In computing, different levels of representation have different advantages and are complementary. Low-level representations are more efficient. But high- level representations are moreflexible, easier to develop and easier to change. In the London Underground example, the low-level representation lacks the awareness, which is explicit in the high-level representation, of the goal of getting help, which is the purpose of pressing the alarm signal button. If some- thing goes wrong with the low-level representation, for example if the button doesn’t work or the driver doesn’t get help, then the passenger might not realise there is a problem. Moreover, if the environment changes, and there are new kinds of emergencies, or newer and better ways of dealing with emergencies, then it is harder to modify the low-level representation to adapt to the changes. In computing, the high-level representation is typically developedfirst, some- times not even as a program but as an analysis of the program requirements. This high-level representation is then transformed, either manually or by means of another program called a compiler, into a low-level, more efficiently executable representation.
The reverse process is also possible. Low-level programs can sometimes be decompiled into equivalent high-level programs. This is useful if the low-level program needs to be changed, perhaps because the environment has changed or because the program has developed a fault. The high-level representation can then be modified and recompiled into a new, improved, lower-level form.
However, this reverse process is not always possible. Legacy systems, devel- oped directly in low-level languages and modified over a period of many years, may not have enough structure to identify their goals precisely and to decompile them into higher-level form. But even then it may be possible to decompile them partially and to approximate them with higher-level programs. This process of rational reconstruction can help to improve the maintenance of the legacy system, even when wholesale reimplementation is not possible.
The relationship between intuitive and
deliberative thinking
This relationship between high-level and low-level programs in computing has similarities with the relationship between deliberative and intuitive thinking in people.
Compiling a high-level program into a lower-level program in computing is similar to the migration from deliberative to intuitive thinking that takes place, for example, when a person learns to use a keyboard, play a musical instrument or drive a car. In computing, compiling a high-level program or specification is normally done by reasoning in advance, before the more efficient program is implemented. But in human thinking, it is more common to collapse an explicit high-level representation into a lower-level shortcut after an extended period of repeated use. Decompiling a low-level program into a higher-level program is similar to the process of reflecting on subconscious knowledge and representing it in con- scious terms– for example, when a linguist constructs a formal grammar for a natural language. Whereas a native speaker of the language might know the grammar only tacitly and subconsciously, the linguist formulates an explicit model of the grammar consciously and deliberatively. Non-native speakers can learn the explicit grammar, and with sufficient practice eventually compile the grammar into more efficient and spontaneous form.
Conclusions
Computational Logic is a wide-spectrum language of thought, which can represent both high-level goals and beliefs, as well as low-level stimulus– response associations. An intelligent agent can use the high-level representation when time allows, and the low-level representation when time is limited. It can also use both representations simultaneously.
An agent may have inherited its stimulus–response associations at birth, and finely tuned them to its own personal experiences. If so, then it can reasonably rely upon them when new situations are similar to situations that the agent and its designer or ancestors have successfully dealt with in the past.
An intelligent agent, on the other hand, might also be able to reflect upon its behaviour and formulate an understanding of the consequences of its actions. The agent can use this higher-level understanding, to help it better achieve its fundamental goals, especially in new situations that are unlike situations that have arisen in the past.
In the more advancedChapter A5, I show how the resolution rule of inference can be used to perform not only forward and backward reasoning when they are needed in the current situation, but also similar kinds of reasoning in advance. This kind of reasoning in advance can be viewed as compiling high-level representations of goals and beliefs into more efficient, lower-level form.
The ability to combine the two levels of representation combines their individual strengths and compensates for their individual weaknesses.
Abduction
Most changes in the world pass us by without notice. Our sensory organs and perceptual apparatusfilter them out, so they do not clutter our thoughts with irrelevancies. Other changes enter our minds as observations. We reason for- ward from them to deduce their consequences, and we react to them if neces- sary. Most of these observations are routine, and our reactions are spontaneous. Many of them do not even make it into our conscious thoughts.
But some observations are not routine: the loud bang in the middle of the night, the pool of blood on the kitchenfloor, the blackbird feathers in the pie. They demand explanation. They could have been caused by unobserved events, which might have other, perhaps more serious consequences. The loud bang could be thefiring of a gun. The pool of blood could have come from the victim of the shooting. The blackbird feathers in the pie could be an inept attempt to hide the evidence.
Even routine observations can benefit from explanation: Why do the Sun, the Moon and the stars rise in the East and set in the West? Why does the door stick? Why do the apples drop before they are ready to eat? Explaining routine observations helps us to discover new connections between otherwise unrelated phenomena, predict the future and reconstruct the past.
An agent might explain its observations by using its existing beliefs or by using new hypothetical beliefs. Both kinds of explanation deductively imply the observations, because if the explanations are true, then the observations are true. Forward reasoning is a natural way to justify explanations after they have been found, but backward reasoning is normally a much better way of actually finding them. As Sherlock Holmes explained to Dr. Watson, in A Study in Scarlet:
“I have already explained to you that what is out of the common is usually a guide rather than a hindrance. In solving a problem of this sort, the grand thing is to be able to reason backward. That is a very useful accomplishment, and a very easy one,
but people do not practise it much. In the everyday affairs of life it is more useful to reason forward, and so the other comes to be neglected. There arefifty who can reason synthetically for one who can reason analytically.”
“I confess,” said I, “that I do not quite follow you.”
“I hardly expected that you would. Let me see if I can make it clearer. Most people, if you describe a train of events to them, will tell you what the result would be. They can put those events together in their minds, and argue from them that something will come to pass. There are few people, however, who, if you told them a result, would be able to evolve from their own inner consciousness what the steps were which led up to that result. This power is what I mean when I talk of reasoning backward, or analytically.”
Backward reasoning can be used to find explanations, whether the resulting explanations use existing beliefs or generate new hypothetical beliefs. Forward reasoning, in contrast, makes sense only when deducing consequences from existing beliefs or hypotheses. To use forward reasoning to explain an obser- vation, you have to make a guess in the dark, generate a hypothesis, and then check whether or not the hypothesis has any relevance to the observation. With backward reasoning, the hypothesis is generated automatically and guaranteed to be relevant.
But the main problem with explaining an observation is, not so much the problem of generating relevant explanations, but the problem of deciding which is the best explanation, given that there can be many alternative, candidate explanations for the same observation. We will see later that the problem of determining the best explanation is similar to the problem of determining the best plan for achieving a goal.
Hypothetical beliefs come in two forms: in the form of general rules (or conditionals) and in the form of specific facts. Hypotheses in the form of general rules represent connections between several observations; and the process of generating hypotheses in the form of rules is known as induction. Generating hypotheses by induction is hard, and includes the case of generating a scientific theory, like the laws of celestial motion. We shall return to the problem of induction briefly in the concluding chapter of this book.
Hypotheses in the form of facts, on the other hand, represent possible underlying causes of observations; and the process of generating them is known as abduction. Typically, a hypothesis generated by abduction is trig- gered by the desire to explain one or more particular observations. The more observations the hypothesis explains, the better the explanation. Similarly, in deciding between different plans of action, the more goals a plan achieves, the better.
Abduction is possible only for an agent who has an open mind and is willing to entertain alternative hypotheses. It is not possible for a close-minded agent,
who thinks he knows it all. The simplest way to have an open mind, but to keep the candidate hypotheses within manageable bounds, is to restrict them to open predicates, to which selective closed-world assumptions and negation as failure do not apply.
The term abduction was introduced by the logician Charles Sanders Peirce (1931). He illustrated the difference between deduction, induction and abduc- tion with the following example:
Deduction: All the beans from this bag are white. These beans are from this bag: Therefore These beans are white. Induction: These beans are from this bag.
These beans are white.
Therefore All the beans from this bag are white. Abduction: All the beans from this bag are white.
These beans are white.
Therefore These beans are from this bag.
Generating abductive hypotheses and deciding between them includes the classic case in which Sherlock Holmes solves a crime byfirst identifying all the hypothetical suspects and then eliminating them one by one, until only one suspect remains. To put it in his own words (from The Adventure of the Beryl Coronet): “It is an old maxim of mine that when you have excluded the impossible, whatever remains, however improbably, must be the truth.”
Sherlock Holmes described his reasoning technique as deduction. But deduction in logic leads from known facts or observations to inescapable conclusions. If the beliefs used to deduce the conclusions are true, then the conclusions must also be true. Abduction, on the other hand, can lead from true observations and other beliefs to false hypotheses. For this reason, abductive inference is said to be fallible or defeasible. We will see inChapter 15that the distinction between deduction and abduction is blurred when conditionals are interpreted as biconditionals in disguise.