[What follows is the text of the 'Development' chapter - chapter five - of my thesis as it existed in June 1988, when I lost access to the machine on which the work was done. This is an unfinished chapter of an unfinished thesis; I am posting it because people have expressed interest in the explanation game. This is the last form of this chapter, but it isn't the end of my thinking on the matter, and if I were rewriting it now I would add further moves to the set to allow the agents to argue not just about assumptions, but about the merit of the authorities from whom rules of inference are drawn.

A modern implementation would also, of course, have access to the semantic web in order to draw in additional sources of knowledge beyond that stored in a local knowledge base.]

Development

Explanation is a social behaviour

Games are social behaviours which can be modelled

Explanation can be viewed as a game playing activity

One of the models we frequently use in real life situations where a decision has to be made on the the basis of uncertain or conflicting evidence is the dialectic model. In this, one authority proposes a decision, giving an argument which supports it; another authority brings forward objections to the argument, and may propose an alternative decision. This method may continue recursively until there is no further argument which can be advanced.

This is the model which underlies both academic and parliamentary debate, and the proceedings of the law courts. The model supports a ‘decision support’ conception of the Expert System’s role, in addition to a ‘decision making’ one; in the decision support conception, the user is placed in a position analogous to that of a jury, considering the arguments presented by the advocates and making a decision on the basis of them.

We can view this dialectic approach to decision making as a game, with a fixed set of legitimate moves.

Hintikka’s game theoretic logic

This approach seems very promising. It may tie in with game-theoretic logics such as those of Ehrenfeucht [Ehrenfeucht 61] and Hintikka [Hintikka & Kulas, 83 and passim]. Of course, these logics were strictly monotonic. Problem areas where monotonic logics are adequate are of limited interest, and unlikely to give rise to interesting problems of explanation; but it should be possible to develop a provable semantics for a non-montonic extension. The decision procedure for a game-theoretic logic should not raise any particular difficulties; the ‘games’ are zero sum, under complete information.

However, the adoption of a game theoretic explanation mechanism does not commit us to adopting a game theoretic logic; so (although interesting) this line will be pursued only if it proves easy.

The object of an explanation game

If explanation is to be seen as a game, what is to be its objective? If we were to take a positivist approach, we might say that the purpose of explanation was to convey understanding; then the game would be a co-operative one, with the objective of both players being to achieve this end.

But seeing we have rejected this position, the objective of an explanation must be to persuade.

Furthermore, if we accept the argument advanced in Chapter 3 above that explanation is hegemonistic, the explanee must be seen to have an objective in resisting explanation. So now we have a clear idea of what the objective of an explanation game will be: the explainer will win, if the explainee is brought to a point of no longer being able to produce a rational¹ reason for resisting the explanation. Otherwise, if when all the supporting arguments the explainer can bring to bear have been advanced the explanee is still unconvinced, the explainee has won.

Legitimate moves in an explanation game

A possible set of legitimate moves in an explanation game might be:

PRESENT

Present a case, supported by an argument, which may include one or more assumptions.

Generally, in a non-monotonic system, we are dealing with incomplete information (and, indeed, this is generally the case in ‘real life’). Consequently, any conclusion is likely to be based upon one or more unsupported assumptions.

[starting move]

DOUBT

Challenge one or more of the assumptions.

[basic response to PRESENT, REBUT or COUNTER-EXAMPLE]

DOUBT-IRRELEVANT

Claim that, even if the assumption were false, it would make no difference to the decision.

[blocking response to DOUBT]

ASSUMPTION-PROBABLE

Claim that the assumption is probable based on prior experience, or, for example, statistical data.

[weaker response to DOUBT]

REBUT

This is essentially the same as PRESENT, but of an argument based on the opposite assumption to that challenged in the preceding DOUBT.

[response to a PASS following a DOUBT]

COUNTER-EXAMPLE

Present a known case similar to the current one, where the predicate of the assumption which has been challenged holds the opposite value.

[response to ASSUMPTION-PROBABLE]

PASS

A null move in response to any other move. Forces the other player to move. In some sense this might be seen as equivalent to saying ‘so what?’: the opponent has made a move, but there is nothing further which the player wants to advance at this stage. This move is inherently dangerous, since the game ends when the two players pass in successive moves.

[weakest response to anything]

Implementing a game theoretic approach to explanation

Playing the explanation game

The game playing algorithm required to implement an explanation system need not be sophisticated; indeed, it must not be too sophisticated, at least as a game player. Consider: a good game playing algorithm looks ahead to calculate what the probable responses to the moves it makes will be. If it sees that one possible move leads to a dead end, it will not make that move.

But in generating an explanation, we need to explore any path whose conclusion is not immediately obvious. So either the game-playing algorithm should not look ahead more than, perhaps, one ply; or else, if it does so, then when it sees a closed path it should print out a message something of the form:

Critic: Oh yes, I can see that even if the assumption that Carol hasTwoLegs is false it does not affect the assumption that Carol canSwim.

Initially, however, I propose to implement a game-playing algorithm which simply makes the strongest move available to the player, based on a scoring scheme which does not look ahead. The game will proceed something like tennis; the player who last made a PRESENT or REBUT move will have the initiative, the ‘serve’, as it were, and need only defend to win. The other player must try to break this serve, by forcing a DOUBT… PASS sequence, which allows a REBUT play.

Dialectic explanation: the two-player game

With this schema, we can mechanise a dialectic about a case. The game is played by the machine against itself; ‘agents’ in the machine play moves in turn until both sequentially pass, or until the user interrupts. Each move produces a natural language statement on the display Ideally, the user could interrupt at any time, either to request further justification for a move or to halt the process.

As a (simple) example of what might be produced, here is some sample output from a very crude prototype system²:

User: (← Carol Explain CanSwin)

Consultant: What is the value of CanSwim for Carol?

User: Don’t know

Consultant: I found that CanSwim was true of Carol by Default using the following assumptions:

I assumed that CanSwim was true of Carol

My reasons are

CanSwim is true of most Mammals;

Carol is a Mammal;

Therefore it is probable that CanSwim is true of Carol.

Critic: The assumption that CanSwim is true of Carol is unsafe:

Henry is also of type(s) (Person) but CanSwim is false of Henry.

This example, which is from a system considerably less developed than the ideas given above, shows ‘Consultant’ PRESENTing a case based on a single assumption, and ‘Critic’ responding with a COUNTER-EXAMPLE – a move which would not be legal under the scheme given. However, this should give some indication of how the idea might be implemented.

The simple model described above has not achieved all we want, however. The machine, in the form of the agent ‘Consultant’ has attempted to explain to itself, wearing its ‘Critic’ hat. The user’s role has simply been that of passive observer. The first enhancement would be to give the user control of the ‘Critic’; but because the user cannot have the same view of the knowledge base as the machine, the ‘Critic’ will have to guide the user, firstly by showing the user the legal moves available, and secondly by finding supplementary information to support these moves.

Explanation as conversation – a three player game

A better design still might be to allow the machine to carry on its dialogue as before, but to allow the user to interrupt and challenge either of the agents. It seems probable that the most interesting moves the user could make would be DOUBT, and also COUNTER-EXAMPLE, where the user could present an example case not previously known to the machine. Now the user can sit back and watch, if the conversation brings out points which seem relevant; but equally, the user can intervene to steer the conversation.

These ideas have, needless to say, yet to be implemented.

1‘Rational’, here, is of course a fix. In an explanation situation involving two human beings, the explainee might continue to resist even if there is no rational reason for doing so. This situation would be non-deterministic, though, and too difficult for me to deal with.

2This is output from Wildwood version Arden, my experimental prototype object based inference mechanism. The game-playing model is different from (a predecessor of) the one given above.