Towards a category theory approach to analogy: Analyzing re-representation and acquisition of numerical knowledge

Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use t...

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Bibliographic Details
Published in:PLoS computational biology Vol. 13; no. 8; p. e1005683
Main Authors: Navarrete, Jairo A., Dartnell, Pablo
Format: Journal Article
Language:English
Published: United States Public Library of Science 25.08.2017
Public Library of Science (PLoS)
Subjects:
Algorithms
Artificial intelligence
Biology and Life Sciences
Cognition
Cognition & reasoning
Cognition - physiology
Cognitive ability
Computational Biology
Computer applications
Computer Simulation
Educational psychology
Empirical analysis
Funding
Game Theory
Humans
Knowledge
Language
Learning
Mathematical models
Mathematics education
Methods
Models, Theoretical
Natural language processing
Neural circuitry
Neurological research
Social Sciences
Theorems (Mathematics)
Theory
ISSN:1553-7358, 1553-734X, 1553-7358
Online Access:Get full text
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Summary:Category Theory, a branch of mathematics, has shown promise as a modeling framework for higher-level cognition. We introduce an algebraic model for analogy that uses the language of category theory to explore analogy-related cognitive phenomena. To illustrate the potential of this approach, we use this model to explore three objects of study in cognitive literature. First, (a) we use commutative diagrams to analyze an effect of playing particular educational board games on the learning of numbers. Second, (b) we employ a notion called coequalizer as a formal model of re-representation that explains a property of computational models of analogy called "flexibility" whereby non-similar representational elements are considered matches and placed in structural correspondence. Finally, (c) we build a formal learning model which shows that re-representation, language processing and analogy making can explain the acquisition of knowledge of rational numbers. These objects of study provide a picture of acquisition of numerical knowledge that is compatible with empirical evidence and offers insights on possible connections between notions such as relational knowledge, analogy, learning, conceptual knowledge, re-representation and procedural knowledge. This suggests that the approach presented here facilitates mathematical modeling of cognition and provides novel ways to think about analogy-related cognitive phenomena.
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The authors have declared that no competing interests exist.
ISSN:1553-7358
1553-734X
1553-7358
DOI:10.1371/journal.pcbi.1005683