Mental models and deduction

According to the mental-model theory of deductive reasoning, reasoners use the meanings of assertions together with general knowledge to construct mental models of the possibilities compatible with the premises. Each model represents what is true in a possibility. A conclusion is held to be valid if it holds in all the models of the premises. Recent evidence described here shows that the fewer models an inference calls for, the easier the inference is. Errors arise because reasoners fail to consider all possible models, and because models do not normally represent what is false, even though reasoners can construct counterexamples to refute invalid conclusions.     

Mental models and omissive causation

Some causal relations refer to causation by commission (e.g., “A gunshot causes death”), and others refer to causation by omission (e.g., “Not breathing causes death”). We describe a theory of the representation of omissive causation based on the assumption that people mentally simulate sets of possibilities—mental models—that represent causes, enabling conditions, and preventions (Goldvarg & Johnson-Laird, 2001). The theory holds that omissive causes, enabling conditions, and preventions each refer to distinct sets of possibilities. For any such causal relation, reasoners typically simulate one initial possibility, but they are able to consider alternative possibilities through deliberation. These alternative possibilities allow them to deliberate over finer-grained distinctions when reasoning about causes and effects. Hence, reasoners should be able to distinguish between omissive causes and omissive enabling conditions. Four experiments corroborated the predictions of the theory. We describe them and contrast the results with the predictions of alternative accounts of causal representation and inference.     

Mental models and probabilistic thinking

This paper outlines the theory of reasoning based on mental models, and then shows how this theory might be extended to deal with probabilistic thinking. The same explanatory framework accommodates deduction and induction: there are both deductive and inductive inferences that yield probabilistic conclusions. The framework yields a theoretical conception of strength of inference, that is, a theory of what the strength of an inference is objectively: it equals the proportion of possible states of affairs consistent with the premises in which the conclusion is true, that is, the probability that the conclusion is true given that the premises are true. Since there are infinitely many possible states of affairs consistent with any set of premises, the paper then characterizes how individuals estimate the strength of an argument. They construct mental models, which each correspond to an infinite set of possibilities (or, in some cases, a finite set of infinite sets of possibilities). The construction of models is guided by knowledge and beliefs, including lay conceptions of such matters as the “law of large numbers”. The paper illustrates how this theory can account for phenomena of probabilistic reasoning.     

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.     

Mental models of line drawings.

Mental models are internal representations of world structure, used to accomplish cognitive tasks. I postulate specific representations (of objects and images) and associated context (of world and view) for mental models of line drawings. I then analyze the representations and context to predict specific perceptual modes, including the relative strengths of these modes. The predicted modes are supported by a well-known example [from Rock, 1983 The Logic of Perception (Cambridge, MA: MIT Press)] where object perception changes with image orientation.     

Mental models as representations of text

A theory of text representation is outlined which suggests that a text is encoded in a mental model that contains representations of only those individuals and events that are relevant to the interpretation of the text in question. Such models are constructed on-line in response to cues in the text and with reference to knowledge about the world. An experiment is reported which demonstrates that mental models represent the events most probably described in a text. The results confirm previous findings that memory for the content of a passage is not based on the construction of one of its linguistically motivated representations. However, unlike most previous findings, they do support a positive proposal about the nature of the representations on which memory for content is based.     

Mental models and the fan effect.

Explanations of data from fan effect experiments have been based on propositional network models. This article presents findings not readily predicted by such models. In particular, in three experiments we found that, during a speeded-recognition test, subjects retrieved facts about several objects associated with a single location faster than facts about several locations associated with a single object. Indeed, there was no fan effect in the former case despite the fact that there were an equivalent number of associations among concepts in both conditions. We suggest that such data are consistent with a mental model representational account.     

Mental models of learning in distance education

Background. Interview‐based research has shown that students in higher education hold a number of different conceptions of learning and of themselves as learners. There is debate about whether these conceptions constitute a developmental hierarchy. Aims. This study evaluated the Mental Models section of Vermunt and van Rijswijk's (1988) Inventory of Learning Styles (ILS) as a measure of students' conceptions of learning and sought to identify conceptions of learning as qualitatively different patterns of scores. Sample. A random sample of 1,000 students who were taking courses by distance learning with the Open University in the UK. Method. A translated and adapted version of the Mental Models section of the ILS was administered in a postal survey. Complete data were obtained from 441 students and were subjected to principal component analysis, cluster analysis and discriminant analysis. Results. The five scales in the Mental Models section of the ILS were homogeneous and achieved a satisfactory level of internal consistency, but two of the five scales could not be differentiated from each other in the students' responses. A cluster analysis identified four subgroups of students who had different patterns of scores on two discriminant functions. Conclusion. The four mental models identified in this study were broadly similar to those identified by Vermunt (1996) in an interview‐based study. However, these do not seem to constitute a developmental hierarchy, and, following Vermunt, it is suggested that they are better interpreted as aspects of four over‐arching ‘learning styles’ or ‘learning patterns’.     

Mental models and the suppositional account of conditionals

The mental model theory of conditional reasoning presented by P. N. Johnson-Laird and R. M. J. Byrne (2002) has recently been the subject of criticisms (e.g., J. St. B. T. Evans, D. E. Over, & S. J. Handley, 2005). The authors argue that the theoretical conflict can be resolved by differentiating 2 kinds of reasoning, reasoning about possibilities given the truth of assertions and reasoning about the truth of assertions given possibilities. The standard mental model theory accounts for the former kind of reasoning but does not adequately account for the latter, contrary to the suppositional approach favored by J. St. B. T. Evans et al. (2005). The authors thus propose a modified mental model theory of conditionals that reconciles the 2 theoretical approaches. It is demonstrated that this theory is able to explain the key findings that have been opposed to the standard theory by J. St. B. T. Evans et al. and makes new predictions that are empirically verified.     

Mental models in the brain: On context-dependent neural correlates of mental models

In this paper, the concept of context-dependent realisation of mental models is introduced and discussed. Literature from neuroscience is discussed showing that different types of mental models can use different types of brain areas. Moreover, it is discussed that the same occurs for the formation and adaptation of mental models and the control of these processes. This makes that it is hard to claim that all mental models use the same brain mechanisms and areas. Instead, the notion of context-dependent realisation is proposed here as a better manner to relate neural correlates to mental models. It is shown in some formal detail how this context-dependent realisation approach can be related to well-known perspectives based on bridge principle realisation and interpretation mapping realisation.     

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.     

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.     

Mental models and other misconceptions in children’s understanding of the earth

This study investigated the claim (e.g., Vosniadou & Brewer’s, 1992) that children have naive “mental models” of the earth and believe, for example, that the earth is flat or hollow. It tested the proposal that children appear to have these misconceptions because they find the researchers’ tasks and questions to be confusing and ambiguous. Participants were 6- and 7-year-olds (N = 127) who were given either the mental model theorists’ original drawing task or a new version in which the same instructions and questions were rephrased to minimize ambiguity and, thus, possible misinterpretation. In response to the new version, children gave substantially more indication of having scientific understanding and less of having naive mental models, suggesting that the misconceptions reported by the mental model theorists are largely methodological artifacts. There were also differences between the responses to the original version and those reported by Vosniadou and Brewer, indicating that other factors, such as cohort and cultural effects, are also likely to help explain the discrepant findings of previous research.     

Mental models of the earth: A study of conceptual change in childhood

This paper presents the results of an experiment which investigated elementary school children's conceptual knowledge about the earth. First-, 3rd-, and 5th- grade children were asked a series of questions about the shape of the earth. Children's responses to these questions revealed considerable apparent inconsistency. For example, many children said that the earth is round but also stated that it has an end or edge from which people could fall. A great deal of this apparent inconsistency could be explained by assuming that the children used, in a consistent fashion, a mental model of the earth other than the spherical earth model. Five alternative mental models of the earth were identified: the rectangular earth, the disc earth, the dual earth, the hollow sphere, and the flattened sphere. It is argued that these models are constrained by certain presuppositions which children form based on interpretations of their everyday experience. Some of these models (the rectangular earth and the disc earth) seem to be initial models children construct before they are exposed to the culturally accepted information that the earth is a sphere. In the process of knowledge acquisition, children appear to modify their initial models to make them more consistent with the culturally accepted model by gradually reinterpreting their presuppositions. Synthetic models (such as the hollow sphere and the flattened sphere) are generated by children as a solution to the problems arising from the inconsistency between their initial model of a flat earth and the culturally accepted, scientific model of a spherical earth. Children come to understand that the earth is a sphere only when the presuppositions that gave rise to their initial models have been reinterpreted.     

Mental models in word problem-solving: A comparison between American and Korean sixth-grade students

Mental model analysis was conducted in word problem solving using American (n = 42) and Korean (n = 44) sixth-graders. Two levels of mental models–the problem model and the mathematical model–constructed in the process of word problem solving were investigated. Categories for correct and incorrect models were developed to be used in think-aloud protocol analysis. The majority of students who constructed correct problem models classified the problems rapidly according to solution procedures as they read the problems, or restated the problems focusing on the specific words relating them to other statements in the problems. However, significant differences were found between American and Korean sixth-graders' in some categories of problem and mathematical models. While many Korean sixth-graders' problem-solving process steps were proceduralized, this was not the case for American sixth-graders, even for those who had a readily accessible knowledge base of basic mathematical facts.