Heuristic and analytic processes in mental models for conditionals: An integrative developmental theory

This article presents a developmental dual-process theory of the understanding of conditionals that integrates Evans’ heuristic–analytic theory within the revised mental model theory of conditional proposed by Barrouillet, Gauffroy, and Lecas (2008). According to this theory, the interpretation of a conditional sentence is driven by unconscious and implicit heuristic processes that provide individuals with an initial representation that captures its meaning by representing the cases that make it true. This initial model can be enriched with additional models (a process named fleshing out within the mental model theory) through the intervention of conscious and demanding analytic processes. Being optional, these processes construct representations of cases that are only compatible with the conditional, leaving its truth-value indeterminate when they occur. Because heuristic processes are relatively immune to developmental changes, while analytic processes strongly develop with age, the initial model remains stable through development whereas the number of additional models that can be constructed increases steadily. Thus, the dual-process mental model theory predicts in which cases conditionals will be deemed true, indeterminate, or false and how these cases evolve with age. These predictions were verified in children, adolescents and adults who were asked to evaluate the truth value and the probability of several types of conditionals. The results reveal a variety of developmental trajectories in the way different conditionals are interpreted, which can all be accounted for by our revised mental 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。     

Abstract reasoning and the interpretation of basic conditionals

Studies examining the interpretation that is given to if–then statementstypically use what are referred to as basic conditionals, which give contextless relations between two unrelated concrete terms (If the ball is blue, then the shape is square). However, there is some evidence that basic conditionals require a more abstract form of representation. In order to examine this, we presented participants with truth-table tasks involving either basic conditionals or conditionals referring to imaginary categories (If it is a bori, then it has red wings), and standard conditional inference tasks with abstract and familiar premises. As expected, fewer typical defective conditional interpretations were given to basic conditionals. In addition, partial correlations showed a unique relationship between the interpretation of basic conditionals and abstract inferential reasoning. Results suggest that people process basic conditionals as a form of abstract reasoning, and that the interpretation of conditionals must consider the semantic context.     

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.     

Logic,Pragmatics, and Types of Conditionals

Johnson-Laird and Byrne distinguished ten kinds of conditionals. Their framework was the mental models theory and they attributed different combinations of semantic possibilities to those ten types of conditionals. Based on such combinations, the mental models theory has clear predictions for reasoning tasks, including those kinds of conditionals and involving reasoning schemata such as Modus Ponens, Modus Tollens, the affirming the consequent fallacy, and the denying the antecedent fallacy. My aim in this paper is to show that the predictions of the mental logic theory for those reasoning tasks are exactly the same as those of the mental models theory, and that, therefore, such tasks are not useful to decide which of the two theories is correct.     

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。     

Real Objects Can Impede Conditional Reasoning but Augmented Objects Do Not

In this study, Knauff and Johnson‐Laird's (2002) visual impedance hypothesis (i.e., mental representations with irrelevant visual detail can impede reasoning) is applied to the domain of external representations and diagrammatic reasoning. We show that the use of real objects and augmented real (AR) objects can control human interpretation and reasoning about conditionals. As participants made inferences (e.g., an invalid one from "if P then Q" to "P"), they also moved objects corresponding to premises. Participants who moved real objects made more invalid inferences than those who moved AR objects and those who did not manipulate objects (there was no significant difference between the last two groups). Our results showed that real objects impeded conditional reasoning, but AR objects did not. These findings are explained by the fact that real objects may over‐specify a single state that exists, while AR objects suggest multiple possibilities.     

Concessive and semifactual interpretations during reasoning with multiple conditionals

The present research evaluates how people integrate factual ‘if then’ and semifactual ‘even if’ conditional premises in an inference task. The theory of mental models establishes that semifactual statements are represented by two mental models with different epistemic status: ‘A & B’ is conjectured and ‘not-A & B’ is presupposed. However, following the principle of cognitive economy in tasks with a high working memory load such as reasoning with multiple conditionals, people could simplify the deduction process in two ways, by discarding: (a) the presupposed case and/or (b) the epistemic status information. In Experiment 1 and Experiment 2, we evaluated each of these hypotheses. In Experiment 1, participants make inferences from two conditionals: two factual conditionals or one factual and one semifactual, with different representations. In Experiment 2, participants make inferences with a factual conditional followed by two different semifactual conditionals that share the same representations but differ in their epistemic status. Accuracy and latency data suggest that people think of both the conjectured and the presupposed situations, but do not codify the epistemic status of either when the task does not require it. The results are discussed through theoretical predictions about how people make inferences from different connected conditionals.     

Conditional reasoning in context: A developmental dual processes account

The way individuals interpret “if p then q” conditionals varies with content and context, often resulting in a biconditional reading. Surprisingly, truth table tasks reveal the existence of two different types of biconditional interpretations: equivalence, as for promises and threats, and defective biconditional, as for causal conditionals or indicative conditionals involving binary terms. The aim of this study was to determine how the interpretation of indicative conditionals is affected in children, adolescents, and adults, by restricting their context of enunciation to only one possible alternative for both the antecedent and the consequent. Moreover, we wanted to determine what is the exact nature of the biconditional interpretation induced by these restricted contexts. For this purpose, third, sixth, and ninth graders and adults performed a truth-value task on indicative conditionals presented either in restricted on non-restricted contexts. Restricted contexts had no effect on children who have a conjunctive interpretation of the conditional, but elicited a predominant defective biconditional reading in adolescents and adults. These results corroborate the developmental dual process account of conditional reasoning proposed by Gauffroy and Barrouillet (2009).     

Logic programming,probability, and two-system accounts of reasoning: a rejoinder to Oaksford and Chater (2014)

This reply to Oaksford and Chater’s (O&C)’s critical discussion of our use of logic programming (LP) to model and predict patterns of conditional reasoning will frame the dispute in terms of the semantics of the conditional. We begin by outlining some common features of LP and probabilistic conditionals in knowledge-rich reasoning over long-term memory knowledge bases. For both, context determines causal strength; there are inferences from the absence of certain evidence; and both have analogues of the Ramsey test. Some current work shows how a combination of counting defeaters and statistics from network monitoring can provide the information for graded responses from LP reasoning. With this much introduction, we then respond to O&C’s specific criticisms and misunderstandings.     

The Suppression of Inferences From Counterfactual Conditionals

We examine two competing effects of beliefs on conditional inferences. The suppression effect occurs for conditionals, for example, “if she watered the plants they bloomed,” when beliefs about additional background conditions, for example, “if the sun shone they bloomed” decrease the frequency of inferences such as modus tollens (from “the plants did not bloom” to “therefore she did not water them”). In contrast, the counterfactual elevation effect occurs for counterfactual conditionals, for example, “if she had watered the plants they would have bloomed,” when beliefs about the known or presupposed facts, “she did not water the plants and they did not bloom” increase the frequency of inferences such as modus tollens. We report six experiments that show that beliefs about additional conditions take precedence over beliefs about presupposed facts for counterfactuals. The modus tollens inference is suppressed for counterfactuals that contain additional conditions (Experiments 1a and 1b). The denial of the antecedent inference (from “she did not water the plants” to “therefore they did not bloom”) is suppressed for counterfactuals that contain alternatives (Experiments 2a and 2b). We report a new “switched-suppression” effect for conditionals with negated components, for example, “if she had not watered the plants they would not have bloomed”: modus tollens is suppressed by alternatives and denial of the antecedent by additional conditions, rather than vice versa (Experiments 3a and 3b). We discuss the implications of the results for alternative theories of conditional reasoning.     

Content and context effects in children's and adults' conditional reasoning

We have recently shown that children interpret conditional sentences with binary terms (e.g., male/female) in both the antecedent and the consequent as biconditionals (Barrouillet & Lecas, 1998). We hypothesized that the same effect can be obtained with conditionals that do not contain binary terms provided that they are embedded in a context that restricts to only two the possible values on both the antecedent and the consequent. In the present experiment, we asked 12-year-old children, 15-year-old children, and adults to draw conclusions from conditional syllogisms that involved three types of conditional sentence: (1) conditionals with binary terms (BB), (2) conditionals with non-binary terms (NN), and (3) conditionals with non-binary terms embedded in a restrictive context (NNR). As we predicted, BB conditionals elicited more biconditional response patterns than did NN conditionals in all age groups. On the other hand, manipulating the context had the same effect in children but not in adults. Content and context constraints on conditional reasoning along with developmental issues are discussed within the framework of the mental models theory.     

The Relation Between Factual and Counterfactual Conditionals

What is the relation between factual conditionals: If A happened then B happened, and counterfactual conditionals: If A had happened then B would have happened? Some theorists propose quite different semantics for the two. In contrast, the theory of mental models and its computer implementation interrelates them. It postulates that both can have a priori truth values, and that the semantic bases of both are possibilities: states that are possible for factual conditionals, and that were once possible but that did not happen for counterfactual conditionals. Two experiments supported these relations. Experiment 1 showed that, like factual conditionals, certain counterfactuals are true a priori, and others are false a priori. Experiment 2 replicated this result and showed that participants selected appropriate paraphrases, referring, respectively, to real and to counterfactual possibilities, for the two sorts of conditional. These results are contrary to alternative accounts of conditionals.     

Mental models in deductive reasoning

We report research investigating the role of mental models in deduction. The first study deals with conjunctive inferences (from one conjunction and two conditional premises) and disjunctive inferences (from one disjunction and the same two conditionals). The second study examines reasoning from multiple conditionals such as: If e then b; If a then b; If b then c; What follows between a and c? The third study addresses reasoning from different sorts of conditional assertions, including conditionals based on if then, only if, and unless. The paper also presents research on figural effects in syllogistic reasoning, on the effects of structure and believability in reasoning from double conditionals, and on reasoning from factual, counterfactual, and semifactual conditionals. The findings of these studies support the model theory, pose some difficulties for rule theories, and show the influence on reasoning of the linguistic structure and the semantic content of problems.     

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.     

On the basis of belief in causal and diagnostic conditionals

According to the suppositional theory of conditionals, people assess their belief in a conditional statement of the form “if p then q” by conducting a mental simulation on the supposition of p in which they assess their degree of belief in q. This leads to them to the judge the probability of a conditional statement to be equal to the conditional probability, P(q|p). Evidence for this conditional probability hypothesis has been adduced in earlier studies for abstract, causal, and counterfactual conditionals. For the realistic conditionals, it is natural to assume that people perform such mental simulations by building causal mental models from prior causes to later effects. However, in the present study we show that the conditional probability hypothesis extends to diagnostic conditionals, which relate effects to causes. This new finding presents a major challenge for theoretical accounts of the mental processing of conditional statements.     

The Causal Structure of Utility Conditionals

The psychology of reasoning is increasingly considering agents' values and preferences, achieving greater integration with judgment and decision making, social cognition, and moral reasoning. Some of this research investigates utility conditionals, ‘‘if p then q’’ statements where the realization of p or q or both is valued by some agents. Various approaches to utility conditionals share the assumption that reasoners make inferences from utility conditionals based on the comparison between the utility of p and the expected utility of q. This article introduces a new parameter in this analysis, the underlying causal structure of the conditional. Four experiments showed that causal structure moderated utility‐informed conditional reasoning. These inferences were strongly invited when the underlying structure of the conditional was causal, and significantly less so when the underlying structure of the conditional was diagnostic. This asymmetry was only observed for conditionals in which the utility of q was clear, and disappeared when the utility of q was unclear. Thus, an adequate account of utility‐informed inferences conditional reasoning requires three components: utility, probability, and causal structure.     

Pronounced inferences: A study on inferential conditionals

An experimental study is reported which investigates the differences in interpretation between content conditionals (of various pragmatic types) and inferential conditionals. In a content conditional, the antecedent represents a requirement for the consequent to become true. In an inferential conditional, the antecedent functions as a premise and the consequent as the inferred conclusion from that premise. The linguistic difference between content and inferential conditionals is often neglected in reasoning experiments. This turns out to be unjustified, since we adduced evidence on the basis of a quantitative and a qualitative analysis that this difference has a manifest psychological relevance. For the inferential conditionals, participants appear to retrieve the order of events of the original content conditional on which it was based, before they start reasoning with it. The implications of this finding for reasoning research and linguistics will be discussed.     

The Mental Model Theory of Conditionals: A Reply to Guy Politzer

This paper replies to Politzer’s (2007) criticisms of the mental model theory of conditionals. It argues that the theory provides a correct account of negation of conditionals, that it does not provide a truth-functional account of their meaning, though it predicts that certain interpretations of conditionals yield acceptable versions of the ‘paradoxes’ of material implication, and that it postulates three main strategies for estimating the probabilities of conditionals.