Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bradley Bassler O. (1998) Leibniz on intension, extension, and the representation of syllogistic inference. Synthese 116(2): 117–139
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: 79–127
Englebretsen G. (1992) Linear diagrams for syllogisms (with relationals). Notre Dame Journal of Formal Logic 33(1): 37–69
Glashoff K. (2010) An intensional Leibniz semantics for Aristotelian logic. Review of Symbolic Logic 3(2): 262–272
Głazowska K. (1958) The structure of valid n-term syllogisms. Studia Logica 8: 249–257
Hammer E. (1994) Reasoning with sentences and diagrams. Notre Dame Journal of Formal Logic 35(1): 73–87
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.
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.
La Palme Reyes M., Macnamara J., Reyes Gonzalo E. (1994) Functoriality and grammatical role in syllogisms. Notre Dame Journal of Formal Logic 35(1): 41–66
Lemon O., Pratt I. (1998) On the insufficiency of linear diagrams for syllogisms. Notre Dame Journal of Formal Logic 39(4): 573–580
Łukasiewicz J. (1951) Aristotle’s syllogistic from the standpoint of modern formal logic. Clarendon Press, Oxford
Mendelson E. (1997) Introduction to mathematical logic. (4th ed.). Chapman & Hall/CRC, London
Meredith C. A. (1953) The figures and moods of the n-term aristotelian syllogism. Dominican Studies 6: 42–47
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.
Roberts, D. D. (1973). The existential graphs of Charles S. Peirce. In Approaches to semiotics (Vol. 27, p. 168). The Hague: Mouton.
Shin S.-J. (1994) The logical status of diagrams. Cambridge University Press, Cambridge
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.
Smyth M. B. (1971) A diagrammatic treatment of syllogistic. Notre Dame Journal of Formal Logic 12(4): 483–488
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Pagnan, R. A Diagrammatic Calculus of Syllogisms. J of Log Lang and Inf 21, 347–364 (2012). https://doi.org/10.1007/s10849-011-9156-7
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10849-011-9156-7