Conditional reasoning and the competence-performance issue: A developmental analysis of a training task

Empirical investigations of conditional reasoning have generally found that both children and young adults perform poorly on tasks that require the selection or evaluation of those propositions that test the truth status of conditional statements (if p then q). Earlier work (D. O'Brien & W. F. Overton, Journal of Experimental Child Psychology 1980, 30, 44–60) suggested that poor performances with these tasks by young adults show improvement following the introduction of evidence that contradicts earlier faulty inferences, and this improvement generalizes to other conditional reasoning tasks. The effects of the contradiction training were not found with younger subjects. The present research is an extension of the contradiction training paradigm. Ten-, fourteen-, and eighteen-year-olds were tested to assess developmental differences in improvement with an evaluation and a conditional syllogism task. Significant improvement in performance was found for the twelfth grade students following the contradiction training, and this generalized across tasks. This effect was not found for the two younger groups. The usual poor performance of the oldest group is considered to be a false negative assessment of their conditional reasoning competency. Further, it is suggested that several correct performances of younger reasoners are false positive assessments of their conditional reasoning competency.     

Conditional reasoning by mental models: chronometric and developmental evidence

The aim of this article is to verify two predictions resulting from the mental models theory of conditional reasoning. First, the denial of antecedent (DA) and modus tollens (MT) inferences should take longer to verify than modus ponens (MP) and affirmation of consequent (AC) because the former require subjects to flesh out the initial model whereas the latter do not. This prediction was confirmed in two reaction time experiments in adults. In line with Evans' proposal (Evans, J. St. B. T. (1993). The mental model theory of conditional reasoning: critical appraisal and revision. Cognition, 48, 1-20), there was a strong directionality effect: inferences from antecedent to consequent (MP and DA) took less time to verify than the inferences in the opposite direction (AC and MT). Second, the development of conditional reasoning should result from the increasing capacity to construct and coordinate more and more models. As a consequence, the pattern of conditional inference production should evolve with age from a one-model conjunctive pattern (production of MP and AC more frequent than DA and MT) to a three-model conditional production pattern (higher production rate for MP and MT than for DA and AC). This prediction was confirmed using an inference production task in children, adolescents, and adults.     

Conditional reasoning following contradictory evidence: A developmental analysis

Recent evidence suggests that young adults do not correctly understand the logical relationship of the conditional (if p the q) as it applies to hypothesis testing, and most training procedures have not been productive. However, the introduction of contradictory evidence following faulty inferences has led to accurate inferences with conditional statements. Third and seventh grade and college studients (9, 13, and 21 years of age, respectively) were tested to assess developmental differences in improvement following contradiction training and to test whether improved performance transfers to other conditional reasoning tasks. Significant improvement in conditional reasoning was found for the young adult group following the introduction of contradictory evidence, and the positive effect of the treatment transferred across tasks. The third grade students showed no effects from the introduction of the contradiction, but the seventh graders were often confused by the introduction of the contradiction. Seventh grade and college student performances were generally worse than that of the third graders for the positive instances (p · q), but while the contradiction training improved college studients' performance it did not affect the seventh graders. The results are discussed in terms of changes in cognitive structures.     

Conditional reasoning and causation

An experiment was conducted to investigate the relative contributions of syntactic form and content to conditional reasoning. The content domain chosen was that of causation. Conditional statements that described causal relationships (if mean value of cause, then mean value of effect) were embedded in simple arguments whose entailments are governed by the rules of truth-functional logic (i.e., modus ponens, modus tollens, denying the antecedent, and affirming the consequent). The causal statements differed in terms of the number of alternative causes and disabling conditions that characterized the causal relationship. (A disabling condition is an event that prevents an effect from occurring even though a relevant cause is present). Subjects were required to judge whether or not each argument's conclusion could be accepted. Judgements were found to vary systematically with the number of alternative causes and disabling conditions. Conclusions of arguments based on conditionals with few alternative causes or disabling conditions were found to be more acceptable than conclusions based on those with many.     

Conditional reasoning and conditionalization

In solving conditional reasoning problems, reasoners are assumed to compute the probability of the conclusion, conditionalizing first on the categorical premise, giving the knowledge-based component, and conditionalizing then on the conditional-statement premise, from which the assumption-based component is derived. Because reasoners find it difficult to compute the second-step conditionalization except when the conditional-statement premise is found to be related to the result of the first-step conditionalization as for modus ponens or, possibly, for modus tollens, the knowledge-based component generally dominates reasoning performance. After representing all the possible cases in which conditional-argument forms may appear, this approach was found to be consistent with the results from the 3 experiments reported in this study, whereas 2 alternative hypotheses account for only some of the results.     

Conditional reasoning processes in a logical deduction game

Two experiments examined the role of conditional reasoning in the logical deduction game, Mastermind. An analysis suggested that Modus Tollens (MT) reasoning could be used to determine the code structure, for example, in determining if any of the colours in the code are repeated. Consistent with this analysis, Experiment 1 showed that only MT errors are correlated with the number of hypotheses advanced in Mastermind. A subsequent analysis showed that conditional reasoning such as Affirming the Consequent (AC) and Denying the Antecedent (DA) could lead to particularly damaging inferences only when the code was four different colours. When that was known before play, Experiment 2 showed that AC errors, but not MT errors, were significantly correlated with Mastermind hypotheses advanced. A stepwise multiple regression analysis supported these findings: When the solvers knew they were playing a four-colour code, there was a slight diminution in the variance explained by MT errors, and a significant increase in the variance explained by AC errors. An analysis of the number of different possible codes that could be consistent with hypotheses actually played showed that the number of such codes is far fewer when the code consists of four different colours than when its structure is not known. This analysis suggests that reasoners are therefore unlikely to discover many alternative causes for the feedback given when the code consists of four different colours, and it is under these conditions that humans are most likely to engage in AC reasoning.     

Structural representation and surrogative reasoning

It is argued that a number of important, and seemingly disparate, types of representation are species of a single relation, here called structural representation, that can be described in detail and studied in a way that is of considerable philosophical interest. A structural representation depends on the existence of a common structure between a representation and that which it represents, and it is important because it allows us to reason directly about the representation in order to draw conclusions about the phenomenon that it depicts. The present goal is to give a general and precise account of structural representation, then to use that account to illuminate several problems of current philosophical interest — including some that do not initially seem to involve representation at all. In particular, it is argued that ontological reductions (like that of the natural numbers to sets), compositional accounts of semantics, several important sorts of mental representation, and (perhaps) possible worlds semantics for intensional logics are all species of structural representation and are fruitfully studied in the framework developed here.     

Interpretation and matching bias in a reasoning task

Subjects were required to construct verifying and falsifying cases of conditional rules in which the presence and absence of negative components was varied. Their responses gave some indication of consistent interpretation of the rules, generally conforming to Wason's (1966) idea of a “defective” truth table. Much of their behaviour, however, seemed to be determined by a task variable in the form of a tendency to construct instances which matched, rather than altered, the values named in the rules.     

Supposition and representation in human reasoning

We report the results of three experiments designed to assess the role of suppositions in human reasoning. Theories of reasoning based on formal rules propose that the ability to make suppositions is central to deductive reasoning. Our first experiment compared two types of problem that could be solved by a suppositional strategy. Our results showed no difference in difficulty between problems requiring affirmative or negative suppositions and very low logical solution rates throughout. Further analysis of the error data showed a pattern of responses, which suggested that participants reason from a superficial representation of the premises in these arguments and this drives their choice of conclusion. Our second experiment employed a different set of suppositional problems but with extremely similar proofs in terms of the rules applied and number of inferential steps required. As predicted by our interpretation of reasoning strategies employed in Experiment 1, logical performance was very much higher on these problems. Our third experiment showed that problems that could be solved by constructing an initial representation of the premises were easier than problems in which this representation was not sufficient. This effect was independent of the suppositional structure of the problems. We discuss the implications of this research for theories of reasoning based on mental models and inference rules.     

Eye movements in a simple spatial reasoning task

We report two experiments in which participants read a question about the spatial relationship between two letters, then viewed a visual display containing the letters and were required to respond to the question. The format of the question influenced the nature of the eye movements generated to the visual display. Participants also had a tendency to make additional eye movements in order to generate a fixation sequence that corresponded to the order of the letters in the question. This demonstrates an influence of stored information on eye movement generation, and suggests that the scanpath plays a role in structuring the visual information to facilitate reasoning.     

Reducing cognitive complexity in a hypothetico-deductive reasoning task

The confusion/non-consequential thinking explanation proposed by Newstead, Girotto, and Legrenzi (1995) for poor performance on Wason's THOG problem (a hypothetico-deductive reasoning task) was examined in three experiments with 300 participants. In general, as the cognitive complexity of the problem and the possibility of non-consequential thinking were reduced, correct performance increased. Significant but weak facilitation (33-40% correct) was found in Experiment 1 for THOG classification instructions that did not include the indeterminate response option. Substantial facilitation (up to 75% correct) was obtained in Experiment 2 with O'Brien et al.'s (1990) one-other-THOG classification instruction. In Experiment 3, a revised version of O'Brien et al.'s pre-test problem format also led to substantial facilitation, even with the use of the standard three-choice THOG classification instruction. These findings are discussed in terms of Newstead et al.'s theoretical proposal and possible attentional factors.     

Conditional reasoning with a spatial content requires visuo-spatial working memory

In previous research, Toms, Morris, and Ward (1993) have shown that conditional reasoning is impaired by a concurrent task calling on executive functions but not by concurrent tasks that load on the slave systems of the working memory system as conceptualised by Baddeley and Hitch (1974). The present article replicates and extends this previous work by studying problems based on spatial as well as nonspatial relations. In the study 42 participants solved 16 types of spatial or nonspatial problems, both in a single-task condition and under concurrent matrix tapping, a task loading the visuo-spatial sketch pad. The findings were consistent with those of Toms et al. (1993) for problems with a nonspatial content. However, when the content was spatial, and only then, a dual-task impairment was observed: processing time of the first premise was lengthened, especially for problems with negations in the antecedent term, the consequent term, or both; moreover, the number of correctly solved problems with negations in both terms was smaller. The implications of these findings for the mental models theory and the mental logic theory are discussed.     

Conditional reasoning,frequency of counterexamples,and the effect of response modality

Geiger and Oberauer (2007) found that when asked to reason with conditionals, people are very sensitive to information about the relative frequency of exceptions to conditional rules and quite insensitive to the relative number of disabling conditions. They asked participants to rate their degree of certainty in a conclusion. In the following studies, we investigated the possibility that this kind of response encourages a more probabilistic mode of processing compared with the usual dichotomous response. In Study 1, participants were given a variant of the problems used by Geiger and Oberauer with either the samescaled response format or a dichotomouscategorical response. The results with the scaled response were identical to those of Geiger and Oberauer. However, the results with the categorical response presented a very different profile. In Study 2, we presented similar problems using only frequency information, followed by a set of abstract conditional reasoning problems. The participants who performed better on the abstract problems showed a significantly different response profile than those who did worse on the abstract problems in the categorical response condition. No such difference was observed in the scaled response condition. These results show that response modality strongly affects the way in which information is processed in otherwise identical inferential problems and they are consistent with the idea that scaled responses promote a probabilistic mode of processing.     

Effects of anxiety on inferential reasoning task performance

Three experiments were conducted in which high anxiety and low anxiety subjects were required to construct inferences. In Experiment 1 there was no anxiety-related performance deficit when inferring a necessary anaphoric relation, a process argued to be automatic. Experiments 2 and 3 involved the verification of unnecessary inferences, a process argued to involve the utilization of the working memory system. In both Experiments 2 and 3 there was an anxiety-related performance deficit. The results are consistent with a working memory-oriented account of anxiety-related performance effects, as deficits were restricted to capacity-demanding tasks.     

Explaining inappropriate strategy selection in a simple reasoning task

People's strategy selections appear to reflect attempts to maximize performance by selecting the most effective option for a particular task or format. Theories that account for such behaviour will be named rational models of strategy selection. However, it is possible to find instances where people are apparently biased towards using less effective strategies, and such behaviour appears to go against these models. Two experiments are reported in which participants were instructed to use first one, and then the other of two possible strategies for solving a compass point directions task (the instructed phase), and were subsequently permitted to use any strategy (the free‐choice phase). A substantial minority of participants selected the less effective spatial strategy during the free‐choice phase. Overall, it was found that people who rely on the spatial strategy when given a free‐choice tend to be those who: (1) have not been given particular incentive to perform as well as possible; (2) have difficulty executing the better alternative, cancellation and (3) are particularly prone to making errors at the spatial strategy. Hence, although evidence was found in support of rational models of strategy selection, it is also suggested that these must additionally take account of the motivational and conceptual difficulties that people may have with a task.     

The effect of emotion on interpretation and logic in a conditional reasoning task

The effect of emotional content on logical reasoning is explored in three experiments. Theparticipants completed a conditional reasoning task (If p, then q) with emotional and neutral contents. In Experiment 1, existing emotional and neutral words were used. The emotional value of initially neutral words was experimentally manipulated in Experiments 1B and 2, using classical conditioning. In all experiments, participants were less likely to provide normatively correct answers when reasoning about emotional stimuli, compared with neutral stimuli. This was true for both negative (Experiments 1B and 2) and positive contents (Experiment 2). The participants' interpretations of the conditional statements were also measured (perceived sufficiency, necessity, causality, and plausibility). The results showed the expected relationship between interpretation and reasoning. However, emotion did not affect interpretation. Emotional and neutral conditional statements were interpreted similarly. The results are discussed in light of current models of emotion and reasoning.     

Indeterminacy,empirical evidence,and methodological pluralism

Roth (1987) effectively distinguishes Quinean indeterminacy of translation from the more general underdetermination of theories by showing how indeterminacy follows directly from holism and the role of a shared environment in language learning. However, Roth is mistaken in three further consequences he draws from his interpretation of indeterminacy. Contra Roth, natural science and social science are not differentiated as offering theories about the shared environment and theories about meanings respectively; the role of the environment in language learning does not justify an empiricist sense of objective evidence; and his advocacy of methodological pluralism does not appropriately sustain the project of social scientific methodology in response to holism and indeterminacy.This paper has benefited from comments by Paul Roth and Terry Winant on an earlier draft, and by the two anonymous referees for Synthese.