Cognitive Processes in Prepositional Reasoning

ed in Proof 3 and that ANDS reproduced in the earlier example. However, the comparison between the subject's proof and ANDS's proof of the same theorem also points up a number of dissimilarities. The first of these is that some of the subject's statements never appear in ANDS's assertion or subgoal trees. This is true, for example, of the sentence in Line c of Table 3 ("if. . . there is an M and a P, there will always be an R"), of the statement in the first half of Line e, and of the very similar one in Line j ("Anytime you see both the letters M and P on a blackboard, then you can be sure that there is no R"). What makes these statements initially puzzling is that they are of the form IF p, q and IF p, NOT q, and it is somewhat unlikely that the subject believed both of these sentences to be true at the same time. But because the first of them is never repeated in the proof, it can plausibly be considered a slip of the tongue or a temporary misunderstanding of the premise, which is later abandoned in favor of the second type of sentence. The factors responsible for this error are unclear, and ANDS makes no attempt to duplicate it. Lines e and j by themselves are easier to understand. These sentences are the inverse of the original premise; that is, from If not (M and P) then R the subject has inferred If M and P then not R. This inference is not valid on most formal interpretations of IF and cannot be deduced from the rules in Table 2. Nevertheless, the inverse does follow if the premise is understood as a biconditional—Not (M and P) if and only if R—as might be appropriate in certain contexts (Fillenbaum, 1977; Geis & Zwicky, 1971). For sentences of the type used here, a substantial minority of subjects accepts the inverse as valid on the basis of a premise conditional (Pollard & Evans, 1980). This behavior could be simulated by providing ANDS with the corresponding deduction rule (see the section on Extensions below), though for the present ANDS sticks to the classical interpretation of IF. Note that such a rule would have to work in a forward direction to account for the protocol, because the inverse does not seem to be motivated by any obvious subgoal. Indeed, the inverse plays no direct role in the proof at all, if this analysis of the subject's reasoning is correct.