Individual differences in strategies for syllogistic reasoning

Current theories of reasoning such as mental models or mental logic assume a universal cognitive mechanism that underlies human reasoning performance. However, there is evidence that this is not the case, for example, the work of Ford (1995), who found that some people adopted predominantly spatial and some verbal strategies in a syllogistic reasoning task. Using written and think-aloud protocols, the present study confirmed the existence of these individual differences. However, in sharp contrast to Ford, the present study found few differences in reasoning performance between the two groups, in terms of accuracy or type of conclusion generated. Hence, reasoners present an outward appearance of ubiquity, despite underlying differences in reasoning processes. These findings have implications for theoretical accounts of reasoning, and for attempts to model reasoning data. Any comprehensive account needs to account for strategic differences and how these may develop in logically untrained individuals.     

Activation of end-terms in syllogistic reasoning

We report five experiments showing that the activation of the end-terms of a syllogism is determined by their position in the composite model of the premises. We show that it is not determined by the position of the terms in the rule being applied (Ford, 1994), by the syntactic role of the terms in the premises (Polk & Newell, 1995; Wetherick & Gilhooly, 1990), by the type of conclusion (Chater & Oaksford, 1999), or by the terms from the source premise (Stenning & Yule, 1997). In our first experiment we found that after reading a categorical premise, the most active term is the last term in the premise. In Experiments 2, 3, and 4 we demonstrated that this pattern of activity is due to the position of the concepts in the model of the premises, regardless of the delay after reading the premises (150 or 2000 msec) or the quantity of the quantifiers (universal or existential). The fifth experiment showed that the pattern switches around after participants evaluate a conclusion. We propose that the last element in the model maintains a higher level of activity during the comprehension process because it is generally used to attach the incoming information. After this process, the first term becomes more active because it is the concept to which the whole representation is referred. These results are predicted by the mental model theory (Johnson-Laird & Byrne, 1991), but not by the verbal reasoning theory (Polk & Newell, 1995), the graphical methods theory (Yule & Stenning, 1992), the attachment-heuristic theory (Chater & Oaksford, 1999), or the mental rules theory (Ford, 1994).     

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.     

Relative informativeness of quantifiers used in syllogistic reasoning

Three experiments tested a possible resolution of the probability heuristics model (PHM) of syllogistic reasoning proposed by Chater and Oaksford (1999), with their experimental results apparently showing that the generalized quantifier few was not as informative as suggested theoretically. Modifying the interpretation of few to take into account the distinction between positive and negative quantifiers (Moxey & Sanford, 1993) indicated two orderings over the quantifiers all, most, few, some, none, and some...not that are more consistent with the results. Experiments 1-3 tested these orderings empirically by having participants rank whether a quantifier applied to a particular probabilistic state of affairs. Experiments 1 and 2 showed that participants agreed on when a quantifier applied and that the empirically derived informativeness orderings were consistent with the proposed modifications of the order. Experiment 3 showed that this finding was robust even when response competition was eliminated.     

Inhibitory mechanism of the matching heuristic in syllogistic reasoning

A number of heuristic-based hypotheses have been proposed to explain how people solve syllogisms with automatic processes. In particular, the matching heuristic employs the congruency of the quantifiers in a syllogism — by matching the quantifier of the conclusion with those of the two premises. When the heuristic leads to an invalid conclusion, successful solving of these conflict problems requires the inhibition of automatic heuristic processing. Accordingly, if the automatic processing were based on processing the set of quantifiers, no semantic contents would be inhibited. The mental model theory, however, suggests that people reason using mental models, which always involves semantic processing. Therefore, whatever inhibition occurs in the processing implies the inhibition of the semantic contents.     

On the role of imagery in linear syllogistic reasoning

Summary The functional role of imagery in linear syllogistic reasoning has not yet been convincingly established. Shortcomings of previous theories and research are discussed. A conceptual analysis of the imagery position leads to the differentiation of modality-specific, analogical-representational, and process perspectives. To obtain evidence relevant to the first and third of these perspectives, a Stroop-type interference paradigm was used in combination with self-paced successive presentation of task components (premises and question of linear syllogisms). Effects of interference information and task components upon response time were consistent with the process reconceptualization of the imagery position.     

Logic and belief across the lifespan: the rise and fall of belief inhibition during syllogistic reasoning

Popular reasoning theories postulate that the ability to inhibit inappropriate beliefs lies at the heart of the human reasoning engine. Given that people's inhibitory capacities are known to rise and fall across the lifespan, we predicted that people's deductive reasoning performance would show similar curvilinear age trends. A group of children (12‐year‐olds), young adults (20‐year‐olds), and older adults (65+‐year‐olds) were presented with a classic syllogistic reasoning task and a decision‐making questionnaire. Results indicated that on syllogisms where beliefs and logic conflicted, reasoning performance showed the expected curvilinear age trend: Reasoning performance initially increased from childhood to early adulthood but declined again in later life. On syllogisms where beliefs and logic were consistent and sound reasoning did not require belief inhibition, however, age did not affect performance. Furthermore, across the lifespan we observed that the better people were at resisting intuitive temptations in the decision‐making task, the less they were biased by their beliefs on the conflict syllogisms. As with the effect of age, one's ability to override intuitions in the decision‐making task did not mediate reasoning performance on the no‐conflict syllogisms. Results lend credence to the postulated central role of inhibitory processing in those situations where beliefs and logic conflict.     

The source of belief bias effects in syllogistic reasoning.

In studies of the belief bias effect in syllogistic reasoning, an interaction between logical validity and the believability of the conclusion has been found; in essence, logic has a larger effect on unbelievable than on believable conclusions. Two main explanations have been proposed for this finding. The selective scrutiny account claims that people focus on the conclusion and only engage in logical processing if this is found to be unbelievable; while the misinterpreted necessity account claims that subjects misunderstand what is meant by logical necessity and respond on the basis of believability when indeterminate syllogisms are presented. Experiments 1 and 2 compared the predictions of these two theories by examining whether the interaction would disappear if only determinate syllogisms were used. It did, thus providing strong support for the misinterpreted necessity explanation. However, the results are also consistent with a version of the mental models theory, and so Experiment 3 was carried out to compare these two explanations. The mental models theory received strong support, as it did also in the follow-up Experiments 4 and 5. It is concluded that people try to construct a mental model of the premises but, if there is a believable conclusion consistent with the first model they produce, then they fail to construct alternative models.     

Response demands and the recruitment of heuristic strategies in syllogistic reasoning

Two experiments investigated whether dealing with a homogeneous subset of syllogisms with time-constrained responses encouraged participants to develop and use heuristics for abstract (Experiment 1) and thematic (Experiment 2) syllogisms. An atmosphere-based heuristic accounted for most responses with both abstract and thematic syllogisms. With thematic syllogisms, a weaker effect of a belief heuristic was also observed, mainly where the correct response was inconsistent with the atmosphere of the premises. Analytic processes appear to have played little role in the time-constrained condition, whereas their involvement increased in a self-paced, unconstrained condition. From a dual-process perspective, the results further specify how task demands affect the recruitment of heuristic and analytic systems of reasoning. Because the syllogisms and experimental procedure were the same as those used in a previous neuroimaging study by Goel, Buchel, Frith, and Dolan (2000), the result also deepen our understanding of the cognitive processes investigated by that study.     

Response demands and the recruitment of heuristic strategies in syllogistic reasoning

Two experiments investigated whether dealing with a homogeneous subset of syllogisms with time-constrained responses encouraged participants to develop and use heuristics for abstract (Experiment 1) and thematic (Experiment 2) syllogisms. An atmosphere-based heuristic accounted for most responses with both abstract and thematic syllogisms. With thematic syllogisms, a weaker effect of a belief heuristic was also observed, mainly where the correct response was inconsistent with the atmosphere of the premises. Analytic processes appear to have played little role in the time-constrained condition, whereas their involvement increased in a self-paced, unconstrained condition. From a dual-process perspective, the results further specify how task demands affect the recruitment of heuristic and analytic systems of reasoning. Because the syllogisms and experimental procedure were the same as those used in a previous neuroimaging study by Goel, Buchel, Frith, and Dolan (2000), the result also deepen our understanding of the cognitive processes investigated by that study.     

Phonological and visual distinctiveness effects in syllogistic reasoning: Implications for mental models theory

Two experiments are reported in which the representational distinctiveness of terms within categorical syllogisms was manipulated in order to examine the assumption of mental models theory that abstract, spatially based representations underpin deduction. In Experiment 1, participants evaluated conclusion validity for syllogisms containing either phonologically distinctive terms (e.g., harks, paps, and fids) or phonologically nondistinctive terms (e.g., fuds, fods, and feds). Logical performance was enhanced with the distinctive contents, suggesting that the phonological properties of syllogism terms can play an important role in deduction. In Experiment 2, participants received either the phonological materials from Experiment 1 or syllogisms involving distinctive or nondistinctive visual contents. Logical inference was again enhanced for the distinctive contents, whether phonological or visual in nature. Our findings suggest a broad involvement of multimodal information in syllogistic reasoning and question the assumed primacy of abstract, spatially organized representations in deduction, as is claimed by mental models theorists.     

Confidence judgments in syllogistic reasoning: the role of consistency and response cardinality

In two experiments, we examined the resolution of confidence judgments in syllogistic reasoning and their heuristic bases. Based on the assumptions of Koriat's Self-Consistency Model of confidence, we expected the confidence judgments to be related to conclusion consensuality, reflecting the role of consistency as a heuristic cue to confidence. In Experiment 1, the participants evaluated 24 syllogisms with conclusions that varied with respect to validity and consensuality. In Experiment 2, the participants produced conclusions to 64 pairs of premises. The correlation between confidence and reasoning accuracy was low. In both experiments confidence was related to the consensuality of the responses. For consensually correct items, correlation between confidence and accuracy was positive; however, for consensually incorrect items it was negative. In Experiment 2, confidence was lower for syllogisms with higher response cardinality, or syllogisms that elicited a greater variety of conclusions.     

Effects of belief and logic on syllogistic reasoning: Eye-movement evidence for selective processing models

Studies of syllogistic reasoning have demonstrated a nonlogical tendency for people to endorse more believable conclusions than unbelievable ones. This belief bias effect is more dominant on invalid syllogisms than valid ones, giving rise to a logic by belief interaction. We report an experiment in which participants' eye movements were recorded in order to provide insights into the nature and time course of the reasoning processes associated with manipulations of conclusion validity and believability. Our main dependent measure was people's inspection times for syllogistic premises, and we tested predictions deriving from three contemporary mental-models accounts of the logic by belief interaction. Results supported recent "selective processing" theories of belief bias (e.g., Evans, 2000; Klauer, Musch, & Naumer, 2000), which assume that the believability of a conclusion biases model construction processes, rather than biasing the search for falsifying models (e.g., Oakhill & Johnson-Laird, 1985) or a response stage of reasoning arising from subjective uncertainty (e.g., Quayle & Ball, 2000). We conclude by suggesting that the eye-movement analyses in reasoning research may provide a useful adjunct to other process-tracing techniques such as verbal protocol analysis.     

Characterizing belief bias in syllogistic reasoning: A hierarchical Bayesian meta-analysis of ROC data

The belief-bias effect is one of the most-studied biases in reasoning. A recent study of the phenomenon using the signal detection theory (SDT) model called into question all theoretical accounts of belief bias by demonstrating that belief-based differences in the ability to discriminate between valid and invalid syllogisms may be an artifact stemming from the use of inappropriate linear measurement models such as analysis of variance (Dube et al., Psychological Review, 117(3), 831–863, 2010). The discrepancy between Dube et al.’s, Psychological Review, 117(3), 831–863 (2010) results and the previous three decades of work, together with former’s methodological criticisms suggests the need to revisit earlier results, this time collecting confidence-rating responses. Using a hierarchical Bayesian meta-analysis, we reanalyzed a corpus of 22 confidence-rating studies (N =?993). The results indicated that extensive replications using confidence-rating data are unnecessary as the observed receiver operating characteristic functions are not systematically asymmetric. These results were subsequently corroborated by a novel experimental design based on SDT’s generalized area theorem. Although the meta-analysis confirms that believability does not influence discriminability unconditionally, it also confirmed previous results that factors such as individual differences mediate the effect. The main point is that data from previous and future studies can be safely analyzed using appropriate hierarchical methods that do not require confidence ratings. More generally, our results set a new standard for analyzing data and evaluating theories in reasoning. Important methodological and theoretical considerations for future work on belief bias and related domains are discussed.     

Spatial associations in relational reasoning: Evidence for a SNARC-like effect

Relational reasoning (A > B, B > C, therefore A > C) shares a number of similarities with numerical cognition, including a common behavioural signature, the symbolic distance effect. Just as reaction times for evaluating relational conclusions decrease as the distance between two ordered objects increases, people need less time to compare two numbers when they are distant (e.g., 2 and 8) than when they are close (e.g., 3 and 4). Given that some remain doubtful about such analogical representations in relational reasoning, we determine whether numerical cognition and relational reasoning have other overlapping behavioural effects. Here, using relational reasoning problems that require the alignment of six items, we provide evidence showing that the subjects' linear mental representation affects motor performance when evaluating conclusions. Items accessible from the left part of a linear representation are evaluated faster when the response is made by the left, rather than the right, hand and the reverse is observed for items accessible from the right part of the linear representation. This effect, observed with the prepositions to the left of and to the right of as well as with above and below, is analogous to the SNARC (Spatial Numerical Association of Response Codes) effect, which is characterized by an interaction between magnitude of numbers and side of response.     

Evidence for an explanation advantage in naïve biological reasoning

The present studies compare young children’s explanations and predictions for the biological phenomenon of contamination. In Study 1, 36 preschoolers and 24 adults heard vignettes concerning contamination, and were asked either to make a prediction or to provide an explanation. Even 3-year-olds readily supplied contamination-based explanations, and most children mentioned an unseen mechanism (germs, contact through bodily fluids). Moreover, unlike adults who performed at ceiling across both explanation and prediction tasks, children were significantly more accurate with their explanations than their predictions. In Study 2, we varied the strength of cues regarding the desirability of the contaminated substance (N = 24 preschoolers). Although desirability affected responses, for both levels of desirability participants were significantly more accurate on explanation than prediction questions. Altogether, these studies demonstrate a significant “explanation advantage” for children’s reasoning in the domain of everyday biology.     

Some men like it black,some women like it pink: consumer implications of differences in male and female website design

• The World Wide Web doubles in size roughly every 2–3 months and dramatic claims are made about the effectiveness of Web‐based commercial efforts. The centrality of non‐price mechanisms of differentiation to the perception, enjoyment and ease of use felt using websites is acknowledged but the only statistically rigorous studies of factors such as form and content have been conducted within a universalist paradigm of aesthetics. This paper reports on an interactionist approach to web aesthetics involving an analysis of 60 male‐ and female‐produced websites. The analysis reveals statistically significant differences between the male‐ and female‐produced websites on 13 out of the 23 factors analysed. These differences span issues of navigation as well as linguistic and visual content. The paper argues that the appeal of websites can be maximised if they mirror the needs and interests of their target populations and that websites targeted at male or female dominated markets need to reflect the aesthetic diversity found in the male‐ and female‐produced websites analysed here. It also presents information on the demographics of the IT profession, showing that there is a potential imbalance between the percentage of women involved online and those involved in the IT profession. This suggests that the male domination of the IT profession could be a barrier to the effective mirroring of female Website preferences.

Copyright © 2006 John Wiley & Sons, Ltd.     

Evidence of deontic reasoning in 3- and 4-year-old children

Deontic reasoning is reasoning about what one may, ought, or ought not do in a given set of circumstances. Virtually all of our social institutions and child-rearing practices presume the capacity to reason about deontic concepts, such as what is permitted, obligated, or prohibited. Despite this, very little is known about the development of deontic reasoning. Two experiments were conducted that contrasted children’s reasoning performance on deontic and indicative reasoning tasks (i.e., the reduced array selection version of the Wason card selection task). Like adults, children as young as 3 years of age were found to adopt a violation-detecting strategy more often when reasoning about the deontic case than when reasoning about the indicative case. These results indicate that violation detection emerges as an effective deontic reasoning very early in human development.