Quarterly Journal of Experimental Psychology

A good deal of energy is currently being expended into discovering the fundamental machinery underlying deductive reasoning. Is it based upon mental models (arrays) or deduction rules (propositions)? The appeal of finding a “grand unified theory” of reasoning is obvious, but the likelihood of achieving this must also be considered.

This paper discusses the use of experimental psychology in attempts to discover the processes associated with the fundamental reasoning mechanism. One particular problem is that individuals can use different strategies to solve reasoning problems. The consequences of this are assessed in relation to: (1) the assumptions underlying the experiments, (2) the choice of tasks and task presentations intended to enable the fundamental reasoning processes to be viewed directly, and (3) the power status of the theories and the nature of the evidence required to show that either theory is superior. Under close scrutiny the debate appears to be unresolvable by using empirical techniques. However, although the main conclusions are negative, it is suggested that approaches that directly investigate individual differences are likely to be useful alternatives.

The present study examined performance on Wason's four-card abstract selection task. Baseline performance is very poor, usually less than 10% correct; and this task has a long record of resistance to facilitation. It was hypothesized that the two primary sources of difficulty are selective encoding of the problem information and the lack of satisfactory analytic processing. Three experiments were conducted to test this hypothesis. In Experiment 1, performance was improved by explicating the implication rule. The majority of subjects, however, still failed to make the correct selection. Subjects were required in Experiment 2 to provide reasons for their selection or non-selection of each of the cards. This response procedure, paired with an explicated rule, led to further improvements in performance (over 50% correct selections). In Experiment 3, the influence of the type of selection instruction (true-false vs. violation) was examined. Paired with an explicated rule and the reasons response format, violation instructions led to one of the highest correct selection rates ever observed for any version of the selection task: over 80% correct. Because of the importance of this result, it was replicated twice. The results of these three experiments are discussed in terms of Johnson-Laird and Byrne's mental models theory and Evans's two-stage model of reasoning.

Cheng and Holyoak (1985) proposed that realistic reasoning in deontic contexts is based on pragmatic schemas such as those for assessing compliance with or violation of permission and obligation rules, and that the evocation of these schemas can facilitate performance in Wason's (1966) selection task. The inferential rules in such schemas are intermediate in generality between the content-independent rules proposed by logicians and specific cases stored in memory. In one test of their theory, Cheng and Holyoak demonstrated that facilitation could be obtained even for an abstract permission rule that is devoid of concrete thematic content. Jackson and Griggs (1990) argued on the basis of several experiments that such facilitation is not due to evocation of a permission schema, but, rather, results from a combination of presentation factors: the presence of explicit negatives in the statement of cases and the presence of a violation-checking context. Their conclusion calls into question both the generality of content effects in reasoning and the explanation of these effects. We note that Jackson and Griggs did not test whether the same combination of presentation factors would produce facilitation for an arbitrary rule that does not involve deontic concepts, as their proposal would predict. The present study tested this prediction. Moreover, we extended Jackson and Griggs’ comparisons between performance with an abstract permission rule versus an arbitrary rule, introducing clarifications in the statement of each. No facilitation was observed for an arbitrary rule even when explicit negatives and a violation-checking context were used, whereas strong facilitation was found for the abstract permission rule under the same conditions. Performance on the arbitrary rule was not improved even when the instructions indicated that the rule was conditional rather than biconditional. In contrast, a small but reliable degree of facilitation was obtained for the abstract permission rule, with violation-checking content even in the absence of explicit negatives. The theory of pragmatic reasoning schemas can account for both the present findings and those reported by Jackson and Griggs.

Cheng and Holyoak's abstract permission schema version of Wason's selection task and the standard abstract version of the task were examined in two experiments, each a factorial design with type of problem (permission vs. standard), presence or absence of a checking context, explicit or implicit negatives on the not-p and not-q cards, and presence or absence of a rule clarification statement as factors. The original permission problem violation-type instruction was employed in Experiment 1, and Margolis's not-p and not-q violation instruction (Griggs & Jackson, 1990) was used in Experiment 2. Subjects were 640 university undergraduates, with each subject solving only one problem. The major findings for permission tasks were: (1) facilitation for the abstract permission version was replicated but found to be dependent upon the presence of explicit negatives on the not-p and not-q cards; and (2) this facilitation was enhanced by the Margolis not-p and not-q instruction. Per Girotto, Mazzocco, and Cherubini (1992), these findings and the observed error patterns are consistent with pragmatic schema theory. The major findings for the standard version of the task were: (1) none of the factors significantly impacted proportion correct [performance was poor, ≤10% correct in 15 of 16 conditions] and (2) the number of not-p & not-q incorrect selections was increased significantly for the not-p and not-q instruction. These results are discussed in terms of Manktelow and Over's argument that the standard abstract task and the permission schema version are actually different problems.

Two experiments are reported which compare conditional reasoning with three types of rule. These consist of two types of rule that have been widely studied previously, if p then q and p only if q, together with a third type, q if p. In both experiments, the p only if q type of rule yields a different pattern of performance from the two other types of rule. Experiment 1 is an abstract rule-evaluation task and demonstrates differential effects of temporal order and of suppositional bias. Experiment 2 investigates rule generation, rephrasing, and comparison, and demonstrates differential effects of temporal order and of thematic content. An analysis of the results is offered in terms of biases and mental models. Effects of rule form and context can be explained as reflecting the different sequences in which mental models are created for each rule form. However, it is necessary to consider the internal structure of individual mental models to account for effects arising from temporal ordering of rules.

Little is known about the role of working memory in conditional reasoning. This paper reports three experiments that examine the contributions of the visuo-spatial scratch pad (VSSP), the articulatory loop, and the central executive components of Baddeley and Hitch's (1974) model of working memory to conditional reasoning. The first experiment employs a spatial memory task that is presented concurrently with two putative spatial interference tasks (tapping and tracking), articulatory suppression, and a verbal memory load. Only the tracking and memory load impaired performance, suggesting that these tap the VSSP and central executive, respectively. Having established the potency of these interference tasks two further experiments examined the effects of tapping and tracking (Experiment 2) and articulation and memory load (Experiment 3) on a conditional reasoning task. Neither tracking nor tapping affected the number of inferences accepted or response latency. Articulation also failed to affect conditional reasoning but memory load selectively reduced acceptance of modus tollens inferences. These results are discussed in terms of both rule-based and mental models theories of reasoning. While these data cannot discriminate between the two perspectives they provide support for one of the central assumptions in each: that some errors in reasoning are attributable directly to working memory demands. Taken together these experiments suggest that conditional reasoning requires an abstract working memory medium for representation; it does not require either the VSSP or the articulatory loop. It is concluded that the central executive provides the necessary substrate.

It was hypothesized that subjects misrepresent the THOG problem by confusing data and hypotheses. An abstract version of the problem in which the given exemplars and the hypothetical ones were designated by two different labels was used in three experiments. Experiment 1 showed that this version elicits a better performance than the standard version of the problem. Experiments 2 and 3 confirmed these results, by ruling out a possible alternative account of the facilitatory effect obtained in Experiment 1. The present results are discussed in relationship to the general issues of content effects and non-consequentialism in reasoning.

Subjects participating in Wason's rule discovery task (1960) overwhelmingly try to confirm rather than refute their currently held hypothesis. Such a strategy is often inadequate and runs counter to the canons of scientific methodology. The present study was designed to investigate subjects’ differential evaluation of test strategies and outcome. One-hundred and sixty students participated in two experiments in which they had to judge someone else's potential test items in Wason's task. Experiment 1 demonstrated that exposure to various histories has a mediating effect on the strength of the confirmation bias. In Experiment 2, subjects knew the researcher's rule and thus whether each proposed test item would lead to confirmation or refutation of the hypothesis under consideration. The preferred items were those that alerted the subject to an incorrect hypothesis (refutation) and those that turned out to be positive instances of the rule sought after, with the combination of the two (a negative test leading to refutation) being most highly evaluated.

A well-documented characteristic of rule discovery behaviour is subjects’ infrequent use of negative testing. Previous attempts at increasing the use of negative testing have met with little success. In an evaluation task, we found that subjects appreciate the benefits of negative testing and disconfirmation (Kareev & Halberstadt, this issue). Further, when given the choice, subjects prefer to begin their inquiry by employing a reception mode of inquiry, and only later switch to a generative strategy (Halberstadt & Kareev, 1992). In the present study we had subjects solve two rule-discovery problems. For the training problem, 180 subjects were assigned either to the traditional generation mode, in which subjects had to generate number triplets, or to a reception mode, in which subjects were presented with number triplets by the experimenter. For the subsequent test problem both groups used the traditional generation mode. Results revealed that subjects trained by the reception mode were more likely to use non-positive tests and more likely to solve the second problem. Apparently, training under the less demanding reception mode enabled subjects to realize the potential relevance of nonpositive testing.

An intriguing finding in the hypothesis-testing literature concerns a large increase in the proportion of subjects who discover a rule when they are asked to determine two rules rather than that rule alone. This finding is based on Wason's (1960) “2 4 6” task, in which subjects try to discover a rule (ascending numbers) by generating and testing number triples. They are initially given an example (“2, 4, 6”) of the rule that leads to overly specific hypotheses. With single-goal (SG) instructions, subjects try to discover the correct rule and are told whether each triple proposed fits the rule. With dual-goal (DG) instructions, correct and incorrect categories are labelled, respectively, as DAX and MED. Subjects try to discover both rules and are told whether each proposed triple is DAX or MED. Two explanations of why DG subjects do better at rule discovery than SG subjects are tested: the quantity of information and the testing of complementary rules using the prevalent positive-test strategy. Results support the latter explanation: DG subjects outperform SG subjects only if they know the rules are complementary, and that SG subjects’ performance does not improve when required to test more triples before announcing their first rule. A third explanation, the positivity of the linguistic label of the feedback, is ruled out. Understanding the superiority of DG instructions might suggest a general method for enhancing rule discovery.

People routinely focus on one hypothesis and avoid consideration of alternative hypotheses on problems requiring decisions between possible states of the world–-for example, on the “pseudodiagnosticity” task (Doherty, Mynatt, Tweney, & Schiavo, 1979). In order to account for behaviour on such “inference” problems, it is proposed that people can hold in working memory, and operate upon, but one alternative at a time, and that they have a bias to test the hypothesis they think true. In addition to being an ex post facto explanation of data selection in inference tasks, this conceptualization predicts that there are situations in which people will consider alternatives. These are:

1. “action” problems, where the alternatives are possible courses of action;

2. “inference” problems, in which evidence favours an alternative hypothesis.

Experiment 1 tested the first prediction. Subjects were given action or inference problems, each with two alternatives and two items of data relevant to each alternative. They received probabilistic information about the relation between one datum and one alternative and picked one value from among the other three possible pairs of such relations. Two findings emerged; (1) a strong tendency to select information about only one alternative with inferences; and (2) a strong tendency, compared to inferences, to select information about both alternatives with actions.

Experiment 2 tested the second prediction. It was predicted that data suggesting that one alternative was incorrect would lead many subjects to consider, and select information about, the other alternative. For actions, it was predicted that this manipulation would have no effect. Again the data were as predicted.

Previous work has shown that people use anchor-and-adjust heuristics to forecast future data points from previous ones in the same series. We report three experiments that show that they use different versions of this heuristic for different types of series. To forecast an untrended series, our subjects always took a weighted average of the long-term mean of the series and the last data point. In contrast, the way that they forecast a trended series depended on the serial dependences in it. When these were low, people forecast by adding a proportion of the last difference in the series to the last data point. When stronger serial dependences made this difference less similar to the next one, they used a version of the averaging heuristic that they employed for untrended series. This could take serial dependences into account and included a separate component for trend. These results suggest that people use a form of the heuristic that is well adapted to the nature of the series that they are forecasting. However, we also found that the size of their adjustments tended to be suboptimal. They overestimated the degree of serial dependence in the data but underestimated trends. This biased their forecasts.