Cultural preferences for formal versus intuitive reasoning

The authors examined cultural preferences for formal versus intuitive reasoning among East Asian (Chinese and Korean), Asian American, and European American university students. We investigated categorization (Studies 1 and 2), conceptual structure (Study 3), and deductive reasoning (Studies 3 and 4). In each study a cognitive conflict was activated between formal and intuitive strategies of reasoning. European Americans, more than Chinese and Koreans, set aside intuition in favor of formal reasoning. Conversely, Chinese and Koreans relied on intuitive strategies more than European Americans. Asian Americans' reasoning was either identical to that of European Americans, or intermediate. Differences emerged against a background of similar reasoning tendencies across cultures in the absence of conflict between formal and intuitive strategies.     

Quantifying disablers in reasoning with universal and existential rules

People accept conclusions of valid conditional inferences (e.g., if p then q, p therefore q) less, the more disablers (circumstances that prevent q to happen although p is true) exist. We investigated whether rules that through their phrasing exclude disablers evoke higher acceptance ratings than rules that do not exclude disablers. In three experiments we re-phrased content-rich conditionals from the literature as either universal or existential rules and embedded these rules in Modus Ponens and Modus Tollens inferences. In Experiments 2 and 3, we also used abstract rules. The acceptance of conclusions increased when the rule was phrased with “all” instead of “some” and the number of disablers had a higher impact on existential rules than on universal rules. Further, the effect of quantifier was more pronounced for abstract rules and when tested within subjects. We discuss the relevance of phrasing, quantifiers and knowledge on reasoning.     

Young children's reasoning about the order of past events

Four studies are reported that employed an object location task to assess temporal-causal reasoning. In Experiments 1-3, successfully locating the object required a retrospective consideration of the order in which two events had occurred. In Experiment 1, 5- but not 4-year-olds were successful; 4-year-olds also failed to perform at above-chance levels in modified versions of the task in Experiments 2 and 3. However, in Experiment 4, 3-year-olds were successful when they were able to see the object being placed first in one location and then in the other, rather than having to consider retrospectively the sequence in which two events had happened. The results suggest that reasoning about the causal significance of the temporal order of events may not be fully developed before 5 years.     

The impact of anxiety on analogical reasoning

The effect of state anxiety on analogical reasoning was investigated by examining qualitative differences in mapping performance between anxious and non-anxious individuals reasoning about pictorial analogies. The working-memory restriction theory of anxiety, coupled with theories of analogy that link complexity of mapping with working-memory capacity, predicts that high anxiety will impair the ability to find correspondences based on relations between multiple objects relative to correspondences based on overlap of attributes between individual objects. Anxiety was induced in one condition by a stressful speeded subtraction task administered prior to the analogy task. Anxious participants produced fewer relational responses and more attribute responses than did non-anxious participants, both in the absence of explicit instructions to find relational mappings (Experiment 1) and after receiving such instructions (Experiment 2). The findings support the postulated links among anxiety, working memory, and the ability to perform complex analogical mapping.     

The specificity of terms affects conditional reasoning

Conditional inferences can be phrased with unspecific terms (“If a person is on a diet, then the person loses weight. A person is on a diet. The person loses weight”) or specific terms (“If Anna is on a diet, then Anna loses weight. Anna is on a diet. Anna loses weight”). We investigate whether the specificity of terms affects people's acceptance of inferences. In Experiment 1, inferences with specific terms received higher acceptance ratings than inferences with unspecific terms. In Experiments 2 and 3, we used the same problems as in Experiment 1 but also problems with unspecific terms in the conditional and specific terms in the categorical and vice versa. When the conditional and the categorical had the same specificity, results were as in Experiment 1. When the specificity of the conditional and the categorical mismatched, acceptance ratings were lower. Our results illustrate the importance of phrasing on reasoning.     

Experts and laymen grossly underestimate the benefits of argumentation for reasoning

Many fields of study have shown that group discussion generally improves reasoning performance for a wide range of tasks. This article shows that most of the population, including specialists, does not expect group discussion to be as beneficial as it is. Six studies asked participants to solve a standard reasoning problem—the Wason selection task—and to estimate the performance of individuals working alone and in groups. We tested samples of U.S., Indian, and Japanese participants, European managers, and psychologists of reasoning. Every sample underestimated the improvement yielded by group discussion. They did so even after they had been explained the correct answer, or after they had had to solve the problem in groups. These mistaken intuitions could prevent individuals from making the best of institutions that rely on group discussion, from collaborative learning and work teams to deliberative assemblies.     

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.     

Multiple layers of information processing in deductive reasoning: combining dual strategy and dual-source approaches to reasoning

The idea that inferential performance cannot be analyzed within a single model has been suggested within two theoretical contexts. The dual strategy model suggests that people reason using different approaches to processing statistical information. The dual-source model suggests that people reason probabilistically using both statistical information and some intuition about logical form. Each model suggests that people have different approaches to processing information while making inferences. The following studies examined whether these different forms of information processing were equally present during reasoning. Participants were given a series of problems designed to distinguish counterexample from statistical reasoners. They were then given a series of MP or AC inferences for which identical statistical information was provided. Results show that MP inferences were considered to be deductively valid more often than equivalent AC inferences. The effect of logical form was independent of reasoning strategy, and of relatively equivalent size for both counterexample and statistical reasoners. The second study examined explicitly probabilistic inferences, and showed smaller effects of logical form and of reasoning strategy, although with a complex set of interactions. These results show that understanding the way that people use information when making inferences requires a multidimensional approach.     

Effects of training and instruction on analytic and belief-based reasoning processes

Two studies are reported which demonstrate that analytic responding on everyday reasoning problems can be increased and bias eliminated after training on the law of large numbers (Fong, Krantz, & Nisbett, 1986 Fong, G. T., Krantz, D. H. and Nisbett, R. E. 1986. The effects of statistical training on thinking about everyday problems. Cognitive Psychology, 18: 253–292. [Crossref], [Web of Science ®] , [Google Scholar]). Critical thinking problems involving belief-consistent, neutral, and inconsistent conclusions were presented. Belief bias was eliminated when a written justification of argument strength was elicited. However, belief-based responding was still evident when evaluations of the arguments were elicited using rating scales. This finding demonstrates a dissociation between analytic and belief-based responding as a function of response format. In Experiment 2 an instructional condition designed to foster decontextualised reasoning was included but was ineffective in reducing the degree to which judgements were biased by beliefs. It was concluded that training which makes available the analytic strategies necessary to evaluate a problem has the potential to facilitate performance only if the requested response triggers conscious deliberation of the evidence.     

Shared and distinct cue utilization for metacognitive judgements during reasoning and memorisation

Metacognitive research is dominated by meta-memory studies; meta-reasoning research is nascent. Accessibility – the number of associations for a stimulus – is a reliable heuristic cue for Feeling of Knowing when answering knowledge questions. We used a similar cue, subjective accessibility, for exposing commonalities and differences between meta-reasoning and meta-memory. In Experiment 1, participants faced solvable Compound Remote Associate problems mixed with unsolvable random word triads. We collected initial Judgement of Solvability (iJOS), final JOS (fJOS) and confidence. Experiment 2 focused on confidence, controlling for potential interactions among judgements. In Experiment 3, the participants memorised the same triads and rated Ease of Learning and Judgement of Learning. sAccessibility was associated with all judgements. Notably, it reliably predicted memory judgements and confidence in the provided solutions. However, it was unreliable for judging solvability (iJOS and fJOS). The findings highlight the importance of studying meta-reasoning for exposing the biasing factors in reasoning processes and for getting a broad perspective on metacognitive processes.     

Supporting the formal verification of mathematical texts

The formal verification of mathematical texts is one of the most interesting applications for computer systems. In fact, we argue that the expert language of mathematics is the natural choice for achieving efficient mathematician–machine interaction. Our empirical approach, the analysis of carefully authored textbook proofs, forces us to focus on the language and the reasoning pattern that mathematician use when presenting proofs to colleagues and students. Enabling a machine to understand and follow such language and argumentation is seen to be the key to usable and acceptable math assistant systems. In this paper, we first perform an analysis of three textbook proofs by hand; we then describe a computational framework that aims at mechanising such an analysis. The resulting proof-of-concept implementation is capable of processing simple textbook proofs and constitutes promising steps towards a natural mathematician–machine interface for proof development and verification.     

Implication and reasoning in mental state attribution: Comments on Jane Heal's theory of co-cognition

Simulation theory explains third-person mental state attribution in terms of an attributor's ability to imaginatively mimic other people's mental processes. Jane Heal's version of simulation theory, which she calls a theory of “co-cognition,” maintains that one can know and can predict others’ beliefs primarily by thinking about what their antecedent beliefs imply. I argue that Heal's account of belief attribution elides crucial differences between reasoning and merely discovering relations among propositions.     

Independent effects of relevance and arousal on deductive reasoning

Emotional content can have either a deleterious or a beneficial impact on logicality. Using standard deductive-reasoning tasks, we tested the hypothesis that the interplay of two factors – personal relevance and arousal – determines the nature of the effect of emotional content on logicality. Arousal was assessed using measures of skin conductance. Personal relevance was manipulated by asking participants to reason about semantic contents linked to an emotional event that they had experienced or not. Findings showed that (1) personal relevance exerts a positive effect on logicality while arousal exerts a negative effect, and that (2) these effects are independent of each other.     

Deciding between theories of how reasoning develops is hard

Although Sloutsky agrees with our interpretation of our data, he argues that the totality of the evidence supports his claim that children make inductive generalisations on the basis of similarity. Here we take issue with his characterisation of the alternative hypotheses in his informal analysis of the data, and suggest that a thorough Bayesian analysis, although practically very difficult, is likely to result in a more finely balanced outcome than he suggests.     

A formal framework for characterizing querying algorithms

Algorithmic procedures have been devised for constructing a knowledge space by querying experts. The queries submitted to the expert consist of assertions that are to be accepted or rejected. The present paper provides a characterization of the algorithms that may be used to draw inferences from previously collected answers. It is based on the notion of a closure on the set of all assertions, and its extension to a set containing for each assertion a positive and a negative instance, representing acceptance and rejection, respectively. The developed characterization emphasizes the significance of the well-known QUERY and PS-QUERY procedures. Potential applications of the presented results in contexts other than knowledge space theory are pointed out.     

Interference between cues requires a causal scenario: Favorable evidence for causal reasoning models in learning processes

In an interference-between-cues design (IbC), the expression of a learned Cue A–Outcome 1 association has been shown to be impaired if another cue, B, is separately paired with the same outcome in a second learning phase. The present study examined whether IbC could be caused by associative mechanisms independent of causal reasoning processes. This was achieved by testing participants in two different learning situations. In the Causal Scenario condition, participants learned in a diagnostic situation in which a common cause (Outcome 1) caused two disjoint effects, namely Cues A and B. In the Non-Causal Scenario condition, the same IbC design and stimulus conditions were used. However, instructions provided no causal frame to make sense of how cues and outcomes were related. IbC was only found in the Causal Scenario condition. This result is consistent with Causal Reasoning Models of causal learning and raises important difficulties for associative explanations of IbC.     

Formal reasoning in late adulthood: The role of semantic content and metacognitive strategy

Two experiments explored the availability of deductive or formal reasoning in late adulthood. In Experiment 1, fifty young (M=19.0 years) and 50 elderly adults (M=81.0 years) were assessed using adaptations of Wason's selection task and rated task content for familiarity, affect, and agreement. In Experiment 2, 100 young (M=21.0 years) and 100 elderly adults (M=81.0 years) were similarly assessed, with half of the subjects in each age group receiving a metacognitive strategy to facilitate reasoning. Results from Experiment 1 indicated equivalent reasoning among the groups on problems employed in earlier developmental research. In contrast, problems constructed to entail affect resulted in poorer performance by older adults. In Experiment 2, both young and older adults who used the metacognitive strategy reasoned equally acrossall problems. In both experiments, familiarity and agreement did not play a role in deductive reasoning performance, but affect seemed to be an interfering factor. Results are discussed in terms of competence-procedure and stability-decrement models of adult cognitive development.     

Conditional reasoning with negations: Implicit and explicit affirmation or denial and the role of contrast classes

' We report two studies on the effect of implicitly versus explicitly conveying affirmation and denial problems about conditionals. Recently Evans and Handley (1999) and Schroyens et al. (1999b, 2000b) showed that implicit referencing elicits matching bias: Fewer determinate inferences are made, when the categorical premise (e.g., B) mismatches the conditional's referred clause (e.g., A). Also, the effect of implicit affirmation (B affirms not-A) is larger than the effect of implicit denial (B denies A). Schroyens et al. hypothesised that this interaction is due to uncertainty in the case-wise affirmation of the contrast class of negated elements involved in implicit affirmations. In Experiment 1 we tested this hypothesis by manipulating the set size of the conditional clauses. The results confirm that binary sets, where the contrast class is a singleton, eliminate the differential effect of implicit affirmation and denial. With non-binary sets the interaction is not modulated by the scope of the contrast class (3, 5, 9 elements). Experiment 2 further investigated the role of contrast classes by using class inclusion to construct implicit affirmations (Mammal vs Mammal or Monkey) and implicit denial (No-Mammal vs Mammal or Monkey), in addition to the standard implicit problems mediated by contrast-class inclusion [(No-)Mammal/No-Mammal; Reptile; Snake). Findings indicate that class inclusion (Mammal/Monkey; Reptile/ Snake) only marginally affects performance, and is independent of the type of problem. This would suggest that the implicitness problem-type interaction is dependent on constructing contrast classes. However, the experiment failed to replicate the interaction, even on the subset of problems repeating the abstract letter/number format of Experiment 1. Moreover, with the natural binary set-sizes (vowels/consonants) the implicitness effect was eliminated entirely.     

Traditional difference-score analyses of reasoning are flawed

Studies of the belief bias effect in syllogistic reasoning have relied on three traditional difference score measures: the logic index, belief index, and interaction index. Dube, Rotello, and Heit (2010, 2011) argued that the interaction index incorrectly assumes a linear receiver operating characteristic (ROC). Here, all three measures are addressed. Simulations indicated that traditional analyses of reasoning experiments are likely to lead to incorrect conclusions. Two new experiments examined the role of instructional manipulations on the belief bias effect. The form of the ROCs violated assumptions of traditional measures. In comparison, signal detection theory (SDT) model-based analyses were a better match for the form of the ROCs, and implied that belief bias and instructional manipulations are predominantly response bias effects. Finally, reanalyses of previous studies of conditional reasoning also showed non-linear ROCs, violating assumptions of traditional analyses. Overall, reasoning research using traditional measures is at risk of drawing incorrect conclusions.     

Matching bias in syllogistic reasoning: Evidence for a dual-process account from response times and confidence ratings

We examined matching bias in syllogistic reasoning by analysing response times, confidence ratings, and individual differences. Roberts’ (2005) “negations paradigm” was used to generate conflict between the surface features of problems and the logical status of conclusions. The experiment replicated matching bias effects in conclusion evaluation (Stupple & Waterhouse, 2009), revealing increased processing times for matching/logic “conflict problems”. Results paralleled chronometric evidence from the belief bias paradigm indicating that logic/belief conflict problems take longer to process than non-conflict problems (Stupple, Ball, Evans, & Kamal-Smith, 2011). Individuals’ response times for conflict problems also showed patterns of association with the degree of overall normative responding. Acceptance rates, response times, metacognitive confidence judgements, and individual differences all converged in supporting dual-process theory. This is noteworthy because dual-process predictions about heuristic/analytic conflict in syllogistic reasoning generalised from the belief bias paradigm to a situation where matching features of conclusions, rather than beliefs, were set in opposition to logic.