Developmental and content effects in reasoning with causal conditionals

Two predictions derived from Markovits and Barrouillet's (2001) developmental model of conditional reasoning were tested in a study in which 72 twelve-year-olds, 80 fifteen-year-olds, and 104 adults received a paper-and-pencil test of conditional reasoning with causal premises ("if cause P then effect Q"). First, we predicted that conditional premises would induce more correct uncertainty responses to the Affirmation of the consequent and Denial of the antecedent forms when the antecedent term is weakly associated to the consequent than when the two are strongly associated and that this effect would decrease with age. Second, uncertainty responding to the Denial of the antecedent form ("P is not true") should be easier when the formulation of the minor premise invites retrieval of alternate antecedents ("if something other than P is true"). The results were consistent with the hypotheses and indicate the importance of retrieval processes in understanding developmental patterns in conditional reasoning with familiar premises.     

Conditional reasoning with causal premises: Evidence for a retrieval model

This study examined the hypothesis that a key process in conditional reasoning with concrete premises involves on-line retrieval of information about potential alternate antecedents. Participants were asked to solve reasoning problems with causal conditional premises (If cause P then effect Q). These premises were inserted into short contexts. The availability of potential alternatives was varied from one context to another by adding statements that explicitly invalidated one or more of these alternatives (i.e., other causes that lead to the effect (Q). The invalidated alternatives differed in the degree of their semantic association to the consequent term (Q). The results show that the effect of invalidating one or more potential alternatives on the two uncertain logical forms, AC and DA, was largely determined by their relative associative strength. These results strongly support a model for conditional reasoning with causal premises that supposes that a key element in responding to the uncertain logical forms is on-line retrieval of at least one potential alternative antecedent.     

Reasoning from an incompatibility: False dilemma fallacies and content effects

In the present studies, we investigated inferences from an incompatibility statement. Starting with two propositions that cannot be true at the same time, these inferences consist of deducing the falsity of one from the truth of the other or deducing the truth of one from the falsity of the other. Inferences of this latter form are relevant to human reasoning since they are the formal equivalent of a discourse manipulation called the false dilemma fallacy, often used in politics and advertising in order to force a choice between two selected options. Based on research on content-related variability in conditional reasoning, we predicted that content would have an impact on how reasoners treat incompatibility inferences. Like conditional inferences, they present two invalid forms for which the logical response is one of uncertainty. We predicted that participants would endorse a smaller proportion of the invalid incompatibility inferences when more counterexamples are available. In Study 1, we found the predicted pattern using causal premises translated into incompatibility statements with many and few counterexamples. In Study 2A, we replicated the content effects found in Study 1, but with premises for which the incompatibility statement is a non-causal relation between classes. These results suggest that the tendency to fall into the false dilemma fallacy is modulated by the background knowledge of the reasoner. They also provide additional evidence on the link between semantic information retrieval and deduction.     

Is inferential reasoning just probabilistic reasoning in disguise?

Oaksford, Chater, and Larkin (2000) have suggested that people actually use everyday probabilistic reasoning when making deductive inferences. In two studies, we explicitly compared probabilistic and deductive reasoning with identical if-then conditional premises with concrete content. In the first, adults were given causal premises with one strongly associated antecedent and were asked to make standard deductive inferences or to judge the probabilities of conclusions. In the second, reasoners were given scenarios presenting a causal relation with zero to three potential alternative antecedents. The participants responded to each set of problems under both deductive and probabilistic instructions. The results show that deductive and probabilistic inferences are not isomorphic. Probabilistic inferences can model deductive responses only using a limited, very high threshold model, which is equivalent to a simple retrieval model. These results provide a clearer understanding of the relations between probabilistic and deductive inferences and the limitations of trying to consider these two forms of inference as having a single underlying process.     

Chronometric evidence for memory retrieval in causal conditional reasoning: The case of the association strength effect

According to many models of conditional reasoning, correct responses to the uncertain forms affirmation of consequent (AC) and denial of antecedent (DA) rely on the retrieval of an alternative antecedent from semantic memory. The main prediction issuing from this hypothesis of online retrieval is that the associative strength of the relevant information in long-term memory affects the latency of its retrieval and then of the correct response of uncertainty to AC and DA. This prediction was tested in 64 adults who performed a syllogism evaluation task with familiar causal conditional premises. As predicted, correct responses of uncertainty to AC and DA were not only more frequent but also faster when the antecedent term was weakly rather than strongly associated with the consequent. In line with the semantic framework, we also observed that this strength effect in response times was reversed for incorrect responses of certainty to AC.     

Pragmatic Schemas and the Selection Task: To Reason or Not to Reason

Cheng and Holyoak (1985) have proposed that people possess classes of linguistically based schemas that have an internal structure that is determined by pragmatic considerations. They found that when permission schemas (“If you want to do P, then you must do Q”) are used in the selection task, the success rate is much superior to what is usually observed. According to Cheng and Holyoak, this is due to the fact that the permission schema is defined by a set of production rules that give the same answers to problems of conditional inference as those of formal logic. In order to test this hypothesis specifically, 160 university students were given one of two tests. The first contained two sets of inferential reasoning tasks, one using a permission schema, the second using a relation of multiple causality. The second test employed the same two conditional relations, but in an appropriate context. The results indicated that subjects did better on the reasoning task with the schema of multiple causality when presented in context, but, as predicted, their performance was much worse on the inferential reasoning task with the permission schema, which generated a higher proportion of logically incorrect responses. These results suggest that contrary to what has been affirmed, permission schemas might not have a logical structure that is equivalent to conditional logic. A second experiment examined selection task performance using the same two relations in context. Performance on the permission schema was superior to that found with the relation of multiple causality. This confirmed previous results indicating that permission schemas do improve selection task performance, but also suggests that this effect is not related to understanding of conditional reasoning.     

条件推理中否定前件下信念偏差发生阶段的ERP研究

以日常生活中的条件推理语句为实验材料,采用大、小前提和结论依次呈现的“推断-判断”范式,利用事件相关电位(event-related brain potential, ERP)技术探讨了条件推理中否定前件下信念偏差效应的脑内时程动态变化。结果发现：在行为反应上,较信念促进,信念阻碍下的正确率更低反应时更长;在脑电上,两条件(信念阻碍和信念促进)诱发的ERP波形仅在大前提加工阶段出现明显的分离。这表明该推理下的信念偏差效应可能早在对大前提的语义表征阶段就已发生。     

On problems of context and attribution in verbal reasoning

Investigated the effect of the verb on inferences in reasoning tasks with conditionals. Subjects were 60 pupils, both male and female, aged 17 to 18 years. Six verbs (buy, have, understand, ignore, hate, avoid) served as independent variables in conditional tasks consisting of two premises. The results which are statistically, highly significant, show an effect due to the verb depending upon the logical form of the task (2Î = 86.1, df= 30). indicate that certain semantic characteristics implicit in verbs determine the way in which a reasoning task is interpreted. A second experiment investigated why verbs differ in this way. Interviews were carried out with subjects using the verbs ‘buy’ and ‘ignore’. It is suggested that implicit meanings acquired through processes of social attribution play an essential role in verbal reasoning. In the present case, such attributions concern the depositional and episodic character of verbs and appear to be responsible for the interpretation of the premises of our tasks. It is concluded that any logical model aiming at an adequate representation of language in reasoning must take these implicit social attributions into account.     

A mental model analysis of young children's conditional reasoning with meaningful premises

Mental model theory has been used to explain many differing phenomena in adult reasoning, including the extensively studied case of conditional reasoning. However, the current theory makes predictions about the development of conditional reasoning that are not consistent with data. In this article, young children's performance on conditional reasoning problems and the justifications given are analysed. A mental model account of conditional reasoning is proposed that assumes that (1) young children can reason with two models and (2) the fleshing out of conditionals involves activation of information in semantic memory that uses the minor premise as a retrieval cue.     

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.     

The origin of conditional logic: does a cheater detection module exist?

The domain-specific hypothesis of L. Cosmides (1989) and L. Cosmides and J. Tooby (1989, 1992) positing that conditional logic has its origin in the evolution of social exchange and in the detection of potential cheaters was tested against a more domain-general hypothesis positing that adult reasoning is logical and that errors in conditional reasoning arise from misunderstandings, not from a lack of logicality. The results of 5 experiments with undergraduate students (n = 682 for Experiments 1-4; n = 188 for Experiment 5), which involved a series of selection tasks that yielded specific predictions about participant performance, were not consistent with the cheater detection hypothesis. Findings supported the misunderstandings hypothesis and imply that adults possess general-purpose logical competence versus domain-specific modules.     

Priming divergent thinking promotes logical reasoning in 6- to 8-year olds: But more for high than low SES students

Divergent thinking is a component of creativity. In the following study, we argue that this form of thinking also underlies logical reasoning. A total of 205 early elementary school children in Grades 1 and 2, from high and moderately low SES environments, were given a short-term prime for divergent thinking and simple reasoning problems. Overall, receiving this prime significantly improved logical reasoning at both grade levels. High and low SES students had similar levels of working memory, inhibitory control, performance on the divergent thinking task, and levels of logical reasoning without the prime. However, also consistent with our predictions, only high SES students showed overall improved logical reasoning following the divergent thinking prime, with the SES difference concentrated in the younger students. These results suggest that environmental differences in openness to alternatives and divergent thinking might underlie developing SES differences in levels of logical thinking.     

Reasoning with premises that are not empirically true: evidence for the role of inhibition and retrieval

Two studies examined conditional reasoning with false premises. In Study 1, 12- and 16-year-old adolescents made "if-then" inferences after producing an alternative antecedent for the major premise. Older participants made more errors on the simple modus ponens inference than did younger ones. Reasoning with a false premise reduced this effect. Study 2 examined the relation between performance on a negative priming task (S. P. Tipper, 1985) and reasoning with contrary-to-fact premises in 9- and 11-year-olds. Overall, there was a correlation between the relative effect of negative priming on reaction times and the number of knowledge-based responses to the reasoning problems. The results of these studies are consistent with the idea that reasoning with premises that are not true requires an interaction between information retrieval and inhibition.     

Working memory and counterexample retrieval for causal conditionals

The present study is part of recent attempts to specify the characteristics of the counterexample retrieval process during causal conditional reasoning. The study tried to pinpoint whether the retrieval of stored counterexamples (alternative causes and disabling conditions) for a causal conditional is completely automatic in nature or whether the search process also demands executive working memory (WM) resources. In Experiment 1, participants were presented with a counterexample generation task and a measure of WM capacity. We found a positive relation between search efficiency, as measured by the number of generated counterexamples in limited time, and WM capacity. Experiment 2 examined the effects of a secondary WM load on the retrieval performance. As predicted, burdening WM with an attention-demanding secondary task decreased the retrieval efficiency. Both low and high spans were affected by the WM load but load effects were less pronounced for the most strongly associated counterexamples. Findings established that in addition to an automatic search component, the counterexample retrieval draws on WM resources.     

Developmental trends in everyday conditional reasoning: the retrieval and inhibition interplay

Two experiments examined developmental patterns in children’s conditional reasoning with everyday causal conditionals. In Experiment 1, a group of pre-, early, young, and late adolescents generated counterexamples for a set of conditionals to validate developmental claims about the counterexample retrieval capacity. In Experiment 2, participants in the same age range were presented with a conditional reasoning task with similar conditionals. Experiment 1 established that counterexample retrieval increased from preadolescence to late adolescence. Experiment 2 showed that acceptance rates of the invalid affirmation of the consequent inference gradually decreased in the same age range. Acceptance rates of the valid modus ponens inference showed a U-shaped pattern. After an initial drop from preadolescence to early adolescence, modus ponens acceptance ratings increased again after the onset of adolescence. Findings support the claim that the development of everyday conditional reasoning can be characterized as an interplay between the development of a counterexample retrieval and inhibition process.     

The Speech and Vocalization Patterns of Boys with ADHD Compared with Boys with Dyslexia and Boys Without Learning Disabilities

The domain-specific hypothesis of L. Cosmides (1989) and L. Cosmides and J. Tooby (1989, 1992) positing that conditional logic has its origin in the evolution of social exchange and in the detection of potential cheaters was tested against a more domain-general hypothesis positing that adult reasoning is logical and that errors in conditional reasoning arise from misunderstandings, not from a lack of logicality. The results of 5 experiments with undergraduate students (n = 682 for Experiments 1-4; n = 188 for Experiment 5), which involved a series of selection tasks that yielded specific predictions about participant performance, were not consistent with the cheater detection hypothesis. Findings supported the misunderstandings hypothesis and imply that adults possess general-purpose logical competence versus domain-specific modules.     

The development of reasoning with causal conditionals.

A total of 512 children in Grades 1 through 6 received a conditional inference task using causal conditionals (If cause P, then effect Q) and a generation of alternatives task. The inference task used premises for which there were few or many possible alternative causes. Results show a steady age-related increase in uncertainty responses to the two uncertain logical forms, affirmation of consequent (AC) and denial of antecedent (DA), and an increase in production of disabling conditions for modus ponens. More uncertainty responses were produced to AC and DA with premises with many possible alternatives. Individual differences in inference production were related to numbers of alternatives produced in the generation task. Results support the idea that both developmental and individual differences in reasoning can be at least partially explained by differential access to knowledge stored in long-term memory.     

Learning conditional frequencies in a probability learning task

The study was prompted by a theoretical discussion of probability learning by Estes (1976). In three separate experiments, subjects were presented with frequency information in the form of wins and losses among 3 teams, and later predicted future wins and losses. Frequencies were devised so that conditional win frequencies for a pair of teams were either inconsistent or consistent with marginal win frequencies for each team. In experiment 1, when subjects predicted future events on the basis of known past frequencies, predictions were generally based on conditional frequencies. In experiment 2 six blocks of observations were presented, with predictions following each block. What little learning did occur was in the direction of the conditional frequencies. Subjects in experiment 3 were able to learn conditional frequencies when given explicit instructions to do so. Results were discussed in terms of a two-stage hypothesis generation model that might operate within the framework of an associative theory of probability learning.     

The mental representation of causal conditional reasoning: mental models or causal models

In this paper, two experiments are reported investigating the nature of the cognitive representations underlying causal conditional reasoning performance. The predictions of causal and logical interpretations of the conditional diverge sharply when inferences involving pairs of conditionals—such as if P₁then Q and if P₂then Q—are considered. From a causal perspective, the causal direction of these conditionals is critical: are the P_icauses of Q; or symptoms caused byQ. The rich variety of inference patterns can naturally be modelled by Bayesian networks. A pair of causal conditionals where Q is an effect corresponds to a “collider” structure where the two causes (P_i) converge on a common effect. In contrast, a pair of causal conditionals where Q is a cause corresponds to a network where two effects (P_i) diverge from a common cause. Very different predictions are made by fully explicit or initial mental models interpretations. These predictions were tested in two experiments, each of which yielded data most consistent with causal model theory, rather than with mental models.     

Suppressing valid inferences with conditionals

Three experiments are reported which show that in certain contexts subjects reject instances of the valid modus ponens and modus tollens inference form in conditional arguments. For example, when a conditional premise, such as: If she meets her friend then she will go to a play, is accompanied by a conditional containing an additional requirement: If she has enough money then she will go to a play, subjects reject the inference from the categorical premise: She meets her friend, to the conclusion: She will go to a play. Other contexts suppress the conditional fallacies. The first experiment demonstrates the effects of context on conditional reasoning. The second experiment shows that the inference suppression disappears when the categorical premise refers to both of the antecedents, such as: She meets her friend and she has enough money. In this case, subjects make both the valid inferences and the fallacies, regardless of the contextual information. The third experiment establishes that when subjects are given general information about the duration of a situation in which a conditional inducement was uttered, such as: If you shout then I will shoot you, they reject both the valid inferences and the fallacies. The results suggest that the interpretation of premises plays an even more central role in reasoning than has previously been admitted.