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From Blanché’s Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory

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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.

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  1. Institut de Recherche en Informatique de Toulouse (IRIT), Université Paul Sabatier, 118 route de Narbonne, 31062, Toulouse Cedex 9, France

    Didier Dubois & Henri Prade

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  1. Didier Dubois
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Correspondence to Henri Prade.

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Dubois, D., Prade, H. From Blanché’s Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory. Log. Univers. 6, 149–169 (2012). https://doi.org/10.1007/s11787-011-0039-0

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