Abstract
This paper contains two traditions of diagrammatic studies namely one, the Euler–Venn–Peirce diagram and the other, following tradition of Aristotle, the square of oppositions. We put together both the traditions to study representations of singular propositions (through a diagram system Venn-i, involving constants), their negations and the inter relationship between the two. Along with classical negation we have incorporated negation of another kind viz. absence (taking a cue from the notion of ‘abhãva’ existing in ancient Indian knowledge system). We have also considered the changes that take place in the context of open universe.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Barwise, J., Etchemendy, J.: Visual information and valid reasoning. In: Allwein, G., Barwise, J. (eds.) Logical Reasoning with Diagrams, pp. 3–25. Oxford University Press, Oxford (1990)
Bernhard P.: Visualization of the square of opposition. Logica Universalis 2, 31–41 (2008)
Béziau, J.Y., Payette, G. (eds.) The square of opposition. In: A General Framework for Cognition. Peter Lang, Bern (2012)
Choudhury L., Chakraborty M.K.: On representing Open Universe. Stud. Logic 5(1), 96–112 (2012)
Choudhury, L., Chakraborty, M.K.: On extending Venn diagram by augmenting names of individuals. In: Blackwell, A., et al. (eds.) Diagrams 2004, LNAI 2980, pp. 142–146 (2004)
Choudhury, L., Chakraborty, M.K.: Comparison between spider diagrams and venn diagrams with individuals. In: Proceedings of the Workshop Euler Diagrams 2005. INRIA, Paris (2005)
Choudhury, L., Chakraborty, M.K.: Singular propositions and their negations in diagrams published in the proceedings of DLAC 2013. In: CEUR Workshop Proceedings, vol. 1132 (2013). http://ceur-ws.org/
Euler, L.: Letters a une princesse d’allemagne, Sur divers sujets de physique et de philosophie. Letters No. 102–108, vol. 2. Basel Birkhauser (1761)
Hammer E.: Logic and Visual Information. CSLI Pubs., USA (1995)
Hopcroft J.E., Ullman J.D.: Formal Languages and Their Relations to Automata. Addison-Wesley, London (1969)
Horn L.R.: A Natural History of Negation. CSLI Pub, USA (2001)
Khomiskii, Y.: William of Sherwood, Singular Proposition and the Hexagon of Opposition. In: Béziau, J.Y., Payette, G. (eds.) The Square of Opposition. A general Framework for Cognition, pp. 43–57. Peter Lang, Bern (2012)
Larkin J.H., Simon H.A.: Why a diagram is (Sometimes) Worth Ten Thousand Words. Cognit. Sci. 11, 65–99 (1987)
Krishna M.B.: Logic, Language and Reality. Motilal Banarasidass. Pub, New Delhi (1990)
Peirce, C.S.: Collected Papers of C.S.Peirce. iv, HUP (1933)
Russell B.: Philosophy of Logical Atomism: Logic and Knowledge. Unwin Hyman, London (1988)
Sharma, S.S.: Interpreting square of oppositions with the help of diagrams. In: Béziau, J.Y., Payette, G. (eds.) The Square of Opposition. A general Framework for Cognition, pp. 174–192. Peter Lang, Bern (2012)
Shin S.J.: The Logical Status of Diagrams. CUP, Cambridge (1994)
Stapleton, G.,Taylor J., Thompson S., Howse, J.: The expressiveness of spider diagrams augmented with constants. J. Vis. Lang. Comput. 20(1), 30–49 (2009)
Stapleton G., Howse J., Taylor J.: A decidable constraint diagram reasoning system. J. Logic Comput. 15(6), 975–1008 (2005)
Stapleton, G.: Incorporating negation into visual logics: a case study using Euler diagrams. Vis. Lang. Comput., 187–194 (2007)
Swoboda N., Allwein, G.: Heterogeneous reasoning with Euler/Venn diagrams containing named constants and FOL. Electron. Not. Theor. Comput. Sci. 134, 153–187 (2005)
Tadeusz C.: On certain peculiarities of singular propositions. Mind 64, 392–395 (1955)
Venn J.: On the diagrammatic and mechanical representation of propositions and reasoning. Philos. Mag. J. Sci. Ser. 5 10(59), 1–18 (1880)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Choudhury, L., Chakraborty, M.K. Singular Propositions, Negation and the Square of Opposition. Log. Univers. 10, 215–231 (2016). https://doi.org/10.1007/s11787-016-0145-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11787-016-0145-0