A cognitive model of discovering commutativity

Markus Guhe; Alison Pease; Alan Smaill

A cognitive model of discovering commutativity

Markus Guhe, Alison Pease, Alan Smaill

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

Mathematics is often seen as the uncovering of eternal truths that exist independently of the human mind. However, even if this epistemological view is correct, the mathematics that humans can know can only be the result of cognitive processes. We investigate this ability of the human mind to make mathematical discoveries. More precisely, we present a cognitive model of how the ability to use metaphors and analogies plays a key role in such discoveries. As a proof of concept we present an ACT-R model that uses path-mapping and that is capable of discovering the commutativity property of addition.

Original language	English
Title of host publication	Proceedings of the 31st Annual Conference of the Cognitive Science Society
Pages	727-732
Number of pages	6
Publication status	Published - 2009

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CogMod: A congnitive model of axiom formulation and reformulation with application to AI and software engineering
Smaill, A. & Clark, A.
EPSRC
1/05/08 → 30/04/11
Project: Research

Cite this

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title = "A cognitive model of discovering commutativity",

abstract = "Mathematics is often seen as the uncovering of eternal truths that exist independently of the human mind. However, even if this epistemological view is correct, the mathematics that humans can know can only be the result of cognitive processes. We investigate this ability of the human mind to make mathematical discoveries. More precisely, we present a cognitive model of how the ability to use metaphors and analogies plays a key role in such discoveries. As a proof of concept we present an ACT-R model that uses path-mapping and that is capable of discovering the commutativity property of addition.",

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AU - Pease, Alison

AU - Smaill, Alan

PY - 2009

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N2 - Mathematics is often seen as the uncovering of eternal truths that exist independently of the human mind. However, even if this epistemological view is correct, the mathematics that humans can know can only be the result of cognitive processes. We investigate this ability of the human mind to make mathematical discoveries. More precisely, we present a cognitive model of how the ability to use metaphors and analogies plays a key role in such discoveries. As a proof of concept we present an ACT-R model that uses path-mapping and that is capable of discovering the commutativity property of addition.

AB - Mathematics is often seen as the uncovering of eternal truths that exist independently of the human mind. However, even if this epistemological view is correct, the mathematics that humans can know can only be the result of cognitive processes. We investigate this ability of the human mind to make mathematical discoveries. More precisely, we present a cognitive model of how the ability to use metaphors and analogies plays a key role in such discoveries. As a proof of concept we present an ACT-R model that uses path-mapping and that is capable of discovering the commutativity property of addition.

M3 - Conference contribution

SP - 727

EP - 732

BT - Proceedings of the 31st Annual Conference of the Cognitive Science Society

ER -

A cognitive model of discovering commutativity

Abstract

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CogMod: A congnitive model of axiom formulation and reformulation with application to AI and software engineering

Cite this