# Philosophy, Computing, and Artificial Intelligence

PHI 319. Two Famous Experiments in Psychology.

Computational Logic and Human Thinking
Chapter 2 (38-53)

In this lecture, we consider two famous experiments in psychology. These experiments seem to show something interesting about reasoning in human beings. Note, though, that nothing directly follows about whether the logic programming/agent model is adequate. The goal in AI is to model intelligence, not necessarily human intelligence. The experiments are interesting nevertheless because human intelligence is the clearest example of intelligence.

"Reasoning about a rule"," P. C. Wason. The Quarterly Journal of Experimental Psychology, 20:3,1968, 273-281. The "Wason Selection Task" refers to an experiment Peter Wason performed in 1968.

"The subjects [in a pilot study (Wason, 1966)] were presented with the following sentence, 'if there is a vowel on one side of the card, then there is an even number on the other side,' together with four cards each of which had a letter on one side and a number on the other side. On the front of the first card appeared a vowel (P), on the front of the second a consonant (P), on the front of the third an even number (Q), and on the front of the fourth an odd number (Q). The task was to select all those cards, but only those cards, which would have to be turned over in order to discover whether the experimenter was lying in making the conditional sentence. The results of this study, and that of a replication by Hughes (1966), showed the same relative frequencies of cards selected. Nearly all subjects select P, from 60 to 75 per cent. select Q, only a minority select not-Q and hardly any select not-P. Thus two errors are committed: the consequent is fallaciously affirmed and the contrapositive is withheld. This type of task will be called henceforth the 'selection task'" (Wason 1968: 273-274). The subject is asked to make a certain selection from among presented options. This task is posed in terms of cards the subject can see. There are four cards, with letters on one side and numbers on the other. The cards are lying on a table with only one side of each card showing:

The task is to select those and only those cards that must be turned over to determine whether the following statement is true: If there is a d on one side, then there is a 3 on the other side.

Most people do far better on tasks that are formally equivalent but have more meaningful content. For example, suppose that the task is to enforce the policy that

You must be at least twenty-one years old to drink in a bar

This task is equivalent to checking cases to determine the truth of the conditional

If a person is drinking alcohol in a bar, then the person is at least twenty-one years old

Given the following description of the cases

card 1: person is drinking (alcholic) beer
card 2: person is a senior citizen
card 3: person is drinking (non-alcoholic) soda
card 4: person is a primary school child

most people know what to do. They know, for example, that given the "person is a primary school child," they must determine whether the "person is drinking alcohol in a bar."

## How to Explain the Observed Results

What is the explanation for these asymmetrical experimental results with respect to the task posed in terms of these two conditionals? If thinking is computation, and in particular if the computations in logic programming are a good model of reasoning, then one might think that subjects would be equally good at reasoning with both of these conditionals.

Why might one think this?

Because determining logical consequence is an innate part of the logic programming/agent model. It is an assumption of the model that this ability is not learned.

### A Hypothesis about Logic from Evolutionary Psychology

The evolutionary psychologist Leda Cosmides challenges this assumption for human beings.

To explain asymmetrical experimental results, she suggests that humans have evolved with a specialized algorithm to detect cheaters in social contracts. The idea is that the ability to reason about the connections between states in the world is not an instance of a single capacity. Rather, domain specific capacities develop in human beings at different ages and result in different competencies. (Further, it might be that this way of being intelligent evolved in human beings from earlier, more primitive domain specific capacities. It might be that the evolution of human intelligence was a matter of the ability to cobble together ancestral capacities, for, say, route planning, to serve novel ends such as abstract mathematical reasoning. (Many mathematicians appear to rely on something like "geometrical intuition" to guide their thinking even about mathematical questions that bear no evident resemblance to navigational plotting.))

Since cooperation has survival value from an evolutionary perspective, and since cooperation is stable as long as cheaters are detected and deterred, it might be that one domain for reasoning is what might be called the "domain of social morality." If there were such a domain specific capacity for reasoning about cheaters, maybe this explains why people do better with the "alcohol" conditional than with the "cards with numbers and letters" conditional. Evolution has given humans the intelligence that makes them good at detecting cheaters.

### Domain Specific Deduction and Logical Deduction

To understand Cosmides' hypothesis, it is necessary to consider what logic is about.

A textbook answer is that logic is about logical consequence. In reasoning, deduction is an activity in which an agent draws out implications of a set of premises. He or she reasons from premises to conclusions. Some but not all deductions are logical deductions. In logical deductions, the implications are logical consequences of the premises. In other deductions, the implications are implications but not logical consequences of the premises.

An example may help clarify the distinction between deductions and logical deductions.

In reasoning about an electrical circuit, one might reason from the premise that the switch is open to the conclusion that the lamp is off. This is a deduction, but it is not a logical deduction. The conclusion is a reasonable implication of the premise given how states are typically connected in electrical circuits, but the conclusion is not a logical consequence of the premise.

Logical deductions are deductions in accordance with rules of logic. There is controversy among philosophers about what the rules of logic are, but it is not part of our purpose to worry about this. For the sake of illustration, we take Disjunction-Introduction (∨I) and Disjunction-Elimination (∨E) as examples of such rules. These two deduction rules may be stated as follows:

 P ------- ∨I P ∨ Q Q ------- ∨I P ∨ Q [P]¹ [Q]² . . . . . . P ∨ Q C C ------------------------- ∨E, 1, 2 C

∨I says that a disjunction is a logical consequence of either of its disjuncts.

∨E is a little less straightforward. It says that given deductions of a conclusion from the disjuncts of a disjunction, the conclusion is a consequence of the disjunction. If the deductions of the conclusion are logical deductions, then the conclusion is a logical consequence of the disjunction. If the deductions of the conclusion from the disjuncts are not logical deductions, then the deduction of the conclusion from the disjunction is not a logical deduction.

### The Capacity for Logical Deduction

Now it is possible to get a little clearer on the hypothesis from evolutionary psychology.

The idea is that the capacity to deduce connections between states in some domains is something human beings naturally develop. The capacity for logical deduction, however, is not a capacity restricted to a domain. It is a capacity to draw implications in any domain. According to the hypothesis from evolutionary psychology, human beings do not naturally develop this capacity. Although it is something most human beings can learn if they put in the time and effort, it is not something they acquire naturally as they become adults, like, say, their adult teeth.

### An Alternative Explanation of the Observed Results

Robert Kowalski (in Computational Logic and Human Thinking) rejects the explanation of the results of the experiment in terms of the hypothesis from evolutionary psychology. Instead, he tries to understand the import of the Wason experiment in terms of the formula

"Natural language understanding = translation into logical form + general purpose reasoning" (Computational Logic and Human Thinking, 217).

This formula is not straightforward to understand, but the idea is that subjects in the experiment make the selections they do (not because they have not developed the capacity for logical deduction but) because they understand the conditionals according to the framework of the logic programming/agent model. This understanding is not what the experimenters expect.

We will consider Kowalski's argument in more detail in a subsequent lecture. We can see now, though, that Kowalski is trying to do something we are not. He is trying to defend the idea that the logic programming/agent model is a good model of human intelligence.

"Suppressing valid inferences with conditionals," R.M.J. Byrne. Cognition, 31, 1989, 61-83. The "Suppression Task" refers to an experiment Ruth Byrne conducted in 1989. Like the Wason Selection Task, the Suppression Task seems to show something about reasoning.

In the experiment, the subjects are asked to consider the following two statements:

If she has an essay to write, then she will study late in the library
She has an essay to write

On the basis of these two statements, most people in the experiment draw the conclusion that

She will study late in the library

If the library is open, then she will study late in the library

many people in the experiment, about 40%, "suppress" (or retract) their previous conclusion. According to classical logic, this "suppression" is a mistake. The conclusion (She will study late in the library) still follows as a logical consequence of the stated premises.

The argument has the following logical form:

1. If P, then Q      If she has an essay to write, then she will study late in the library
2. P                       She has an essay to write
3. R                       If the library is open, then she will study late in the library
----                      ----
4. Q                      She will study late in the library

Like Disjunction-Introduction and Disjunction-Elimination, Conditional-Elimination is traditional rule of logic. The conclusion is a logical consequence of premises (1) and (2). The deduction from these premises proceeds by the rule of Conditional-Elimination (→ E):

P         If P, then Q                P       PQ
------------------ → E        ------------ → E
Q                                         Q

This is what is called is sometimes called monoticity. A "logic" (set of rules for deduction) is monotonic just in case

if P1 ⊢ φ, then P1 U P2 ⊢ φ
The addition of the third premise does nothing to change this fact. It is just extra information. If a conclusion is a logical consequence of a set of premises, then it remains a logical consequence no matter how many additional premises are added to the original set of premises.

## How to Explain the Observed Results

What explains the results observed in the "Suppression Task" experiment?

### Kowalski's Explanation

Robert Kowalski suggests, again, that the subjects do not understand the sentences in the way the experimenters expect and do not reason in the way the experimenters expect.

We will consider here the part of Kowalski's solution that seems to apply to the mind of any rational agent. The more specific part of his solution we will consider in a subsequent lecture.

Kowalski suggests that the subjects in the "Suppression Task" understand the premises and the conclusion in such a way that the premises are defeasible reasons to believe the conclusion. Further, they understand the new information to defeat this reasoning.

The logic programming/agent model (as we are currently understanding it as a way to answer queries in terms of backward chaining) does not implement defeasible reasoning.

This is a problem. It does not seem likely that the reasoning in any rational agent is restricted to the reasoning in logical deductions. Certainly this does not seem true for human beings.

### Conclusive and Defeasible Reasoning

We can distinguish two kinds of reasoning: conclusive reasoning and defeasible reasoning.

In conclusive reasoning, the reasoning is the reasoning in a logical deduction. Backward chaining in the logic programming/agent model (as we are currently understanding it) provides an example. If a query is answered positively, there is a logical deduction of the query from premises taken from the KB. So we can think that the agent is reasoning from premises in the KB to the conclusion that the query is true. This reasoning is conclusive because additional beliefs in the KB do not undermine it. The conclusion remains a logical consequence.

Defeasible reasoning is much more difficult to characterize. This makes it difficult to implement this reasoning on machine. To implement it, we need to understand it.

It seems easiest to understand defeasible reasoning in the case in which the agent is reasoning from premises to a conclusion. In this case, the reasoning is defeasible if new beliefs can make it rational to retract the belief in the conclusion while at the same time retaining the belief in the premises. This might explain the experimental results in the Suppression Task.

An example of defeasible reasoning helps make this sort of reasoning a little clearer.

### An Undercutting Defeater

Suppose someone has the following beliefs:

• Ornithologists are reliable sources of information about birds
• Herbert is an ornithologist
• Herbert says that not all swans are white

Based on these premises, it is reasonable to draw the conclusion and to believe that

• Not all swans are white

The conclusion is not a logical consequence of the premises. It is possible for the conclusion to be false even if the premises are true. Even so, the conclusion is reasonable.

If, however, one were later to come to know that Herbert is incompetent, this new information would undercut the reasoning to the conclusion that not all swans are white. What the agent comes to know about Herbert defeats the premises in the above argument as a reason for him to believe that not all swans are white. In these circumstances, it is rational for the agent to keep his belief in the premises but to retract his belief in the conclusion of the argument.

This seems to be an instance of how human beings form and retract beliefs. The question is how to characterize it so that it might be implemented in its general form on a machine.

### Justification for Belief

There is another example that looks like but may not be an instance of defeasible reasoning.

Suppose that I form the belief that some object is red because it looks red. The proposition

The object is red

is not a logical consequence of the proposition

The object looks red to me.

Still, in ordinary circumstances, the object looking red makes it rational to believe it is red.

Suppose I form the belief in these circumstances but later I acquire new information. Suppose I come to know that the object is illuminated by a red light and that red lights make white objects look red. This new information does not change the way the object looks. It still looks red to me. It might even be red, but no longer is it rational for me to believe that it is red.

In this "looks red/is red" example, it is not clear that any reasoning is undercut because it is not clear that What happens, it seems, is that instead of forming the belief by reasoning, the agent has an experience (the object looking red to him) that justifies him in believing the propositional content of this experience (that the object is red).

Another way to think about this is in terms of impressions. An impression is the way things appear to the agent. So someone can have the impression that the object is red because this is how it looks to him (as opposed, say, to being told by someone that the object is red or measuring the wavelength of the reflected light). Normally when someone gets the impression that some object is red because it looks red, this experience justifies him in believing (or makes it rational for the agent to believe) that the object is red.

This justification the experience provides does not guarantee that the propositional content of the impression is true. The object might look but not be red. Further, as the "looks red/is red" example shows, this justification can be defeated. If it is, then proposition that object is red is no longer part of the agent's evidence. He can no longer use it in reasoning.
the agent forms the belief that the object is red by reasoning on the basis of the premise and belief that the object looks red. Rather, it seems that forming the belief in such circumstances is an instance of correct cognizing. It is rational for the agent to do.

It is still true that new information can defeat the agent's justification for the belief (the rationality of the agent holding the belief), but this defeat does not seem to be a matter of undercutting some reasoning in which the agent engaged to form the belief.

This example, it seems, tell us something about justification. Sometimes the justification consists in reasoning. This is what happens in the "ornithologist" example. Sometimes the justification consists in an experience. This is what happens in the "looks red/is red" example.

### An Rebutting Defeater

In addition to undercutting defeaters, there are rebutting defeaters.

Suppose that I form the belief that all A's are B's because I have seen many A's and they have all been B's. This conclusion is not a logical consequence of the premise. Still, in the absence of contrary information, the premise makes it reasonable for me to believe that all A's are B's.

Now, though, suppose I see an A that is not a B. It is still rational for me to believe that the A's I saw in the past were B's, but no longer is it rational for me to believe that all A's are B's. When I see A that is not a B, this new information rebuts my belief that all A's are B's.

Again, this seems to be an instance of how humans form and retract beliefs.

## What we have Accomplished in this Lecture

We looked at two experiments in psychology (the Selection Task and the Suppression Task) that challenge assumptions about human reason. Further, we looked at the beginnings of Robert Kowalski's responses to these two experiments. In doing this, we looked at a hypothesis from evolutionary psychology that understands the ability to deduce logical consequences as a skill that must be learned. We also looked at conclusive and defeasible reasoning.