### 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 language | English |
---|---|

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 |

Publisher | Springer |

Pages | 365-381 |

Volume | 10871 |

ISBN (Electronic) | 9783319913766 |

ISBN (Print) | 9783319913759 |

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 |
---|---|

ISSN (Print) | 0302-9743 |

### Conference

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

Abbreviated title | Diagrams 2018 |

Country | United Kingdom |

City | Edinburgh |

Period | 18/06/18 → 22/06/18 |

Internet address |

### Bibliographical note

The final authenticated version is available online at https://doi.org/10.1007/978-3-319-91376-6_34## Fingerprint Dive into the research topics of 'Euler Diagrams Through the Looking Glass: From Extent to Intent'. Together they form a unique fingerprint.

## Profiles

## James Burton

- School of Computing, Engineering & Maths - Senior Lecturer
- Centre for Secure, Intelligent and Usable Systems

Person: Academic

## 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). Springer. https://doi.org/10.1007/978-3-319-91376-6_34