1. Reasoning with Stored Knowledge

In chapter 3 we drew a distinction between two views of artificial intelligence: a performance model, concerned with reproducing the superficial aspects of human-like behaviour, and an internal representation model, covering most serious work in AI, which is concerned with representing knowledge that underlies and gives rise to overt behaviour. In the present chapter we are going to discuss the semantic network (sometimes also called an associative network) as a means of reasoning about such stored knowledge.

Coming upon the word 'reasoning' in a book such as this, it is all too tempting to leap to premature conclusions about what is involved. In particular, you should note that deductive reasoning, whatever Aristotle and Sherlock Holmes may have thought of it, may not always be the most appropriate form of reasoning for the task in hand. Therefore, before we look in detail at semantic nets, we shall briefly and informally say something about how human beings reason. For a much more thorough treatment of human reasoning, you might look at, for example, chapter 10 of John Anderson's Cognitive Psychology and Its Implications.

In fact, there is no single uniform way in which humans reason. In differing circumstances, given different sets of known facts and goals, we use different tactics to reach solutions to our problems: we generalize, we explain, we deduce, we visualize, and so on. Although some reasoning strategies may not in fact be logically sound, they may in some circumstances be better than logic in getting us to the answers we need. Let us consider some concrete problems and how we go about solving them.

In the first place, we like to think that we live in a reassuringly orderly and predictable world. Indeed, it is only because it is in the main orderly and predictable that we are able to navigate our way through each day without too much conscious effort. Our behaviour and our perceptions, then, are largely based on expectation: on the one hand, we have learned concepts and can recognize further instances of them; on the other hand, we expect all further instances to be much like the ones we have experienced before. If we know that this is a dog, or this is a picnic, or that is a handshake, it is because we have seen innumerable instances of the same thing before: it is another one of the same, and we expect this dog to be much like any other dog, this picnic to happen much like any other, that handshake to have the same social function as any other handshake. This form of reasoning is called induction (or more familiarly a type of 'learning') and is typical of the kind of reasoning we do in our everyday lives, from childhood on, in extending and refining our knowledge about the world. It is in just such a way, in fact, that, according to Schank and Abelson (1977, chapter 9), we acquire those scripts for understanding everyday situations -- like picnics -- that we mentioned in section 3.3.4. above. The typical form that inductive reasoning takes is:

   if P is true of a,
   and P is true of b,
   and P is true of c,>
   and ... P is true of n,
   then infer that P is true of all other entities
           of the same kind as a, b, c, ... n

So if, in the course of our lives, every swan we see is white, we might inductively infer that all swans are white. In this case, it is not a totally reliable form of inference, as the discovery in Australia of black swans showed to a seventeenth-century Europe used to seeing only white swans.

Inductive reasoning provides an account of how we are able to make generalizations and therefore how we recognize new objects or interpret the social acts of others, but it does not account for other types of inference we may use in the course of our everyday lives. Suppose I know that every time Bill has an argument with his wife he goes out to a bar and gets drunk. If I then meet Bill reeling drunkenly in the street I may assume that "Bill's been arguing with his wife again". I may be right, but not necessarily so: he may have been out drinking for some wholly different reason. What I am doing is reasoning back from a state of affairs that I can perceive to a state or action that could plausibly have produced it. This second kind of inference is an instance of abduction and, like induction, is not a reliable form of inference, though often both useful and necessary in our everyday lives, where we more commonly think of it as a form of 'explanation'. Its form is:

   if b (normally) follows from a,
   and b is known to be true,
   then infer a to be true

Though abductive reasoning is, strictly speaking, not logical reasoning, it is often both an extremely useful and a highly plausible form of inference. As in the case of Bill's drunkenness, it provides a mechanism for understanding people's behaviour and analyzing the motives for their actions. Perhaps surprisingly, it is also frequently used in solving professional problems by experts in engineering, medicine, and other skilled professions. For example, a doctor knows that someone suffering from, say, influenza would have a temperature, an inflamed throat, muscular pain, and so on. The patient the doctor is examining has all of these symptoms; therefore the doctor has reason to suspect that the patient may be suffering from a bout of 'flu. We shall look at this kind of reasoning in more detail in chapter 7.

Suppose now I were to ask the question "Is Moscow north or south of New York?" or "Are there more white notes lying between the nearest black note to C on the piano keyboard and between the nearest black note to F above it, or between F and the nearest black note to B above it?" You would probably begin by visualizing a map of the world or a piano keyboard and then, in the first case, working out which city is to the north and, in the second, counting off the white notes. In both instances you would be reasoning with visual or spatial rather than with logical representations of the problem. You might, in each case, come up with perfectly good answers, though the answers would not have been arrived at by logical inference. (There is a very rich literature on spatial inferencing; you might like to look at Anderson, 1990, chapter 4, for a resumé of some recent research into visual and spatial reasoning.)

You may already have encountered deductive reasoning in the form of the classical Aristotelian syllogism, typically of the form:

   All Xs are Ys
   A is an X
   Therefore A is also a Y

You can no doubt intuitively recognize the validity of the following syllogism,

   Premise 1:   All canaries are birds
   Premise 2:   Tweetie is a canary
   Conclusion:  Therefore Tweetie is a bird

as perhaps you can of

   Premise 1:   No one who is lazy is rich.
   Premise 2:   Desmond isn't rich.
   Conclusion:  Therefore Desmond is lazy.

In the second example, you may be surprised to know that, even though you may intuitively feel, as for the first syllogism, the conclusion to be true, it does not follow logically from the premises. It is a curious fact about human reasoning that we tend to believe valid -- even though they may not be -- those conclusions which are consonant with our taken-for-granted assumptions about the world, while rejecting -- even though they may be logically valid -- those conclusions of which we disapprove. Of course, much of our everyday reasoning is deductive -- if the kettle whistles, the water has boiled; the kettle is whistling now, therefore the water has boiled -- but we are seldom explicitly aware of it. Our second syllogism, on the other hand, points up the complexity of actual human reasoning, and the error of assuming that we can model human inferencing strategies purely on logic.