Understanding causal conditionals: A study of individual differences

Previous studies have suggested that a minority of university students, of lower cognitive ability, are inclined to interpret abstract conditional statements, if p then q, as if they were conjunctions: p and q. In the present study we administered the conditional truth table task to a large sample of students (n = 160), but using realistic, everyday causal conditionals. We also measured their general intelligence. While individual differences were found, these were not consistent with some participants adopting a conjunctive interpretation of such statements. Rather, it appears that students of lower cognitive ability are rather likely to assume that a conditional implies its converse, so that it means also if q then p. The results are discussed with reference to the suppositional theory of conditionals and our more general account of hypothetical thinking.     

Inferential confusion in obsessive-compulsive disorder: the inferential confusion questionnaire

The current article represents the further validation of the construct of inferential confusion amongst clinical samples. Inferential confusion is proposed to be a meta-cognitive confusion particularly relevant to obsessive compulsive disorder (OCD) that leads a person to confuse an imagined possibility with an actual probability. As such, it conceptualizes OCD as a form of belief disorder similar to a delusion or overvalued idea that is a product of distorted reasoning processes. In contrast, other cognitive models of OCD emphasize a phobic model of development in OCD, and thus consider the exaggerated interpretation of intrusions as an essential element in OCD. The present study administered a revised version of the Inferential Confusion Questionnaire, and the Obsessive Belief Questionnaire (OBQ), to a total of 183 participants in three clinical groups and a non-clinical control group. Results suggest that OCD, at least in part, follows a non-phobic model of development with inferential confusion significantly related to obsessive-compulsive symptoms independently of cognitive domains as measured by the OBQ, and mood states. Further, scores on inferential confusion were particularly high in those with OCD and delusional disorder as compared to anxious and non-clinical controls.     

“Meaningful” social inferences: Effects of implicit theories on inferential processes

Perceivers’ shared theories about the social world have long featured prominently in social inference research. Here, we investigate how fundamental differences in such theories influence basic inferential processes. Past work has typically shown that integrating multiple interpretations of behavior during social inference requires cognitive resources. However, three studies that measured or manipulated people’s beliefs about the stable versus dynamic nature of human attributes (i.e., their entity vs. incremental theory, respectively) qualify these past findings. Results revealed that, when interpreting others’ actions, perceivers’ theories selectively facilitate the consideration of interpretations that are especially theory-relevant. While experiencing cognitive load, entity theorists continued to incorporate information about stable dispositions (but not about dynamic social situations) in their social inferences, whereas incremental theorists continued to incorporate information about dynamic social situations (but not about stable traits). Implications of these results for how perceivers find meaning in behavior are discussed.     

A necessity illusion for modal inferences from conditionals

Three experiments examined how people reason about what is possible or necessary when a conditional is true. Participants were asked to indicate whether it was necessary, possible or impossible for a specific instance to conform to one of the truth-table cases (pq, p¬q, ¬pq and ¬p¬q) (¬ = not), given the truth of the conditional. It was found that most participants, inconsistently, judged the pq case as necessary but the ¬pq or ¬p¬q cases as possible. Logically, these two kinds of judgments are contradictory. Moreover, a true conditional doesn’t imply that a specific instance under the conditional must be pq . Therefore, people demonstrate a necessity illusion for pq cases which contradicts their commitment to the possibility of ¬pq or ¬p¬q cases. Existing accounts of conditionals are unable to explain the contradiction and the necessity illusion. We propose an inference dissociation account and explore the theoretical implications of this necessity illusion.     

Enhancing adolescent girls’ argument skills in reasoning about personal and non-personal decisions

The present study sought to evaluate (a) the effectiveness of an intervention in developing adolescents’ argument skills regarding a decision on a topic of high potential personal relevance (teen pregnancy) or one of general social relevance (capital punishment), and (b) differential effects of the two topics in promoting the generalization of skills to a new topic. Thirty 14–15-year-old adolescent girls participated in an intervention on one of the two topics. The 16 sessions of the intervention were identical except for topic. Argument skills were assessed on both topics at pretest and posttest. Both interventions were effective in developing rudimentary argument skills, but only the intervention focusing on the personally relevant topic resulted in transfer to the less personal topic. Transfer in the opposite direction did not occur.     

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.     

Asymmetric transfer effects between cognitive and affective task disturbances

Task-irrelevant features of a stimulus can disturb performance on a given task, and this can occur for cognitive reasons such as irrelevant stimulus position, and affective reasons such as high stimulus valence. The human brain adapts to such disturbances in order to ensure successful task performance. Adaptations can occur in a transient manner in response to recent events, and they can also be sustained to account for overall probabilities of disturbances. Here, we study the mutual interplay between affective and cognitive task disturbances under conditions of sustained conflict adaptation. More precisely, we examined the trajectory of finger movements in a speeded classification task and investigated whether adaptation to a high probability of spatial disturbances transfers to the impact of affective disturbances (Experiment 1) and whether adaptation to a high probability of affective disturbances transfers to the impact of spatial disturbances (Experiment 2). Our observations point towards an asymmetric transfer from adaptation to affective onto the processing of cognitive disturbances, but not the other way around.     

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.     

Conflicts as aversive signals

Theories of human action control deal with the question of how cognitive control is dynamically adjusted to task demands. The conflict monitoring theory of anterior cingulate (ACC) function suggests that the ACC monitors for response conflicts in the ongoing processing stream thereby triggering the mobilization of cognitive control. Alternatively, the outcome evaluation account of ACC function suggests that the ACC monitors for negative performance outcomes, an information that serves as an aversive learning signal for future action selection. Botvinick (2007) recently suggested that both theories might converge on the detection of aversive signals in general. Here, the authors provide first evidence that conflicts are registered as aversive signals. Congruent and incongruent Stroop color-words served as primes, and positive and negative stimuli as targets in an affective priming paradigm. Negative targets were evaluated faster after incongruent than after congruent Stroop primes, and positive targets were evaluated slower after incongruent than after congruent primes. The finding that conflicts are actually registered as aversive signals bridges the gap between competing theories of ACC function and has broad theoretical and behavioral implications as it makes the conflict monitoring theory applicable to a much wider range of situations and tasks.     

Reducing postural sway by concurrently performing challenging cognitive tasks

The present experiment varied cognitive complexity and sensory modality on postural control in young adults. Seventeen participants (23.71 ± 1.99 years) were instructed to stand feet together on a force platform while concurrently performing cognitive tasks of varying degrees of difficulty (easy, moderate and difficult). The cognitive tasks were presented both, auditorily and visually. Auditory tasks consisted of counting the occurrence of one or two letters and repeating a string of words. Visual tasks consisted of counting the occurrence of one or two numbers. With increasing cognitive demand, area of 95% confidence ellipse and ML sway variability was significantly reduced. The visual tasks reduced ML sway variability, whereas the auditory tasks increased COP irregularity. We suggest that these findings are primarily due to an increase in sensorimotor integration as a result of a shift in attentional focus.     

Conflict tasks and the diffusion framework: Insight in model constraints based on psychological laws

Formal models of decision-making have traditionally focused on simple, two-choice perceptual decisions. To date, one of the most influential account of this process is Ratcliff’s drift diffusion model (DDM). However, the extension of the model to more complex decisions is not straightforward. In particular, conflicting situations, such as the Eriksen, Stroop, or Simon tasks, require control mechanisms that shield the cognitive system against distracting information. We adopted a novel strategy to constrain response time (RT) models by concurrently investigating two well-known empirical laws in conflict tasks, both at experimental and modeling levels. The two laws, predicted by the DDM, describe the relationship between mean RT and (i) target intensity (Piéron’s law), (ii) standard deviation of RT (Wagenmakers–Brown’s law). Pioneering work has shown that Piéron’s law holds in the Stroop task, and has highlighted an additive relationship between target intensity and compatibility. We found similar results in both Eriksen and Simon tasks. Compatibility also violated Wagenmakers–Brown’s law in a very similar and particular fashion in the two tasks, suggesting a common model framework. To investigate the nature of this commonality, predictions of two recent extensions of the DDM that incorporate selective attention mechanisms were simulated and compared to the experimental results. Both models predict Piéron’s law and the violation of Wagenmakers–Brown’s law by compatibility. Fits of the models to the RT distributions and accuracy data allowed us to further reveal their relative strengths and deficiencies. Combining experimental and computational results, this study sets the groundwork for a unified model of decision-making in conflicting environments.     

The compatibility heuristic in non-categorical hypothetical reasoning: Inferences between conditionals and disjunctions

A new theory explains how people make hypothetical inferences from a premise consistent with several alternatives to a conclusion consistent with several alternatives. The key proposal is that people rely on a heuristic that identifies compatible possibilities. It is tested in 7 experiments that examine inferences between conditionals and disjunctions. Participants accepted inferences between conditionals and inclusive disjunctions when a compatible possibility was immediately available, in their binary judgments that a conclusion followed or not (Experiment 1a) and ternary judgments that included it was not possible to know (Experiment 1b). The compatibility effect was amplified when compatible possibilities were more readily available, e.g., for ‘A only if B’ conditionals (Experiment 2). It was eliminated when compatible possibilities were not available, e.g., for ‘if and only if A B’ bi-conditionals and exclusive disjunctions (Experiment 3). The compatibility heuristic occurs even for inferences based on implicit negation e.g., ‘A or B, therefore if C D’ (Experiment 4), and between universals ‘All A’s are B’s’ and disjunctions (Experiment 5a) and universals and conditionals (Experiment 5b). The implications of the results for alternative theories of the cognitive processes underlying hypothetical deductions are discussed.     

The influence of clause order,congruency, and probability on the processing of conditionals

Conditional information can be equally asserted in the forms if p, then q (e.g., “if I am ill, I will miss work tomorrow”) and q, if p (e.g., “I will miss work tomorrow, if I am ill”). While this type of clause order manipulation has previously been found to have no influence on the ultimate conclusions participants draw from conditional rules, we used self-paced reading to examine how it affects the real time incremental processing of everyday conditional statements. Experiment 1 revealed that clause order interacts with presuppositional congruency as readers hypothetically represent counterfactual statements. When if p, then q counterfactuals contained a presupposition that was incongruent with prior context, these statements took longer to read than when the presupposition was congruent, but for q, if p conditionals there was no such congruency effect. Experiment 2 revealed that reading times were influenced by the subjective probability of an indicative conditional regardless of clause order, with a penalty observed for low-probability statements relative to high-probability statements in both conditional clause orders. These data reveal a dissociation whereby clause order mediates the effect of suppositional congruency on reading times, but does not mediate the effect of subjective probability.     

Post-error slowing: An orienting account

It is generally assumed that slowing after errors is a cognitive control effect reflecting more careful response strategies after errors. However, clinical data are not compatible with this explanation. We therefore consider two alternative explanations, one referring to the possibility of a persisting underlying problem and one on the basis of the low frequency of errors (orienting account). This latter hypothesis argues that infrequent events orient attention away from the task. Support for the orienting account was obtained in two experiments. Using a new experimental procedure, Experiment 1 demonstrated post-error slowing after infrequent errors and post-correct slowing after infrequent correct trials. In Experiment 2, slowing was observed following infrequent irrelevant tones replacing the feedback signals.     

Conflict detection,dual processes,and logical intuitions: Some clarifications

Recent studies on conflict detection during thinking suggest that reasoners are sensitive to possible conflict between their heuristic judgement and elementary logical or probabilistic principles. I have argued that this conflict sensitivity calls for the postulation of logical intuitions and has implications for the way we conceive the interaction between System-1 and System-2 in dual process theories. In this paper I clarify potential misconceptions about this work, discuss the link with other approaches, and sketch directions for further research.     

A psychological study of unconnected conditionals

Unconnected conditionals, also called irrelevant conditionals, are sentences of form if A, C, whose antecedent and consequent bear no connection. According to the main theories of conditional reasoning, the truth or high probability of an antecedent and a consequent is sufficient to make true or highly probable the corresponding conditional. We tested this assumption and showed that it does not hold for unconnected conditionals. Furthermore, we investigated experimentally the factors which favour the endorsement of irrelevant conditional constructions and found that this rate increases when an analogy can be built between the antecedent and the consequent or when the conditional is asserted before its components.     

Context-specific adjustment of cognitive control: Transfer of adaptive control sets

Cognitive control protects processing of relevant information from interference by irrelevant information. The level of this processing selectivity can be flexibly adjusted to different control demands (e.g., frequency of conflict) associated with a certain context, leading to the formation of specific context–control associations. In the present study we investigated the robustness and transferability of the acquired context–control demands to new situations. In three experiments, we used a version of the context-specific proportion congruence (CSPC) paradigm, in which each context (e.g., location) is associated with a specific conflict frequency, determining high and low control demands. In a learning phase, associations between context and control demands were established. In a subsequent transfer block, stimulus–response mappings, whole task sets, or context–control demands changed. Results showed an impressive robustness of context–control associations, as context-specific adjustments of control from the learning phase were virtually unaffected by new stimuli and tasks in the transfer block. Only a change of the context–control demand eliminated the context-specific adjustment of control. These findings suggest that context–control associations that have proven to be adaptive in the past are continuously applied despite major changes in the task structure as long as the context–control associations remain the same.     

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.     

Thinking about conditionals: A study of individual differences

Recent studies have shown the existence of two qualitatively distinct groups of people based on how they judge the probability of a conditional statement. The present study was designed to test whether these differences are rooted in distinctive means of processing conditional statements and whether they are linked to differences in general intelligence. In the study, each of 120 participants completed three separate cognitive tasks involving the processing of abstract conditional statements--the probability-of-conditionals task, the conditional truth table task, and the conditional inference task--in addition to completing a test of general intelligence (AH4). The results showed a number of predicted effects: People responding with conditional (rather than conjunctive) probabilities on the first task were higher in cognitive ability, showed reasoning patterns more consistent with a suppositional treatment of the conditional, and showed a strongly "defective" truth table pattern. The results include several novel findings and post challenges to contemporary psychological theories of conditionals.