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 language | English |
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Title of host publication | International workshop on Visual Languages and Computing |
Subtitle of host publication | Proceedings of 13th International Conference on Distributed Multimedia Systems, San Francisco, USA |
Place of Publication | Chicago, IL. USA |
Publisher | Knowledge Systems Institute |
Pages | 187-194 |
Number of pages | 8 |
Publication status | Published - 2007 |
Event | 13th 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 Sept 2007 → 8 Sept 2007 |
Conference
Conference | 13th International Conference on Distributed Multimedia Systems, Visual Languages and Computing,DMS'2007 , 6-8th September, 2007, San Francisco, USA |
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Country/Territory | United States |
City | San Francisco |
Period | 6/09/07 → 8/09/07 |
Keywords
- diagrammatic reasoning
- Euler diagrams
- visual logics