### Abstract

Original language | English |
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Title of host publication | 10th International Conference on the Theory and Application of Diagrams |

Editors | P. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz, F. Bellucci |

Place of Publication | Edinburgh |

Pages | 365-381 |

Volume | 10871 |

ISBN (Electronic) | 9783319913766 |

DOIs | |

Publication status | Published - 17 May 2018 |

Event | 10th International Conference on the Theory and Application of Diagrams - Edinburgh , Edinburgh , United Kingdom Duration: 18 Jun 2018 → 22 Jun 2018 Conference number: 10 http://www.diagrams-conference.org/2018/ |

### Publication series

Name | Lecture Notes in Computer Science |
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ISSN (Print) | 0302-9743 |

### Conference

Conference | 10th International Conference on the Theory and Application of Diagrams |
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Abbreviated title | Diagrams 2018 |

Country | United Kingdom |

City | Edinburgh |

Period | 18/06/18 → 22/06/18 |

Internet address |

### Fingerprint

### Bibliographical note

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

*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

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*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.

Research output: Chapter in Book/Conference proceeding with ISSN or ISBN › Conference contribution with ISSN or ISBN › Research › peer-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 -