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Article Dans Une Revue Logica Universalis Année : 2012

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

Résumé

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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Dates et versions

hal-03344980 , version 1 (15-09-2021)

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Didier Dubois, Henri Prade. From Blanché's Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory. Logica Universalis, 2012, 6 (1-2), pp.149-169. ⟨10.1007/s11787-011-0039-0⟩. ⟨hal-03344980⟩
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