The Psychology of Logic. Two Experimental Challenges to the Logic Programming/Agent Model of Intelligence
Computational Logic and Human Thinking, 2
The First Experimental Challenge: the Wason Selection Task
The Wason Selection Task refers to an experiment in psychology that Peter Wason performed in 1968.
In the experiment, the subject is given a "task" to perform. The task is 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
*** MAKE THE SELECTION YOURSELF BEFORE YOU LOOK AT THE ANSWER THE EXPERIMENTERS EXPECTED*** [Hover here to see the answer] The experimenters expect the subjects to select the first and fourth cards. To determine whether the statement is true, selecting these cards is the response classical logic dictates when the sentence is interpreted as having the logical form of a material conditional, φ → ψ. (If the other side of the first card shows something other than a "3," the statement is false. If the other side of the fourth card shows a "d," then the statement is false. For the second and third card, the statement is true no matter what the other side of the card shows.)
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 rule 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 to consider
A, a person is drinking (alcholic)
B, the person is a senior citizen
C, a person is drinking (non-alcoholic) soda
D, the person is a primary school child
most people know to check both A and D. So, e.g., if the "card" is A, it must be turned because if the person is not at least twenty-one years old, the rule has been violated.
How to Explain the Observed Results in the Wason Selection Task
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.
A Hypothesis about Logic from Evolutionary Psychology
The evolutionary psychologist
Leda Cosmides suggests that humans have evolved with a
specialized algorithm to
detect cheaters in social contracts. The idea is that the
ability to reason about consequence is not an instance of a single
capacity. Rather, there are domain specific
capacities to reason about consequence. These 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 is beneficial for the survival of human beings 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 about consequence is what might be called the "domain of social morality." If there were such a domain specific capacity for reasoning about consequence, maybe this explains why people do better with the "alcohol" conditional than with the "card" conditional. Evolution has given humans the intelligence that makes them good at detecting cheaters.
Domain Specific Consequence and Logical Consequence
To understand the import of Cosmides' hypothesis, it is necessary to get straight on what logic is. A textbook answer is that there are a variety of consequence relations and that logic is about logical consequence. In reasoning, deduction is the activity in which an agent draws out the implications of a set of premises. Some deductions are logical deductions. In logical deductions, the implications are logical consequences of the premises. In deductions that are not logical 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 the context of reasoning about electrical circuits, one might reason from the premise that the switch is open to the conclusion that the lamp is not on. This reasoning is a perfectly good deduction, but it is not a logical deduction. Given the relation of consequence and incompatibility in the context of electrical possibility, the conclusion follows. In the context of logical possibility, however, the conclusion does not follow. The conclusion is not a logical consequence of the premise.
The logical deductions are deductions according to laws (the laws of logic) that hold for all consequence relations, not just consequences in the theory of electrical circuits. There is dispute among philosophers about what the laws of logic are. For the sake illustration, we assume that Disjunction-introduction (∨I) and disjunction-elimination (∨E) are logical laws:
P ------- ∨I P ∨ Q
Q ------- ∨I P ∨ Q
[P]¹ [Q]² . . . . . . P ∨ Q R R ----------------------------- ∨E, 1, 2 R
Disjunction-introduction says that a disjunction is a logical consequence of either of its disjuncts. Disjunction-elimination is a little less straightforward, since it is stated in terms of deductions. It says that given logical deductions of a conclusion from each of the disjuncts of a disjunction, the conclusion is a logical consequence of the disjunction.
The Capacity to Recognize Logical Consequence
Now it is possible to get a little clearer on the hypothesis about logic from evolutionary psychology. The idea is that human beings naturally develop the capacity to recognize consequence and incompatibility in certain contexts or domains, such as "domain of social morality." The capacity for logical deduction itself, however, is not something human beings naturally develop. In this, it is unlike the way children natural acquire adult teeth. It is something most human beings can learn if they put in the time and effort, but it is not something they acquire naturally as they mature.
Just why, according to evolutionary psychology, we do not naturally develop the capacity for logical deduction is not immediately clear.
The capacity can be useful. Consider again the electrical circuit example. Suppose someone does not know whether the switch is open or closed but knows it is one or the other, reasons from the assumption it is open to the conclusion that the lamp is not on, and reasons from the assumption that it is closed to this same conclusion. Given that he has capacity for logical deduction, he can use or-elimination (∨E) to create a new deduction from the premise that either the switch is open or closed to the conclusion that the lamp is not on.
Nor is it immediately clear why we would develop sophisticated capacity to recognize consequence in one domain but not have this develop into general purpose capacity to recognize consequence. The hypothesized capacity in the "domain of social morality" appears very sophisticated and to approach or to be the capacity to recognize logical consequence in that domain. Given that a general purpose capacity to recognize logical consequence in more than one "domain" would be useful, it is not obvious why such a capacity does not develop.
An Alternative Explanation of the Observed Results
Robert Kowalksi (the author of CLHT) 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" (198).
Kowalski's formula is not straightforward to understand, but the rough idea that subjects in the experiment go wrong not because they lack the capacity for logical deduction but because they understand the conditionals according to the programming/agent model framework. We will consider Kowalski's argument later in the course once we state the programming/agent model framework in more detail.
The Second Experimental Challenge: The Suppression Task
The Suppression Task is 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
However, given the additional information
If the library is open, then she will study late in the library
many people in the experiment, about 40%, "suppress" (or retract) their earlier conclusion. According to classical logic, however, this "suppression" is a mistake. The conclusion (She will study late in the library) still follows from the stated premises. The argument has the following logical form:
If P, then Q | If she has an essay to write, then she will study late in the library P | She has an essay to write R | If the library is open, then she will study late in the library ===== | ===== Q | She will study late in the library
The conclusion is a logical consequent of the first two premises. The deduction proceeds by the rule of conditional-elimination:
If P, then Q P --------------------- conditional-elimination (→ E) Q
The addition of the third premise does nothing to change this fact. It is just extra information.
How to Explain the Observed Result in the Experiment
What explains the results observed in the experiment?
Robert Kowalski (the author of CLHT) suggests 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 Kowalski's solution in more detail later, but part of his idea seems to be that the reasoning in which the subjects engage in the Suppression Task is defeasible reasoning, not conclusive reasoning. The logic programming/agent model, as it is currently understood as a way to answer queries in terms of backward chaining, does not implement defeasible reasoning. Kowalski, in his response to the Suppression Task, suggests a way to supplement the logic programming/agent model so that it implements both conclusive and defeasible reasoning.
Conclusive and Defeasible Reasoning
Conclusive and defeasible reasons stand in different relations to their conclusions.
Conclusive reasons are reasons to believe because there is a logical deduction from the reason to the belief. In logic programming, backward chaining (as we are currently understanding it) may be understood as an example of conclusive reasoning. If a query is answered positively, there is a logical deduction from the entries in the KB to the query.
Defeasible reasons are more difficult to characterize. They are reasons to believe, but not because there is a logical deduction from the reason to the belief. This means that if some premises are defeasible reasons for some conclusion, new information can make it rational to retract belief in the conclusion while at the same time retaining belief in the premises.
Examples help to clarify the way defeasible reasoning is supposed to work.
Suppose that I form the belief that some object is red because it looks red. The conclusion "The object is red" is not a logical consequence of the premise "The object looks red." There is no logical deduction from this premise to this conclusion, but in the absence of information to the contrary, it is reasonable for me to believe the conclusion. Now suppose that 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. The object might even be red, but no longer is it rational for me to believe that it is red. The new information undercuts my belief that the object is red.
Suppose that I form the belief that all A's are B's because I have seen many A's in the past and they all have been B's. This conclusion is not a logical consequence of the premise. Still, in the absence of contrary information, it is defeasibly reasonable for me to believe that all A's are B's. Now, though, suppose I acquire new information. Suppose I see an A that is not a B. I still believe that the many A's I saw previously are B's, but it is no longer be rational for me to believe that all A's are B's. The new information rebuts my belief that all A's are B's.
Defeasible reasoning appears to be very common in
ordinary, everyday life. So for the logic programming/agent
model framework to be of much use in modeling the intelligence of a rational agent,
it seems that it must be able to model this kind of reasoning. As we are currently
understanding the framework, it is not
capable of modeling defeasible reasoning.