A Diagrammatic Calculus of Syllogisms
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A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
KeywordsSyllogism Venn-Peirce diagram Syllogistic diagram
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- De Morgan A. (1850) On the symbols of logic, the theory of the syllogism, and in particular of the copula, and the application of the theory of probabilities to some questions of evidence. Transactions of the Cambridge Philosophical Society 9: 79–127Google Scholar
- Hammer, E., & Danner, N. (1996). Towards a model theory of Venn diagrams. In Logical reasoning with diagrams, volume 6 of Stud. Logic Comput. (pp. 109–127). New York: Oxford University Press.Google Scholar
- Hobart, M. E., & Richards, J. L. (2008). De Morgan’s logic. In Handbook of the history of logic. British logic in the nineteenth century, volume 4 of Handb. Hist. Log. (pp. 283–329). Amsterdam: Elsevier/North-Holland.Google Scholar
- Łukasiewicz J. (1951) Aristotle’s syllogistic from the standpoint of modern formal logic. Clarendon Press, OxfordGoogle Scholar
- Mendelson E. (1997) Introduction to mathematical logic. (4th ed.). Chapman & Hall/CRC, LondonGoogle Scholar
- Meredith C. A. (1953) The figures and moods of the n-term aristotelian syllogism. Dominican Studies 6: 42–47Google Scholar
- Rayside, D., & Kontogiannis, K. (2001). On the syllogistic structure of object-oriented programming. In Proceedings of the 23rd international conference on software engineering, ICSE’01 (pp. 113–122). Toronto, ON: IEEE Computer Society.Google Scholar
- Roberts, D. D. (1973). The existential graphs of Charles S. Peirce. In Approaches to semiotics (Vol. 27, p. 168). The Hague: Mouton.Google Scholar
- Shin S.-J. (1994) The logical status of diagrams. Cambridge University Press, CambridgeGoogle Scholar
- Shin, S.-J. (1996). Situation-theoretic account of valid reasoning with Venn diagrams. In Logical reasoning with diagrams, Volume 6 of Stud. Logic Comput. (pp. 81–108). New York: Oxford University Press.Google Scholar
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