Causal conditional reasoning and semantic memory retrieval: a test of the semantic memory framework

This study tested and refined a framework that proposes a mechanism for retrieving alternative causes and disabling conditions (Cummins, 1995) during reasoning. Experiment 1 examined the relation between different factors affecting retrieval. The test revealed high correlations between the number of possible alternative causes or disabling conditions and their strength of association and plausibility. Experiment 2 explored the hypothesis that due to a more extended search process, conditional inferences would last longer when many alternative causes or disabling conditions were available. Affirmation of the consequent (AC) and modus ponens (MP) latencies showed the hypothesized pattern. Denial of the antecedent (DA) and modus tollens (MT) inferences did not show latency effects. The experiment also identified an effect of the number of disabling conditions on AC and DA acceptance. Experiment 3 measured efficiency of disabler retrieval by a limited time, disabler generation task. As predicted, better disabler retrieval was related to lower acceptance of the MP and MT inferences.     

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。     

A Probabilistic Interpretation of llIf-Then

This study proposes that subjects interpret thematic conditionals ('if p then q ') probabilistically in solving conditional reasoning problems. Experiment 1 found that subjects' correct responses increased with the perceived probability of q , given p for each of the four forms of conditional arguments: modus ponens (MP), modus tollens (MT), denial of the antecedent (DA), and affirmation of the consequent (AC). Experiment 2 ruled out two alternative explanations based on the comprehensibility of conditionals and on subjects interpreting conditionals as biconditionals. In Experiment 3, subjects solved two types of problems: (a) complete probabilistic problems, such as 'If p then q ; knowing p ; how probable is q ?', and (b) reduced probabilistic problems, such as 'Knowing p ; how probable is q ?' Two sources of information that determine the observable reasoning responses are identified. One source of information is based on one's general knowledge, and another is based on taking all premises into account.     

关于条件推理的ERP研究

以抽象的条件命题作为实验材料,测定13名大学生在完成MP、AC、DA、MT推理（推测判断任务）和基线任务（记忆判断任务）时的事件相关电位（ERP）,初步探讨不同推理类型的脑内时程动态变化。这是使用ERP技术来研究条件推理脑机制的初步尝试。结果发现,五种任务所诱发的ERP早成分均不存在显著差异,在头皮前部的左外侧额区和左颞区,MP与DA推理与基线任务相比,均诱发一个更明显的晚期正成分（450-1100ms）,在右外侧额区则诱发一个更明显的晚期负成分（450~1100ms）;与之相反,MT与AC推理与基线任务相比,在左侧诱发一个更明显的晚期负成分（450~1100ms）,在右侧诱发一个更明显的晚期正成分（450~1100ms）,这一结果可能是由于左右脑在推理中的认知功能以及四种推理类型之间存在的差异所致,同时也表明推测过程主要激活了左右侧的前额部、颞叶等区域,基本支持Goel等人的双加工理论     

情绪状态对大学生条件推理的影响

采用不同情绪效价的电影片断诱发大学生不同的情绪,并运用眼动仪器记录条件推理的过程和结果,探讨了不同情绪状态对条件推理的影响状况。实验采用3（情绪组别：积极情绪、消极情绪、中性情绪）×4（推理形式：MP、DA、AC、MT）的混合实验设计。研究结果发现,中性情绪状态下的条件推理成绩显著地高于积极和消极情绪状态,结果支持抑制假说。     

命题内容对青少年条件推理的影响

选取3个具体内容的条件命题作为实验材料,以小四、初一、高一、大三的学生为被试,探讨了命题内容对青少年条件推理的影响机制及其发展特点。结果表明:(1)对同一年级而言,不同内容的条件命题的相同推理(MP、MT、DA、AC)之间表现出显著的差异;对不同年级而言,相同内容的条件命题的四种推理之间也存在显著的差异。(2)青少年的条件推理过程似乎是一种基于对事件发生概率估计的直觉判断,这一判断过程主要取决于个体知识经验的增长和主体认知水平的提高,而用形式逻辑的标准来衡量个体条件推理能力的高低似乎并不妥当。     

A mixed Rasch model of dual-process conditional reasoning

A fine-grained dual-process approach to conditional reasoning is advocated: Responses to conditional syllogisms are reached through the operation of either one of two systems, each of which can rely on two different mechanisms. System1 relies either on pragmatic implicatures or on the retrieval of information from semantic memory; System2 operates first through inhibition of System1, then (but not always) through activation of analytical processes. It follows that reasoners will fall into one of four groups of increasing reasoning ability, each group being uniquely characterized by (a) the modal pattern of individual answers to blocks of affirming the consequent (AC), denying the antecedent (DA), and modus tollens (MT) syllogisms featuring the same conditional; and (b) the average rate of determinate answers to AC, DA, and MT. This account receives indirect support from the extant literature and direct support from a mixed Rasch model of responses given to 18 syllogisms by 486 adult reasoners.     

Necessity and sufficiency in abstract conditional reasoning

The necessity and sufficiency of the cause relates to the conclusions people draw on everyday conditional inference problems. The current research explores the effects of necessity and sufficiency in an abstract causal context. Three experiments showed that the subjective ratings of necessity and sufficiency diverge from the objective levels: A sufficient and necessary cause is more often labelled as sufficient than a sufficient and not-necessary cause. Likewise, a necessary and sufficient cause is more often labelled necessary than a necessary and not-sufficient cause. In Experiments 1 and 2 we observed that the robust effects of sufficiency on MP and MT, and of necessity on AC and DA found on everyday reasoning generalise to abstract conditionals. There were also partial effects of sufficiency on AC and DA, and of necessity on MP and MT. When the problem presentation is simplified, as in Experiment 3, these partial effects on reasoning disappear. The reasoning results then relate to the objective levels and less to the subjective levels of necessity and sufficiency. This divergence sheds doubt on the idea that reasoners base their inferences on an active assessment of the necessity and/or sufficiency of the causal relation.     

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.     

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.     

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.     

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.     

Bias in Conditional Inference: Implications for Mental Models and Mental Logic

Three experiments are reported in which subjects are given the opportunity to make any of the four inferences associated with conditional statements: modus ponens (MP), denial of the antecedent (DA), affirmation of the consequent (AC), and modus tollens (MT). The primary purpose of the research was to establish the generality and robustness of polarity biases that may be occasioned by systematic rotation of negative components in the conditional rules. In Experiments 1 & 2, three forms of conditionals were used: “if (not) p then (not) q”, “(not) p only if (not) q” and “(not) q if (not) p”. Experiment 1 used a conclusion evaluation task, whereas Experiment 2 used a conclusion production task. In Experiment 3, thematic conditionals were presented with and without a preceding scenario.

The biases investigated were (a) affirmative premise bias—the tendency to draw more inferences from affirmative premises and (b) negative conclusion bias—the tendency to draw more inferences with negative conclusions. The suggestive evidence for affirmative premise bias in the literature was not supported: very little evidence was found for it in the current experiments. Robust findings of negative conclusion bias were, however, found across the three experiments, although the bias was mostly restricted to DA and MT inferences. This suggests that the bias is best regarded as a difficulty with double negation.

The results are discussed with respect to both the mental logic and mental model accounts of propositional reasoning. Neither theory as currently formulated can explain all of our findings, although a plausible revision of each is considered.     

From models to rules: mechanization of reasoning as a way to cope with cognitive overloading in combinatorial problems

It is hypothesized that the transition from unfamiliar problems to familiar, well-learned problems coincides with the transition from a model-based style of reasoning to a rule-based style of reasoning; model-based style of reasoning helps understanding the problem structure, but can overload working memory when the number of models required increases; rule-based style of reasoning avoids cognitive overloading, at the cost of making individuals liable to mechanization errors. In Experiment 1, the number of models required to respond to a verification task affected response latencies with unfamiliar problems, but not with familiar problems, supporting the initial hypothesis. In Experiment 2, participants were prone to mechanization errors when confronted with slightly modified problems in the late stages of the experiment, supporting the hypothesis that they had developed a reasoning rule in the early stages and were blindly applying it. The findings suggest that model-based reasoning and rule-based reasoning serve different purposes and have different costs and benefits, are both available to human reasoners, and familiarization with a problem may induce the transition from the former to the latter. The findings also suggest that mechanization of reasoning may be the first step along a gradient of decreasing cognitive load, whose end-point is automatization, as discussed in theories of automatization of information processing.     

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.     

Story Remembering Among Children

Abstract

The hypothesis that belief in the paranormal is related to reasoning errors was tested. College students were administered the Belief in the Paranormal Scale (Jones, Russell, &; Nickel, 1977) and a syllogistic reasoning test. A slight but statistically significant correlation was observed between BPS scores and the number of errors made on the reasoning test. This relationship was larger but not significantly so for reasoning items with paranormal content than for symbolic content. An a priori comparison indicated that the relationship between BPS scores and reasoning errors was significantly greater for problems that required subjects to determine the validity of hypotheses given statements of evidence than for problems that required subjects to determine the validity of deduced empirical predictions given hypotheses. Thus, belief in the paranormal among college students was very moderately correlated with reasoning ability and was observed most clearly when the reasoning problems contained paranormal content and when they required subjects to determine the validity of hypotheses given evidential statements.     

Pragmatic reasoning schemas

We propose that people typically reason about realistic situations using neither content-free syntactic inference rules nor representations of specific experiences. Rather, people reason using knowledge structures that we term pragmatic reasoning schemas, which are generalized sets of rules defined in relation to classes of goals. Three experiments examined the impact of a “permission schema” on deductive reasoning. Experiment 1 demonstrated that by evoking the permission schema it is possible to facilitate performance in Wason's selection paradigm for subjects who have had no experience with the specific content of the problems. Experiment 2 showed that a selection problem worded in terms of an abstract permission elicited better performance than one worded in terms of a concrete but arbitrary situation, providing evidence for an abstract permission schema that is free of domain-specific content. Experiment 3 provided evidence that evocation of a permission schema affects not only tasks requiring procedural knowledge, but also a linguistic rephrasing task requiring declarative knowledge. In particular, statements in the form if p then q were rephrased into the form p only if q with greater frequency for permission than for arbitrary statements, and rephrasings of permission statements produced a pattern of introduction of modals (must, can) totally unlike that observed for arbitrary conditional statements. Other pragmatic schemas, such as “causal” and “evidence” schemas can account for both linguistic and reasoning phenomena that alternative hypotheses fail to explain.     

Working memory and conditional reasoning

Little is known about the role of working memory in conditional reasoning. This paper reports three experiments that examine the contributions of the visuo-spatial scratch pad (VSSP), the articulatory loop, and the central executive components of Baddeley and Hitch's (1974) model of working memory to conditional reasoning. The first experiment employs a spatial memory task that is presented concurrently with two putative spatial interference tasks (tapping and tracking), articulatory suppression, and a verbal memory load. Only the tracking and memory load impaired performance, suggesting that these tap the VSSP and central executive, respectively. Having established the potency of these interference tasks two further experiments examined the effects of tapping and tracking (Experiment 2) and articulation and memory load (Experiment 3) on a conditional reasoning task. Neither tracking nor tapping affected the number of inferences accepted or response latency. Articulation also failed to affect conditional reasoning but memory load selectively reduced acceptance of modus tollens inferences. These results are discussed in terms of both rule-based and mental models theories of reasoning. While these data cannot discriminate between the two perspectives they provide support for one of the central assumptions in each: that some errors in reasoning are attributable directly to working memory demands. Taken together these experiments suggest that conditional reasoning requires an abstract working memory medium for representation; it does not require either the VSSP or the articulatory loop. It is concluded that the central executive provides the necessary substrate.     

Matching and oddity learning in the pigeon: Transfer effects and the absence of relational learning

Three experiments examined the extent to which pigeons trained on a matching or oddity discrimination with one pair of colours showed transfer when tested on a new matching or oddity discrimination with a new pair of colours. Experiment 1 examined the effects of key spacing and a delay procedure and replicated previous reports that in the transfer stage subjects given the same kind of problem (Non-shift condition) in general learn more rapidly than those given the opposite problem (Shift condition). However, this difference appeared only when pigeons given matching in both training and transfer stages were compared to those shifted from oddity to matching; it did not appear in birds transferred to oddity. Transfer was not significantly affected by key spacing or by the delay.

Experiments 2 and 3 examined transfer from a non-relational conditional discrimination based on one set of colours to a subsequent matching or oddity task based on two new colours. Both a comparison between the results of Experiment 1 and 2 and the corresponding within-experiment comparison from Experiment 3 showed that transfer from conditional training to matching was as great as from prior training on matching, while prior training on oddity produced negative transfer on shift to matching. It was suggested that this negative transfer occurs because pigeons trained on oddity have not learned to override an initial bias towards the odd stimulus in an array. Whatever the correct explanation; the present results provide no support for the claim that pigeons solve matching or oddity discriminations relationally.     

有关条件推理中概率效应的实验研究

通过预备实验选取了四种不同条件概率的条件规则和四种不同前后件概率组合的条件规则作为实验材料,以大学生为被试,考察了两种概率因素(条件概率和前后件概率)对条件推理的演绎形式(MP、DA、AC、MT)以及变通形式(四卡问题)的影响。结果表明,两种概率因素对四种条件推理的影响都非常显著,研究进一步证实了人们对四种推理的认可程度主要与范畴前提的概率成正比的结论;但概率因素对四卡问题的解决影响不明显。