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).     

Is everyday experience dysfunctional for the development of conditional reasoning?

According to “Comprehension theory” improved performance on invalid conditional syllogisms is a function of the ability to dissociate from a biconditional interpretation. Given that biconditional interpretation is typically used in inferring from everyday conditionals (i.e., circumstantial conditionals), the accumulation of everyday experience should reinforce its usage rather than weaken it and, hence, be dysfunctional in solving invalid conditional syllogisms. This study examines the hypothesis that certain kinds of experiences that are unique to schooling account for improved performance on invalid problems with age. The study estimated the independent effects of age and schooling in Grades 5 and 6 on scores obtained on invalid conditional and class syllogisms. The results point to a negative, albeit very small effect of out-of-school experience and to a considerable positive effect of schooling. Hence, contrary to other cognitive tasks in which schooling operates in the same direction as out-of-school experience, in this case, it apparently breaks daily-life interpretational habits and therefore is crucial for the developmental process.     

Reasoning about conditional sentences: development of understanding of cues to quantification

The previous literature has reported that when children are asked to judge the truth or falsity of universally quantified conditional sentences of the form If a thing is P then it is Q they typically give responses, e.g., responding "true" whenever there is a case of P and Q even if there are also cases of P and not-Q. Three experiments are reported that address possible sources of this error. Experiment 1 shows that the error survives on sentences that refer to particular things as well as to things of a particular kind, and further shows that articulating the necessity of the consequent (... then it has to be Q) eliminates the error for adults and reduces it for fifth graders, although it does not affect second grade performance. Experiment 2 shows that for second and fifth graders the error survives to problems that are not universally quantified and for second graders to problems that are not conditionals although are otherwise structurally similar. Experiment 3 compares various verbal formulations of such universally quantified conditionals: Second and fifth graders do not make the error when the quantification is expressed with the surface structure that makes its universality most explicit (all things ...); the error tendency is greatest when the indefinite article is used (if a thing ...); and formulations using any fall in between. We argue that such erroneous evaluations of universally quantified conditionals have more to do with the quantificational aspect than the conditional aspect of the problems; children interpret the indefinite article as existential, although they resist the error when the cue to universal quantification is completely clear. The error appears to result more from the surface-structure form of the stimuli than from an inability of children to appreciate the logic of universally quantified conditionals.     

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.     

Processing of logically valid and logically invalid conditional inferences in discourse comprehension

Two competing theories of processing of conditionals (if-then) were tested. Syntactic theories posit that people only draw inferences conforming to the logically valid modus ponens (MP) schema. Mental models theories predict that people draw MP and invalid affirming-the-consequent (AC) inferences. Three experiments tested these predictions. Participants read short stories that conformed to either the MP or AC form but without conclusions, and they completed either priming or recognition tasks. Results indicate that both MP and AC inferences occur during discourse processing: MP and AC premise forms prime their respective conclusions, participants erroneously judged that they had read the conclusions to MP and AC arguments, and AC inferences did not stem from a biconditional interpretation of conditionals. Findings support mental models theories.     

Reasoning counterfactually: making inferences about things that didn't happen

The authors investigated the relationship between reasoners' understanding of subjunctive conditionals (e.g., if p had happened, then q would have happened) and the inferences they were prepared to endorse. Reasoners who made a counterfactual interpretation of subjunctive statements (i.e., they judged the statement to imply that p and q did not happen) endorsed different inferences than those who did not. Those who made a counterfactual interpretation were more likely to (a) judge the situation in which p and q occurred to be inconsistent with the conditional statement and (b) make negative inferences such as modus tollens (i.e., approximately q therefore approximately p). These findings occurred with familiar and unfamiliar content, affirmative and negative conditionals, and conditional and biconditional relations.     

Comparing the meanings of “if” and “all”

In this study, we compared the everyday meanings of conditionals (“if p then q”) and universally quantified statements (“all p are q”) when applied to sets of elements. The interpretation of conditionals was predicted to be directly related to the conditional probability, such that P(“if p then q”) = P(q|p). Quantified statements were assumed to have two interpretations. According to an instance-focused interpretation, quantified statements are equivalent to conditionals, such that P(“all p are q”) = P(q|p). According to a set-focused interpretation, “all p are q” is true if and only if every instance in set p is an instance of q, so that the statement would be accepted when P(q|p) = 1 and rejected when this probability was below 1. We predicted an instance-focused interpretation of “all” when the relation between p and q expressed a general law for an infinite set of elements. A set-focused interpretation of “all” was predicted when the relation between p and q expressed a coincidence among the elements of a finite set. Participants were given short context stories providing information about the frequency of co-occurrence of cases of p, q, not-p, and not-q in a population. They were then asked to estimate the probability that a statement (conditional or quantified) would be true for a random sample taken from that population. The probability estimates for conditionals were in accordance with an instance-focused interpretation, whereas the estimates for quantified statements showed features of a set-focused interpretation. The type of the relation between p and q had no effect on this outcome.     

A process model of the understanding of uncertain conditionals

To build a process model of the understanding of conditionals we extract a common core of three semantics of if-then sentences: (a) the conditional event interpretation in the coherencebased probability logic, (b) the discourse processingtheory of Hans Kamp, and (c) the game-theoretical approach of Jaakko Hintikka. The empirical part reports three experiments in which each participant assessed the probability of 52 if-then sentencesin a truth table task. Each experiment included a second task: An n-back task relating the interpretation of conditionals to working memory, a Bayesian bookbag and poker chip task relating the interpretation of conditionals to probability updating, and a probabilistic modus ponens task relating the interpretation of conditionals to a classical inference task. Data analysis shows that the way in which the conditionals are interpreted correlates with each of the supplementary tasks. The results are discussed within the process model proposed in the introduction.     

Conflicting desire and the child's theory of mind

We contrast the standard representational theory-of-mind approach to the understanding of mental states with an alternative view that theory-of-mind tasks require executive functioning or the inhibition of more “cognitively salient” information. Two experiments test the hypothesis that 3-year-olds' apparent problems on theory-of-mind tasks are not due to an inability to represent the mental contents of another, but rather lie in the informational structure of the task. In Experiment 1, 3- to 5-year-olds were tested on their understanding of desire in others either when they themselves held a strong and conflicting desire or when they had no strong desire. Results showed that under the condition of having a strong and conflicting desire, only 5-year-olds were able to recognize that another person may desire something different. In contrast, when the children themselves held no strong desire, even 3-year-olds were able to judge another's desire correctly. Experiment 2 compared 3-year-olds' performance on a standard false-belief task with an equivalently structured desire task in which participants had again to inhibit their own strong and conflicting desire. Results showed similar performance on the traditional false-belief task and the new conflicting-desire task.     

Counterfactual antecedent falsity and the epistemic sensitivity of counterfactuals

Why do utterances of counterfactual conditionals typically, but not universally, convey the message that their antecedents are false? I demonstrate that two common theoretical commitments–commitment to the existence of scalar implicature and of informative presupposition—can be supplemented with an independently motivated theory of the presuppositions of competing conditional alternatives to jointly predict this information when and only when it appears. The view works best if indicative and counterfactual conditionals have a closely related semantics, so I conclude by undermining two familiar arguments for a nonunified semantics of indicative and counterfactual conditionals.     

Reasoning About Uncertain Conditionals

There is a long tradition in formal epistemology and in the psychology of reasoning to investigate indicative conditionals. In psychology, the propositional calculus was taken for granted to be the normative standard of reference. Experimental tasks, evaluation of the participants’ responses and psychological model building, were inspired by the semantics of the material conditional. Recent empirical work on indicative conditionals focuses on uncertainty. Consequently, the normative standard of reference has changed. I argue why neither logic nor standard probability theory provide appropriate rationality norms for uncertain conditionals. I advocate coherence based probability logic as an appropriate framework for investigating uncertain conditionals. Detailed proofs of the probabilistic non-informativeness of a paradox of the material conditional illustrate the approach from a formal point of view. I survey selected data on human reasoning about uncertain conditionals which additionally support the plausibility of the approach from an empirical point of view.     

Past Tense and Past Times in Subjunctive Conditionals

Some theories of conditionals maintain that the difference between indicative and subjunctive conditionals involves the standard temporal interpretation of past tense. I provide an argument against such theories. The argument is based on the claim that these views do not correctly predict the correspondence between tense marking and temporal interpretation in certain conditionals.     

Advice conditionals about tips and warnings: interpretations and inferences

Two experiments examine how people interpret and reason about advice conditionals, such as tips, for example, “if you study more your grades will improve”, and warnings, for example, “if you stop exercising you will gain weight”. Experiment 1 showed that when participants reason about whether a tip or warning could be true in different situations, their judgments correspond to a biconditional or conditional interpretation on about half of all trials, but to an enabling or tautology interpretation on many others. Experiment 2 showed that participants make few modus ponens and tollens inferences from tips and warnings, and more modus ponens inferences from tips than warnings. The implications for alternative theories are discussed.     

Embedding If and Only If

Some left-nested indicative conditionals are hard to interpret while others seem fine. Some proponents of the view that indicative conditionals have No Truth Values (NTV) use their view to explain why some left-nestings are hard to interpret: the embedded conditional does not express the truth conditions needed by the embedding conditional. Left-nestings that seem fine are then explained away as cases of ad hoc, pragmatic interpretation. We challenge this explanation. The standard reasons for NTV about indicative conditionals (triviality results, Gibbardian standoffs, etc.) extend naturally to NTV about biconditionals. So NTVers about conditionals should also be NTVers about biconditionals. But biconditionals embed much more freely than conditionals. If NTV explains why some left-nested conditionals are hard to interpret, why do biconditionals embed successfully in the very contexts where conditionals do not embed?     

Triviality For Restrictor Conditionals

I present two Triviality results for Kratzer's standard “restrictor” analysis of indicative conditionals (while also clarifying the sense in which Kratzer's semantics might avoid such results). I both refine and undermine the common claim that problems of Triviality do not arise for Kratzer conditionals since they are not strictly conditionals at all.     

Conditionals Right and Left: Probabilities for the Whole Family

The fact that the standard probabilistic calculus does not define probabilities for sentences with embedded conditionals is a fundamental problem for the probabilistic theory of conditionals. Several authors have explored ways to assign probabilities to such sentences, but those proposals have come under criticism for making counterintuitive predictions. This paper examines the source of the problematic predictions and proposes an amendment which corrects them in a principled way. The account brings intuitions about counterfactual conditionals to bear on the interpretation of indicatives and relies on the notion of causal (in)dependence.     

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.     

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.     

5～8岁儿童二级信念-愿望推理能力的发展

该研究依据信念(正确-错误)和愿望(接近-回避)对儿童的二级信念-愿望推理能力进行了细分,并据此设计了四个二级信念-愿望任务,探讨了480名5～8岁儿童在四个任务上的表现。结果发现,对儿童而言,不同的二级信念-愿望任务的难度不同,由易到难的顺序依次为:二级真实信念接近愿望、二级错误信念接近愿望、二级真实信念回避愿望、二级错误信念回避愿望。     

Extreme elemental processing in a high schizotypy population: Relation to cognitive deficits

The cognitive deficits observed in schizophrenia have been characterized as a failure to utilize task-setting information to guide behaviour, especially in situations in which there is response conflict. Recently, we have provided support for this account; high schizotypy individuals demonstrated inferior biconditional discrimination performance compared to low scorers, but were not impaired on a simple discrimination that did not require the use of task-setting cues. These results may, however, also be explained by the way in which individuals with high schizotypy process stimulus compounds. Here, we examine the initial approaches to solving biconditional and control discrimination tasks of participants with high and low schizotypy scores. In particular, we focus on performance during the first block of training trials to capture processing style before the acquisition of the discrimination tasks. Participants scoring highly on the introvertive anhedonia subscale (which has been allied to the negative and cognitive symptoms of schizophrenia) demonstrated better biconditional performance during the first block of training trials than did low-schizotypy individuals, consistent with a highly elemental approach to stimulus processing. Subsequent recognition tests confirmed this analysis demonstrating that the pattern of performance observed in participants with high schizotypy was associated with a failure to discriminate conjunctions of items that had been seen before from those that had not. These results suggest that the negative/cognitive symptoms of schizophrenia may reflect an extreme bias towards elemental, as opposed to configural, processing of stimulus conjunctions.