A computational model for solving problems from the Raven’s Progressive Matrices intelligence test using iconic visual representations

We describe a computational model for solving problems from Raven’s Progressive Matrices (RPM), a family of standardized intelligence tests. Existing computational models for solving RPM problems generally reason over amodal propositional representations of test inputs. However, there is considerable evidence that humans can also apply imagery-based reasoning strategies to RPM problems, in which processes rooted in perception operate over modal representations of test inputs. In this paper, we present the “affine model,” a computational model that simulates modal reasoning by using iconic visual representations together with affine and set transformations over these representations to solve a given RPM problem. Various configurations of the affine model successfully solve between 33 and 38 of the 60 problems on the Standard Progressive Matrices, which matches levels of performance for typically developing 9- to 11-year-old children. This suggests that, for at least a sizeable subset of RPM problems, it is not always necessary to extract amodal symbols in order to arrive at the correct answer, and iconic visual representations constitute a sufficient form of representation to successfully solve these problems. We intend for the affine model to serve as a complementary computational account to existing propositional models, which together may provide an integrated, dual-process account of human problem solving on the RPM.     

A Brief Proof of the Full Completeness of Shin’s Venn Diagram Proof System

In an article in the Journal of Philosophical Logic in 1996, “Towards a Model Theory of Venn Diagrams,” (Vol. 25, No. 5, pp. 463–482), Hammer and Danner proved the full completeness of Shin’s formal system for reasoning with Venn Diagrams. Their proof is eight pages long. This note gives a brief five line proof of this same result, using connections between diagrammatic and sentential representations.     

The effects of presentation and content on syllogistic reasoning by children with and without specific language impairment

This study examines performance at a syllogistic reasoning task for a group of children (age 10 years) with specific language impairment (SLI) along with age- and language-matched controls. The syllogisms were presented either verbally or verbally/pictorially, and contained two types of item: imaginary versus real, both intended not to evoke strong beliefs. Children with SLI performed worse than age-matched controls, and equivalently to language-matched controls. Patterns of performance indicate this may be due to cognitive ability deficits rather than specific language deficits. For all groups, pictorial presentation interfered with reasoning processes. It is suggested that, for syllogisms, this pictorial information contextualises the interpretation of the task, and that in turn either raises working memory load or evokes belief bias. Additionally, these results suggest that caution should be exhibited before using visual aids to help children with SLI in the classroom.     

The effect of iconicity of visual displays on statistical reasoning: evidence in favor of the null hypothesis

Knowing which properties of visual displays facilitate statistical reasoning bears practical and theoretical implications. Therefore, we studied the effect of one property of visual diplays?– iconicity (i.e., the resemblance of a visual sign to its referent)?– on Bayesian reasoning. Two main accounts of statistical reasoning predict different effect of iconicity on Bayesian reasoning. The ecological-rationality account predicts a positive iconicity effect, because more highly iconic signs resemble more individuated objects, which tap better into an evolutionary-designed frequency-coding mechanism that, in turn, facilitates Bayesian reasoning. The nested-sets account predicts a null iconicity effect, because iconicity does not affect the salience of a nested-sets structure—the factor facilitating Bayesian reasoning processed by a general reasoning mechanism. In two well-powered experiments (N = 577), we found no support for a positive iconicity effect across different iconicity levels that were manipulated in different visual displays (meta-analytical overall effect: log OR = ?0.13, 95 % CI [?0.53, 0.28]). A Bayes factor analysis provided strong evidence in favor of the null hypothesis—the null iconicity effect. Thus, these findings corroborate the nested-sets rather than the ecological-rationality account of statistical reasoning.     

Individual differences in deductive reasoning

Three studies are reported, which examined individual differences in deductive reasoning as a function of intellectual ability and thinking style. Intellectual ability was a good predictor of logical performance on syllogisms, especially where there was a conflict between logic and believability. However, in the first two experiments there was no link between ability and performance on indicative selection tasks, in sharp contrast to previous research. This correlation did, however, return in the final study. Our data are consistent with the claim that the correlation with logical accuracy on abstract selection tasks is found primarily with participants of relatively high ability. At lower levels, pragmatically cued responses are given but those of slightly higher ability divorce the rule from the scenario and respond consistently (though incorrectly) across problems. Self-report questionnaires were generally poor predictors of performance, but a measure of the ability to generate alternative representations proved an excellent predictor. These results are consistent with a mental models approach to reasoning and also have implications for the debate about human rationality.     

小学生数学问题解决中视觉空间表征的研究

本研究区分了两类数学应用题:非视觉化题目与视觉化题目,采用数学测验与个别访谈相结合的方法,考察了54名小学四、五、六年级不同学业水平学生的视觉空间表征。结果表明:图式表征在非视觉化题目与视觉化题目上都极大地促进了问题解决,图像表征妨碍非视觉化题目的解决但与视觉化题目的解决无关,并提出图式表征和图像表征在两类题目上有不同的含义。六年级学生的解题成绩及图式表征有显著的提高,但图像表征与年级因素无关。差生的图式表征能力很差,而在视觉化题目上使用图像表征显著地多于优生及中等生。在非视觉化题目的非视觉空间表征与图式表征之间的转换灵活性上,优生表现了明显的优势。     

Ecological and evolutionary validity: comments on Johnson-Laird,Legrenzi, Girotto,Legrenzi, and Caverni's (1999) mental-model theory of extensional reasoning

The mental-model account of naive probabilistic reasoning by P. N. Johnson-Laird, P. Legrenzi, V. Girotto, M. S. Legrenzi, and J.-P. Caverni (1999) provides an opportunity to clarify several similarities and differences between it and ecological rationality (frequentist) accounts. First, ambiguities in the meaning of Bayesian reasoning can lead to disagreements and inappropriate arguments. Second, 2 conflated effects of using natural frequencies are noticed but not actually tested separately because of an artificial dissociation of frequency representations and natural sampling. Third, similarities are noted between the subset principle and the principle of natural sampling. Finally, some potentially misleading portrayals of the role of evolutionary factors in psychology are corrected. Mental-model theory, rather than better explaining probabilistic reasoning, may be able to use frequency representations as a key element in clarifying its own ambiguous constructs.     

Categorical reasoning from multiple diagrams.

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.     

Learning to Think Iconically in the Human and Social Sciences: Iconic Standards of Understanding as a Pivotal Challenge for Method Development

Theoretically as well as alongside an empirical research idea, this paper outlines conditions for the development of social scientific empirical methods able to further exploit the iconic potential of the image. Reconstructing the role of formal pictorial elements for the standards of understanding within the medium “image” is considered pivotal in this endeavor. Within the context of language, standards of communication have already been extensively researched. The linguistic format of the narrative, for instance, is well studied. Up to now, though, comparable formal vehicles of iconic semantics have only been examined in aesthetics and art history. Nevertheless, standards of iconic understanding are part of our implicit knowledge, are incessantly in use in everyday practice and, thus, the basis of everyday identity formation. With the help of empirical methods based on an iconic logos we can deepen our understanding of orientations, longings, and anxieties of our time that are often silently conveyed by images. Fashion will be outlined as a prototypical field, in which an empirically based development of such methods might start off.     

The probabilistic approach to human reasoning

A recent development in the cognitive science of reasoning has been the emergence of a probabilistic approach to the behaviour observed on ostensibly logical tasks. According to this approach the errors and biases documented on these tasks occur because people import their everyday uncertain reasoning strategies into the laboratory. Consequently participants' apparently irrational behaviour is the result of comparing it with an inappropriate logical standard. In this article, we contrast the probabilistic approach with other approaches to explaining rationality, and then show how it has been applied to three main areas of logical reasoning: conditional inference, Wason's selection task and syllogistic reasoning.     

Counterexample Search in Diagram-Based Geometric Reasoning

Topological relations such as inside, outside, or intersection are ubiquitous to our spatial thinking. Here, we examined how people reason deductively with topological relations between points, lines, and circles in geometric diagrams. We hypothesized in particular that a counterexample search generally underlies this type of reasoning. We first verified that educated adults without specific math training were able to produce correct diagrammatic representations contained in the premisses of an inference. Our first experiment then revealed that subjects who correctly judged an inference as invalid almost always produced a counterexample to support their answer. Noticeably, even if the counterexample always bore a certain level of similarity to the initial diagram, we observed that an object was more likely to be varied between the two drawings if it was present in the conclusion of the inference. Experiments 2 and 3 then directly probed counterexample search. While participants were asked to evaluate a conclusion on the basis of a given diagram and some premisses, we modulated the difficulty of reaching a counterexample from the diagram. Our results indicate that both decreasing the counterexample density and increasing the counterexample distance impaired reasoning performance. Taken together, our results suggest that a search procedure for counterexamples, which proceeds object-wise, could underlie diagram-based geometric reasoning. Transposing points, lines, and circles to our spatial environment, the present study may ultimately provide insights on how humans reason about topological relations between positions, paths, and regions.     

Iconic Representations and Representative Practices

I develop an account of scientific representations building on Charles S. Peirce's rich, and still underexplored, notion of iconicity. Iconic representations occupy a central place in Peirce's philosophy, in his innovative approach to logic and in his practice as a scientist. Starting from a discussion of Peirce's approach to diagrams, I claim that Peirce's own representations are in line with his formulation of iconicity, and that they are more broadly connected to the pragmatist philosophy he developed in parallel with his scientific work. I then defend the contemporary relevance of Peirce's approach to iconic representations, and specifically argue that Peirce offers a useful ‘third way’ between what Mauricio Suárez has recently described as the ‘analytical’ and ‘practical’ inquiries into the concept of representation. As a philosophically minded scientist and an experimentally inclined philosopher, Peirce never divorced the practice of representing from questions about what counts as a representation. I claim that his account of iconic representations shows that it is the very process of representing, construed as a practice which is coextensive with observing and experimenting, that casts light on the nature of representative relations.     

Why the spontaneous images created by the hands during talk can help make TV advertisements more effective

The design of effective communications depends upon an adequate model of the communication process. The traditional model is that speech conveys semantic information and bodily movement conveys information about emotion and interpersonal attitudes. But McNeill (2000) argues that this model is fundamentally wrong and that some bodily movements, namely spontaneous hand movements generated during talk (iconic gestures), are integral to semantic communication. But can we increase the effectiveness of communication using this new theory? Focusing on advertising we found that advertisements in which the message was split between speech and iconic gesture (possible on TV) were significantly more effective than advertisements in which meaning resided purely in speech or language (radio/ newspaper). We also found that the significant differences in communicative effectiveness were maintained across five consecutive trials. We compared the communicative power of professionally made TV advertisements in which a spoken message was accompanied either by iconic gestures or by pictorial images, and found the iconic gestures to be more effective. We hypothesized that iconic gestures are so effective because they illustrate and isolate just the core semantic properties of a product. This research suggests that TV advertisements can be made more effective by incorporating iconic gestures with exactly the right temporal and semantic properties.     

Stimulus equivalence instruction of fraction-decimal relations

Stimulus control technology was applied to the instruction of fraction ratio (e.g., (1/5)) and decimal (e.g., 0.20) relations, with 7 students who demonstrated difficulty in fraction and decimal tasks. The students were trained to match pictorial representations of fractions (B comparison stimuli) to printed counterpart fraction ratios (A sample stimuli), and to match printed decimals (C comparison stimuli) to pictorial representations of counterpart quantities (B sample stimuli). Posttest performance by all participants indicated the emergence of equivalence relations between fractions represented as ratios, decimals, and pictures. Limited generalization of fraction-decimal relations was observed.     

Piktorielle Repräsentationen als unterbestimmte räumliche Modelle

Central for the discussion about the pros and cons of pictorial representations is the indeterminacy problem. Whereas propositional representations can be underdetermined, it is a widespread opinion that pictorial representations are completely determined and committed to details. In contrast to this view, which is held — for example by Dennett, Pylyshyn and Iorger — in the present paper a variable system of commitments is proposed: Users of pictorial representations have alternatives with respect to interpretations and commitments since there are implicit annotations to these representations. The annotations refer to axiomatized geometric systems, which — from a cognitive point of view — can be seen as systems of commitments.     

A Cognitive Theory of Graphical and Linguistic Reasoning: Logic and Implementation

We discuss external and internal graphical and linguistic representational systems. We argue that a cognitive theory of peoples' reasoning performance must account for (a) the logical equivalence of inferences expressed in graphical and linguistic form, and (b) the implementational differences that affect facility of inference. Our theory proposes that graphical representation limit abstraction and thereby aid “processibility”. We discuss the ideas of specificity and abstraction, and their cognitive relevance. Empirical support both comes from tasks which involve the manipulation of external graphics and tasks that do not. For the former, we take Euler's (1772) circles, provide a novel computational reconstruction, show how it captures abstractions, and contrast it with earlier construals and with Johnson-Laird's (1983) mental models representations. We demonstrate equivalence of the graphical Euler system, and the nongraphical mental models system. For tasks not involving manipulation of external graphics, we discuss text comprehension, and the mental performance of syllogisms. By positing an internal system with the same specificity as Euler's circles, we cover the mental models data, and generate new empirical predictions. Finally, we consider how the architecture of working memory explains why such specific representations are relatively easy to store.     

Attentional bias toward negative and positive pictorial stimuli and its relationship with distorted cognitions,empathy, and moral reasoning among men with intellectual disabilities who have committed crimes

The aims of this study were to examine: (a) whether men with intellectual disabilities who have a history of criminal offending attend to affective pictorial stimuli in a biased manner, and (b) whether there is a relationship between an affective attentional bias and offense‐supportive cognitions, empathy, and moral reasoning. Forty‐six men with intellectual disabilities who had a documented history of criminal offending, and 51 men who also had intellectual disabilities, but no such history, were recruited and asked to complete a computer‐based dot‐probe task using affective pictorial stimuli with randomization, along with measures of distorted cognitions, empathy, and moral reasoning. Those with a history of criminal offending endorsed significantly more offense‐supportive cognitions, had significantly lower general empathy, and more “mature” moral reasoning, as well as a significant attentional bias toward affective pictorial stimuli. Attentional bias significantly predicted offense‐supportive cognitions, and vice versa, having controlled for offense history, and Full‐Scale IQ, but this was not the case for empathy or moral reasoning. While the findings require replication, interventions that aim to modify attention bias with this population should be tested.     

Varieties of Pictorial Illusion

This article focuses on a potentially perplexing aspect of our interactions with pictorial representations (including film, paintings, pictures, drawings, photographs, even video games): in some cases, it seems that visual representations can play tricks on our cognitive faculties. We may either come to believe that objects represented in pictures are real or perhaps perceive them as such. The possibility of widespread pictorial illusions has been oft discussed, and discarded, in the aesthetics literature. I support this stance. However, the nature of the illusion is more complicated than is usually considered. I argue that there are five different types of potential illusions and present reasons for rejecting each. I also explore in detail the most persistent illusion: the “object recognition perceptual illusion thesis,” which states that we undergo a perceptual illusion while viewing pictorial representations simply in virtue of seeing objects in the representation. I contend that a rejection of this thesis depends on the nature of perceptual content, an issue with far‐reaching consequences in aesthetics.     

Children's cognitive representation of the mathematical number line

Learning of the mathematical number line has been hypothesized to be dependent on an inherent sense of approximate quantity. Children's number line placements are predicted to conform to the underlying properties of this system; specifically, placements are exaggerated for small numerals and compressed for larger ones. Alternative hypotheses are based on proportional reasoning; specifically, numerals are placed relative to set anchors such as end points on the line. Traditional testing of these alternatives involves fitting group medians to corresponding regression models which assumes homogenous residuals and thus does not capture useful information from between‐ and within‐child variation in placements across the number line. To more fully assess differential predictions, we developed a novel set of hierarchical statistical models that enable the simultaneous estimation of mean levels of and variation in performance, as well as developmental transitions. Using these techniques we fitted the number line placements of 224 children longitudinally assessed from first to fifth grade, inclusive. The compression pattern was evident in mean performance in first grade, but was the best fit for only 20% of first graders when the full range of variation in the data are modeled. Most first graders' placements suggested use of end points, consistent with proportional reasoning. Developmental transition involved incorporation of a mid‐point anchor, consistent with a modified proportional reasoning strategy. The methodology introduced here enables a more nuanced assessment of children's number line representation and learning than any previous approaches and indicates that developmental improvement largely results from midpoint segmentation of the line.