Set space diagrams |
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| Affiliation: | 1. Sapienza University of Rome, Italy;2. University of Padua, Italy;1. Institute of Information Science, Beijing Jiaotong University, Beijing 100044, China;2. Computer & Information Science, University of Pennsylvania, Philadelphia, PA 19104, USA;1. Institute of Preventive Veterinary Medicine, Sichuan Agricultural University, Wenjiang District, Chengdu City, 611130, Sichuan Province, PR China;2. Avian Disease Research Center, College of Veterinary Medicine of Sichuan Agricultural University, Wenjiang, Chengdu City, Sichuan Province, 611130, PR China;3. Key Laboratory of Animal Disease and Human Health of Sichuan Province, Sichuan Agricultural University, Wenjiang, Chengdu City, Sichuan Province, 611130, PR China;1. Laboratory LIIAN/Department of Computer Science, Faculty of Science, BP 1796 Fes-atlas 30000, Morocco;2. Laboratory LESSI/Department of Physics, Faculty of Science, BP 1796, Fes-atlas 30000, Morocco;3. Department of Mathematics and Informatics, Multidisciplinary Faculty, BP 300, Selouane 62702, Nador, Morocco;1. CICS-UBI – Health Sciences Research Centre, University of Beira Interior, Avenida Infante D. Henrique, 6200-506 Covilhã, Portugal;2. I3A – Aragón Institute of Engineering Research, Calle Mariano Esquillor, 50018 Zaragoza, Spain |
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| Abstract: | This paper introduces set space diagrams and defines their formal syntax and semantics. Conventional region based diagrams, like Euler circles and Venn diagrams, represent sets and their intersections by means of overlapping regions. By contrast, set space diagrams provide a certain layout that avoids overlapping geometrical entities. This enables the representation of a good deal of sets without getting diagrams which are cluttered due to overlapping regions. In particular, these diagrams can be employed for illustration purposes, e.g., for showing the laws of Boolean algebras. Additionally, cardinalities are represented and can be easily compared; inferences can be drawn to derive unknown cardinalities from a given knowledge base. The soundness of set space diagrams is shown with respect to their set-theoretic interpretation. |
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| Keywords: | Diagrammatic reasoning Set theory Set space diagrams Boolean algebra Cardinalities Euler circles Venn diagrams |
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