Euler Diagrams Through the Looking Glass: From Extent to Intent

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBNResearchpeer-review

Abstract

Extension and intension are two ways of indicating the fundamental meaning of a concept. The extent of a concept, C, is the set of objects which correspond to C whereas the intent of C is the collection of attributes that characterise it. Thus, intension denotes the set of objects corresponding to C without naming them individually. Mathematicians switch comfortably between these perspectives but the majority of logical diagrams deal exclusively in extension. Euler diagrams indicate sets using curves to depict their extent in a way that intuitively matches the relations between the sets. What happens when we use spatial diagrams to depict intension? What can we infer about the intension of a concept given its extension, and vice versa? We present the first steps towards addressing these questions by defining extensional and intensional Euler diagrams and translations between the two perspectives. We show that translation in either direction leads to a loss of information, yet preserves important semantic properties. To conclude, we explain how we expect further exploration of the relationship between the two perspectives could shed light on connections between diagrams, extension, intension, and well-matchedness.
Original languageEnglish
Title of host publication10th International Conference on the Theory and Application of Diagrams
EditorsP. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz, F. Bellucci
Place of PublicationEdinburgh
Pages365-381
Volume10871
ISBN (Electronic)9783319913766
DOIs
Publication statusPublished - 17 May 2018
Event10th International Conference on the Theory and Application of Diagrams - Edinburgh , Edinburgh , United Kingdom
Duration: 18 Jun 201822 Jun 2018
Conference number: 10
http://www.diagrams-conference.org/2018/

Publication series

NameLecture Notes in Computer Science
ISSN (Print)0302-9743

Conference

Conference10th International Conference on the Theory and Application of Diagrams
Abbreviated titleDiagrams 2018
CountryUnited Kingdom
CityEdinburgh
Period18/06/1822/06/18
Internet address

Fingerprint

semantics

Bibliographical note

The final authenticated version is available online at https://doi.org/10.1007/978-3-319-91376-6_34

Cite this

Stapleton, G., Moktefi, A., Howse, J., & Burton, J. (2018). Euler Diagrams Through the Looking Glass: From Extent to Intent. In P. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz, & F. Bellucci (Eds.), 10th International Conference on the Theory and Application of Diagrams (Vol. 10871, pp. 365-381). (Lecture Notes in Computer Science). Edinburgh. https://doi.org/10.1007/978-3-319-91376-6_34
Stapleton, Gem ; Moktefi, Amirouche ; Howse, John ; Burton, James. / Euler Diagrams Through the Looking Glass: From Extent to Intent. 10th International Conference on the Theory and Application of Diagrams. editor / P. Chapman ; G. Stapleton ; A. Moktefi ; S. Perez-Kriz ; F. Bellucci. Vol. 10871 Edinburgh, 2018. pp. 365-381 (Lecture Notes in Computer Science).
@inproceedings{f2dcfcd0597449af92cf7544758d7b70,
title = "Euler Diagrams Through the Looking Glass: From Extent to Intent",
abstract = "Extension and intension are two ways of indicating the fundamental meaning of a concept. The extent of a concept, C, is the set of objects which correspond to C whereas the intent of C is the collection of attributes that characterise it. Thus, intension denotes the set of objects corresponding to C without naming them individually. Mathematicians switch comfortably between these perspectives but the majority of logical diagrams deal exclusively in extension. Euler diagrams indicate sets using curves to depict their extent in a way that intuitively matches the relations between the sets. What happens when we use spatial diagrams to depict intension? What can we infer about the intension of a concept given its extension, and vice versa? We present the first steps towards addressing these questions by defining extensional and intensional Euler diagrams and translations between the two perspectives. We show that translation in either direction leads to a loss of information, yet preserves important semantic properties. To conclude, we explain how we expect further exploration of the relationship between the two perspectives could shed light on connections between diagrams, extension, intension, and well-matchedness.",
author = "Gem Stapleton and Amirouche Moktefi and John Howse and James Burton",
note = "The final authenticated version is available online at https://doi.org/10.1007/978-3-319-91376-6_34",
year = "2018",
month = "5",
day = "17",
doi = "10.1007/978-3-319-91376-6_34",
language = "English",
isbn = "9783319913759",
volume = "10871",
series = "Lecture Notes in Computer Science",
pages = "365--381",
editor = "P. Chapman and G. Stapleton and A. Moktefi and S. Perez-Kriz and F. Bellucci",
booktitle = "10th International Conference on the Theory and Application of Diagrams",

}

Stapleton, G, Moktefi, A, Howse, J & Burton, J 2018, Euler Diagrams Through the Looking Glass: From Extent to Intent. in P Chapman, G Stapleton, A Moktefi, S Perez-Kriz & F Bellucci (eds), 10th International Conference on the Theory and Application of Diagrams. vol. 10871, Lecture Notes in Computer Science, Edinburgh, pp. 365-381, 10th International Conference on the Theory and Application of Diagrams, Edinburgh , United Kingdom, 18/06/18. https://doi.org/10.1007/978-3-319-91376-6_34

Euler Diagrams Through the Looking Glass: From Extent to Intent. / Stapleton, Gem; Moktefi, Amirouche; Howse, John; Burton, James.

10th International Conference on the Theory and Application of Diagrams. ed. / P. Chapman; G. Stapleton; A. Moktefi; S. Perez-Kriz; F. Bellucci. Vol. 10871 Edinburgh, 2018. p. 365-381 (Lecture Notes in Computer Science).

Research output: Chapter in Book/Conference proceeding with ISSN or ISBNConference contribution with ISSN or ISBNResearchpeer-review

TY - GEN

T1 - Euler Diagrams Through the Looking Glass: From Extent to Intent

AU - Stapleton, Gem

AU - Moktefi, Amirouche

AU - Howse, John

AU - Burton, James

N1 - The final authenticated version is available online at https://doi.org/10.1007/978-3-319-91376-6_34

PY - 2018/5/17

Y1 - 2018/5/17

N2 - Extension and intension are two ways of indicating the fundamental meaning of a concept. The extent of a concept, C, is the set of objects which correspond to C whereas the intent of C is the collection of attributes that characterise it. Thus, intension denotes the set of objects corresponding to C without naming them individually. Mathematicians switch comfortably between these perspectives but the majority of logical diagrams deal exclusively in extension. Euler diagrams indicate sets using curves to depict their extent in a way that intuitively matches the relations between the sets. What happens when we use spatial diagrams to depict intension? What can we infer about the intension of a concept given its extension, and vice versa? We present the first steps towards addressing these questions by defining extensional and intensional Euler diagrams and translations between the two perspectives. We show that translation in either direction leads to a loss of information, yet preserves important semantic properties. To conclude, we explain how we expect further exploration of the relationship between the two perspectives could shed light on connections between diagrams, extension, intension, and well-matchedness.

AB - Extension and intension are two ways of indicating the fundamental meaning of a concept. The extent of a concept, C, is the set of objects which correspond to C whereas the intent of C is the collection of attributes that characterise it. Thus, intension denotes the set of objects corresponding to C without naming them individually. Mathematicians switch comfortably between these perspectives but the majority of logical diagrams deal exclusively in extension. Euler diagrams indicate sets using curves to depict their extent in a way that intuitively matches the relations between the sets. What happens when we use spatial diagrams to depict intension? What can we infer about the intension of a concept given its extension, and vice versa? We present the first steps towards addressing these questions by defining extensional and intensional Euler diagrams and translations between the two perspectives. We show that translation in either direction leads to a loss of information, yet preserves important semantic properties. To conclude, we explain how we expect further exploration of the relationship between the two perspectives could shed light on connections between diagrams, extension, intension, and well-matchedness.

U2 - 10.1007/978-3-319-91376-6_34

DO - 10.1007/978-3-319-91376-6_34

M3 - Conference contribution with ISSN or ISBN

SN - 9783319913759

VL - 10871

T3 - Lecture Notes in Computer Science

SP - 365

EP - 381

BT - 10th International Conference on the Theory and Application of Diagrams

A2 - Chapman, P.

A2 - Stapleton, G.

A2 - Moktefi, A.

A2 - Perez-Kriz, S.

A2 - Bellucci, F.

CY - Edinburgh

ER -

Stapleton G, Moktefi A, Howse J, Burton J. Euler Diagrams Through the Looking Glass: From Extent to Intent. In Chapman P, Stapleton G, Moktefi A, Perez-Kriz S, Bellucci F, editors, 10th International Conference on the Theory and Application of Diagrams. Vol. 10871. Edinburgh. 2018. p. 365-381. (Lecture Notes in Computer Science). https://doi.org/10.1007/978-3-319-91376-6_34