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.     

Mental models and temporal reasoning

We report five experiments investigating reasoning based on temporal relations, such as: “John takes a shower before he drinks coffee”. How individuals make temporal inferences has not been studied hitherto, but we conjectured that they construct mental models of events, and we developed a computer program that reasons in this way.As the program shows, a problem of the form:

1. a before b

2. b before c

3. d while b

4. e while c

What is the relation between d and e?

where a, b, c, etc. refer to everyday events, calls for just one model, whereas a problem in which the second premise is modified to c before b calls for multiple models because a may occur before c, after c, or at the same time as c.

Experiments 1–3 showed that problems requiring one mental model elicited more correct responses than problems requiring multiple models, which in turn elicited more correct answers than multiple model problems with no valid answers. Experiment 4 contrasted the predictions of the model theory with those based on formal rules of inference; its results corroborated the model theory. Experiment 5 confirmed that a premise leading to multiple models took longer to read than the corresponding premise in one-model problems, and that latency to respond correctly was greater for multiple-model problems than for one-model problems. We conclude that the experiments corroborate the mental model theory.     

Working memory and reasoning: An individual differences perspective

This article reports three experiments that investigated the relationship between working memory capacity and syllogistic and five-term series spatial inference. A series of complex and simple verbal and spatial working memory measures were employed. Correlational analyses showed that verbal and spatial working memory span tasks consistently predicted syllogistic and spatial reasoning performance. A confirmatory factor analysis showed that three factors best accounted for the data—a verbal, a spatial, and a general factor. Syllogistic reasoning performance loaded all three factors, whilst spatial reasoning loaded only the general factor. The implications of these findings are discussed in the context of reasoning theories and contemporary accounts of the structure of working memory.     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

Mental models and logical reasoning problems in the GRE

The Graduate Record Examination (GRE) contains a class of complex reasoning tests known as logical reasoning problems. These problems are demanding for human reasoners and beyond the competence of any existing computer program. This article applies the mental model theory of reasoning to the analysis of these problems. It predicts 3 main causes of difficulty, which were corroborated by the results of 4 experiments: the nature of the logical task (Experiment 1), the set of foils (Experiment 2), and the nature of the conclusions (Experiments 3 and 4). This article shows how these factors can be applied to the design of new problems.     

Interpretation of instructions: A source of individual differences in analogical reasoning

Two studies were conducted to identify individual differences in the effect of instruction on strategies used to solve figural/numerical analogies. In Study 1, students aged 9, 11, 13, and 19 years were given incomplete instructions and then were assessed for (a) consistent use of an appropriate rule for solving analogies and (b) the type and number of stimulus attributes that are incorporated in those analogical rules. Use of an analogical rule increased with age and corresponded to higher scores on a psychometric test of reasoning within each age group. In Study 2, analysis of verbal protocols was used to identify the strategies of some 9- and 11-year-olds who showed a peculiar pattern of responding in Study 1. These children attended to relevant attributes but used systematic nonanalogical rules to solve problems. When provided with more specific instructions, most of these children adopted an analogical rule but failed to incorporate relevant attributes. Results indicate that selection or construction of task-relevant solution strategies from incomplete instructions may partially account for differential performance on tests of analogical reasoning.     

Individual differences in mental animation during mechanical reasoning

In three experiments we tested the effects of spatial visualization ability on performance of a motion-verification task, in which subjects were shown a diagram of a mechanical system and were asked to verify a sentence stating the motion of one of the system components. We propose that this task involves component processes of (1) sentence comprehension, (2) diagram comprehension, (3) text-diagram integration, and (4) mental animation. Subjects with law spatial ability made more errors than did subjects with high spatial ability on this task, and they made more errors on items in which more system components had to be animated to solve the problem. In contrast, the high-spatial subjects were relatively accurate on all trials. These results indicate that spatial visualization is correlated with accuracy on the motion-verification task and suggest that this correlation is primarily due to the mental animation component of the task. Reaction time and eye-fixation data revealed no differences in how the high- and low-spatial subjects decomposed the task. The data of the two groups of subjects were equally consistent with a piecemeal model of mental animation, in which components are animated one by one in order of the causal chain of events in the system.     

Mental models in propositional reasoning and working memory's central executive

We examine the role of working memory's central executive in the mental model explanation of propositional reasoning by using two working memory measures: the classical “reading span” test by Daneman and Carpenter (1980 Daneman, M. and Carpenter, P. A. 1980. Individual differences in working memory and reading. Journal of Verbal Learning and Verbal Behavior, 19: 450–466. [Crossref] , [Google Scholar]) and a new measure. This new “reasoning span” measure requires individuals to solve very simple anaphora problems, and store and remember the word solution in a growing series of inferential problems. We present one experiment in which we check the involvement of the central executive in conditional and disjunctive inference tasks and compare predictions of the new reasoning span test with those of the classical reading span test. The results of the experiment confirm that reasoning responses, which according to mental model theory require high cognitive work, are predicted by working memory measures. Results also show that some reasoning responses are probably obtained by means of superficial biases or strategies that do not load working memory. The reasoning span test, which involves the central executive to a greater degree, predicts reasoning performance better than the reading span test. The significance and possibilities of the new measure in studying reasoning are discussed.     

The stress response systems: Universality and adaptive individual differences

Biological reactivity to psychological stressors comprises a complex, integrated system of central neural and peripheral neuroendocrine responses designed to prepare the organism for challenge or threat. Developmental experience plays a role, along with heritable variation, in calibrating the response dynamics of this system. This calibration occurs through setting of response thresholds in the regulatory mechanisms that coordinate the expression and use of trait-specific gene products and environmental elements that build alternative phenotypes. Whereas natural selection tends to favor developmental plasticity when the fitness of alternative phenotypes can be predicted from observable cues, genetic polymorphisms are most likely to be maintained when the advantages of niche specialization are high and organisms can evaluate and select their niches. Well-developed theories of both adaptive phenotypic plasticity and adaptive genetic variation in the stress-response systems have been advanced in the literature. Taken together, these theories strongly suggest that variation in stress-response phenotypes has been shaped by natural selection, is an adaptation to multiniche environments, and involves an integration of genetic influences and condition-sensitivity.     

Beta-MPT: Multinomial processing tree models for addressing individual differences

Traditionally, multinomial processing tree (MPT) models are applied to groups of homogeneous participants, where all participants within a group are assumed to have identical MPT model parameter values. This assumption is unreasonable when MPT models are used for clinical assessment, and it often may be suspect for applications to ordinary psychological experiments. One method for dealing with parameter variability is to incorporate random effects assumptions into a model. This is achieved by assuming that participants’ parameters are drawn independently from some specified multivariate hyperdistribution. In this paper we explore the assumption that the hyperdistribution consists of independent beta distributions, one for each MPT model parameter. These beta-MPT models are ‘hierarchical models’, and their statistical inference is different from the usual approaches based on data aggregated over participants. The paper provides both classical (frequentist) and hierarchical Bayesian approaches to statistical inference for beta-MPT models. In simple cases the likelihood function can be obtained analytically; however, for more complex cases, Markov Chain Monte Carlo algorithms are constructed to assist both approaches to inference. Examples based on clinical assessment studies are provided to demonstrate the advantages of hierarchical MPT models over aggregate analysis in the presence of individual differences.     

The everyday production of knowledge: individual differences in epistemological understanding and juror‐reasoning skill

This study investigated the untested assumption that people's everyday reasoning reflects different understandings of the nature of knowledge and knowing. The epistemological stances of 180 prospective jurors were assessed with an interview that probed the nature and source of the discrepant knowledge claims of two historical accounts. The researchers derived global epistemological levels from these interviews. The jurors also heard trials and offered justifications for their verdict choices. The researchers assessed these justifications for whether subjects could use various reasoning skills successfully. Epistemological level, but not educational level, age, or gender, predicted juror‐reasoning skills and degree of certainty about verdict choice. Epistemological level, mediated by the juror‐reasoning skills, was a better predictor of general argument skill than certainty about verdict choice and the amount of evidence used in arguing for a verdict. The results indicate that epistemological understandings underlie specific juror‐reasoning skills and overall argument ability. Copyright © 2002 John Wiley & Sons, Ltd.     

Probabilistic reasoning in prediction and diagnosis: Effects of problem type,response mode,and individual differences

In prediction, subset relations require that the probability of conjoined events is never higher than that of constituent events. However, people's judgments regularly violate this principle, producing conjunction errors. In diagnosis, the probability of a hypothesis normatively is often higher for conjoined cues. An online survey used a within‐subjects design to explore the degree to which participants (n = 347) differentiated diagnosis and prediction using matched scenarios and both choice and estimation responses. Conjunctions were judged more probable than a constituent in diagnosis (76%) more often than prediction (64%) and in choice (84%) more often than direct estimation (57%), with no interaction of type of task and response mode. Correlation, regression, and path analyses were used to determine the relationships among individual difference variables and the diagnosis and prediction tasks. Among the correlation findings was that time spent on the task predicted higher conjunction probabilities in diagnosis but not prediction and that class inclusion errors predicted increased conjunction errors in choice but not estimation. Need for cognition and numeracy were only minimally related to reasoning about conjunctions. Results are consistent with the idea that people may misapply diagnostic reasoning to the prediction task and consequently commit the conjunction error. Copyright © 2010 John Wiley & Sons, Ltd.     

Mental model construction in linear reasoning: Evidence for the construction of initial annotated models

According to the mental model theory, reasoners build an initial model representing the information given in the premises. In the context of relational reasoning, the question arises as to which kind of representation is used to cope with indeterminate or multimodel problems. The present article presents an array of possible answers arising from the initial construction of complete explicit models, partial explicit models, partial implicit models, a single "isomeric" model, or a single annotated model. Predictions generated from these views are tested in two experiments that vary the problem structure and the number of models consistent with the premises. Analyses of the premise processing times, answering times and accuracy show that the annotated model yields the best fit of the data. Implications of these findings for the mental model theory as developed for relational reasoning are discussed.     

Examining the influence of anecdotal stories and the interplay of individual differences on reasoning

In two experiments, we explored whether anecdotal stories influenced how individuals reasoned when evaluating scientific news articles. We additionally considered the role of education level and thinking dispositions on reasoning. Participants evaluated eight scientific news articles that drew questionable interpretations from the evidence. Overall, anecdotal stories decreased the ability to reason scientifically even when controlling for education level and thinking dispositions. Additionally, we found that article length was related to participants' ratings of the news articles. Our study demonstrates that anecdotes can discourage scientific reasoning while also pointing to the potential influence of article length on judgements of quality.     

Constructing stories of self-growth: how individual differences in patterns of autobiographical reasoning relate to well-being in midlife

Although growth has been a central focus in narrative research, few studies have examined growth comprehensively, as a story that emerges across the interpretation of many events. In this study, we examined how individual differences in autobiographical reasoning (AR) about self-growth relate to traits and well-being in a national sample of midlife adults (N= 88) who ranged in age from 34 to 68. Two patterns of growth-related AR were identified: (1) positive processing, defined as the average tendency to interpret events positively (vs. negatively), and (2) differentiated processing, defined as the extent to which past events are interpreted as causing a variety of forms of self-growth. Results showed that positive processing was negatively related to neuroticism and predicted well-being even after controlling for the average valence of past events. Additionally, differentiated processing of negative events but not positive events was positively related to openness and predictive of well-being. Finally, growth-related AR patterns independently predicted well-being beyond the effects of traits and demographic factors.     

Analyzing individual differences in sentence processing performance using multilevel models

The use of multilevel models is increasingly common in the behavioral sciences for analyzing hierarchically structured data, including repeated measures data. These models are flexible and easily implemented via a variety of commercially available statistical software programs. We consider their application in the context of an eye-movement experiment testing readers' responses to a semantic plausibility manipulation in temporarily ambiguous sentences. Multilevel models were used to study the relationship between working memory capacity and the extent to which readers were disrupted by syntactic misanalysis. This represented a cross-level interaction between an individual difference measure and a sentence-level characteristic. We compare a multilevel modeling approach to a standard approach based on ANOVA.     

The forgotten individual: diagrammatic reasoning in mathematics

Parallelism has been drawn between modes of representation and problem-sloving processes: Diagrams are more useful for brainstorming while symbolic representation is more welcomed in a formal proof. The paper gets to the root of this clear-cut dualistic picture and argues that the strength of diagrammatic reasoning in the brainstorming process does not have to be abandoned at the stage of proof, but instead should be appreciated and could be preserved in mathematical proofs.