A Review of Murphree’s Diagrams
Abstract
Although the literature on logic diagrams is wide and deep, Murphree’s diagrams for assertoric and numerical syllogistic are not as well known; however, we believe they deserve more attention because they have interesting logical (soundness and completeness) and representative (comprehension and clarity) properties. Therefore, following some of the tenets of a research program on diagrammatic reasoning, in this paper we offer a review of these diagrams which, in our opinion, are not as popular as they should be.References
Allwein, G. y Barwise, J. (1996). Logical Reasoning with Diagrams. Nueva York: Oxford University Press.
Basu, A., Stapleton, G., Linker, S., Legg, C., Manalo, E. y Viana, P. (2021). Diagrammatic Representation and Inference: 12th International Conference, Diagrams 2021. Berlin / Heidelberg: Springer Verlag.
Castro-Manzano, J. M. (2016). “From Diagrammatic to Mechanical Reasoning: the Case of Syllogistic”. En P. Arazim, D. Dancak (eds.). The Logica Yearbook 2015. London: College Publications.
(2017a). “Re(dis)covering Leibniz’s Diagrammatic Logic”. En Tópicos. Revista de Filosofía, 52, pp. 89-116.
(2017b). “Remarks on the Idea of Non-Monotonic (Diagrammatic) Inference”. En Open Insight. Revista de Filosofía, 8(14), pp. 243-263.
(2018). “Syllogistic with Jigsaw Puzzle Diagrams”. En P. Chapman, G. Stapleton, A. Moktefi, S. Perez-Kriz, F. Bellucci (eds.). Diagrammatic Representation and Inference. Berlin / Heidelberg: Springer-Verlag.
(2020). “On Why Alpha Graphs are not Logic Diagrams”. En P. Reyes-Cárdenas y D. Herbert (eds.). The Reception of Peirce and Pragmatism in Latin-America. A Trilingual Collection. México: Editorial Torres y Asociados.
(2021). “¿Cuándo decimos que un diagrama es un diagrama lógico? Un estudio comparativo”. En Cogency. Journal of Reasoning and Argumentation, 13(1), pp. 71-103.
Gardner, M. (1958). Logic Machines and Diagrams. New York: McGraw-Hill.
Giardino, V., Linker, S., Burns, R., Bellucci, F., Boucheix, J. M., y Viana, P. (2022). Diagrammatic Representation and Inference: 13th International Conference, Diagrams 2022. Berlin / Heidelberg: Springer Verlag.
Moktefi, A. y Shin, S. (2012). “A History of Logic Diagrams”. En D. M. Gabbay y J. Woods (eds.). Handbook of the History of Logic, vol. 11. Amsterdam: Elsevier North Holland, pp. 611-682.
Murphree, W. (1991). Numerically Exceptive Logic: A Reduction of the Classical Syllogism. Peter Lang.
(1998). “Numerical Term Logic”. En Notre Dame J. Formal Logic, 39(3), pp. 346-362.
Shimojima, A. (1996). “Operational Constraints in Diagrammatic Reasoning”. En G. Allwein y J. Barwise (eds.) Logical Reasoning with Diagrams. Nueva York: Oxford University Press, pp. 27-48.
Shin, S. (1994). The Logical Status of Diagrams. Cambridge: Cambridge University Press.
Szabolcsi, L. y Englebretsen, G. (2008). Numerical Term Logic. Edwin Mellen Press.