and for Psychology. The first is multiple context and the second is novelty. Both are old ideas receiving new, precise definition. Both contribute to the potential, aptitude and resilience of PURR-PUSS as a teachable machine: see Fig. 6.

4.1. POTENTIAL From a strictly theoretical point of view, PURR-PUSS may have sufficient computing power in a single PUSS, if speech actions or the equivalent are available. It was shown by Andreae & Cleary (1976) that PURR-PUSS could be taught to behave like a Universal Turing Machine, given an infinite tape (paper and pencil) in her environment. In particular, it was shown, by the method used, that a single PUSS with speech was capable of modelling any finite state machine. As an open system coupled to the real world, PURR-PUSS has no formal limitations of computational power. So far we have no interesting results


on the theoretical power of a multiple context with threading PUSSes. Our guess is that the "elastic" short-term memory of the threading PUSSes provides PURR-PUSS with much greater power than just finite state machine power.

4.2. APTITUDE

The transfer of learning from one task to another was demonstrated by Andreae & Cleary (1976), where the method of counting on fingers learnt in the task of counting objects was transferred to a second task of counting beads on an abacus by introducing the appropriate context just once. In this way, PURR-PUSS can accumulate experience and apply old methods to new situations. I f PURR-PUSS could not do this, then teacher would have to teach each new task from scratch, which would be most unsatisfactory.

Although, as was mentioned above, a PURR-PUSS with a single PUSS in a suitable environment could be taught to do any task, it seems that teaching a multiple context PURR-PUSS is much easier. There are two reasons which contribute to this greater ease of teaching: first, with a multiple context PURR-PUSS, any task can be taught in more different ways than with a single PUSS system, so it is less critical how teacher teaches a task; secondly, the threading PUSSes can hold information in a more "natural" way, so teacher does not have to work out artificial ways of providing short-term memory.

The use of disapproval enables correction of teaching errors and resolution of ambiguities that teacher unwittingly introduces into his teaching. The novelty-seeking, exploratory behaviour of PURR-PUSS tends to reveal these ambiguities so that teacher can disapprove them.

4.3. RESILIENCE

A new pattern occurring in a well-established situation is usually treated by PURR-PUSS as though it were the expected (i.e. predicted) pattern, and so variations become related by their common contexts. This is a form of noise resistance which can cope to some extent with variety and with error. An important aspect of the storage of events by PUSSes is the fact that the contents of the PUSS memory can never be inconsistent with new behaviour. A sequence of events is either the same as before or different: if the same, nothing is stored, while if there are differences, the events are stored. A PUSS does not convert its stored behaviour into, for example, a minimal state automaton which might then have to be taken to bits in the light of later behaviour to produce a new automaton (Gaines, 1976). A PUSS only adds to what is already stored. Another aspect of resilience is the way in which novelty-seeking causes PURR-PUSS to construct hypotheses back to events which have occurred only once, so that all experience which has been stored tends to be made accessible to future behaviour. PURR-PUSS's novelty-seeking, exploratory behaviour thus causes her to consolidate experience in partially known areas of the environment before exploring farther afield.

4.4. THE BRAIN

The reader may have guessed that we have another reason for designing and testing a teachable machine in the real world. Industrial automation is a big field with important applications and possibilities. It is dwarfed, however, by the field of mental health which so desperately needs an understanding of how the brain works. We hope that PURR-PUSS will make a contribution in this direction too.

This work is supported by the Defence Scientific Establishment of the New Zealand Ministry of Defence.

312 P.M. ANDREAE AND J. H. ANDREAE'

References ANDREAE, J. H. (1977). Thinking with the Teachable Machine. London: Academic Press. ANDREAE, J. H. & CLEARY, J. G. (1976). A new mechanism for a brain. International Journal

of Man-Machine Studies, 8, 89-119. CHOMSKY, N. (1971). Recent contributions to the theory of innate ideas. In SEARLE, J. R., Ed.,

Philosophy of Language. London: Oxford University Press, pp. 121-129. GAINES, B. R. (1976). Behaviour/structure transformations under uncertainty. International

Journal of Man-Machine Studies, 8, 337-365. JACKSON, P. C. (1974). Introduction to Artificial Intelligence. New York: Petrocelli/Charter. KNUTH, D. E. (1973). The Art of Computer Programming, 3. Reading, Mass.: Addison-Wesley. LUCAS, J. R. (1964). Minds, machines and G6del. In ANDERSOn, A. R., Ed., Minds and Machines.

Englewood Cliffs, N.J.: Prentice-Hall, pp. 43-59. PIAG~T, J. (1972). The Child and Reality. London: Frederick Muller.

a teachable machine in the real world

Documents