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.     

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.     

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.     

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.     

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.     

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。     

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.     

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.     

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。     

When will is not the same as should: The role of modals in reasoning with legal conditionals

Naïve reasoners reject logically valid conclusions from conditional rules if they can think of exceptions in which the antecedent is true, but the consequent is not. However, when reasoning with legal conditionals (e.g., “If a person kills another human, then this person should be punished for manslaughter”) people hardly consider exceptions but evaluate conclusions depending on their own sense of justice. We show that participants’ reluctance to consider exceptions in legal reasoning depends on the modal auxiliary used. In two experiments we phrased legal conditionals either with the modal “should” (i.e., “ . . . then this person should be punished”), or with “will” (i.e., “ . . . then this person will be punished”) and presented them as modus ponens or modus tollens inferences. Participants had to decide whether the offender should or will be punished (modus ponens) or whether the offender indeed committed the offence (modus tollens). For modus ponens inferences phrased with “should” we replicate previous findings showing that participants select conclusions on the basis of their own sense of justice (Experiments 1 and 2). Yet, when the legal conditional is phrased with the modal “will” this effect is attenuated (Experiments 1 and 2), and exceptions are considered (Experiment 1). The modal auxiliary did not affect modus tollens inferences.     

Individual differences in conditional reasoning: A dual-process account

Dual-process theories of conditional reasoning predict that relationships among four basic logical forms, and to intellectual ability and thinking predictions, are most evident when conflict arises between experiential and analytic processing (e.g., Stanovich & West, ). To test these predictions, 210 undergraduates were presented with conditionals for which the consequents were either weakly or strongly associated with alternative antecedents (i.e., WA and SA problems, respectively). Consistent with predictions, modus ponens inferences were not related to inferences on the uncertain forms (affirmation of the consequent, denial of the antecedent). On WA problems, modus tollens, affirmation of the consequent, and denial of the antecedent were related to each other and to verbal ability. Modus ponens was linked to verbal ability only when disabling conditions were activated. In accord with the predictions of Stanovich and West (), on most problems, thinking dispositions predicted variance in inferences independently from verbal ability. We argue that a largely automatic experiential processing system governs performance on modus ponens, unless disablers are activated. Consciously controlled analytic processing predominates on the uncertain forms and, under some conditions, on modus tollens.     

The emergence of inferential rules: The use of pragmatic reasoning schemas by preschoolers

This study contrasts the pragmatic view with the natural logic view regarding the origin of inferential rules in conditional reasoning. The pragmatic view proposes that pragmatic rules emerge first, and the generalizations of these produce formal rules. In contrast, the natural logic view proposes that the formal rules emerge first and serve as a core that is then supplemented by pragmatic rules. In an experiment, scenarios involving conditional rules in different contexts, permission and arbitrary, were administered to independent groups of preschool children. To rule out the matching bias [Evans, J. St. B. T., & Lynch, J. S. (1973). Matching bias in the selection task. Br J Psychol 64, 391–397] as a possible explanation of reasoning performance, children were given conditional rules with a negated consequent. The results show that in the arbitrary context modus tollens (MT) was unavailable, and the use of modus ponens (MP) was unstable. In contrast, children in the permission context reliably used both MP and MT. In addition, they realized that a conditional rule does not imply a definite answer when the consequent holds. These findings suggest that, in their explicit forms, pragmatic rules emerge earlier than formal rules and in particular, even as basic a rule as MP is generalized from a context-specific form to a context-general one in preschool children.     

Inferences from counterfactual threats and promises

We examine how people understand and reason from counterfactual threats, for example, "if you had hit your sister, I would have grounded you" and counterfactual promises, for example, "if you had tidied your room, I would have given you ice-cream." The first experiment shows that people consider counterfactual threats, but not counterfactual promises, to have the illocutionary force of an inducement. They also make the immediate inference that the action mentioned in the "if" part of the counterfactual threat and promise did not occur. The second experiment shows that people make more negative inferences (modus tollens and denial of the antecedent) than affirmative inferences (modus ponens and affirmation of the consequent) from counterfactual threats and promises, unlike indicative threats and promises. We discuss the implications of the results for theories of the mental representations and cognitive processes that underlie conditional inducements.     

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     

Reasoning with conditionals: a test of formal models of four theories

The four dominant theories of reasoning from conditionals are translated into formal models: The theory of mental models (Johnson-Laird, P. N., & Byrne, R. M. J. (2002). Conditionals: a theory of meaning, pragmatics, and inference. Psychological Review, 109, 646-678), the suppositional theory (Evans, J. S. B. T., & Over, D. E. (2004). If. Oxford: Oxford University Press), a dual-process variant of the model theory (Verschueren, N., Schaeken, W., & d'Ydewalle, G. (2005). A dual-process specification of causal conditional reasoning. Thinking &Reasoning, 11, 278-293), and the probabilistic theory (Oaksford, M., Chater, N., & Larkin, J. (2000). Probabilities and polarity biases in conditional inference. Journal of Experimental Psychology: Learning, Memory, and Cognition, 26, 883-899). The first three theories are formalized as multinomial models. The models are applied to the frequencies of patterns of acceptance or rejection across the four basic inferences modus ponens, acceptance of the consequent, denial of the antecedent, and modus tollens. Model fits are assessed for two large data sets, one representing reasoning with abstract, basic conditionals, the other reflecting reasoning with pseudo-realistic causal and non-causal conditionals. The best account of the data was provided by a modified version of the mental-model theory, augmented by directionality, and by the dual-process model.     

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.     

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 processing of negations in conditional reasoning: A meta-analytic case study in mental model and/or mental logic theory

We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs.     

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.