An ERP investigation of conditional reasoning with emotional and neutral contents

In two experiments we investigate conditional reasoning using event-related potentials (ERPs). Our goal was to examine the time course of inference making in two conditional forms, one logically valid (Modus Ponens, MP) and one logically invalid (Affirming the Consequent, AC). We focus particularly on the involvement of semantically-based inferential processes potentially marked by modulations of the N400. We also compared reasoning about emotional and neutral contents with separate sets of stimuli of differing linguistic complexity across the two experiments. Both MP and AC modulated the N400 component, suggesting the involvement of a semantically-based inferential mechanism common across different logical forms, content types, and linguistic features of the problems. Emotion did not have an effect on early components, and did not interact with components related to inference making. There was a main effect of emotion in the 800–1050 ms time window, consistent with an effect on sustained attention. The results suggest that conditional reasoning is not a purely formal process but that it importantly implicates semantic processing, and that the effect of emotion on reasoning does not primarily operate through a modulation of early automatic stages of information processing.     

A successive-conditionalization approach to disjunctive and syllogistic reasoning

With p and q each standing for a familiar event, a disjunctive statement, “either p or q”, seems quite different from its material conditional, “if not p then q”. The notions of sufficiency and necessity seem specific to conditional statements. It is surprising, however, to find that perceived sufficiency and necessity affect disjunctive reasoning in the way they affect conditional reasoning. With B and C each standing for a category name, a universal statement, “all B are C”, seems stronger than its logically equivalent conditional statement, “if B then C”. However, the effects of perceived sufficiency or necessity were found to be as pronounced in conditional reasoning as in syllogistic reasoning. Furthermore, two experiments also showed that (a) MP (modus ponens)-comparable disjunctive reasoning was as difficult as MT (modus tollens)-comparable disjunctive reasoning, and that (b) MT-comparable syllogisms were easier to solve than MT problems in conditional reasoning.     

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

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

Feeling we’re biased: Autonomic arousal and reasoning conflict

Human reasoning is often biased by intuitive beliefs. A key question is whether the bias results from a failure to detect that the intuitions conflict with logical considerations or from a failure to discard these tempting intuitions. The present study addressed this unresolved debate by focusing on conflict-related autonomic nervous system modulation during biased reasoning. Participants’ skin conductance responses (SCRs) were monitored while they solved classic syllogisms in which a cued intuitive response could be inconsistent or consistent with the logical correct response. Results indicated that all reasoners showed increased SCRs when solving the inconsistent conflict problems. Experiment 2 validated that this autonomic arousal boost was absent when people were not engaged in an active reasoning task. The presence of a clear autonomic conflict response during reasoning lends credence to the idea that reasoners have a “gut” feeling that signals that their intuitive response is not logically warranted. Supplemental materials for this article may be downloaded from http://cabn.psychonomic-journals.org/content/supplemental.     

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.     

Causal and noncausal conditionals: An integrated model of interpretation and reasoning

We present an integrated model for the understanding of and the reasoning from conditional statements. Central assumptions from several approaches are integrated into a causal path model. According to the model, the cognitive availability of exceptions to a conditional reduces the subjective conditional probability of the consequent, given the antecedent. This conditional probability determines people's degree of belief in the conditional, which in turn affects their willingness to accept logically valid inferences. In addition to this indirect pathway, the model contains a direct pathway: Availability of exceptional situations directly reduces the endorsement of valid inferences. We tested the integrated model with three experiments using conditional statements embedded in pseudonaturalistic cover stories. An explicitly mentioned causal link between antecedent and consequent was either present (causal conditionals) or absent (arbitrary conditionals). The model was supported for the causal but not for the arbitrary conditional statements.     

Conditionals and directionality: On the meaning of if vs. only if

The aim of this study was to test the predictions of the current theories of reasoning about the comprehension of conditional statements. We used two types of conditional statement that are logically equivalent: if p then q and p only if q . The model theory of reasoning considers that these conditional forms differ in their initial meaning, because the negative contingency is considered only in the p only if q form. Mental-rule theories maintain that the interpretation of p only if q depends on a rephrasing of the statement as: if not q then not p . Alternatively, a directional bias may explain the differences between if p then q and p only if q . We report three experiments that demonstrate the existence of a directional bias in the comprehension of the conditionals. The results were not predicted by either the mental-rules theories or the model theory; they could, however, be easily assimilated by the model theory.     

充分条件句语义关系知觉对条件推理的影响

作者通过实验考察了大学生被试对五种充分条件句语义关系知觉对其条件推理的影响。两个实验的结果表明,被试对条件句中前后件之间语义关系的知觉理解影响和调节其相应的条件推理的成绩。实验1新发现,被试对充分条件句后件对前件必要性的知觉理解存在难易差异,对许可句和定义句的后件必要性容易知觉,对偶然句、义务句和因果句的后件必要性难以知觉。实验2新发现,被试对充分条件句后件对前件必要性的知觉理解的难易差异导致被试在否定后件式推理成绩上的差异,对许可句和定义句的否定后件式推理成绩显著高于对偶然句、义务句和因果句的否定后件式推理成绩,对充分条件句否定后件式推理成绩随对后件必要性知觉增加而增加。     

On the nature and development of conditional reasoning in early adolescence

Two studies investigated the conditional reasoning capabilities of eighth grade learners. In Study 1, we analysed conditional reasoning performances for differences in learners' abilities to solve problems correctly and propensities to be tricked into responding to problems in a biconditional manner. There seemed to be a developmental progression in conditional reasoning ability. Most young adolescents reason using memory of domain-specific memories. However, pragmatic inferential rules may serve as an intermediate level of abstration in reasoners as they progress from the ability to reason using only domain-specific experience to the ability to use content-free syntactic rules. In addition, correlation between scores on the Test of Logical Thinking and conditional reasoning performances suggested that ability to reason deductively using inferential rules at progressively higher levels of abstraction is related to cognitive development. In Study 2, we assessed the effectiveness of an instructional application of pragmatic inferential rule theory for development of conditional reasoning abilities. Pragmatic reasoning skill was developed throug engagement in Prolog programming activities involving hierarchical knowledge domains.     

Language and reasoning: a study of temporal factors

The paper is concerned with the testing of psycholinguistic hypotheses by the use of deductive reasoning tasks. After reviewing some of the problems of interpretation which have arisen with particular reference to conditional rules, an experiment is presented which measures comprehension and verification latencies in addition to response frequencies in a truth table evaluation task.The experiment tests a psycholinguistic hypothesis concerning the different usage of the logically equivalent forms of sentence: If p then q and p only if q with respect to the temporal order of the events p and q. It is proposed that the former sentence is more natural when the event p precedes the event q in time, and the latter more natural when the opposite temporal relation holds.Although significant support is found for the hypothesis in the analysis of the latency data, it is only distinguished from an alternative explanation by detailed analysis of response frequencies, thus indicating the general usefulness of the paradigm adopted.     

条件推理的语义关系表达形式效应

作者用以大学生为被试的实验考察, 基本条件句语义关系表达形式(充分关系、必要关系和析取关系表达形式)和作为心理模型外显建构的可能性判断任务对条件推理的可能影响。实验结果发现, 条件推理的语义关系表达形式效应显著, 条件句语义关系表达形式对被试条件推理有显著的影响, 条件推理成绩随条件句语义关系表达的外显程度增加而增加; 被试在可能性判断任务中对条件句所含心理模型的外显建构并没有明显改善条件推理的成绩; 在有可能性判断任务条件下, 被试外显心理模型建构的成绩变化模式并不能一致地预测条件推理成绩的变化模式。这些结果说明, 人们的条件推理可能并不是完全基于心理模型建构, 而是还受对条件句前后件之间语义关系理解的影响; 条件句表达形式中语义关系的外显内隐模式影响对条件句语义关系的知觉理解难易, 从而影响相应条件推理的成绩。     

Recognition of proofs in conditional reasoning

Relatively little is known about those who consistently produce the valid response to Modus Tollens (MT) problems. In two studies, people who responded correctly to MT problems indicated how “convinced” they were by proofs of conditional reasoning conclusions. The first experiment showed that MT competent reasoners found accurate proofs of MT reasoning more convincing than similar “proofs” of invalid reasoning. Similarly, there was a tendency for MT competent reasoners to find an initial counterfactual supposition more convincing than did people who were less competent in MT. The second experiment showed that when individuals produced the correct MT response, and found correct MT proofs to be more convincing than “bogus” proofs, they were also less likely to find the conclusions to Denying the Antecedent, or Affirming the Consequent problems valid, compared to individuals who could not discriminate between valid and bogus MT proofs. These findings are discussed in terms of both their implications for the mental logic and mental models positions, and individual differences in System 1 and System 2 reasoning.     

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.     

Reasoning about highly emotional topics: Syllogistic reasoning in a group of war veterans

Previous studies have generally found that emotion impairs logical reasoning. However, laboratory experiments have typically involved relatively mild levels of emotion where affect is not linked to personal experience. In this study we examined how army veterans reasoned about syllogisms of three types: neutral, generally emotional, and combat-related emotional. We also measured intensity of combat experience. Veterans were more likely to provide logically accurate answers when reasoning about combat-related compared to neutral problems. Participants with more intense combat experiences showed a reduced advantage in reasoning about combat-related emotional problems.     

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

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

Domain-specific reasoning: social contracts, cheating, and perspective change.

What counts as human rationality: reasoning processes that embody content-independent formal theories, such as propositional logic, or reasoning processes that are well designed for solving important adaptive problems? Most theories of human reasoning have been based on content-independent formal rationality, whereas adaptive reasoning, ecological or evolutionary, has been little explored. We elaborate and test an evolutionary approach. Cosmides' (1989) social contract theory, using the Wason selection task. In the first part, we disentangle the theoretical concept of a "social contract" from that of a "cheater-detection algorithm". We demonstrate that the fact that a rule is perceived as a social contract--or a conditional permission or obligation, as Cheng and Holyoak (1985) proposed--is not sufficient to elicit Cosmides' striking results, which we replicated. The crucial issue is not semantic (the meaning of the rule), but pragmatic: whether a person is cued into the perspective of a party who can be cheated. In the second part, we distinguish between social contracts with bilateral and unilateral cheating options. Perspective change in contracts with bilateral cheating options turns P & not-Q responses into not-P & Q responses. The results strongly support social contract theory, contradict availability theory, and cannot be accounted for by pragmatic reasoning schema theory, which lacks the pragmatic concepts of perspectives and cheating detection.     

条件推理和选择任务的关系：选择任务中的条件推理逻辑

要求大学生被试在相同的情境和规则下先后完成选择任务和条件推理任务,从而系统考察两项条件命题任务之间的关系。结果表明,当规则的语义表征意义为条件命题和反条件命题时,两项任务的反应模式具有一致性;当为双向条件和非条件命题时,两项任务的反应模式出现了分歧,而且四种推理形式和四张卡片之间不存在直接的对应关系。两项条件命题任务之间的关系表现在,它们可能享有共同的语义关系表征空间,但推理过程和策略有所不同。     

How our brains reason logically

The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as “all”, “some”, “none”, and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic.

A Probabilistic Approach to Conditional Reasoning Development

How likely is the glass to break, given that it is heated? The present study asks questions such as this with or without the premise if the glass is heated, it breaks. A reduced problem (question without premise) measures the statistical dependency (conditional probability) of an event to occur, given that another has occurred. Such statistical dependency represents knowledge-based reasoning (inferring from “glass heated” to “its breaking”) and is a component of the response to the complete problem (question with premise). The complete problems therefore measure not only knowledge-based reasoning in terms of statistical dependencies (inductive component) but assumption-based reasoning (deductive component). Two experiments revealed: a) Knowledge-based reasoning continues to develop and attains adult levels at 7th grade for the problems tested, and b) assumption-based reasoning (deductive component) is reliable only for secondary school students (7th graders).