Reasoning with conditionals containing negated constituents.

Three experiments investigated matching bias in conditional reasoning tasks. Matching bias occurs when Ss ignore negations and match named items. Experiment 1 used an abstract and a thematic version of Evans's (1972) construction task. Results showed that matching may be due to an interaction between task demands and constructing contrast classes when interpreting negations. Experiment 2, which used Wason's (1968) selection task, introduced a manipulation to ease contrast-class construction. Confirmation plus falsification dominated over matching. Experiment 3 introduced two other manipulations to aid contrast-class construction with abstract material. Confirmation was facilitated, matching was suppressed, and falsification remained unchanged. These results suggest that matching occurs only when insufficient or ambiguous information prevents the intended interpretation of negations.     

Context and rule manipulations on the Wason selection task

‘Food and drinks’ is a thematic content known not to produce differential performance to abstract content on the Wason selection task. To examine the effects of context on problem responses, this content was set in a ‘diet’ context, predicted to produce differential performance, and this context was compared both with the ‘food and drinks’ presentation previously used and with abstract content. Additionally, both conditional and universal rules were used, producing six cells to the design, 12 subjects being tested in each cell. Results revealed a significant difference between the rules (in the form a rule by content interaction), content having a significant effect only when the conditional rules were used. For these rules, subjects made significantly more correct solutions in the diet condition than in the abstract condition, whereas there was no evidence of differential performance between the (other) thematic and the abstract condition. Although it is admitted that no satisfactory explanation of the rule differences seems apparent, the effect of context observed is encouraging for this line of research. It is concluded that, as subjects are shown to be capable of coding the general idea of a counter-example into relevant specific selections, they are quite capable of solving the task, but that they fail to do so unless the solution is cued by, and its outcome would be consistent with, their pre-existing belief structures.     

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.     

The elusive matching bias effect in the disjunctive selection task

When reasoning with conditional statements (i.e., if [not] p then [not] q), for example when solving Wason's selection task, subjects tend to display matching bias: Options which match the entities named in the rule tend to be selected irrespective of whether this is logically appropriate. Recently, there have been suggestions that the underlying causes of matching bias reflect a general phenomenon that applies to many types of logical rule, not just conditionals. A study is reported in which performance is investigated for selection tasks with categorical or disjunctive rules. Although matching bias was clearly present for categorical rules, inverted matching bias was identified for disjunctive rules, calling into question the generality of the phenomenon and its explanations. In addition, performance at one task was not correlated with performance at the other, calling into question recent cognitive capacity accounts of selection task performance.     

MATCHING BIAS IN THE SELECTION TASK

A previous study (Evans, 1972) found that subjects tend to match rather than alter named values when constructing verifying and falsifying cases of conditional rules. It was suggested that this tendency (‘matching bias’) might account for the responses normally observed in Wason's (1968, 1969) ‘selection task’. This suggestion was tested by giving subjects the selection task with conditional rules in which the presence and absence of negative components was systematically varied, to see whether subjects consistently attempted to verify the rules (Wason's theory) or whether they continued to choose the matching values despite the presence of negatives, which would reverse the logical meaning of such selections. Significant matching tendencies were observed on four independent measures, and the overall pattern, with matching bias cancelled out, gave no evidence for a verification bias, indicating instead that the logically correct values were most frequently chosen.     

The Influence of Linguistic Form on Reasoning: The Case of Matching Bias

A well-established phenomenon in reasoning research is matching bias : a tendency to select information that matches the lexical content of propositional statements, regardless of the logically critical presence of negations. Previous research suggested, however, that the effect might be restricted to reasoning with conditional statements. This paper reports two experiments in which participants were required to construct or identify true and false cases of propositional rules of several kinds, including universal statements, disjunctions, and negated conjunctions. Matching bias was observed across all rule types but largely restricted to problems where participants were required to falsify rather than to verify the rules. A third experiment showed a similar generalization across linguistic forms in the Wason selection task with only if conditionals substituted for universals. The results are discussed with reference to contemporary theories of propositional reasoning.     

The Impact of Necessity and Sufficiency in The Wason Four-Card Selection Task

Performance in the Wason card selection task is often improved given thematic content. Such content effects have been considered evidence against human rationality. We propose that the role of content lies in specifying premises underlying "if P, then Q" rules. Unlike thematic rules, abstract conditional rules do not explicitly provide material interpretation (P is a sufficient but not necessarily a necessary condition for Q), resulting in nonnormative responses. When necessity–sufficiency relations were explicated, normative responses were elicited and effects of other logically irrelevant components disappeared. The results suggest that content effects are compatible with human rationality.     

Rephrasing between Disjunctives and Conditionals: Mental Models and the Effects of Thematic Content

Two experiments are reported thatinvestigate whether the logical equivalence of conditionals and disjunctives is paralleled by a psychological equivalence. In these experiments, subjects rephrased from one form into the other. Experiment 1 demonstrated strong effects of familiarity and causality of rule content. Similar findings were found in Experiment 2 with a different conditional rule syntax. An account of the experiments is given in terms of mental models theory: In this account, task performance can be seen to depend upon the extent to which the model sets used by subjects to generate rephrasings are complete, task content being the most important factor affecting model set completion. A 'Minimal Completion' strategy is proposed to operate in the absence of thematic content. The experiments also falsify the long-held assumption that conditionals with negative antecedents are always interpreted as their disjunctive equivalents. This raises doubts about the mental models explanation for matching bias in conditional reasoning.     

Rapid-response versus free-time selection tasks using different logical connectives

When reasoning with conditional statements (i.e., if [not] p then [not] q), people tend to display matching bias: Options that match the entities named in the rule are selected even when logically inappropriate. Three different Wason selection tasks were administered under free-time and rapid-response formats. For the latter, individual cards were presented for one second, and required a response within a further one second. Previous research using these formats (Roberts & Newton, 2001) has shown that this increases matching bias, in line with the action of preconscious heuristic processes which direct attention towards relevant aspects of a problem, but whose action can be overturned if there is sufficient time to apply analytic reasoning processes. The selection tasks administered included a standard abstract conditional task, a disjunctive version (i.e., either [not] p or [not] q), and a conditional task in which the cards showed explicitly negated values. Both conditional tasks demonstrated matching bias, but under rapid-response presentation, matching bias only increased for the standard conditional and disjunctive tasks. Overall, the data support Evans’ (e.g., 2006) heuristic-analytic framework albeit with some caveats, and it is suggested that the broad question, of whether individual selection task formats show or do not show matching bias, requires more detailed investigation.     

The emergence of inferential rules: The use of pragmatic reasoning schemas by preschoolers

This study contrasts the pragmatic view with the natural logic view regarding the origin of inferential rules in conditional reasoning. The pragmatic view proposes that pragmatic rules emerge first, and the generalizations of these produce formal rules. In contrast, the natural logic view proposes that the formal rules emerge first and serve as a core that is then supplemented by pragmatic rules. In an experiment, scenarios involving conditional rules in different contexts, permission and arbitrary, were administered to independent groups of preschool children. To rule out the matching bias [Evans, J. St. B. T., & Lynch, J. S. (1973). Matching bias in the selection task. Br J Psychol 64, 391–397] as a possible explanation of reasoning performance, children were given conditional rules with a negated consequent. The results show that in the arbitrary context modus tollens (MT) was unavailable, and the use of modus ponens (MP) was unstable. In contrast, children in the permission context reliably used both MP and MT. In addition, they realized that a conditional rule does not imply a definite answer when the consequent holds. These findings suggest that, in their explicit forms, pragmatic rules emerge earlier than formal rules and in particular, even as basic a rule as MP is generalized from a context-specific form to a context-general one in preschool children.     

Reasoning with three types of conditional: Biases and mental models

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.     

Evoking the permission schema: The impact of explicit negation and a violation-checking context

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.     

Transfer of conditional reasoning: Effects explanations and initial problem types

Transfer of reasoning on Wason's (1966) selection task was explored in three experiments. Experiment 1 tested the effects of problem explanations and verbalization instructions on transfer from abstract or thematic problems to abstract problems. Explanations facilitated transfer only when the initial problems were abstract; verbalization did not produce transfer between problems. Experiment 2 explored the effects of problem similarity and explanations on transfer between problems. Although transfer occurred following explanations, no effect of similarity was found for thematic problems. In both of these experiments, the thematic effect (Wason & Shapiro, 1971) was observed. Experiment 3 examined the effects of explanations to abstract or thematic problems on transfer to subsequent abstract or thematic problems. Transfer of reasoning occurred from both initial problem types, particularly to problems of the same type; however, transfer occurred to a greater extent from abstract problems than from thematic problems. The results are discussed in terms of problem similarity and Cheng and Holyoak's (1985) pragmatic reasoning schema hypothesis.     

Implicit learning: Robustness in the face of psychiatric disorders

The performance of a group of psychiatric inpatients on two different cognitive tasks was compared with that of a control group of college undergraduates. The task in the first experiment was implicit learning of a complex, synthetic grammar; the task in the second experiment was explicit learning of relatively simple letter-to-number matching rules. In the first experiment, differences between the normals and the psychiatrically impaired were found on the preliminary memorization task but not on the implicit grammar learning task; in the second experiment, differences were observed on all phases of the experiment, with the inpatients performing no better than chance. These findings provide support for the hypothesis that, under appropriate conditions, individuals suffering from serious disorders may show no deficits when working with complex and abstract stimulus domains while showing serious performance problems when working with relatively simple, concrete stimuli. The key factor is that the former were presented as tasks that tap nonreflective, implicit processes, whereas the latter were put forward as ones that recruit conscious, explicit processes.The experiments are based in part on studies reported in Abrams (1987). Preparation of this article was supported in part by a grant from the City University of New York PSC-CUNY Research Award Program, Brooklyn College of CUNY.     

Working memory involvement in dual-task performance: Evidence from the backward compatibility effect

In three experiments, the authors supported the hypothesis that parallel response activation seen in dual-task performance results from holding Task 2 rules in working memory (WM) while performing Task 1. To this end, the authors used the backward compatibility effect (BCE; quicker primary responses when the Task 2 response is compatible with codes of Task 1) as a marker for parallel response activation and manipulated WM load. Increasing the number of primary task rules from two to four did not modulate BCE, replicating Hommel and Eglau (2002), but a higher load condition, involving six primary task rules, reduced the BCE to nonsignificant levels. Experiment 3 further showed that WM is loaded by rules associating abstract stimulus categories to responses, and not by rules tt associate individual stimuli to responses (S-R rules).     

Concrete problems in the abstract deontic selection task - and how to solve them

The abstract deontic selection task was introduced by Cheng and Holyoak with the aim of demonstrating that people possess abstract reasoning schemas for processing deontic rules about what an individual must, must not, may, or need not do. Solving this task requires people to detect possible rule violators. The average solution rate across several studies, while being substantially higher than that with abstract nondeontic tasks, did not reach the level obtained with concrete deontic tasks. A task analysis based on the deontic principles by Beller uncovers several problems with the formulation of the original task. They concern the presentation of the deontic rule as well as the instructions (focusing on rule following) and result in a specific selection behaviour. Three experiments replicate the difficulties with the original task and show that task performance increases when the formulation problems are resolved. The best performance was obtained with a task that combined a genuine violation detection instruction with a genuine permission rule. Interestingly, permissions are weak deontic rules that, if taken literally, cannot be violated in a deontic sense. Therefore, people must interpret these rules as implying a strong deontic constraint (i.e., a ban), which then constitutes the basis for solving the task. The results provide novel insights into the interpretation of deontic rules and into the role that these content-specific, but abstract, tasks can play for the study of reasoning processes.     

Interactions between view changes and shape changes in picture-picture matching

Four experiments are reported in which pictures of different morphs of novel, complex, 3-D objects, similar to objects which we must identify in the real world, were presented. We investigated how changes of viewpoint influence our ability to discriminate between morphs. View changes had a powerful effect on performance in picture-picture matching tasks when similarly shaped morphs had to be discriminated. Shape changes were detected faster and more accurately when morphs were depicted from the same rather than different views. In contrast, view change had no effect when dissimilarly shaped morphs had to be discriminated. This interaction between the effects of view change and shape change was found both for simultaneous stimulus presentation and for sequential presentation with interstimulus intervals up to 3600 ms. The interaction was found after repeated presentations of the stimuli before the matching task and after practice at the matching task as well as after no such pre-exposure to the stimuli or to the task. The results demonstrate the difficulty in activating abstract, view-insensitive representations to help to achieve object constancy, even when matching over long interstimulus intervals or after stimuli have already been seen many times.     

Verbal Counting Moderates Perceptual Biases Found in Children's Cardinality Judgments

A crucial component of numerical understanding is one's ability to abstract numerical properties regardless of varying perceptual attributes. Evidence from numerical match-to-sample tasks suggests that children find it difficult to match sets based on number in the face of varying perceptual attributes, yet it is unclear whether these findings are indicative of incomplete numerical abstraction abilities early in development or instead are driven by specific demands of the matching task. In this study, we explored whether perceptual biases would be found in data from a numerical task invoking verbal representations of number and whether these biases are moderated by verbal counting behavior. Three- to 6-year-old children classified as proficient counters (cardinal principle knowers) participated in a number cardinality task in which they were asked to identify which of 2 arrays—either perceptually homogeneous or heterogeneous in appearance—contained a specific number of animals (e.g., “12 animals”). Results revealed an overall performance bias for homogeneous trials in this cardinality task, such that children were better able to exactly identify the target cardinality when items within the sets were perceptually identical. Further analyses revealed that these biases were found only for those children who did not explicitly verbally count during the task. In contrast, performance was unaffected by the perceptual attributes of the array when the child spontaneously counted. Together, results reveal that cardinality judgments are negatively impacted by perceptual variation, but this relationship is muted in those children who engage in verbal counting.     

The effect of thematic content on the ‘Wason selection task’

This paper concerns the differential effects of use of ‘thematic’, rather than abstract (symbolic), content on the ‘Wason selection task’. An effect of thematic content has been reported several times, originally by Wason & Shapiro (1971), but Manktelow & Evans (1979) report five experiments that failed to obtain an effect and argue against the validity of the content effect in general. However, it is pointed out that four of their experiments use a novel content and that there are previous reports of non-effective content in the literature. It is concluded that a particular type of thematic content cannot be treated as a ‘random sample’ of thematic content in general, and that their argument thus rests upon their failure to produce an effect of the specific (’towns and transport’) content used by Wason and Shapiro. This produces an essentially empirical controversy which is settled in two ways. First, Manktelow and Evans’s criticisms of two previous replications are shown to be misleading. Second, an experiment is reported that exactly copies the Wason and Shapiro design and produces a significant effect of content. It is concluded that the Manktelow and Evans result most probably was due to a Type 2 error. Finally, a hypothesis is developed to account for both the effect of certain types of content and the lack of effect of others, including that used in Manktelow and Evans’s first four experiments.