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

Dubois, D; Prade, H

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

Dubois, D Prade, H

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Publication Type:: Journal Article
Citation:: Logica Universalis, 2012, 6 (1-2), pp. 149 - 169
Issue Date:: 2012-06-01

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Field	Value	Language
dc.contributor.author	Dubois, D	en_US
dc.contributor.author	Prade, H https://orcid.org/0000-0003-4586-8527	en_US
dc.date.issued	2012-06-01	en_US
dc.identifier.citation	Logica Universalis, 2012, 6 (1-2), pp. 149 - 169	en_US
dc.identifier.issn	1661-8297	en_US
dc.identifier.uri	http://hdl.handle.net/10453/114000
dc.description.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. © 2011 Springer Basel AG.	en_US
dc.relation.ispartof	Logica Universalis	en_US
dc.relation.isbasedon	10.1007/s11787-011-0039-0	en_US
dc.title	From Blanché's Hexagonal Organization of Concepts to Formal Concept Analysis and Possibility Theory	en_US
dc.type	Journal Article
utslib.citation.volume	1-2	en_US
utslib.citation.volume	6	en_US
utslib.for	0101 Pure Mathematics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Software
pubs.organisational-group	/University of Technology Sydney/Strength - CAI - Centre for Artificial Intelligence
utslib.copyright.status	closed_access
pubs.issue	1-2	en_US
pubs.publication-status	Published	en_US
pubs.volume	6	en_US

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. © 2011 Springer Basel AG.

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http://hdl.handle.net/10453/114000