### Abstract

Many diagrammatic logics based on Euler diagrams have been defined with the aim of making precise reasoning easier for people. In such logics it is unusual to find the negation operator (¬) included. This is likely to impact the usability of the logics when users try to make statements that are naturally phrased using the ¬ operator. Furthermore, if one wishes to use semantic tableaux methods for the purposes of establishing entailment then including ¬ is essential. Thus, there are good reasons for extending existing diagrammatic logics to include ¬ explicitly. In this paper, we take Euler diagrams and extend the notation to include the ¬ operator, as well as 'or' and 'and'. Various expressiveness results for the logic are established. We present a sound and complete set of reasoning rules for the logic, drawing parallels with existing completeness proof strategies and highlighting differences that arise due to including negation.

Original language | English |
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Title of host publication | Proceedings of the 13th International Conference on Distributed Multimedia Systems, DMS 2007 |

Place of Publication | USA |

Publisher | Knowledge Systems Institute |

Pages | 187-194 |

Number of pages | 8 |

ISBN (Print) | 9781891706219 |

Publication status | Published - 1 Jan 2007 |

Event | Proceedings of the 13th International Conference on Distributed Multimedia Systems, DMS 2007 - San Francisco Bay, USA, 6-8 September, 2007 Duration: 1 Jan 2007 → … |

### Conference

Conference | Proceedings of the 13th International Conference on Distributed Multimedia Systems, DMS 2007 |
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Period | 1/01/07 → … |

### Keywords

- Diagrammatic logics
- Euler diagrams

## Fingerprint Dive into the research topics of 'Incoporating negation into visual logics: a case study using Euler diagrams'. Together they form a unique fingerprint.

## Cite this

Stapleton, G., & Masthoff, J. (2007). Incoporating negation into visual logics: a case study using Euler diagrams. In

*Proceedings of the 13th International Conference on Distributed Multimedia Systems, DMS 2007*(pp. 187-194). Knowledge Systems Institute. http://www.ksi.edu/seke/Proceedings/dms/DMS2007_Proceedings.pdf