Abstract
We propose an algorithmic procedure for the automatic analysis of syllogisms with negative terms based on the modified version of Shin’s Venn-I diagram. Our computational procedure can automatically generate all the possible conclusions derivable from the two premises of a given syllogism with negative terms. Our approach relies on the reformulation of the logic behind the relations between points, lines, and surfaces in the Venn diagram by employing conditional propagation rules.
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Notes
- 1.
The term surface is called zone in the classical Venn and Euler diagram literature.
- 2.
Our proposal also works without assuming existential import. We only need to eliminate 24 point-to-line propagation rules introduced in Sect. 2.2. Another possibility is to keep the rules without assigning valuation 1 to the points. Obviously, the combination of those two solutions is also possible.
- 3.
Please visit https://sites.google.com/view/mehdimirzapour/publications for getting access to the spreadsheet and the codes.
References
Moktefi, A., Pietarinen, A.V.: On the diagrammatic representation of existential statements with Venn diagrams. J. Logic Lang. Inf. 24(4), 361–374 (2015)
Moktefi, A., Shin, S.J.: A history of logic diagrams. In: Gabbay, D.M., Pelletier, F.J., Woods, J. (eds.) Logic: A History of Its Central Concepts, pp. 611–682. North-Holland, Amsterdam (2012)
Shin, S.J.: The Logical Status of Diagrams. Cambridge University Press, Cambridge (1994)
Acknowledgement
We would like to show our gratitude to Gholamreza Zakiani for his enlightening suggestions in the early stage of this paper.
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Mirzapour, M., Retoré, C. (2018). Venn Diagram and Evaluation of Syllogisms with Negative Terms: A New Algorithm. In: Chapman, P., Stapleton, G., Moktefi, A., Perez-Kriz, S., Bellucci, F. (eds) Diagrammatic Representation and Inference. Diagrams 2018. Lecture Notes in Computer Science(), vol 10871. Springer, Cham. https://doi.org/10.1007/978-3-319-91376-6_66
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DOI: https://doi.org/10.1007/978-3-319-91376-6_66
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