Abstract
This paper extends Shin’s[1] and Hammer’s[2]work by bringing in the names of individuals within Venn diagram and proving thereby the soundness and completeness results. History: Beginning with Euler (1772) diagrams have evolved in the hands of Venn(1880) and Peirce(1896). Each had the aim of making the relationship between sets and binary properties of emptiness and non-emptiness more and more clear. In recent years Shin(1994), Hammer(1995) and House et al(2001) have regenerated interest in diagrams by formalizing the logic of diagrams.
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References
Shin, S.-J.: The logical status ofdiagrams. CUP (1994)
Hammer, E.M.: Logic and visual information. CSLI Pub., Stanford (1995)
Euler, L.: Letters a une Princesse d’Allegmagne (1772)
Peirce, C.S.: Collectedpapers of C.S. Peirce, vol. iv, HUP (1933)
Venn, G.: Symbolic Logic (1881)
Howse, J., Molina, F., Taylor, J., Stuart, K.: Spider Diagrams a Diagrammatic Reasoning System. Journal of Visual Languages and Computing 12(3), 299–324 (2001)
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Choudhury, L., Chakraborty, M.K. (2004). On Extending Venn Diagram by Augmenting Names of Individuals. In: Blackwell, A.F., Marriott, K., Shimojima, A. (eds) Diagrammatic Representation and Inference. Diagrams 2004. Lecture Notes in Computer Science(), vol 2980. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-25931-2_14
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DOI: https://doi.org/10.1007/978-3-540-25931-2_14
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