Cognitive Properties of Representations: A Framework

Cheng, Peter; Garcia, Grecia Garcia; Raggi, Daniel; Stockdill, Aaron; Jamnik, Mateja

doi:10.1007/978-3-030-86062-2_43

Cited by 4 publications

(5 citation statements)

References 21 publications

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“…Finally, we note that this research was conducted as part of a wider project that is developing automated systems for the selection of representations for individual problem solvers with varying levels of competence on different classes of problems [13], [14], [15]. One aspect of the project is to devise a measure of the cognitive cost of representations [5], which can be used to assess the relative difficulty a user will likely experience with alternative representations. We note that RIST/RISN may provide an addition route to such assessments though the analysis of the contents of the schemas and the nature of their networks.…”

Section: Discussionmentioning

confidence: 99%

Representational Interpretive Structure: Theory and Notation

Cheng

Stockdill

Garcia

et al. 2022

Diagrammatic Representation and Inference

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A cognitive theory of the interpretive structure of visual representations (RIST) was proposed by Cheng (2020), which identified four classes of schemas that specify how domain concepts are encoded by graphical objects. A notation (RISN) for building RIST models as networks of these schemas was also introduced. This paper introduces common RIST/RISN network structures -idioms -that occur across varied representations. A small-scale experiment is presented in which three participants successfully modelled their own interpretation of three diverse representations using RIST/RISN and idioms.

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Section: Discussionmentioning

confidence: 99%

Representational Interpretive Structure: Theory and Notation

Cheng

Stockdill

Garcia

et al. 2022

Diagrammatic Representation and Inference

Self Cite

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“…45, 122]. 6 In contrast, when reasoning with the Hasse diagram, we think about paths, links, the vertical orientation, and levels of scales. Some indication that image schemas are implicitly used to cognitively structure diagrams is provided by the informal language researchers use when describing how Hasse diagrams should be used for reasoning [4,8,9,21,22].…”

Section: Discussionmentioning

confidence: 99%

“…The term visuo-implies an agent with a certain body and perceptual faculties. Cheng et al [6] also take as a given which relations between symbols of a given representation are meaningful, and should be used for inference. One of our contributions here is that what counts as a meaning-carrying relationship, or valid inference, can be explained in terms of blends with image schemas.…”

Section: Discussionmentioning

confidence: 99%

“…In this section we will briefly summarise the theory of observational advantage of Stapleton et al [27], and a cognitively-inspired framework for the analysis of representations, developed by Cheng et al [6]. The former work put forth a formal criterion to compare the effectiveness of two notations of any kind; including diagrammatic or sentential.…”

Section: Related Workmentioning

confidence: 99%

“…Regarding other work with similar goals to ours, Cheng et al [6] develop a comprehensive formal framework for characterising the formal and cognitive properties of representations, ultimately aiming to build an AI system to automatically select effective representations for particular problem solving tasks. They systematically classify cognitive properties of representation systems, allowing them also to discuss cognitive cost, and thus effectiveness, of using a certain representation system for solving a problem.…”

Section: Related Workmentioning

confidence: 99%

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Euler vs Hasse Diagrams for Reasoning About Sets: A Cognitive Approach

Bourou

Schorlemmer

Plaza

2022

Lecture Notes in Computer Science

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The literature on diagrammatic reasoning includes theoretical and experimental work on the effectiveness of diagrams for conveying information. One influential theoretical contribution to this field proposes that a notation that is more effective than another would have an observational advantage over it; that is, it would make certain pieces of information observable—by means of some visual, meaning-carrying relationships—that were not observable in the other. Although the notion of observational advantage captures a relevant aspect of the benefit of using one notation over another, we present here an example where this notion is not sufficient to distinguish between a more and a less effective diagram. We suggest to take the theory of observational advantage one step further by linking it to cognitive theories of human conceptualisation and reasoning. Following our previous work, we propose that the act of observing facts about set theory from the geometry of a diagram can be modeled as a conceptual blend of image schemas with parts of the geometric configuration of a diagram. Image schemas are elementary mental structures that crystallize early embodied experiences, allowing agents to make sense of what they perceive by conceptualising it in terms of these structures (e.g., container, link, scale etc.). With our approach, we can extend the theory of observational advantage to take into account the cognitive complexity of the act of observation. Concretely, we present an example of an Euler and a Hasse diagram, and we posit that, while their observational advantage is equivalent, the Hasse diagram requires a much more complex network of conceptual blends to model certain observations made from it. Thus, to reason about certain set-theoretic claims, a Hasse diagram is less cognitively effective than an Euler diagram with equivalent observational advantage. We believe our approach contributes to the theoretical discussion on what factors affect the effectiveness of a diagram, and provides new avenues for the exploration of how the embodied experiences of the users contribute to the way they reason with diagrams.

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