Incorporating Negation into Visual Logics

A Case Study Using Euler Diagrams

Gem Stapleton, Judith Masthoff

Research output: Chapter in Book/Report/Conference proceedingConference contribution

18 Citations (Scopus)

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 v 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 languageEnglish
Title of host publicationInternational workshop on Visual Languages and Computing
Subtitle of host publicationProceedings of 13th International Conference on Distributed Multimedia Systems, San Francisco, USA
Place of PublicationChicago, IL. USA
PublisherKnowledge Systems Institute
Pages187-194
Number of pages8
Publication statusPublished - 2007
Event13th International Conference on Distributed Multimedia Systems, Visual Languages and Computing,DMS'2007 , 6-8th September, 2007, San Francisco, USA - San Francisco, United States
Duration: 6 Sep 20078 Sep 2007

Conference

Conference13th International Conference on Distributed Multimedia Systems, Visual Languages and Computing,DMS'2007 , 6-8th September, 2007, San Francisco, USA
CountryUnited States
CitySan Francisco
Period6/09/078/09/07

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Semantics
Acoustic waves

Keywords

  • diagrammatic reasoning
  • Euler diagrams
  • visual logics

Cite this

Stapleton, G., & Masthoff, J. (2007). Incorporating Negation into Visual Logics: A Case Study Using Euler Diagrams. In International workshop on Visual Languages and Computing: Proceedings of 13th International Conference on Distributed Multimedia Systems, San Francisco, USA (pp. 187-194). Chicago, IL. USA: Knowledge Systems Institute.

Incorporating Negation into Visual Logics : A Case Study Using Euler Diagrams. / Stapleton, Gem; Masthoff, Judith.

International workshop on Visual Languages and Computing: Proceedings of 13th International Conference on Distributed Multimedia Systems, San Francisco, USA. Chicago, IL. USA : Knowledge Systems Institute, 2007. p. 187-194.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Stapleton, G & Masthoff, J 2007, Incorporating Negation into Visual Logics: A Case Study Using Euler Diagrams. in International workshop on Visual Languages and Computing: Proceedings of 13th International Conference on Distributed Multimedia Systems, San Francisco, USA. Knowledge Systems Institute, Chicago, IL. USA, pp. 187-194, 13th International Conference on Distributed Multimedia Systems, Visual Languages and Computing,DMS'2007 , 6-8th September, 2007, San Francisco, USA, San Francisco, United States, 6/09/07.
Stapleton G, Masthoff J. Incorporating Negation into Visual Logics: A Case Study Using Euler Diagrams. In International workshop on Visual Languages and Computing: Proceedings of 13th International Conference on Distributed Multimedia Systems, San Francisco, USA. Chicago, IL. USA: Knowledge Systems Institute. 2007. p. 187-194
Stapleton, Gem ; Masthoff, Judith. / Incorporating Negation into Visual Logics : A Case Study Using Euler Diagrams. International workshop on Visual Languages and Computing: Proceedings of 13th International Conference on Distributed Multimedia Systems, San Francisco, USA. Chicago, IL. USA : Knowledge Systems Institute, 2007. pp. 187-194
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