We present a meta-analytic review on the processing of negations in conditional reasoning about affirmation problems (Modus Ponens: “MP”, Affirmation of the Consequent “AC”) and denial problems (Denial of the Antecedent “DA”, and Modus Tollens “MT”). Findings correct previous generalisations about the phenomena. First, the effects of negation in the part of the conditional about which an inference is made, are not constrained to denial problems. These inferential-negation effects are also observed on AC. Second, there generally are reliable effects of (...) a negation in the clause referred to by the categorical premise, and these referred-negation effects are constrained to the logically fallacious AC and DA inferences. All findings are presented and discussed in relation to contemporary mental model (MM) and mental logic (ML) theories. It is argued that a double-negation elimination hypothesis provides a sufficient explanation of inferential-negation effects within both MM theory and ML theory, if the latter is extended by a validating search for counter examples. Both MM and ML theories adhere to a processing scheme that allows them to incorporate an account of referred-negation effects based on the thesis that counter-example frequency is modulated by the scope of a contrast class delineated by a false affirmative. We conclude that MM and ML theories provide adequate processing schemes to accommodate for the explanatory hypotheses, at least in principle. In practice, both approaches remain equivocal as regards the connectivity and interactivity with long-term memory knowledge invoked in generating, manipulating, and testing the mental representations of negative state of affairs. (shrink)

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. It is shown that, although these sentences are known to have a diagrammatic expression (in the form of the Gergonne circles) which constitute a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) It is hypothesized that the quantified sentences have an abstract underlying representation common to the formulas and their associated sets of diagrams (models). Nine predictions are derived (three semantic, two pragmatic, and four mixed) regarding people's assessment of how well each of the five diagrams expresses the meaning of each of the quantified sentences. The results from three experiments, using Gergonne's circles or an adaptation of Leibniz lines as external representations, are reported and shown to support the predictions. (shrink)

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). (shrink)

When interpreting the meanings of visual features in information visualizations, observers have expectations about how visual features map onto concepts (inferred mappings.) In this study, we examined whether aspects of inferred mappings that have been previously identified for colormap data visualizations generalize to a different type of visualization, Venn diagrams. Venn diagrams offer an interesting test case because empirical evidence about the nature of inferred mappings for colormaps suggests that established conventions for Venn diagrams are counterintuitive. Venn diagrams represent classes (...) using overlapping circles and express logical relationships between those classes by shading out regions to encode the concept of non-existence, or none. We propose that people do not simply expect shading to signify non-existence, but rather they expect regions that appear as holes to signify non-existence (the hole hypothesis.) The appearance of a hole depends on perceptual properties in the diagram in relation to its background. Across three experiments, results supported the hole hypothesis, underscoring the importance of configural processing for interpreting the meanings of visual features in information visualizations. (shrink)

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. (shrink)

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology (...) and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain. (shrink)

Diagrams are a form of spatial representation that supports reasoning and problem solving. Even when diagrams are external, not to mention when there are no external representations, problem solving often calls for internal representations, that is, representations in cognition, of diagrammatic elements and internal perceptions on them. General cognitive architectures—Soar and ACT-R, to name the most prominent—do not have representations and operations to support diagrammatic reasoning. In this article, we examine some requirements for such internal representations and processes in cognitive (...) architectures. We discuss the degree to which DRS, our earlier proposal for such an internal representation for diagrams, meets these requirements. In DRS, the diagrams are not raw images, but a composition of objects that can be individuated and thus symbolized, while, unlike traditional symbols, the referent of the symbol is an object that retains its perceptual essence, namely, its spatiality. This duality provides a way to resolve what anti-imagists thought was a contradiction in mental imagery: the compositionality of mental images that seemed to be unique to symbol systems, and their support of a perceptual experience of images and some types of perception on them. We briefly review the use of DRS to augment Soar and ACT-R with a diagrammatic representation component. We identify issues for further research. (shrink)

Some regularities enjoy only an attenuated existence in a body of training data. These are regularities whose statistical visibility depends on some systematic recoding of the data. The space of possible recodings is, however, infinitely large – it is the space of applicable Turing machines. As a result, mappings that pivot on such attenuated regularities cannot, in general, be found by brute-force search. The class of problems that present such mappings we call the class of “type-2 problems.” Type-1 problems, by (...) contrast, present tractable problems of search insofar as the relevant regularities can be found by sampling the input data as originally coded. Type-2 problems, we suggest, present neither rare nor pathological cases. They are rife in biologically realistic settings and in domains ranging from simple animat behaviors to language acquisition. Not only are such problems rife – they are standardly solved! This presents a puzzle. How, given the statistical intractability of these type-2 cases, does nature turn the trick? One answer, which we do not pursue, is to suppose that evolution gifts us with exactly the right set of recoding biases so as to reduce specific type-2 problems to type-1 mappings. Such a heavy-duty nativism is no doubt sometimes plausible. But we believe there are other, more general mechanisms also at work. Such mechanisms provide general strategies for managing problems of type-2 complexity. Several such mechanisms are investigated. At the heart of each is a fundamental ploy – namely, the maximal exploitation of states of representation already achieved by prior, simpler learning so as to reduce the amount of subsequent computational search. Such exploitation both characterizes and helps make unitary sense of a diverse range of mechanisms. These include simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription”. In addition, the most distinctive features of human cognition – language and culture – may themselves be viewed as adaptations enabling this representation/computation trade-off to be pursued on an even grander scale. (shrink)

Modern logic provides accounts of both interpretation and derivation which work together to provide abstract frameworks for modelling the sensitivity of human reasoning to task, context and content. Cognitive theories have underplayed the importance of interpretative processes. We illustrate, using Wason's [Q. J. Exp. Psychol. 20 (1968) 273] selection task, how better empirical cognitive investigations and theories can be built directly on logical accounts when this imbalance is redressed. Subjects quite reasonably experience great difficulty in assigning logical form to descriptively (...) interpreted rules in this task and materials, though not to deontically interpreted ones. The main empirical contrasts in reasoning performance are precisely between these interpretations, so better semantic theory can explain the main empirical effects. However, a more adequate notion of logical form than that typically employed in the psychology of reasoning is required, and we offer a richer alternative. Prima facie evidence that subjects do in fact experience the predicted difficulties in interpreting descriptive materials is provided by analyses of socratic tutoring dialogues. Experimental verification that these difficulties do in fact affect subjects' performance in the standard task is provided by six novel experimental conditions each designed to test different aspects of the semantic predictions. The results bear out the predictions. The semantic distinction between descriptive and deontic rules interacts with the task specifics to provide powerful generalisations about reasoning which surface in detailed explanations of many disparate observations. We conclude that semantic analyses have more direct benefits for psychological investigation than is usually credited, and conversely, that the extraordinary pragmatic circumstances of psychological experiments yield much thought provoking data for semantic analysis. © 2004 Cognitive Science Society, Inc. All rights reserved.Subjects quite reasonably experience great difficulty in assigning logical form to descriptively interpreted rules in this task and materials, though not to deontically interpreted ones. The main empirical contracts in reasoning performance are precisely between these interpretatins, so better semantic theory can explain the main empirical effects. Howevers, a more adequate nation of logical from than that typically employed in the psychology of reasoning in required, and we offer a richer alternative.Prima facie evidence that subjects do in fact experience the predicted difficulties in interpreting descriptive materials is provided by analyses of socratic tutoring dialogues. Experimental verification that these difficulties do in fact affect subjects' performance in the standard task is provided by six novel experimental conditions each designed to test different aspects of the semantic predications.The resluts bear out the predictions. The semantic distinction between descriptive and deontic rules interacts with the task specifics to provide powerful generalisations about reasoning which surface in detailed explanations of many disparate observations. We conclude that semantic analyses have more direct benefits for psychological investigation than is usually credited, and conversely, that the extraordinary pragmatic circumstances of psychological experiments yield much thought provoking data for semantic analysis. (shrink)

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used (...) a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re‐evaluates current theories of syllogistic reasoning in the light of these results. (shrink)

We present a set-theoretic model of the mental representation of classically quantified sentences (All P are Q, Some P are Q, Some P are not Q, and No P are Q). We take inclusion, exclusion, and their negations to be primitive concepts. We show that although these sentences are known to have a diagrammatic expres- sion (in the form of the Gergonne circles) that constitutes a semantic representation, these concepts can also be expressed syntactically in the form of algebraic formulas. (...) We hypothesized that the quantified sen- tences have an abstract underlying representation common to the formulas and their associated sets of dia- grams (models). We derived 9 predictions (3 semantic, 2 pragmatic, and 4 mixed) regarding people’s as- sessment of how well each of the 5 diagrams expresses the meaning of each of the quantified sentences. We report the results from 3 experiments using Gergonne’s (1817) circles or an adaptation of Leibniz (1903/ 1988) lines as external representations and show them to support the predictions. (shrink)

Self‐explaining is an effective metacognitive strategy that can help learners develop deeper understanding of the material they study. This experiment explored if the format of material (i.e., text or diagrams) influences the self‐explanation effect. Twenty subjects were presented with information about the human circulatory system and prompted to self‐explain; 10 received this information in text and 10 in diagrams. Results showed that students given diagrams performed significantly better on post‐tests than students given text. Diagrams students also generated significantly more self‐explanations (...) that text students. Furthermore, the benefits of self‐explaining were much greater in the diagrams condition. To discover why diagrams can promote the self‐explanation effect, results are interpreted with reference to the multiple differences in the semantic, cognitive and affective properties of the texts and diagrams studied. (shrink)

This article proposes a theoretical framework for external representation based problem solving. The Tic‐Tac‐Toe and its isomorphs are used to illustrate the procedures of the framework as a methodology and test the predictions of the framework as a functional model. Experimental results show that the behavior in the Tic‐Tac‐Toe is determined by the directly available information in external and internal representations in terms of perceptual and cognitive biases, regardless of whether the biases are consistent with, inconsistent with, or irrelevant to (...) the task. It is shown that external representations are not merely inputs and stimuli to the internal mind and that they have much more important functions than mere memory aids. A representational determinism is suggested—the form of a representation determines what information can be perceived, what processes can be activated, and what structures can be discovered from the specific representation. (shrink)

We argue that existing learning algorithms are often poorly equipped to solve problems involving a certain type of important and widespread regularity that we call “type-2 regularity.” The solution in these cases is to trade achieved representation against computational search. We investigate several ways in which such a trade-off may be pursued including simple incremental learning, modular connectionism, and the developmental hypothesis of “representational redescription.”.

Theorems in automated theorem proving are usually proved by formal logical proofs. However, there is a subset of problems which humans can prove by the use of geometric operations on diagrams, so called diagrammatic proofs. Insight is often more clearly perceived in these proofs than in the corresponding algebraic proofs; they capture an intuitive notion of truthfulness that humans find easy to see and understand. We are investigating and automating such diagrammatic reasoning about mathematical theorems. Concrete, rather than general diagrams (...) are used to prove particular concrete instances of the universally quantified theorem. The diagrammatic proof is captured by the use of geometric operations on the diagram. These operations are the inference steps of the proof. An abstracted schematic proof of the universally quantified theorem is induced from these proof instances. The constructive -rule provides the mathematical basis for this step from schematic proofs to theoremhood. In this way we avoid the difficulty of treating a general case in a diagram. One method of confirming that the abstraction of the schematic proof from the proof instances is sound is proving the correctness of schematic proofs in the meta-theory of diagrams. These ideas have been implemented in the system, called Diamond, which is presented here. (shrink)

Theories concerning the structure, or format, of mental representation should (1) be formulated in mechanistic, rather than metaphorical terms; (2) do justice to several philosophical intuitions about mental representation; and (3) explain the human capacity to predict the consequences of worldly alterations (i.e., to think before we act). The hypothesis that thinking involves the application of syntax-sensitive inference rules to syntactically structured mental representations has been said to satisfy all three conditions. An alternative hypothesis is that thinking requires the construction (...) and manipulation of the cognitive equivalent of scale models. A reading of this hypothesis is provided that satisfies condition (1) and which, even though it may not fully satisfy condition (2), turns out (in light of the frame problem) to be the only known way to satisfy condition (3). (shrink)

Depictive expressions of thought predate written language by thousands of years. They have evolved in communities through a kind of informal user testing that has refined them. Analyzing common visual communications reveals consistencies that illuminate how people think as well as guide design; the process can be brought into the laboratory and accelerated. Like language, visual communications abstract and schematize; unlike language, they use properties of the page (e.g., proximity and place: center, horizontal/up–down, vertical/left–right) and the marks on it (e.g., (...) dots, lines, arrows, boxes, blobs, likenesses, symbols) to convey meanings. The visual expressions of these meanings (e.g., individual, category, order, relation, correspondence, continuum, hierarchy) have analogs in language, gesture, and especially in the patterns that are created when people design the world around them, arranging things into piles and rows and hierarchies and arrays, spatial-abstraction-action interconnections termed spractions. The designed world is a diagram. (shrink)

In contrast to Constructivist Views, which construe perceptual cognition as an essentially reconstructive process, this article recommends the Deictic View, which grounds perception in perceptual-demonstrative reference and the use of deictic tracking strategies for acquiring and updating knowledge about individuals. The view raises the problem of how sensory-motor tracking connects to epistemic and integrated forms of tracking. To study the strategies used to solve this problem, we report a study of the ability to track distal individuals when only their directions (...) can be perceived and not their locations. We introduce a new experimental paradigm named the 'Modified Traveling Salesman Problem' (MTSP), which requires subjects to visit n invisible targets in a 2D display once each. Surprisingly, subjects are competent at this task for up to 10 targets. We consider two types of tracking strategies that subjects might use: 'location-based' strategies and 'deictic direction-based' strategies. A number of observations suggest that subjects used the latter, at least for larger numbers of targets. We hypothesize that subjects used perceptual-demonstrative reference and deictic strategies (i) to perform the sensory-motor tracking of directional segments, (ii) to bind the segments with their updated status in the task, and (iii) to perform the epistemic tracking of invisible targets by means of perception-based inferences. (shrink)

The aim of this article is to strengthen links between cognitive brain research and formal logic. The work covers three fundamental sorts of logical inferences: reasoning in the propositional calculus, i.e. inferences with the conditional “if...then”, reasoning in the predicate calculus, i.e. inferences based on quantifiers such as “all”, “some”, “none”, and reasoning with n-place relations. Studies with brain-damaged patients and neuroimaging experiments indicate that such logical inferences are implemented in overlapping but different bilateral cortical networks, including parts of the (...) fronto-temporal cortex, the posterior parietal cortex, and the visual cortices. I argue that these findings show that we do not use a single deterministic strategy for solving logical reasoning problems. This account resolves many disputes about how humans reason logically and why we sometimes deviate from the norms of formal logic. (shrink)

The possibility of ideography is an empirical question. Prior examples of graphic codes do not provide compelling evidence for the infeasibility of ideography, because they fail to satisfy essential cognitive requirements that have only recently been revealed by studies of representational systems in cognitive science. Design criteria derived from cognitive principles suggest how effective graphic codes may be engineered.

In Volume 33:1 of the Notre Dame Journal of Formal Logic, a system for diagramming syllogistic inferences using straight line segments is presented by Englebretsen. In light of recent research on the representational power of diagrammatic representation systems by the authors, we point out some problems with the proposal, and indeed, with any proposal for representing logically possible situations diagrammatically. We shall first outline the proposed linear diagrammatic system of Englebretsen, and then show by means of counterexamples that it is (...) inadequate as a representation scheme for general logical inferences (the task for which the system is intended). We also show that modifications to the system fail to remedy the problems. The considerations we present are not limited to the particular proposal of Englebretsen; we thus draw a more general moral about the use of spatial relations in representation systems. (shrink)

We elaborate on the approach to syllogistic reasoning based on “case identification” (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition ( ecthesis ), and that there are traces of this method in the strategies described by a number of psychologists, from St rring (1908) to the present day. We hypothesised that by rendering individual cases explicit (...) in the premises, the chance that reasoners would engage in a proof by exposition would be enhanced, and thus performance improved. To do so, we used syllogisms with singular premises (e.g., this X is Y ). This resulted in a uniform increase in performance as compared to performance on the associated standard syllogisms. These results cannot be explained by the main theories of syllogistic reasoning in their current state. (shrink)

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed‐world reasoning of particular interest for (...) human cognition. Byrne's “suppression” data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine‐grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3‐valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning. (shrink)

Mechanical systems have structural organizations—parts, and their relations—and functional organizations—temporal, dynamic, and causal processes—which can be explained using text or diagrams. Two experiments illustrate the role of arrows in diagrams of mechanical systems. In Experiment 1, people described diagrams with or without arrows, interpreting diagrams without arrows as conveying structural information and diagrams with arrows as conveying functional information. In Experiment 2, people produced sketches of mechanical systems from structural or functional descriptions. People spontaneously used arrows to indicate functional processes (...) in diagrams. Arrows can play a powerful role in augmenting structural diagrams to convey dynamic, causal, or functional information. (shrink)

One of the most debated questions in psychology and cognitive science is the nature and the functioning of the mental processes involved in deductive reasoning. However, all existing theories refer to a specific deductive domain, like syllogistic, propositional or relational reasoning.Our goal is to unify the main types of deductive reasoning into a single set of basic procedures. In particular, we bring together the microtheories developed from a mental models perspective in a single theory, for which we provide a formal (...) foundation. We validate the theory through a computational model (UNICORE) which allows fine‐grained predictions of subjects' performance in different reasoning domains.The performance of the model is tested against the performance of experimental subjects—as reported in the relevant literature—in the three areas of syllogistic, relational and propositional reasoning. The computational model proves to be a satisfactory artificial subject, reproducing both correct and erroneous performance of the human subjects. Moreover, we introduce a developmental trend in the program, in order to simulate the performance of subjects of different ages, ranging from children (3–6) to adolescents (8–12) to adults (>21). The simulation model performs similarly to the subjects of different ages.Our conclusion is that the validity of the mental model approach is confirmed for the deductive reasoning domain, and that it is possible to devise a unique mechanism able to deal with the specific subareas. The proposed computational model (UNICORE) represents such a unifying structure. (shrink)

This paper outlines a method to assess the effectiveness of diagrams, from semiotic foundations. In doing so, we explore the Peircian notion of signification, as applied to diagrammatic representations. We review a history of diagrams, with particular emphasis on schematics used for representing systems, and uncover the neglect of semiotic analysis of diagrammatic representations. Through application of category theory to the Peircian triadic model, we propose a set of quantitative quality measures for diagrams, and a framework for their assessment, based (...) on the properties of their encoding, pragmatic and perceptual morphisms. These measures include diagram complexity, utility, aesthetics and expert assessment of semiotic content, together with qualitative feedback. We consider the diagrams as an aid to cognitive processes, rather than a purely communication media. This utility-focused perspective on diagram quality dimensions allows for fresh insights into the creation of effective diagrams. (shrink)

In this paper, the theory of syllogistic reasoning proposed by Johnson-Laird is shown to be inadequate and an alternative theory is put forward. Protocols of people attempting to solve syllogistic problems and explaining to another person how they reached their conclusions were obtained. Two main groups of subjects were identified. One group represented the relationship between classes in a spatial manner that was supplemented by a verbal representation. The other group used a primarily verbal representation. A detailed theory of the (...) processes for both groups is given. (shrink)

This paper describes Peirce's systems of logic diagrams, focusing on the so-called ''existential'' graphs, which are equivalent to the first-order predicate calculus. It analyses their implications for the nature of mental representations, particularly mental models with which they have many characteristics in common. The graphs are intended to be iconic, i.e., to have a structure analogous to the structure of what they represent. They have emergent logical consequences and a single graph can capture all the different ways in which a (...) possibility can occur. Mental models share these properties. But, as the graphs show, certain aspects of propositions cannot be represented in an iconic or visualisable way. They include negation, and the representation of possibilities qua possibilities, which both require representations that do not depend on a perceptual modality. Peirce took his graphs to reveal the fundamental operations of reasoning, and the paper concludes with an analysis of different hypotheses about these operations. (shrink)

Abstract“Natural syllogisms” are arguments formally identifiable with categorical syllogisms that have an implicit universal affirmative premise retrieved from semantic memory rather than explicitly stated. Previous studies with adult participants (Politzer, 2011) have shown that the rate of success is remarkably high. Because their resolution requires only the use of a simple strategy (known as ecthesis in classic logic) and an operational use of the concept of inclusion (the recognition that an element that belongs to a subset must belong to the (...) set but not vice versa), it was hypothesized that these syllogisms would be within the grasp of non‐adult participants, provided they have acquired the notion of deductive validity. Here, 11‐year‐old children were presented with natural syllogisms embedded in short dialogs. The first experiment showed that their performance was equivalent to adults' highest level of performance in standard experiments on syllogisms. The second experiment, while confirming children's proficiency in solving natural syllogisms, showed that they outperformed children who solved non‐natural matched syllogisms in the same experimental setting. The results are also in agreement with the argumentation theory of reasoning. (shrink)

Interpretation is the process whereby a hearer reasons to an interpretation of a speaker's discourse. The hearer normally adopts a credulous attitude to the discourse, at least for the purposes of interpreting it. That is to say the hearer tries to accommodate the truth of all the speaker's utterances in deriving an intended model. We present a nonmonotonic logical model of this process which defines unique minimal preferred models and efficiently simulates a kind of closed-world reasoning of particular interest for (...) human cognition. Byrne's “suppression” data (Byrne, 1989) are used to illustrate how variants on this logic can capture and motivate subtly different interpretative stances which different subjects adopt, thus indicating where more fine-grained empirical data are required to understand what subjects are doing in this task. We then show that this logical competence model can be implemented in spreading activation network models. A one pass process interprets the textual input by constructing a network which then computes minimal preferred models for (3-valued) valuations of the set of propositions of the text. The neural implementation distinguishes easy forward reasoning from more complex backward reasoning in a way that may be useful in explaining directionality in human reasoning. (shrink)

Semantic studies on diagrammatic notations (Barwise & Etchemendy, ; Shimojima, ; Stenning & Lemon, ) have revealed that the “non-deductive,” “emergent,” or “perceptual” effects of diagrams (Chandrasekaran, Kurup, Banerjee, Josephson, & Winkler, ; Kulpa, ; Larkin & Simon, ; Lindsay, ) are all rooted in the exploitation of spatial constraints on graphical structures. Thus, theoretically, this process is a key factor in inference with diagrams, explaining the frequently observed reduction of inferential load. The purpose of this study was to examine (...) the empirical basis for this theoretical suggestion, focusing on the reality of the constraint-exploitation strategy in actual practices of diagrammatic reasoning. Eye movements were recorded while participants used simple position diagrams to solve three- or four-term transitive inference problems. Our experiments revealed that the participants could exploit spatial constraints on graphical structures even when (a) they were not in the position of actually manipulating diagrams, (b) the semantic rule for the provided diagrams did not match their preferences, and (c) the constraint-exploitation strategy invited a partly adverse effect. These findings indicate that the hypothesized process is in fact robust, with the potential to broadly account for the inferential advantage of diagrams. (shrink)

The goal of this study was to explore two accounts for why sketching during learning from text is helpful: sketching acts like other constructive strategies such as self-explanation because it helps learners to identify relevant information and generate inferences; or that in addition to these general effects, sketching has more specific benefits due to the pictorial representation that is constructed. Seventy-three seventh-graders were first taught how to either create sketches or self-explain while studying science texts. During a subsequent learning phase, (...) all students were asked to read an expository text about the greenhouse effect. Finally, they were asked to write down everything they remembered and then answer transfer questions. Strategy quality during learning was assessed as the number of key concepts that had either been sketched or mentioned in the self-explanations. The results showed that at an overall performance level there were only marginal group differences. However, a more in-depth analysis revealed that whereas no group differences emerged for students implementing either strategy poorly, the sketching group clearly outperformed the self-explanation group for students who applied the strategies with higher quality. Furthermore, higher sketching quality was strongly related to better learning outcomes. Thus, the study's results are more in line with the second account: Sketching can have a beneficial effect on learning above and beyond generating written explanations; at least, if well deployed. (shrink)

Six characteristics of effective representational systems for conceptual learning in complex domains have been identified. Such representations should: (1) integrate levels of abstraction; (2) combine globally homogeneous with locally heterogeneous representation of concepts; (3) integrate alternative perspectives of the domain; (4) support malleable manipulation of expressions; (5) possess compact procedures; and (6) have uniform procedures. The characteristics were discovered by analysing and evaluating a novel diagrammatic representation that has been invented to support students' comprehension of electricity—AVOW diagrams (Amps, Volts, Ohms, (...) Watts). A task analysis is presented that demonstrates that problem solving using a conventional algebraic approach demands more effort than AVOW diagrams. In an experiment comparing two groups of learners using the alternative approaches, the group using AVOW diagrams learned more than the group using equations and were better able to solve complex transfer problems and questions involving multiple constraints. Analysis of verbal protocols and work scratchings showed that the AVOW diagram group, in contrast to the equations group, acquired a coherently organised network of concepts, learnt effective problem solving procedures, and experienced more positive learning events. The six principles of effective representations were proposed on the basis of these findings. AVOW diagrams are Law Encoding Diagrams, a general class of representations that have been shown to support learning in other scientific domains. (shrink)