Logica Universalis 6 (1-2):149-169 (2012)

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Abstract
The paper first introduces a cube of opposition that associates the traditional square of opposition with the dual square obtained by Piaget’s reciprocation. It is then pointed out that Blanché’s extension of the square-of-opposition structure into an conceptual hexagonal structure always relies on an abstract tripartition. Considering quadripartitions leads to organize the 16 binary connectives into a regular tetrahedron. Lastly, the cube of opposition, once interpreted in modal terms, is shown to account for a recent generalization of formal concept analysis, where noticeable hexagons are also laid bare. This generalization of formal concept analysis is motivated by a parallel with bipolar possibility theory. The latter, albeit graded, is indeed based on four graded set functions that can be organized in a similar structure
Keywords Square of opposition  Blanché hexagon  Piaget group  propositional connectives  formal concept analysis  possibility theory
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DOI 10.1007/s11787-011-0039-0
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References found in this work BETA

A Useful Four-Valued Logic.N. D. Belnap - 1977 - In J. M. Dunn & G. Epstein (eds.), Modern Uses of Multiple-Valued Logic. D. Reidel.
On the 3d Visualisation of Logical Relations.Hans Smessaert - 2009 - Logica Universalis 3 (2):303-332.
“Setting” N-Opposition.Régis Pellissier - 2008 - Logica Universalis 2 (2):235-263.
On Ignorance and Contradiction Considered as Truth-Values.Didier Dubois - 2008 - Logic Journal of the IGPL 16 (2):195-216.

View all 21 references / Add more references

Citations of this work BETA

The Power of the Hexagon.Jean-Yves Béziau - 2012 - Logica Universalis 6 (1-2):1-43.
Logical Geometries and Information in the Square of Oppositions.Hans5 Smessaert & Lorenz6 Demey - 2014 - Journal of Logic, Language and Information 23 (4):527-565.
A Cube of Opposition for Predicate Logic.Jørgen Fischer Nilsson - 2020 - Logica Universalis 14 (1):103-114.
Why the Logical Hexagon?Alessio Moretti - 2012 - Logica Universalis 6 (1-2):69-107.

View all 12 citations / Add more citations

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