### Abstract

Original language | English |
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Title of host publication | Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002 |

Place of Publication | Berlin Heidelberg |

Publisher | Springer-Verlag |

Pages | 146-160 |

Number of pages | 15 |

Volume | 2317 |

ISBN (Print) | 9783540435617 |

DOIs | |

Publication status | Published - 1 Jan 2002 |

Event | Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002 - Callaway Gardens, GA, USA, April 18-20, 2002 Duration: 1 Jan 2002 → … |

### Publication series

Name | Lecture Notes in Computer Science |
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### Conference

Conference | Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002 |
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Period | 1/01/02 → … |

### Fingerprint

### Keywords

- Visual languages
- Euler diagrams

### Cite this

*Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002*(Vol. 2317, pp. 146-160). (Lecture Notes in Computer Science). Berlin Heidelberg: Springer-Verlag. https://doi.org/10.1007/3-540-46037-3_7

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*Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002.*vol. 2317, Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg, pp. 146-160, Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002, 1/01/02. https://doi.org/10.1007/3-540-46037-3_7

**Corresponding regions in Euler diagrams.** / Howse, John; Stapleton, Gem; Flower, Jean; Taylor, John.

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

TY - GEN

T1 - Corresponding regions in Euler diagrams

AU - Howse, John

AU - Stapleton, Gem

AU - Flower, Jean

AU - Taylor, John

PY - 2002/1/1

Y1 - 2002/1/1

N2 - Euler diagrams use topological properties to represent set-theoretical concepts and thus are `intuitive' to some people. When reasoning with Euler diagrams, it is essential to have a notion of correspondence among the regions in different diagrams. At the semantic level, two regions correspond when they represent the same set. However, we wish to construct a purely syntactic definition of corresponding regions, so that reasoning can take place entirely at the diagrammatic level. This task is interesting in Euler diagrams because some regions of one diagram may be missing from another. We construct the correspondence relation from `zones' or minimal regions, introducing the concept of `zonal regions' for the case in which labels may differ between diagrams. We show that the relation is an equivalence relation and that it is a generalization of the counterpart relations introduced by Shin and Hammer.

AB - Euler diagrams use topological properties to represent set-theoretical concepts and thus are `intuitive' to some people. When reasoning with Euler diagrams, it is essential to have a notion of correspondence among the regions in different diagrams. At the semantic level, two regions correspond when they represent the same set. However, we wish to construct a purely syntactic definition of corresponding regions, so that reasoning can take place entirely at the diagrammatic level. This task is interesting in Euler diagrams because some regions of one diagram may be missing from another. We construct the correspondence relation from `zones' or minimal regions, introducing the concept of `zonal regions' for the case in which labels may differ between diagrams. We show that the relation is an equivalence relation and that it is a generalization of the counterpart relations introduced by Shin and Hammer.

KW - Visual languages

KW - Euler diagrams

U2 - 10.1007/3-540-46037-3_7

DO - 10.1007/3-540-46037-3_7

M3 - Conference contribution with ISSN or ISBN

SN - 9783540435617

VL - 2317

T3 - Lecture Notes in Computer Science

SP - 146

EP - 160

BT - Diagrammatic Representation and Inference, Second International Conference, Diagrams 2002

PB - Springer-Verlag

CY - Berlin Heidelberg

ER -