Mental representation and hypothetico-deductive reasoning: The case of the THOG problem

Summary This article reports three experiments that deal with the source of the difficulty of Wason's (1977) THOG problem. The solution of this problem demands both the postulation of hypotheses and a combinatorial analysis of their consequences. Experiment 1 showed that the generation of the hypotheses is not in itself sufficient to solve the problem. Experiment 2 showed that a version presenting a plausible context for separating the level of data from that of hypotheses produced a better performance than both the original abstract version and a thematic version lacking the plausible context separating the levels. Experiment 3 gave evidence that this context can produce facilitation even with the geometric material of the classic version. This experiment also showed that a pictorial presentation of data and a verbal presentation of hypotheses affect performance negatively. The results demonstrate the role of problem representation in problem solving, and, in particular, the role of homogeneity in representing data and hypotheses in hypothetico-deductive reasoning.     

No interpretation without representation: the role of domain-specific representations and inferences in the Wason selection task

The Wason selection task is a tool used to study reasoning about conditional rules. Performance on this task changes systematically when one varies its content, and these content effects have been used to argue that the human cognitive architecture contains a number of domain-specific representation and inference systems, such as social contract algorithms and hazard management systems. Recently, however, Sperber, Cara & Girotto (Sperber, D., Cara, F., & Girotto, V. (1995). Relevance theory explains the selection task. Cognition, 57, 31-95) have proposed that relevance theory can explain performance on the selection task - including all content effects - without invoking inference systems that are content-specialized. Herein, we show that relevance theory alone cannot explain a variety of content effects - effects that were predicted in advance and are parsimoniously explained by theories that invoke domain-specific algorithms for representing and making inferences about (i) social contracts and (ii) reducing risk in hazardous situations. Moreover, although Sperber et al. (1995) were able to use relevance theory to produce some new content effects in other domains, they conducted no experiments involving social exchanges or precautions, and so were unable to determine which - content-specialized algorithms or relevance effects - dominate reasoning when the two conflict. When experiments, reported herein, are constructed so that the different theories predict divergent outcomes, the results support the predictions of social contract theory and hazard management theory, indicating that these inference systems override content-general relevance factors. The fact that social contract and hazard management algorithms provide better explanations for performance in their respective domains does not mean that the content-general logical procedures posited by relevance theory do not exist, or that relevance effects never occur. It does mean, however, that one needs a principled way of explaining which effects will dominate when a set of inputs activate more than one reasoning system. We propose the principle of pre-emptive specificity - that the human cognitive architecture should be designed so that more specialized inference systems pre-empt more general ones whenever the stimuli centrally fit the input conditions of the more specialized system. This principle follows from evolutionary and computational considerations that are common to both relevance theory and the ecological rationality approach.     

THOG: The anatomy of a problem

Summary Three experiments are reported on the attempts to solve a novel hypothetico-deductive problem. Its solution demands both the postulation of hypotheses about its structure and a combinatorial analysis upon the consequences of these hypotheses. The majority of subjects (students) failed to solve the problem because they argued from the properties of stimuli rather than from hypotheses about their conceptual status. The results suggest that a familiarity with the logical structure of the problem and the elicitation of appropriate hypotheses failed to correct this intuitive approach. These findings are discussed in relation to Piaget's theory of formal operations, and (very tentatively) in relation to habitual styles of thought.     

Sources of difficulty in deductive reasoning: The THOG task

The THOG task presents four designs constructed from two shapes and two colours. Subjects are told that the experimenter has written down one of the shapes and one of the colours and are provided the rule that if, and only if, any design has either the shape or the colour, but not both, written down, then it is a THOG. Finally, they are given an exemplar and are asked to classify the remaining designs. Successful solution requires construction of hypotheses, reasoning under each hypothesis, and comparison of the results under each to reach a final conclusion. Few subjects are able to provide adequate responses on the standard version of the task. We present the results of four experiments, with 160 undergraduates each presented with one of eight versions of the task. Experiments 1 and 2 indicate that (1) some subjects think that the properties that are written down are identical to those of the exemplar, although these are not the same subjects who exhibit the modal error pattern, (2) many subjects correctly understand the disjunction of the rule but fail to consider the hypotheses, and (3) poor initial encoding of the problem is not easily corrected. Experiment 3 investigates the sufficiency of the claim of Griggs and Newstead (1982) that appropriate problem solution follows from explicit presentation of all problem information (including use of positive labels for properties that are not written down), and Experiment 4 investigates the necessity of the claim. The results of Experiments 3 and 4 show that presenting positive category labels does increase the frequency of correct solution; however, positive category labels are not necessary for such improvement. Separation of the labels of the THOG rule from those of the exemplar, or informing subjects that only one other design is a THOG, also increases the frequency of successful solution. The results suggest that many people have some fairly sophisticated reasoning skills. but application of these skills is easily discouraged when the features of the task lead to poor initial encoding.     

Analogical transfer in the THOG task

The influences of surface and structural similarity on analogical transfer were examined with 318 undergraduate participants in four experiments using Needham and Amado's (1995) Pythagoras THOG problem as the source problem and Wason's standard abstract THOG task as the target problem. In Experiments 1-3, systematic changes in surface similarity between the source and target problems were introduced by changing the named exemplar, the dimensional values, and the dimensions, respectively, in the target problem. Significant transfer was obtained in all three experiments. In Experiment 4, we explored the basis of this transfer by examining three versions of the Pythagoras THOG problem, factorially combining its facilitating features as source problems. Results indicated that the inclusion of a hypothesis generation request was necessary for significant transfer. The implications of our findings for using transfer versus facilitation as the performance criterion for deductive reasoning are considered.     

Facilitation and analogical transfer in the THOG task

This study was concerned with Wason's THOG task, a hypothetico-deductive reasoning problem for which performance is typically very poor (<20% correct). Recently, however, Needham and Amado (1995) and Koenig and Griggs (2004) have observed both facilitation and spontaneous analogical transfer effects for the Pythagoras version of this task. Based on their findings, Koenig and Griggs concluded that in addition to the separation of the data (the properties of the designated THOG) from the hypotheses that need to be generated (the possible combinations of properties written down), an explicit request to generate these hypotheses is necessary to obtain significant analogical transfer. In the present study we extended the generalisability of this conclusion in three experiments with 214 undergraduate participants using O'Brien et al.'s (1990) Blackboard version of the task. We discuss the relationship of the results to dual process theories of reasoning and propose that analogical transfer may be a better criterion than task facilitation for judging participants' task understanding.     

Naming the parents of the THOG: Mental representation and reasoning

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.     

The effect of instructions on performance in the Wason selection task

The effect of instructions on performance on the standard abstract form of Wason’s selection task was examined. Instructions to determine whether or not the statement is violated did not lead to an increase in correct responding, contrary to previous suggestions that such instructions would induce falsification strategies, but rather to an increase in verification bias. Instructions to determine whether the statement is true or false led to increased variability in performance, supporting the suggestion that such instructions are inherently ambiguous. Thus, the results demonstrate that the form of instructions can have a significant effect on performance in the selection task. Verification bias did better as an explanation of the data than did matching bias, which only fared well when its predictions coincided with those of verification bias. A substantial proportion of the data was unaccounted for by either of these strategies, which is consistent with the findings of a number of other recent studies.     

Perspective effects in nondeontic versions of the Wason selection task

Perspective effects in the Wason four-card selection task occur when people choose mutually exclusive sets of cards depending on the perspective they adopt when making their choice. Previous demonstrations of perspective effects have been limited to deontic contexts--that is, problem contexts that involve social duty, like permissions and obligations. In three experiments, we demonstrate perspective effects in nondeontic contexts, including a context much like the original one employed by Wason (1966, 1968). We suggest that perspective effects arise whenever the task uses a rule that can be interpreted biconditionally and different perspectives elicit different counterexamples that match the predicted choice sets. This view is consistent with domain-general theories but not with domain-specific theories of deontic reasoning--for example, pragmatic reasoning schemas and social contract theory--that cannot explain perspective effects in nondeontic contexts.     

The effects of realism on Wason's THOG problem

Summary In this series of experiments the effects of phrasing Wason's THOG problem in realistic terms were investigated. Experiments 1 and 2 used realistic materials of very different kinds, but neither version of the problem produced any facilitation compared with the original abstract version. Experiment 3 used a version of the problem in which the correct answer was cued in by the realistic material, and a significant improvement was found. Experiment 4 used a version of the problem similar to that used in Experiment 3 and again improved performance was found; since the subjects in this experiment were eight- and nine-year-old children, the facilitation almost certainly was not the result of improved logical ability. The results of Experiment 5, however, suggested that it was difficult to cue in adults to give the logically incorrect answer. It is concluded that realism improves performance on this problem only when the realistic material cues in the correct answer from memory. A review of the research that makes use of other reasoning paradigms suggests that this conclusion may hold true for these as well.     

De-confusing the THOG problem: the Pythagorean solution.

Sources of facilitation for Needham and Amado's (1995) Pythagoras version of Wason's THOG problem were systematically examined in three experiments with 174 participants. Although both the narrative structure and figural notation used in the Pythagoras problem independently led to significant facilitation (40-50% correct), pairing hypothesis generation with either factor or pairing the two factors together was found to be necessary to obtain substantial facilitation (> 50% correct). Needham and Amado's original finding for the complete Pythagoras problem was also replicated. These results are discussed in terms of the "confusion theory" explanation for performance on the standard THOG problem. The possible role of labelling as a de-confusing factor in other versions of the THOG problem and the implications of the present findings for human reasoning are also considered.     

Falsification cueing in collective reasoning: example of the Wason selection task

This paper focuses on the effectiveness of groups, as opposed to individuals, in benefiting from falsification cueing in solving the Wason selection task. Consistent with the idea that groups use information that often individuals fail to use, Experiment 1 showed that groups (but not individuals) that received falsification cueing focused more on cue‐consistent evidence in their reasoning. Experiments 2 and 3 showed that the increment in focus on cue‐consistent evidence is moderated by the distribution of the falsification cue within a group. Finally, Experiment 3 demonstrated that the cue distribution affects collective focus on cue‐consistent evidence through the content of the group discussion, namely through mentioning the cue during the discussion. Copyright © 2008 John Wiley & Sons, Ltd.     

Matching versus optimal data selection in the Wason selection task

It has been reported as a robust effect that people are likely to select a matching case in the Wason selection task. For example, they usually select the 5 case, in the Wason selection task with the conditional “if an E, then a not-5”. This was explained by the matching bias account that people are likely to regard a matching case as relevant to the truth of the conditional (Evans, 1998). However, because a positive concept usually constructs a smaller set than its negative one does (a rarity assumption), it is more effective to get information on the truth of the conditional in a positive set than in a negative set. Thus the optimal data selection account can also explain the effect. The set size of Q and matching by introducing negation were manipulated independently in four experiments. From the results it was inferred that the so-called matching bias was an amalgam of two different cognitive components—relevance judgement by matching and optimal data selection.     

Conditional reasoning and the Wason selection task: Biconditional interpretation instead of reasoning bias

Two experiments were conducted to show that the IF … THEN … rules used in the different versions of Wason's (1966 Wason, P. C. 1966. “Reasoning”. In New horizons in psychology I, Edited by: Foss, B. M. Harmondsworth, , UK: Penguin.  [Google Scholar]) selection task are not psychologically—though they are logically—equivalent. Some of these rules are considered by the participants as strict logical conditionals, whereas others are interpreted as expressing a biconditional relationship. A deductive task was used jointly with the selection task to show that the original abstract rule is quite ambiguous in this respect, contrary to deontic rules: the typical “error” made by most people may indeed be explained by the fact that they consider the abstract rule as a biconditional. Thus, there is no proper error or bias in the selection task as it is still argued, but a differential interpretation of the rule. The need for taking into account a pragmatic component in the process of reasoning is illustrated by the experiments.     

Facilitation and transfer with narrative thematic versions of the THOG task

This article reports two experiments investigating the use of narrative form in the presentation of thematic versions of Wason's (1977) THOG problem. Experiment 1 demonstrated that narrative thematic versions that use actions of characters to present the elements of the problem are easier to solve than the classic version. This result was found both for a problem that used thematic examples and for a problem that used the same geometric figures as the classic THOG. Results also suggested that the presence of a character who creates the comparison properties to be used in applying the disjunction rule was useful in separating those properties from the properties of the positive example. Experiment 2 demonstrated that the solution of a narrative thematic version of the THOG could lead to improved performance on the classic abstract THOG, but only when the examples in the narrative version were the geometric figures. Issues of transfer with the THOG problem are discussed.     

Working memory limitation as a source of confusion in the abstract THOG task

Limitations of working memory are proposed as a major determinant of problem difficulty in the THOG task. This task is a logical reasoning task which uses an exclusive disjunction and requires hypothetico-deductive reasoning. Four experiments with students of mathematics or psychology were used to test the hypotheses that, first, guiding participants' attention facilitates the task and, second, the use of paper and pencil as external problem representation reliefs working memory load. Focusing participants' attention upon a critical aspect of the task does not improve solution rates. Students of mathematics were better than students of psychology, but only if they were allowed to use paper and pencil or to work on the task repeatedly. These results partially support the working memory hypothesis. They point toward the importance of training and practice in relatively simple meta-cognitive skills in logical reasoning. Received: 20 March 2000 / Accepted: 22 January 2001     

Thinking about THOG: Sources of error in a deductive reasoning problem

Summary Three experiments are reported which investigated performance on a number of variants of the THOG problem. Collectively, these experiments indicated that subjects are more accurate (a) when the problem is phrased in a way that clearly separates the properties of the positive instance provided from the properties about which hypotheses must be generated; and (b) when subjects are required to generate hypotheses about what might be the chosen properties. It is suggested that people have little difficulty in carrying out the various thought processes that are required to reach the correct solution to the standard THOG problem, but that it is beyond most people to carry out all of these processes simultaneously.     

Reasoning versus text processing in the Wason selection task: A nondeontic perspective on perspective effects

We argue that perspective effects in the Wason four-card selection task are a product of the linguistic interpretation of the rule in the context of the problem text and not of the reasoning process underlying card selection. In three experiments, participants recalled the rule they used in either a selection or a plausibility rating task. The results showed that (1) participants tended to recall rules compatible with their card selection and not with the rule as stated in the problem and (2) recall was not affected by whether or not participants performed card selection. We conclude that perspective effects in the Wason selection task do not concern how card selection is reasoned about but instead reflect the inferential text processing involved in the comprehension of the problem text. Together with earlier research that showed selection performance in nondeontic contexts to be indistinguishable from selection performance in deontic contexts (Almor & Sloman, 1996; Sperber, Cara, & Girotto, 1995), the present results undermine the claim that reasoning in a deontic context elicits specialized cognitive processes.     

On the representation of task information in task switching: Evidence from task and dimension switching

Task switching research has revealed that task changes lead to a performance switch cost. The present study focuses on the organization of task components in the task set. Three different views of task set organization have been distinguished and evidence in favor of each of these has been reported in the literature. In four experiments, we orthogonally varied the categorization task (magnitude and parity) and the stimulus dimension on which the categorization was to be made. Experiments 1, 2, and 4 used Stroop-like number stimuli, whereas Experiment 3 used global-local stimuli to define the stimulus dimension. In Experiments 2-4, the cue-stimulus interval was also varied. The findings showed that a change of any component resulted in a cost, without any reliable difference in the size of these costs. These results are consistent with the flat view on task-set organization, which assumes that the task set binds all elements in an unstructured representation, which is completely reconfigured each time a change to the task set is required. The implications of these findings are discussed in relation to other findings and the different views on task-set organization.     

Sharing-rule and detection of free-riders in cooperative groups: Evolutionarily important deontic reasoning in the Wason Selection task

Taking a Darwinian approach, we propose that people reason to detect free-riders on the Wason Selection task with the sharing-rule; If one receives the resource, one is an in-group member (standard), or If one is an in-group member, one receives the resource (switched). As predicted, taking the resource-provider's perspective, both undergraduates and children (11 to 12 years old) checked for the existence of out-group members taking undeserved resource. Changing the perspective to that of the resource-recipient did not alter the selection pattern in undergraduates, although the prediction was that another type of free-riding—failure to share by resource-provider—would be checked as well. However, by removing confounding factors in the materials, both undergraduates and children checked for both types of free-riding, which fully supports the prediction. These results indicate that the sharing-rule elicits a thematic content effect that cannot be explained by preceding deontic reasoning theories.