“Setting” n-Opposition

Logica Universalis 2 (2):235-263 (2008)
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Abstract

Our aim is to show that translating the modal graphs of Moretti’s “n-opposition theory” (2004) into set theory by a suited device, through identifying logical modal formulas with appropriate subsets of a characteristic set, one can, in a constructive and exhaustive way, by means of a simple recurring combinatory, exhibit all so-called “logical bi-simplexes of dimension n” (or n-oppositional figures, that is the logical squares, logical hexagons, logical cubes, etc.) contained in the logic produced by any given modal graph (an exhaustiveness which was not possible before). In this paper we shall handle explicitly the classical case of the so-called 3(3)-modal graph (which is, among others, the one of S5), getting to a very elegant tetraicosahedronal geometrisation of this logic

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Citations of this work

The power of the hexagon.Jean-Yves Béziau - 2012 - Logica Universalis 6 (1-2):1-43.
Schopenhauer’s Partition Diagrams and Logical Geometry.Jens Lemanski & Lorenz Demey - 2021 - In A. Basu, G. Stapleton, S. Linker, C. Legg, E. Manalo & P. Viana (eds.), Diagrams 2021: Diagrammatic Representation and Inference. 93413 Cham, Deutschland: pp. 149-165.
On the 3d visualisation of logical relations.Hans Smessaert - 2009 - Logica Universalis 3 (2):303-332.
Metalogical Decorations of Logical Diagrams.Lorenz Demey & Hans Smessaert - 2016 - Logica Universalis 10 (2-3):233-292.

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