The Wason Selection Task Revisited
Computational Logic and Human Thinking, 16
The Wason Selection Task was an experiment that seemed to some to show that human beings are terrible at logic and hence that logic is not a promising platform for artificial intelligence. Humans are the primary examples of the intelligence that characterizes a rational agent. So if they are terrible at logic, their intelligence must have another basis.
Kowlaski's Explanation of the Experimental Results
According to Kowalski, this interpretation of the experimental result stems from the failure to appreciate that
natural language understanding = translation into logical form + general purpose reasoning
The experiment, as it is usually understood, assumes that the sentence in the task is a material conditional (φ → ψ). However, the way the subjects respond in the experiment suggests that they do not understand the sentence this way. The subjects do not translate into logical form in the way the experiment expects.
For Kowalski's response to the Wason Selection Task to be successful, he needs to explain the observed results in which the subjects appear to reason with respect to the conditional. In addition, he needs to explain why subjects appear to reason "correctly" with respect to conditionals with more meaningful content.
Translation into Logical Form
In the logic programming/agent model, according to Kowalski, the agent's response depends on whether the conditional is understood as a goal or a belief. The distinction is in function, not form. So, in classical logic, there is no distinction between goals and beliefs. The experimenters expect only two responses
modus ponens: from observation φ ("d"), check for ψ ("3") on the other side
modus tollens: from observation ¬ψ ("7), check for ¬φ ("something other than "d") on the other side
Most people correctly perform modus ponens, but they fail to perform modus tollens. In addition, they affirm the consequent (which is a mistake from the point of view of classical logic):
affirm the consequent: from observation ψ ("3"), check for φ ("d") on the other side
Kowalski tries to explain these results in terms of the translation into logical form in the logic/programming agent model.
Reading Conditionals as Biconditionals
In the logic programming/agent model, it is natural to think of beliefs with the same head as biconditionals. Suppose, for example, that the agent believes there are two ways for the grass to be wet
The grass is wet if the sprinkler
The grass is wet if it rained
According to classical logic, it does not follow that
The grass is wet if, and only if, the sprinkler was on or it rained
From classical logic, all that follows is
The grass is wet if the sprinkler was on or it rained
Yet,since the agent knows of no other way for the grass to be wet, it is natural for him to treat the two beliefs as the biconditional.
Moreover, the same is true of the subjects in the Wason Selection Task: it is natural for them to treat
There is a "3" on the other side if there is a "d" on one side
as a biconditional. This helps explain why many people in the experiment affirm the consequent: they naturally interpret the sentence as a belief and hence in problem solving treats it as a biconditional.
Reading Conditionals as Maintenance Goals
According to Kowalski, the logic programming/agent model also explains why subjects do better with "meaningful" conditionals, such as
If a person is drinking in a bar, then the person is at least twenty-one years of old
This sentence is naturally interpreted along the lines of a maintenance goal.
This explains why subjects perform modus tollens with these "meaningful" conditionals. If the agent observes an underage person, the agent will need to make sure the antecedent fails. So he will attempt to observe whether the person is drinking. If the person is drinking, then the rule the agent is trying to enforce is violated.
The observation of the truth of the consequent of the rule the agent is trying to enforce does not trigger reasoning. This helps explains why the subjects do not affirm the consequent.
Deriving a Negative Conclusion is Difficult
Kowalski must also explain why only a minority of subjects realize that it is necessary to turn over the card showing "7" to make sure that "d" is not on the other side. What the subjects observe is
the fourth card has the number 7 on the number side.
From this observation, in order to perform modus tollens with the belief
if a card X has letter d on the letter side, then the card X has number 3 on the number side
the subject must derive the negative conclusion
it is not the case that the fourth card has number 3 on the number side
In the logic programming/agent model, the only way to introduce a negative conclusion is to reason to failure. So the agent must identify the right negative statement to test. The observation
the fourth card has the number 7 on the number side
provides no clear indication of the right negative statement to test for failure. For this reason, agents have trouble moving from the observation to the right negative statement.
Kowalski says that this helps explain why the subjects in the experiment fail to perform modus tollens.