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 wellmatchedness.
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. PerezKriz, F. Bellucci 
Place of Publication  Edinburgh 
Publisher  Springer 
Pages  365381 
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.diagramsconference.org/2018/ 
Publication series
Name  Lecture Notes in Computer Science 

ISSN (Print)  03029743 
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/10.1007/9783319913766_34Fingerprint 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