Sets for foundational representations? A design case study with probability and distributions

Cheng, Peter C-H (2018) Sets for foundational representations? A design case study with probability and distributions. SetVR 2018: International Workshop on Set Visualization and Reasoning, Edinburgh, UK, 18 June 2018. Published in: Sato, Yuri and Shams, Zohreh, (eds.) Proceedings of International Workshop on Set Visualization and Reasoning (SetVR 2018). 1-11. CEUR Workshop Proceedings ISSN 1613-0073

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Ideas about sets are foundational to our understanding of many knowledge domains. And cognitive science tells us that the representation (notation or visualization) we use to encode the knowledge of a domain substantially determines what we can think and how easily we can reason about that do-main. Therefore, how a representation encodes ideas about sets may sub-stantially determine how readily we can comprehend, solve problems and learn about its domain. So, how should we design representations for knowledge rich domains to ensure that concepts about sets are readily ac-cessible and also effectively integrated with the domain’s other concepts? A case study is presented in which a representation for sets (Set Space Dia-grams) is taken as a foundation for a representation for probability theory (Probability Space Diagrams) and then further extended as a representation for statistical distributions (Distribution Space Diagrams). Together the three representations constitute a unified framework that conceptually inte-grates knowledge across the three domains.

Item Type: Conference Proceedings
Keywords: Set, probability, statistical distributions, notations, visualization, dia-grams, knowledge recodification
Schools and Departments: School of Engineering and Informatics > Informatics
Subjects: B Philosophy. Psychology. Religion > BC Logic
Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Q Science > QA Mathematics > QA0075 Electronic computers. Computer science
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Depositing User: Peter Cheng
Date Deposited: 25 Apr 2018 13:39
Last Modified: 25 Jun 2018 13:09

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