Categorical Reasoning from Multiple Diagrams

2005 ◽  
Vol 58 (2) ◽  
pp. 333-376 ◽  
Author(s):  
Maxwell J. Roberts ◽  
Elizabeth D. A. Sykes

Syllogistic reasoning from categorical premise pairs is generally taken to be a multistep process. Quantifiers ( all, no, some, some …not) must be interpreted, representations constructed, and conclusions identified from these. Explanations of performance have been proposed in which errors may occur at any of these stages. The current paper contrasts (a) representation explanations of performance, in which errors occur because not all possible representations are constructed, and/or mistakes are made when doing so (e.g., mental models theory), and (b) conclusion identification explanations, in which errors occur even when information has been correctly and exhaustively represented, due to systematic difficulties that people may have when identifying particular conclusions, or in identifying conclusions in particular circumstances. Three experiments are reported, in which people identified valid conclusions from diagrams analogous to Euler circles, so that the first two stages of reasoning from premise pairs were effectively removed. Despite this, several phenomena associated with reasoning from premise pairs persisted, and it is suggested that whereas representation explanations may account for some of these phenomena, conclusion identification explanations, which have never previously been considered, are required for others.

2007 ◽  
Author(s):  
Cristina Vargas ◽  
Sergio Moreno-Rios ◽  
Candida Castro ◽  
Geoffrey Underwood

Author(s):  
John R. Wilson ◽  
Andrew Rutherford

This review points out confusion surrounding the concept and use of mental models from the viewpoints of both human factors and psychology. Noted are the ways in which the notion is conceived according to the needs and approaches of different specialties, and the relationships of mental models to other forms of knowledge representation are considered. The manner in which the human factors community has and should utilize the concept in applications across a number of fields is addressed and discussed in relation to the psychological perspective.


2002 ◽  
Vol 5 (2) ◽  
pp. 125-140 ◽  
Author(s):  
Juan A. García-Madruga ◽  
Francisco Gutiérrez ◽  
Nuria Carriedo ◽  
Sergio Moreno ◽  
Philip N. Johnson-Laird

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.


2009 ◽  
Vol 8 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Mark van de Wouw ◽  
Chris Kik ◽  
Theo van Hintum ◽  
Rob van Treuren ◽  
Bert Visser

The loss of variation in crops due to the modernization of agriculture has been described as genetic erosion. The current paper discusses the different views that exist on the concept of genetic erosion in crops. Genetic erosion of cultivated diversity is reflected in a modernization bottleneck in the diversity levels that occurred during the history of the crop. Two stages in this bottleneck are recognized: the initial replacement of landraces by modern cultivars; and further trends in diversity as a consequence of modern breeding practices. Genetic erosion may occur at three levels of integration: crop, variety and allele. The different approaches in the recent literature to measure genetic erosion in crops are reviewed. Genetic erosion as reflected in a reduction of allelic evenness and richness appears to be the most useful definition, but has to be viewed in conjunction with events at variety level. According to the reviewed literature, the most likely scenario of diversity trends during modernization is the following: a reduction in diversity due to the replacement of landraces by modern cultivars, but no further reduction after this replacement has been completed.


1982 ◽  
Vol 34 (1) ◽  
pp. 1-29 ◽  
Author(s):  
P. N. Johnson-Laird

There are two conflicting views about the nature of thought: it is invariably rational or invariably irrational. Bartlett argued that thinking is a high level skill, and this idea suggests an obvious third possibility: thought is sometimes rational and sometimes irrational. This view is defended in the present paper, which argues that the doctrine of logical infallibility is either falsified by the results of some experiments on syllogistic reasoning or else empirically vacuous. There is no need to postulate a mental logic of the sort that Piaget and others have proposed. The rapid implicit inferences of daily life depend on the ability to interpret sentences by constructing mental models of the states of affairs that they describe. Deliberate deductions depend on the further ability to search for alternative models that violate putative conclusions. All that you need to know to assess validity is the fundamental semantic principle of deduction: an inference is valid if, and only if, its conclusion is true in every situation in which its premises are true and there is no way of interpreting the premises so as to render the conclusion false. This principle guides the construction of all logics though it is not explicitly stated in any of them. The paper concludes by examining the ways in which people differ in their ability to reason, the practical need to improve this ability, and some of the pedagogical implications of the present studies.


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