Cheng and Holyoak's (1985) most persuasive evidence for pragmatic reasoning schemas theory has been that an abstract permission version of Wason's selection task yields higher rates of solution than a nonpragmatic control. Experiment 1 presented two problem sets, one modelled after Cheng and Holyoak's abstract permission problem, which is relatively rich in extraneous features, and one after Wason's, relatively impoverished, Standard problem. Each problem set varied type of rule (permission, obligation, or nonpragmatic) and task type (to reason from or about a rule). Results revealed that enriched problems were solved more often than impoverished ones, that reasoning-from problems were solved more often than reasoning-about problems, and that there was a benefical interaction between enriching features and the permission rule. Experiment 2 demonstrated that although explicit negatives were crucial for solution of reasoning-from permission problems, they played no role in solution of the nonpragmatic-rule problems with enriched features. Experiment 3 provided a replication of the enriched reasoning-about problems and the enriched reasoning-from permission problem, again revealing no beneficial effect for obligation-rule problems, and further revealing no influence of instructions to provide a brief written justification of responses. We argue that the results show that the scope of pragmatic reasoning schemas theory needs to be narrowed, that although a permission rule does have an effect an obligation rule does not, and that some beneficial task features are independent of anything explained by the pragmatic reasoning schema theory.
 
 

INTRODUCTION
Cheng and Holyoak and their associates (Cheng and Holyoak, 1985, 1989; Cheng, Holyoak, Nisbett & Oliver, 1986; Holland, Holyoak, Nisbett & Thagard, 1986; Holyoak &Cheng, in press; Kroger, Cheng, & Holyoak, 1993) have proposed a pragmatic-reasoning-schema theory. Their theory claims that people induce and store domain-specific inference forms in clusters called pragmatic reasoning schemas as a result of repeated exposure to particular classes of content. A pragmatic reasoning schema is defined in terms of classes of goals and content (e.g., permissions, obligations and causations) and is context-sensitive in that it applies only when its goals and content are present; in other words, a schema becomes available when a situation warrants it.

 According to the pragmatic-schemas theory, reasoning with thematically familiar materials typically uses pragmatic schemas, and Holland et al. (1986) wrote of their negative conclusion concerning any role for a content-independent mental logic. For example, pragmatic-schemas theory eschews logical inference schemas such as modus ponens. As advocates of a mental-logic theory (e.g., Braine & O'Brien, 1991; Braine, O'Brien, Samuels, Noveck, Lea, Fisch, & Yang, in press; Noveck, Lea, Davidson, & O'Brien, 1990; O'Brien, 1993, in press), we are motivated to address (a) the empirical evidence for the pragmatic-schemas theory, and (b) the extent to which this evidence should be taken as weighing against a role for content-independent processes such as those of mental logic.

 Only two pragmatic schemas have been presented so far - -one for permissions and another for obligations. Most of the empirical investigations have concerned the permission schema, which articulates four production rules that reflect the four inference patterns that are traditionally associated with a conditional proposition:
 
 

Rule 1. If the action is to be taken, then the precondition must be satisfied.

 Rule 2. If the action is not to be taken, then the precondition need not be satisfied.

 Rule 3. If the precondition is satisfied, then the action may be taken.

Rule 4. If the precondition is not satisfied, then the action must not be taken.
 
 

Interest in the selection task stems largely from findings of a content effect, that is, that several realistic-content versions of the task elicit the correct responses. Part of the appeal of the pragmatic-schema theory is that it provides an apparently straightforward explanation for the content effect; most of the realistic-content versions that have elicited the correct patterns can be understood as presenting veiled pragmatic rules, and this is the case for the most reliably facilitative problems. For example, the facilitative postal and drinking-age problems have rules like If a letter is sealed then it has a 50 lire stamp on it (Johnson-Laird, Legrenzi and Legrenzi, 1972) and If a person is drinking beer then the person must be over 19 years of age (Griggs and Cox, 1982).

 An additional reason for interest in pragmatic-schema theory is that Cheng and Holyoak (1985) presented the first abstract-content version of the selection task that leads to the correct response pattern. This problem provided the most compelling evidence in favor of their theory because it suggested the possibility that the permission rule alone (i.e., without familiar content) is sufficient to account for the improvement in performance; Cheng and Holyoak claimed that their abstract permission version elicited correct response patterns because the wording in the problem's rule triggered the entire permission schema, whereas the merely descriptive rule in their control problem does not. Their two problems are shown in the Appendix.

 Cheng and Holyoak (1985) employed a repeated-measures design, with 61% of their subjects solving the abstract permission problems when it was given first (55% overall) and 19% solving the control problem when it was given first (30% overall). Although Cheng and Holyoak viewed the superior performance on the abstract permission problem as resulting from the pragmatic nature of its rule, which is lacking in the control problem, there were several confounds that could provide alternative interpretations. First, the abstract permission problem required subjects to assume the role of an authority who is seeking out violators (hereafter referred to as the checking context) whereas the control problem did not. Second, whereas there was a consistent use of explicit negatives in the abstract permission problem, the control problem introduced explicit negatives only parenthetically in two cards. In the abstract permission problem, the second paragraph said "one side of the card indicates whether or not a person has taken action A, and the other indicates whether or not the same individual has fulfilled precondition P" (italics added), and the second and fourth cards were presented as "has not taken action A," and "has not fulfilled precondition P." The control problem simply said "every card has a letter on one side and a number on the other" and the second and fourth cards were presented as "B (i.e., not A)", and "7 (i.e. not 4)." Third, the abstract permission problem stated the rule a second time when it said "in other words, in order to be permitted to do action A, one must first have fulfilled prerequisite P," whereas their control version had no such rephrasing (hereafter referred to as rule clarification). Fourth, the task's information was not presented in an order that was consistent across the two tasks. For instance, in the abstract permission problem, the rule was introduced first followed by the cards; in the control problem, the content of the cards was introduced before the regulation. Overall, the fatures of the abstract permission problem were enriched, and those of the control problem were impoverished, in relation to one another. (Note that the abstract permission problem contained 121 words, whereas the control problem contained only 81 words.) Collectively, these differences in task features confounded assessment of the independent variable of interest, i.e., the pragmatic vs. nonpragmatic nature of the rules in the two problems.

 Although several recent investigations (Jackson & Griggs, 1990; Girotto, Mazzocco, & Cherubini, 1992; Kroger et al., 1993; Griggs & Cox, 1993) have addressed the extent to which task features other than the pragmatic nature of its rule might be responsible for solution of the abstract permission problem, these studies contain confounds and difficulties of their own. For example, Jackson and Griggs (1990) reported that correct responses on the abstract permission problem were suppressed either (a) when the instruction to assume the role of a regulative authority (i.e., the checking context) was removed, or (b) when the explicit negatives in the cards were replaced with implicit negative, e.g., replacing "has not fulfilled Precondition P" with "Has fulfilled Precondition Q." Although they found that presenting explicit negatives in their control problem did not lead to increases in solution, they failed to present a nonpragmatic problem with a checking context. Thus, their conclusion that task solution stemmed from explicit negatives together with a checking context remained untested. Further, their comparisons between pragmatic-rule and control problems did not address the other confounds of Cheng and Holyoak (1985). Nevertheless, these findings presented pragmatic reasoning schemas theory with a serious challenge because they suggested the possibility that the superior performance on the abstract permission problem compared to the control problem was due not to the pragmatic nature of its rule, but to other extraneous task features.

 Girotto et al. (1992), Griggs & Cox (1993), and Kroger et al. (1993) argued that the Jackson and Griggs (1990) data should not count against pragmatic schemas theory. Collectively, the three articles have supported a deontic relevance hypothesis that includes three provisos.¹First, a problem with a permission rule will be solved only when the production rules are evoked (and a checking context can aid their evocation). Second, explicit negatives in the cards can be helpful only once the production rules have been evoked because the negative information can aid recognition of the correspondence between the cards and the production rules. Thus, the explicit negatives should lead to solution only when a pragmatic-rule evokes the permission schema's production rules, and they should not lead to solution of a nonpragmatic-rule problem.

 Third, the final proviso concerns a difference between the sorts of tasks that have led to solution with deontic content and Wason's original selection task. Note that the title of Wason's seminal article introducing the selection tasks was "Reasoning about a rule" (Wason, 1968), signaling the task's metalogical nature. Cheng and Holyoak's (1985) abstract permission problem, as well as the realistic-content versions that have led reliably to high rates of correct response patterns, required instead reasoning from a rule that was presented as true, and thus lacked the metalogical status of the original task. The abstract permission and control problems on the one hand, and Wason's selection task on the other, are thus fundamentally different kinds of tasks in that the former concern reasoning from a given rule (to find potential violators of the rule) and the latter reasoning about a rule (to identify cases that might falsify a hypothesis). Claims that pragmatic-content problems have led to solution of the selection task thus are misleading, and as Kroger et al. (1993) noted, a pragmatic schema should not lead to solution of a metalogical hypothesis-testing selection task. The third proviso of the deontic relevance hypothesis is that a pragmatic-rule problem should be solved when it requires reasoning from a rule, but it should not on a task requiring reasoning about a rule. Performance on nonpragmatic-rule problems, however, should not benefit from the presentation of a checking context, explicit negatives, or the use of a reasoning-from task. As Kroger et al. stated, these "favourable presentation factors will be useless for facilitating performance with an arbitrary rule" (p. 633).

 In addition to these predictions concerning which problems will be solved, Girotto et al. (1992), Kroger et al. (1993), and Griggs and Cox (1993) proposed that a reported difference in error patterns between the abstract permission and the control problems when they are presented with implicit negatives lends support to the pragmatic-schema deontic-relevance account: Whereas the usual modal error pattern on nonpragmatic problem versions is the selection of the cards showing p and q (where the rule has the form if p then q), for the abstract permission problem the modal response is to select only the p card. The pragmatic-schemas theorists argued that because the permission rule of the abstract permission problem elicits the production rules of the permission schema, it triggers a search for violators to the rule. The q card does not correspond to a production rule that can violate the rule, and so is not selected. When the problem's rule does not elicit the production rules, the q card often is selected on linguistic matching grounds.

 Taken together, the results of Jackson and Griggs (1990), Girotto et al. (1992), Kroger et al. (1993) and Griggs and Cox (1993) show that the reasoning-from permission-rule problems led to correct solutions more often than the corresponding nonpragmatic control problems when the permission-rule problem presents explicitly the negatives in the cards.² Further, adding explicit negatives to a nonpermission-rule control problem has not led to task solution. Interpretation of these findings is problematic, however, because these investigations placed the control problems at a disadvantage in comparison to the permission-rule problems. Girotto et al. (1992) and Kroger et al. (1993) presented problems that inherited the sorts of confounds found in Cheng and Holyoak (1985). In Girotto et al., for example, the control problem did not contain a checking context, whereas the abstract permission problem did; generally, the features of their permission-rule problem were richer than those of their nonpragmatic-rule problem. The Kroger et al. problems all presented a checking context, but the permission-rule problem with explicit negatives contained 156 words, whereas the comparable non-pragmatic-rule problem contained only 104, and the control problem thus was relatively impoverished.

 The problems in Griggs and Cox were the first not to inherit most of the confounds of the original Cheng and Holyoak (1985) problems, although the permission-rule problems stated that "one side of the card indicates whether or not a person has taken Action `A'..." (italics added, p. 643), whereas the control problems stated "every card has a letter on one side..." (p. 642). The way in which their problems were constructed, however, led to nonpragmatic control problems that differed from all previous versions. The control problems were constructed to conform to the permission-rule problem, so that the information in the two problems was presented in the same order. This resulted in control problems that were pragmatically peculiar in that they presented the rule prior to the cards to which the rule refers. Every other nonpragmatic problem in the literature had presented the cards before the rule, which strikes us as much more sensible. Note that presenting the permission rule before the cards does not make the rule difficult to understand, but presenting the nonpragmatic rule before the cards makes it impossible to comprehend until the rest of the problem has been read. Clearly, the nonpragmatic control problem made processing demands that the permission-rule problem did not, and thus is less user-friendly than the permission-rule problem.

 The extent to which providing a checking context is important is equivocal. Jackson and Griggs found that (1990) removing the checking context from a permission-rule problem suppressed solution to the low rates usually associated with the control problem; Griggs and Cox (1993), however, found that the checking context did not have a statistically significant effect either on a permission-rule problem or on a control problem, although the highest rates of solution were on reasoning-from permission-rule problems with explicit negatives and a checking context. ³ The studies of Girotto et al. (1992) and Kroger et al. (1993) did not address the possible role of checking context, because the former presented a checking context only on pragmatic-rule problems and not on control problems, and the latter presented a checking context on all problems. Again, as we described above, comparisons of permission-rule to control problems in all these studies is problematic, confounding assessment of any interactions with checking context.

 We turn now to whether the facilitative effect of pragmatic rules is limited to reasoning-from problems, as Kroger et al. predicted. Yachanin (1986), Yachanin and Tweney (1982), Chrostowski and Griggs (1985), Cheng and Holyoak (1989), and Griggs (1984) presented both reasoning-from and reasoning-about tasks both with pragmatic rules and with rules that are not obviously pragmatic. Correct answers occurred significantly more often on the pragmatic-rule problems only, and the superior performance on the pragmatic-rule problems was significantly greater on the reasoning-from than on the reasoning-about tasks. Most of these studies were motivated not by an interest in pragmatic schemas, however, but in a memory-cueing hypothesis, and their pragmatic-rule problems used familiar content (e.g., the drinking-age problem for permission, and a problem with the rule "If a worker's risk is 7 or more, then the worker must wear a hard hat" for obligation), whereas the nonpragmatic-rule problem used unfamiliar content (e.g., the widget problem). Thus, the reported difference between the pragmatic-rule and nonpragmatic-rule problems was confounded with the familiarity and unfamiliarity of the content, and the difference between reasoning-from and reasoning-about tasks on the pragmatic-rule problems vs. its absence on the nonpragmatic-rule problems may have been influenced by the content differences.

 Jackson and Griggs (1990) investigated differences between reasoning-from and reasoning-about tasks using abstract permission and control problems as well as an abstract obligation problem, also varying implicit vs. explicit negatives. In their design half of the subjects were presented an abstract permission problem together with a control problem and the other half an abstract obligation problem together with a control problem. They reported that none of the differences between reasoning-from and reasoning-about achieved statistical significance except on the control problem with explicit negatives when it was presented with the abstract permission problem, where there were more correct responses on the reasoning-from problem than on the reasoning-about problem. These results are not those Kroger et al. (1993) predicted, i.e., that there should be an effect on the pragmatic-rule problems, but not on the control problems, and Jackson and Griggs viewed their finding as anomalous, particularly given the absence of such an effect on problems with implicit negatives. ⁴ Jackson and Griggs's problems, however, inherited the confounds from the original problems presented by Cheng and Holyoak (1985). Moreover, the reasoning-from and reasoning-about comparisons contained further confounds, e.g., their permission reasoning-about problem was noticeably longer than (163 vs. 121 words), and presented its information in a different order from, its reasoning-from counterpart.

Kroger et al. (1993) presented both reasoning-from and reasoning-about problems, both for a permission rule and for a nonpragmatic rule. Their comparisons between reasoning-from and reasoning-about were without apparent confounds, although, as described above, the comparisons between permission-rule and nonpragmatic-rule problems were confounded. Their data supported their prediction, with the permission-rule reasoning-from problem with explicit negatives solved much more often than the comparable reasoning-about problem, and with neither version of nonpragmatic-rule problem solved. In sum, the findings on reasoning-from vs. reasoning-about problems are equivocal, and, like much of the empirical work on abstract-content versions of the pragmatic-rule problems, plagued by confounds, making unclear the extent to which the predictions of pragmatic-schemas theory are accurate.

 Although pragmatic-schemas theory has claimed that reasoning with meaningful materials typically uses pragmatic schemas, the only schema described so far other than the permission schema is an obligation schema, and only two studies have presented an abstract obligation problem. Both Jackson and Griggs (1990) and Girotto et al. (1992) reported fewer subjects solving their abstract obligation problems than their abstract permission problems, although these comparisons did not achieve statistical significance. Girotto et al. reported more correct responses to an abstract obligation problem than to a control problem; in Jackson and Griggs's repeated-measures design this comparison failed to achieve significance when problems presented first were compared (p = .073), but when all problems were considered the obligation-rule problem was solved more often than the control problem (p < .05). Both of these studies, however, transferred all of the confounds of their permission-rule vs. nonpragmatic-rule comparisons to the comparison between obligation-rule and nonpragmatic-rule problems. The present investigation was motivated to examine the predictions of pragmatic-schema theory without the sorts of confounds that we have described. Would problems with a permission rule be solved more often than control problems as long as the negatives in the cards are presented explicitly and the problem requires reasoning from a rule? Would obligation-rule problems follow the same pattern as the permission-rule problems? Would the p-only and p and q patterns occur as predicted on the reasoning-from problems when the cards present implicit negatives? Our strategy was to approach this study from the point of view of two extremes -- one extreme represented by the abstract problem that has led to the best performance (the abstract permission problem) and the other extreme by the abstract problem that has led to the worst performance (Wason's standard problem). Thus we constructed two sets of problems. One, referred to as the enriched problem set, was constructed to be maximally similar in wording and structure to the abstract permission problem; the other set, referred to as the impoverished problem set, was constructed to be maximally similar in wording and structure to Wason's standard problem. Within each of these two problem sets we constructed both reasoning-from and reasoning-about problems, each with a permission rule, with an obligation rule, and with a nonpragmatic rule.

Method

 Subjects. Three hundred and thirty six undergraduates participated in order to fulfill laboratory requirements for the introductory psychology class at New York University.

Procedure. Each subject was presented a single problem and subjects were run in small groups. Twenty four subjects were assigned randomly to each of fourteen problems. Subjects were asked to justify briefly their response in writing.

Materials. One problem was the abstract permission problem from Cheng and Holyoak (1985) and one was Wason's standard problem (as presented by Jackson and Griggs, 1990). The remaining twelve problems were constructed to fill a 2 (Levels of Task Features: Enriched vs. Impoverished) x 2 (Task Type: Reasoning-from vs. Reasoning-about) x 3 (Rule Type: Permission vs. Obligation vs. Nonpragmatic) design.

 The enriched problem set was modeled on the abstract permission problem and the impoverished problem set on the standard problem, and the enriched problems include several features that distinguish them from their impoverished counterparts. The enriched problems require subjects to assume the role of an authority who is seeking out violators, they provide a rule clarification, and their cards are presented with explicit negatives. Further, the order in which problem information is presented differs between the enriched and impoverished sets, and the instructions of the enriched problems make the need to search for violators more clearly than do the Impoverished problems.

 To arrive at a set of coherent problems, some minor modifications were required of the abstract permission problem so that parallel nonpragmatic versions could be constructed. For example, if a nonpragmatic problem were to follow exactly the same format as the abstract permission problem, it would introduce the rule about cards without explaining what is on the cards, something that is not readily interpretable (as was the case in the problems presented by Griggs and Cox, 1993). Therefore, the six newly constructed enriched set problems first present the description of the cards, followed by the role-playing instructions, then the rule, the task instructions, and finally the cards. The enriched reasoning-from problems are shown as Problems 3, 4, and 5 in the Appendix. The only difference in the reasoning-about problems is that the second paragraph was changed to:
 
 

Suppose that you are an authority trying to find out what regulation these four cards are obeying. You want to check the hypothesis that the regulation is:

You know that these four cards are following the regulation. In order to check whether your hypothesis is wrong, which of the cards would you need to turn over?

The impoverished problem set was modeled on Wason's standard problem, which was presented in a single paragraph, made no mention of role-playing and presented the cards with implicit negatives. Here, again, modifications were necessary so that parallel pragmatic-rule problems could be accommodated. For example, to begin a permission problem with:
 
 

Below are four cards. Every card shows on one side what Action a person has taken and on the other side what Precondition that person has fulfilled.

Your task is to decide which of the cards you need to turn over in order to find out whether a certain rule is being followed.

You know that the four people represented below are supposed to follow this rule. However, you are not sure whether the four people are following this rule. Turn over only those cards that you need in order to check that the rule is being followed.

Results and Discussion

The proportions of correct responses on the abstract permission and Wason's standard problems were .58 and .04, respectively, replicating previous findings for these problems. These values are similar to the values on the comparable problems in the set constructed here, i.e., the enriched reasoning-from permission problem (.67 correct) and the impoverished reasoning-about nonpragmatic problem (.08 correct), respectively. Thus, the alterations we made in these two tasks in order to construct the enriched and impoverished problem sets did not appreciably affect performance, and subsequent analyses were computed using only the twelve problems of the enriched and impoverished sets.

 The proportions of correct responses on each of the twelve problems are shown in Table 1. The data are nominal frequency counts, and were analyzed with a log-linear multiway frequency analysis (MFA), which is analogous to ANOVA, and yields a likelihood-ratio statistic G ² which is asymptotically distributed as chi-square (see Tabachnick and Fidell, 1989). A three-way analysis, 2 (Level of Task Features) X 2 (Task type) X 3 (Rule Type), revealed two significant main effects. One was for Level of Task Features, G ² (1) = 18.69, p < .001, with more correct responses on enriched than on impoverished problems (.38 vs. .15). The other significant main effect was for Task Type, G ² (1) = 8.06, p < .005, with more correct responses on reasoning-from than on reasoning-about problems (.33 vs. .19). This second finding differed from results reported by Jackson and Griggs, who did not find a significant difference between reasoning-about and reasoning-from versions on pragmatic-rule problems, but was consistent with findings from Kroger et al. (1993). The effect for Rule Type was not significant, but there was a significant interaction of Rule Type x Level of Task Features, G ² (2) = 6.02, p < .05. Thus, whether the rule was pragmatic or not was of less importance than whether the problem contained other extraneous enriching features, and whether the rule required reasoning from a given rule rather than assessing when the truth of a rule can be evaluated. No other interaction was significant.

The proportions of correct responses for the Rule Type X Level of Task Features interaction are shown in Table 1. Post-hoc analyses of the Rule Type X Level of Task Features (p < .05) revealed that the only significant pairwise comparison among the rules was between the enriched permission problems and the combined set of enriched obligation and nonpragmatic problems. Thus, the rate of the correct response pattern on pragmatic-rule reasoning-from problems was not higher than on the nonpragmatic reasoning-from problems, and the finding of a superior performance on the permission-rule problem relied on the relatively poor performance on the obligation-rule problems. Indeed, performance on the obligation-rule versions yielded little support for the pragmatic-schemas theory; the permission rule had a salutary effect, but only when compared to the obligation and nonpragmatic versions taken together, and only when the other extraneous task features of the enriched problem set were present.

The most common erroneous response patterns were those reported by previous researchers (see reviews by Evans, 1982, 1989; Evans, Newstead, & Byrne, 1993), either selecting only the card showing the value referred to in the rule's antecedent (the p-only response), or the cards showing the values referred to both in the rule's antecedent and in its consequent (the p and q response). ⁵ Proportions of these response patterns are shown in Table 2. The predictions about error patterns of the pragmatic-schemas theory (Girotto et al., 1992; Kroger et al., 1993) pertain only to the reasoning-from problems: A reasoning-from permission-rule problem with implicit negatives in the cards should elicit the production rules for the permission schema, leading to selection of the p card, but the lack of an explicit negative for the not-q card should disguise its deontic relevance and block the use of the appropriate production rule. The prevalent response on such a problem thus should be p-only. The same argument should apply equally to an obligation-rule problem, thus predicting the same response pattern. On nonpragmatic problems, which should not evoke a pragmatic schema, the p and q pattern should predominate.

 In the present experiment, the relevant reasoning-from problems with implicit negatives are in the impoverished problem set. Inspection of Table 2 reveals both some support for the pragmatic-schemas predictions and some lack of support. The P-only response occurred significantly more often on the permission problem than on the nonpragmatic problem, chi² (1) = 4.54, p < .05, as predicted by the theory, and the P and Q response was made less often on the permission problem than on the nonpragmatic problem, although this comparison did not achieve significance. Responses on the obligation problem, however, were nearly identical to those on the nonpragmatic problem rather than the permission problem, which is opposite to what pragmatic-schemas theory predicts.
 

In summary, although the enriched reasoning-from permission problem (comparable to Cheng-and-Holyoak's abstract permission problem) leads two-thirds of subjects to the correct response (thus replicating the original finding), the permission rule is only partially responsible; both task type and task features are more important. The obligation rule is no more likely than the nonpragmatic rule to lead to task solution. Taken together with the results reported earlier (Jackson and Griggs, 1990; Griggs and Cox, 1993; Kroger et al., 1993), the only pragmatic rule with any reliable salutary influence is the permission rule, and then only for the reasoning-from task and only when some enriching task features are present. Moreover, the collective rate of correct response patterns was significantly higher on both of the enriched nonpragmatic problems (.31) than on the impoverished nonpragmatic problems (.10), indicating that one or more of the extraneous task features that came from Cheng-and-Holyoak's abstract permission problem also facilitate solution on the enriched nonpragmatic problems. ⁶
 
 

Experiment 1 revealed that some enriching task features that have nothing to do with the pragmatic nature of the rules played a large role in eliciting correct responses to these problems. In the present experiment we investigate a possible source of this salutary effect. Given that the findings reported by Jackson and Griggs (1990), Girotto et al. (1992), Griggs and Cox (1993), and Kroger et al. (1993) indicate the necessity for the explicit presentation of negative information in the cards for solution of the abstract permission problem, we focus here on the role of negatives, both in permission-rule and in nonpragmatic-rule problems.

 Previous investigations of the influence of negatives manipulated implicit vs. explicit presentation of negative information only in the cards; negative information in the text of the pragmatic-rule problems was generally presented explicitly in the permission-rule problems and not at all in the nonpragmatic-rule problems. In their nonpragmatic problems, for example, Griggs and Cox (1993) presented "every card has a letter on one side and a number on the other," whereas on their permission-rule problem they presented "one side of the card indicates whether or not a person has taken Action `A', the other indicates whether or not the same individual has fulfilled precondition `P'" (italics added, pp. 642-643). This difference in wording provided two possible sources of problem difficulty. First, when a permission-rule problem presented explicit negatives in the text, subjects may have been unprepared for the kind of cards they would see when the cards presented negatives implicitly. Second, when a nonpragmatic-rule problem presented no negatives in the text, subjects may have been unprepared for any sort of negatives in the cards. ⁷

 Three problem sets were constructed, one modeled on the enriched reasoning-from permission problem, one on the impoverished reasoning-from permission problem, and one on the enriched reasoning-from nonpragmatic problem. In each of these problem sets, explicit vs. implicit negatives were manipulated, both in the text of the problem and in the cards, resulting in a 2 (Explicit vs. Implicit negatives in the text) X 2 (Explicit vs. Implicit negatives in the cards) matrix for each of the three sorts of problems. This design allows assessment of any possible role of negative information independently of the other enriching task features.

 An additional enriched reasoning-from permission problem was constructed to test a possibility raised by Jackson and Griggs (1990) and by Girotto et al. (1992) that the wording in the enriched reasoning-from permission problem may prompt subjects to interpret has taken Action B to mean has taken Action B and perhaps Action A as well and has fulfilled Precondition Q to mean has fulfilled Precondition Q and perhaps Precondition P as well. Of course, has fulfilled Precondition Q must imply has not fulfilled Precondition P for a subject to solve the task. Jackson and Griggs included a condition in which the phrase "each person has taken one action and fulfilled one precondition," and found it did not influence performance, but Girotto et al. argued that this wording might have been insufficient to block the misinterpretation. In the present manipulation we included the words "has taken only one action ..." (italics added); any subject misinterpreting this would not be paying attention.

Method

 Subjects. Two-hundred-and-forty undergraduate students participated to fulfill a requirement of the introductory psychology course at New York University.

 Materials and Procedure. The procedure was the same as in Experiment 1. Ten new problems were constructed. Nine were constructed to complete the three 2 X 2 matrices based on manipulations to the enriched reasoning-from permission problem, the impoverished reasoning-from permission problem, and the enriched reasoning-from nonpragmatic problem, which were presented in Experiment 1. The tenth problem was an enriched reasoning-from permission problem designed to test the possible misinterpretation of the cards identified by Girotto et al. (1992).

The six new permission problems required to complete the two matrices for the enriched- and impoverished-reasoning-from permission problems were prepared as follows. Whenever explicit negative information was required in the text, the first two sentences of the original enriched reasoning-from permission problem were used. Whenever implicit negative information was required in the text, the first two sentences of the original impoverished reasoning-from permission problem were used. (Only the second sentence of each pair of sentences is critical). The same sources were used to manipulate negative information with respect to the cards: The cards from the original enriched reasoning-from permission problem were used to express negatives explicitly whereas the cards in the original impoverished reasoning-from permission problem were used to express negatives implicitly. Paragraph construction and general presentation of both the enriched and impoverished permission problem sets remained unchanged otherwise. The other two problems that completed the two 2 x 2 matrices were the enriched- and the impoverished-reasoning-from permission problems from Experiment 1, and no new subjects were presented these two problems here.

 The nonpragmatic set consisted of three new problems. (The enriched reasoning-from nonpragmatic problem from Experiment 1 completed the 2 x 2 matrix.) One was identical to the enriched reasoning-from nonpragmatic problem of Experiment 1 except that the second and fourth cards presented negative information implicitly, and this problem presented negative information implicitly throughout. (Despite efforts to match the presentation of the enriched nonpragmatic problem to its companion pragmatic problems in Experiment 1, the original enriched nonpragmatic problems did not use negatives explicitly in the text.) The cards in this problem appeared as "has the letter A," "has the letter B," "has the number 4," "has the number 7." The text in the two remaining problems was changed only in the first paragraph and appeared as follows:

Below are pictures of four cards. One side of each card has the letter A or does not have the letter A and the other side of each card has the number 4 or does not have the number 4.

The tenth new problem, motivated to address the possible misinterpretation of the implicit negatives in the cards of the permission-rule problems identified by Girotto et al. (1992), was identical to the enriched reasoning-from permission problem with explicit negatives only in the text, except for the following additional sentence (third overall): "Each person has taken only one Action and fulfilled only one Precondition."
 
 

Results and Discussion

We turn first to the permission-rule problems. The enriched reasoning-from permission problem with the extra sentence ("Each person has taken only one Action and fulfilled only one Precondition") yielded a proportion of correct responses that was identical to its counterpart without the added sentence (the proportion of correct responses was .17 on each problem) and proportions of incorrect response patterns that were nearly identical to its counterpart. Subsequent analyses refer to the eight Permission problems that vary with respect to explicit and implicit negatives in the text and cards.

 The proportions of correct responses on the six new tasks are summarized in Table 3, together with those on the two reasoning-from permission problems of Experiment 1. A 2 (Problem version: Originally Enriched vs. Originally Impoverished) X 2 (Text: explicit vs. implicit negative information) X 2 (Cards: explicit vs. implicit negative information) MFA was computed, revealing two significant main effects and no interactions. Whereas there was a significant main effect for Cards, G ² (1) = 33.95, p < .001, with more correct responses on problems with explicitly negative cards than on those with implicitly negative cards (.50 vs. .11), there was no effect for Text. The role of explicit negatives thus seems to concern how the exemplars were perceived rather than what the problem structure led subjects to expect. There was also a main effect for problem version, G ² (1) = 4.23, p < .05, with more correct responses on enriched problems than on impoverished problems (.38 vs. 24). Thus, in addition to, and independent from, the explicit negatives in the cards, the enriched problem set still contained features that encouraged task solution. Adding explicit negatives to the cards increased rates of correct performance (from .08 to .40), and further enriching the pragmatic-rule problems further improved performance (correct solutions rose from .40 to .61). This improvement from .40 to .61 is not attributable to the task features addressed by Kroger et al. (1993), and it not clear that pragmatic-schemas theory readily can account for it.
 

Note: n = 24 per cell. Figures in bold indicate that they were gathered in Experiment 1.

Note: n = 24 per cell. Figure in bold indicate that it was gathered in Experiment 1.

Note: n = 48 per problem.

Two concerns motivated this experiment. First, performance in Experiment 1 on the enriched reasoning-about obligation problems yielded an unexpectedly low rate of solution (13% vs. 33% for permission and 29% for nonpragmatic). ⁸ A second concern is that asking subjects in the earlier experiments to provide a brief justification for their responses may have affected performance (Griggs, personal communication); Dominowski (1990) reported that requiring explanations of responses on selection task problems can lead to a higher rate of solution, and Platt and Griggs (1993) reported that the beneficial effects of requiring explanations are greatest on problems that are easier to solve anyway. For these two reasons we presented each of the three enriched reasoning-about problems (permission, obligation, and nonpragmatic) in two conditions: One in which subjects were required to provide a brief written justification of their responses, and another in which such justifications were not required. In addition, the enriched reasoning-from permission problem from Experiment 1 was presented, with some subjects in the with-explanation condition and others in the without-explanations condition. This problem was included because it was the problem solved most often, and any beneficial effect of requiring an explanation should thus occur on this problem.

Method

 Subjects. One hundred and sixty undergraduate students participated to fulfill a laboratory requirement in the introductory psychology class at Baruch College.

 Procedure. Each subject was presented a single problem (n = 20 per problem). Subjects were run in groups of twenty to thirty, with each group assigned either to the with-explanations or to the without-explanations condition. In the with-explanations condition, subjects were instructed to provide "a brief written explanation of your answers;" no such instructions were provided to the without-explanations group. Otherwise, all instructions and procedures were identical to those in the previous experiments.

 Materials. Three enriched reasoning-about problems were presented, as well as the enriched reasoning-from permission problem from Experiment 1. The three new problems were identical to the enriched reasoning-about problems in Experiment 1 except that they replaced the definite article the with the existential quantifier some in the sentence "You know that these four cards are following some regulation."

Results and Discussion

The proportions of correct responses for the enriched reasoning-about problems are shown in Table 6. A 3 (Permission vs. Obligation vs. Nonpragmatic) x 2 (With-explanation vs. Without-explanation) MFA analysis revealed no statistically significant effects. The proportion of subjects solving each problem was greater than would expected by chance alone (p < .01), except for the obligation without-explanation problem; when data for the obligation without-explanation problem were summed with those for the obligation with-explanation problem, however, the solution rate exceeded what would be expected by chance alone (.175 vs. .0625, p < .005).
 
 

Note: n = 20 per cell.

We turn now to the enriched reasoning-from permission problem. Given the concern that the influence of requiring a justification may be greatest on the easiest problems, this is the problem for which the with-explanation vs. without-explanation comparison is most important. Forty-five percent of the subjects solved the problem in the without-explanations condition and 50% in the with-explanations condition; our instruction to provide a brief written justification of responses thus does not appear to be responsible to the response trends we reported in the earlier experiments. This absence of an effect for requiring an explanation is somewhat different from what Dominowski (1990) and Platt and Griggs (1993) reported. In those studies, however, subjects were asked to provide a justification for each card, whereas in the present study they were given only a global instruction, which possibly could account for the absence of such an effect here.
 
 

The present investigation provides some support for the predictions of the pragmatic-schemas theory. First, no problem was solved by a majority of subjects unless it contained a pragmatic rule. Second, as Kroger et al. (1993) predicted, pragmatic-rule problems generally were solved only when they were reasoning-from problems with explicitly presented negatives in the cards. Third, neither the explicit negatives nor the reasoning-from task aided solution of the nonpragmatic-rule problems. These findings are consistent with the claims that (a) a reasoning-from problem with a pragmatic rule elicits the production rules for the pragmatic schema, with the explicit negatives in the cards then revealing their deontic relevance and allowing the production rules to be matched, and (b) neither the search-for-violators aspect of the reasoning-from task nor the use of explicit negatives should facilitate solution on a problem without a pragmatic rule. Several of the findings, however, are not explained by this pragmatic-schemas account.

 Consider first the failure of the obligation rule to facilitate task solution. The theory has made claims to being a general account of how people reason typically. To date, however, pragmatic-schemas theory has provided only two examples of domain-specific schemas, one for permissions and one for obligations, and thus far the only pragmatic rule that has led reliably to task solution (with any set of task features) is the permission rule; although Girotto et al. (1992) found that obligation-rule problems were easier than control problems, Jackson and Griggs (1990) reported weaker facilitation for the obligation-rule problems than for the permission-rule problems, and the present study found no significant facilitative effect for the obligation rule. Further, the results of the present Experiment 1 show no evidence on obligation-rule problems for the error patterns predicted by pragmatic-schemas theory for the pragmatic-rule reasoning-from problems with implicit-negative cards. The evidence for the theory thus rests on only a single reliable schema (for permissions), on only a single sort of task (the reasoning-from analog to the selection task), and then only in conjunction with certain other task features. In order to provide an account of how people reason typically, pragmatic-schemas theory will need to provide (a) more than a single reliable schema, (b) on some tasks additional to the reasoning-from task, and (c) with propositions other than deontic conditionals. Results reported by Markovits and Savary (1992) cast doubt concerning how well the effects of the permission rule will generalize to other tasks; they presented universally quantified conditional syllogisms with a permission rule as the major premise (drawn from the postal-rule problem of Johnson-Laird, Legrenzi and Legrenzi, 1972), and found that the pragmatic rule had no beneficial effect. Further, Griggs (1989) and Platt and Griggs (1993) found a majority of subjects were able to solve several abstract-content versions of the selection tsk that did not contain any deontic rule, showing that task solution need not rely on a pragmatic rule.

 Consider next the effects of the enriched problems. The p-only response was made more often on the permission-rule reasoning-from problems with implicit negatives than on the corresponding nonpragmatic-rule problems only when the permission-rule problems contained the enriched features. To apply the pragmatic-schemas explanation of the influences of the other task features, one would need to assume that the features of the enriched problems evoked the permission schema. Inspection of the rates of task solution, however, show that the features of the enriched problems elicited task solution both on the permission-rule problems and on the nonpragmatic-rule problems; this indicates that the influence of the enriched features concerns neither evoking a pragmatic rule nor making the cards deontically relevant, and the influence of the enriched problem set therefore seems to be outside the scope of the account given by the pragmatic-schemas theory.

The present investigation does not address directly what it is about the enriched problems that led to a higher rate of solution either on the permission-rule or nonpragmatic-rule problems, nor does it address whether the permission-rule and nonpragmatic-rule problems were influenced by the same feature(s) of the enriched problems in the same way. The enriched problems differed from the impoverished problems in several ways, including the presence vs. absence of a checking context and of a rule-clarification statement, the presentation of information in four paragraphs vs. in a single paragraph, and the wording of the task instructions ("In order to check whether the regulation has been violated, which of the cards would you turn over? Turn over those cards, and only those cards, that you need to check to be sure" vs. "Turn over only those cards that you need in order to check that the rule is being followed"). Pollard and Evans (1987), Politzer & Nguyen-Xuan (1992), Gigerenzer & Hug, 1992, and Manktelow and Over (1991) presented problems with nonabstract materials that provided evidence that a checking context may play a crucial role, as did Jackson and Griggs (1990) with abstract materials, although Griggs and Cox (1993) provided little reason to think that this is an important feature on abstract-content problems of the sort discussed here (and no support for the importance of the addition of a rule-clarification statement). The ways in which the other features are important are as yet unclear. The instructions of the enriched problems, for example, make the need for a search-for-violators more explicit than do the instructions of the impoverished problems, but the pragmatic-schemas theory provides no reason for this to influence the nonpragmatic-rule problems.

 Note that adding the enriched features to permission-rule problems without the explicit negatives in the cards did not help, and adding explicit negatives to the nonpragmatic-rule problems with or without the enriched features did not help. That the role of the explicitly negative cards is limited to the permission-rule problems--where they play a crucial role--indicates that the permission-rule problems are in some way processed differently from the nonpragmatic-rule problems.

 Griggs & Cox (1993) and Manktelow & Over (1991) have argued that problems with deontic rules constitute a different sort of task from those with nonpragmatic rules. As Manktelow and Over noted, indicative conditionals (such as those in the nonpragmatic-rule problems) describe states of affairs and thus can be true or false, but can hardly be violated. Deontic conditionals, however, concern intentions about actions and contingencies, and although a deontic conditional can be violated, asking whether it is true or false can be problematic. For example, finding someone driving a car at 100 kilometers per hour does not falsify the regulation that if someone drives in an urban area, then they may not exceed 60 kilometers per hour; finding a violator to a deontic rule does not necessarily falsify that rule. Alternatively, consider a possible scientific hypothesis such as If an object is dropped in a vacuum at the surface level of Mars, then it travels at a speed of 13 meters per second per second. In this case, the results on an experiment showing an object falling at a different accelerating velocity under these conditions would not be thought merely to violate the proposition, but to falsify it. Nature does not issue speeding tickets. Deontic regulations and natural laws both may be expressed in the form of conditionals, but counterexamples have different implications for the two sorts of propositions. The original selection task, with its requirement to reason about a hypothetical rule, is of interest because it bears a relation to scientific hypothesis testing. The absence in the results reported here of any difference between the reasoning-from and reasoning-about conditions for the nonpragmatic-rule problems may be because these problems, unlike the reasoning-from permission-rule problems, fail to make clear to subjects what it is that they are being asked to judge.

 One difference between the results reported here and those in the previous literature requires some comment: Whereas the enriched nonpragmatic-rule problems here were solved by one-third of the subjects, hardly any subjects solved any control problem in Griggs and Cox (1993), even though their control problems were constructed to share the features of the abstract permission problem. As described in the introduction to this article, the control problem in Griggs and Cox presented the rule about the cards before introducing the cards to which the rule refers, which made the rule impossible to understand when it was first read.

 Part of the motivation for the present investigation, as stated in the Introduction, was to assess some theoretical claims made by pragmatic-schemas theorists, in particular with regard to their generally negative view of any role for content-independent reasoning processes of the sort proposed by mental-logic theory. Does an influence of problem content impeach a role for some content-free processes? The original articles that presented pragmatic-schemas theory (Cheng & Holyoak, 1985; Cheng et al., 1986; Holland et al., 1986) provided a stronger set of claims than the more recent articles have (Kroger et al., 1993; Girotto et al., 1992; Griggs & Cox, 1993; Holyoak & Cheng, in press). The original articles, for example, included a claim of typicality, i.e., that ordinary reasoning typically uses inductively acquired pragmatic schemas. In contrast, Kroger et al. said nothing of typicality and claimed only that facilitation of the abstract permission problems requires its pragmatic rule. Further, in their only comment on mental logic, Kroger et al. merely noted that the content-free processes of mental logic cannot by themselves explain the role of permission content on these problems. We agree with their conclusion that the content-independent inferences of mental logic do not explain the influence of permission content on these problems; note, however, that the pragmatic schemas alone also do not provide a complete account of the data reported here, and some of the features that influence performance are content independent. More is going on with these problems than pragmatic schemas alone can explain.

 In principle, the inferences available from the production rules of the permission schema are compatible with the inferences available from the content-independent inference schemas of mental logic. It is beyond the scope of this article to describe our mental-logic theory of conditionals (for a detailed description see Braine & O'Brien, 1991). Suffice it to say that mental logic does not provide sufficient resources to solve a selection task (see discussion in O'Brien, in press). The production rules of the permission schema, however, provide additional inference mechanisms available for reasoning-from problems that both block selection of not-p cases and of q cases and select not-q cases, and these additional inferences do not contravene anything available on the content-independent mental-logic schemas. Whereas the pragmatic-schemas theory presented by Cheng and Holyoak (1985) and the theory of deontic reasoning presented by Manktelow and Over (1991) describe inferences that are particular to a certain sort of conditionals, the content-independent schemas of mental logic describe inferences that are available for all sorts of conditionals. Ordinary conditional reasoning includes both content-independent inferences available on mental logic and content-specific inferences of the sort described by pragmatic-schemas theory or a theory of deontic reasoning, and the content-specific inferences extend the available inferences beyond those available on mental logic alone.

 Finally, given the findings reported here, how should the data reported by Cheng and Holyoak (61% solution on the abstract permission problem vs. 19% on the control problem) be viewed? As recent articles by pragmatic-schemas theorists have noted, a permission rule by itself does nothing to elicit solution, and only 8% of subjects reported here solved the least successful permission-rule problems. Adding explicit negatives to the cards in the reasoning-from problems increased the percentage of subjects solving the problem to 40%, and further adding the enriched features increased the percentage to 61%, which is the same value reported by Cheng and Holyoak (1985) for the abstract permission problem. The enriched features thus increased the number of subjects solving the task by slightly more than 50%, and they thus play a crucial role in achieving the level of success Cheng and Holyoak had reported. The results reported here suggest that if Cheng and Holyoak (1985) had presented an impoverished permission-rule problem and an enriched nonpragmatic-rule problem, rather than an enriched permission-rule problem and an impoverished nonpragmatic-rule problem, no more subjects would have solved the permission-rule problem than the nonpragmatic-rule problem. The conclusions that could have been drawn would have been quite different, as would the subsequent literature.
 
 

¹ Deontology is a branch of philosophy that is concerned with what is morally obligated and permitted.

² Girotto et al. (1992) reported that an explicit negative need not be presented with the word not when subjects were presented a checklist of preconditions with the one mentioned in the rule explicitly not checked, subjects still tended to solve the permission-rule problem.

³ Griggs and Cox (1993) also reported that the presence or absence of a rule-clarification statement influence neither pragmatic-rule nor nonpragmatic-rule problems.

⁴ Although the comparison between reasoning-from and reasoning-about did not achieve statistical significance for the control problem when it was presented with the Obligation problem, when these data are combined with those for the control problem presented with the Obligation problem, the control problem overall showed significantly more solutions for the reasoning-from version than for the reasoning-about version (19% vs. 6%, chi ²(1) = 4.78, p < .05).

⁵ The only other error pattern occurring with greater-than-chance frequency was to select the two cards referring to values not mentioned in the rule (the not-p and not-q response pattern). This pattern constituted 17% of responses both on the enriched and the impoverished reasoning-from nonpragmatic problems and 21% of the responses on the enriched reasoning-about obligation problems. Subjects' written justifications indicate that these responses follow from an unsound strategy in which those cards whose information matched that in either the antecedent or consequent clause of the rule are assumed to be following the rule, so there is no need for further checking, whereas those cards that do not match were potential violators.

⁶ A reviewer of an earlier version of this article expressed concern about the use of the definite article the in the first sentence of the last paragraph of the enriched reasoning-about problems, i.e., You know that these four cards a following the regulation. To allay concern that this might have led subjects to think that the regulation being tested was in fact being followed, we presented three new enriched reasoning-about problems that substituted the existential quantifier some for the definite article the to 65 University of Minnesota undergraduates. The data for these problems were very similar to those reported here.

⁷ Kroger et al. (1993) presented problems with explicit negatives both in the text and in the cards, although they did not systematically manipulate them. There was no apparent influence of the explicit negatives in the text.

⁸ The solution rate for the reasoning-about problem was sufficiently low that one reviewer of an earlier version of this article thought we had made a mistake in what we reported in Table 1.

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Original manuscript received 15 December 1993

Accepted revision received 9 May 1995
 
 

The problems for the 2 (Level of Task Features: Enriched vs. Impoverished) X 2 (Task Type: Reasoning-from vs. Reasoning-about) x 3 (Task Rule: Permission vs. Obligation vs. Nonpragmatic) design.

------------------------------------------------------------------------------------

 1. The abstract permission problem from Cheng and Holyoak (1985, Experiment 2):
 
 

Suppose you are an authority checking whether or not people are obeying certain regulations. The regulations all have the general form, "If one is to take action 'A', then one must first satisfy precondition 'P'." In other words, in order to be permitted to do "A", one must first have fulfilled prerequisite "P."

 The cards below contain information on four people: One side of the card indicates whether or not a person has taken action "A", the other indicates whether or not the same individual has fulfilled precondition "P". In order to check that a certain regulation is being followed, which of the cards below would you turn over? Turn over only those that you need to check to be sure.
 
 

(The four cards show "has taken action A," "has not taken action A," "has fulfilled precondition P," "has not fulfilled precondition P.")

2. The control problem from Cheng and Holyoak (1985, Experiment 2):
 
 

Below are four cards. Every card has a letter on one side and a number on the other. Your task is to decide which of the cards you need to turn over in order to find out whether or not a certain rule is being followed. The rule is: "If a card has an 'A' on one side, then it must have a '4' on the other side." Turn over only those cards that you need to check to be sure.
 
 

(The four cards show the letters "A," "B (i.e., not A)," "4," and "7 (i.e., not 4)".)
 
 

3. Enriched Reasoning-from Permission problem:
 
 

Below are pictures of four cards containing information about four people. One side of each card shows whether or not a person has taken Action A, and the other side shows whether or not the same person has fulfilled Precondition P.
 
 

Suppose that you are an authority checking whether or not these four people are obeying a certain regulation. The regulation is:
 
 

If one is to take Action A, then one must first satisfy Precondition P. In other words, in order to be permitted to do Action A, one must first have fulfilled Prerequisite P.
 
 

In order to check whether the regulation has been violated, which of the cards would you turn over? Turn over those cards, and only those cards, that you need to check to be sure.
 
 

(The four cards show "has taken Action A," "has not taken Action A," "has fulfilled Precondition P," and "has not fulfilled Precondition P.")
 
 

4. The Enriched Reasoning-from Obligation problem:
 
 

Below are pictures of four cards containing information about four people. One side of each card shows whether or not a person is faced with Situation I, and the other side shows whether or not the same person has taken Action C.
 
 

Suppose that you are an authority checking whether or not these four people are obeying a certain regulation. The regulation is:
 
 

If Situation I arises, then Action C must be done. In other words, if Situation I comes about, then one is obliged to complete Action C.
 
 

In order to check whether the regulation has been violated, which of the cards would you turn over? Turn over those cards, and only those cards, that you need to check to be sure.

(The four cards show "Situation I has arisen," Situation I has not arisen," "Action C has been taken," "Action C has not been taken.")
 
 

5. The Enriched Reasoning-from Nonpragmatic: problem:
 
 

Below are pictures of four cards. One side of each card has a letter (either the letter A or some other letter) and the other side has a number (either the number 5 or some other number).
 
 

Suppose that you are an authority checking whether or not these four cards are obeying a certain regulation. The regulation is:

If a card has a letter A on one side, then it must have the number 5 on the other side. In other words, a card can have the letter A on one side only if it has the number 5 on the other side.
 
 

In order to check whether the regulation has been violated, which of the cards would you need to turn over? Turn over those cards, and only those cards, that you need to check to be sure.
 
 

(The four cards show "has the letter A," "does not have the letter A," "has the number 5," "does not have the number 5.")
 
 

6. The Enriched Reasoning-about Permission problem:
 
 

Below are pictures of four cards containing information about four people. One side of each card shows whether or not a person has taken Action A, and the other side shows whether or not the same person has fulfilled Precondition P.
 
 

Suppose that you are an authority trying to find out what regulation these four cards are obeying. You want to check the hypothesis that the regulation is:
 
 

If one is to take Action A, then one must first satisfy Precondition P. In other words, in order to be permitted to do Action A, one must first have fulfilled Prerequisite P.
 
 

You know that these four cards are following the regulation. In order to check whether your hypothesis is wrong, which of these cards would you need to turn over?
 
 

(The four cards show "has taken Action A," "has not taken Action A," "has fulfilled Precondition P," and "has not fulfilled Precondition P.")
 
 

7. The Enriched Reasoning-about Obligation problem:
 
 

Below are pictures of four cards containing information about four people. One side of each card shows whether or not a person is faced with Situation I, and the other side shows whether or not the same person has taken Action C.
 
 

Suppose that you are an authority trying to find out what regulation these four cards are obeying. You want to check the hypothesis that the regulation is:
 
 

If Situation I arises, then Action C must be done. In other words, if Situation I comes about, then one is obliged to complete Action C.
 
 

You know that these four cards are following the regulation. In order to check whether your hypothesis is wrong, which of these cards would you need to turn over?
 
 

(The four cards show "Situation I has arisen," Situation I has not arisen," "Action C has been taken," "Action C has not been taken.")
 
 

8. The Enriched Reasoning-about Nonpragmatic problem:
 
 

Below are pictures of four cards. One side of each card has a letter (either the letter A or some other letter) and the other side has a number (either the number 5 or some other number).
 
 

Suppose that you are an authority trying to find out what regulation these four cards are obeying. You want to check the hypothesis that the regulation is:
 
 

If a card has a letter A on one side, then it must have the number 5 on the other side. In other words, a card can have the letter A on one side only if it has the number 5 on the other side.
 
 

You know that these four cards are following the regulation. In order to check whether your hypothesis is wrong, which of these cards would you need to turn over?
 
 

(The four cards show "has the letter A," "does not have the letter A," "has the number 5," "does not have the number 5.")
 
 

9. The Impoverished Reasoning-about Nonpragmatic problem:
 
 

Below are four cards. One side of each card has a letter (for example, an 'A' or a 'B') and the other side has a number (for example, a '4' or a '7'). Your task is to decide which of the cards you need to turn over in order to find out whether a certain rule is true or false. The rule is: "If a card has an 'A' on one side, then it must have a '4' on the other side." You know that the four cards below are following some rule. However, you are not sure whether the above rule is true or false for these four cards. Turn over only those cards that you need to check to determine whether the rule is true or false for the four cards.
 
 

(The four cards show "A," "B," "4" and "7.")
 
 

10. The Impoverished Reasoning-about Permission problem:
 
 

Below are four cards containing information about four people. One side of each card tells you an Action a person has taken (for example, Action A or Action B) and the other side tells you a Precondition that person has satisfied (for example, Precondition P or Precondition Q). Your task is to decide which of the cards you need to turn over in order to find out whether a certain rule is true or false. The rule is: " If one is to take Action A, then one must first satisfy Precondition P." You know that the four people represented below are following some rule. However, you are not sure whether the above rule is true or false for these four people. Turn over only those cards that you need to check to determine whether the rule is true or false for the four people represented on the four cards.
 
 

(The four cards show "Has taken Action A," "Has taken Action B," "Has satisfied Precondition P" and "Has satisfied Precondition Q.")
 
 

11. The Impoverished Reasoning-about Obligation problem:
 
 

Below are four cards containing information about four people. One side of each card tells you a Situation a person has faced (for example, Situation I or Situation J) and the other side tells you an Action that person has taken (for example, Action C or Action D). Your task is to find out whether a certain rule is true or false. The rule is "If Situation I arises, then Action C must be done." You know that the four people represented below are following some rule. However, you are not sure whether the above rule is true or false for these four people. Turn over only those cards that you need to determine whether the rule is true or false for the four people represented on the four cards.
 
 

(The four cards show "Situation I has arisen," "Situation J has arisen," "Action C has been taken," and Action D has been taken.")
 
 

12. The Impoverished Reasoning-from Nonpragmatic problem:
 
 

Below are four cards. One side of each card has a letter (for example, an 'A' or a 'B') and the other side has a number (for example, a '4' or a '7'). Your task is to decide which of the cards you need to turn over in order to find out whether a certain rule is being followed. The rule is: "If a card has an 'A' on one side, then it must have a '4' on the other side." You know that the four people represented below are supposed to follow this rule. However, you are not sure whether the four people are following this rule. Turn over only those cards that you need in order to check that the rule is being followed.
 
 

(The four cards show "A," "B," "4" and "7.")
 
 

13. The Impoverished Reasoning-from Permission problem:
 
 

Below are four cards containing information about four people. One side of each card tells you an Action a person has taken (for example, Action A or Action B) and the other side tells you a Precondition that person has satisfied (for example, Precondition P or Precondition Q). Your task is to decide which of the cards you need to turn over in order to find out whether a certain rule is being followed. The rule is: " If one is to take Action A, then one must first satisfy Precondition P." You know that the four people represented below are supposed to follow this rule. However, you are not sure whether the four people are following this rule. Turn over only those cards that you need in order to check that the rule is being followed.
 
 

(The four cards show "Has taken Action A," "Has taken Action B," "Has satisfied Precondition P" and "Has satisfied Precondition Q.")
 
 

14. The Impoverished Reasoning-from Obligation problem:
 
 

Below are four cards containing information about four people. One side of each card tells you a Situation a person has faced (for example, Situation I or Situation J) and the other side tells you an Action that person has taken (for example, Action C or Action D). Your task is to find out whether a certain rule is being followed. The rule is "If Situation I arises, then Action C must be done." You know that the four people represented below are supposed to follow this rule. However, you are not sure whether the four people are following this rule. Turn over only those cards that you need in order to check that the rule is being followed.
 
 

(The four cards show "Situation I has arisen," "Situation J has arisen," "Action C has been taken," and Action D has been taken.")

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Correspondence concerning this article can be directed to Ira Noveck at CREA-Ecole Polytechnique, 1, rue Descartes, 75005 Paris, France, email: noveck@poly.polytechnique.fr or to David O'Brien, Department of Psychology, Box G-1126, Baruch College of CUNY, 17 Lexington Avenue, New York, NY 10010, USA.

This article is based in part on the first author's doctoral dissertation at New York University completed under the supervision of Martin Braine, to whom both authors are grateful. The authors also express their gratitude to Francesco Cara, Jonathan St. B. T. Evans, Vittorio Girotto, Murray Glanzer, Jackie Goodnow, Richard Griggs, Brooke Lea, Larry Maloney, Guy Politzer, Gay Snodgrass, Dan Sperber, and the members of CREA, for many helpful conversations and comments, and to Peter Wason for devising the original task.

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