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The Cube of Opposition: A Structure Underlying Many Knowledge Representation Formalisms

Dubois, Didier and Prade, Henri and Rico, Agnès The Cube of Opposition: A Structure Underlying Many Knowledge Representation Formalisms. (2015) In: 24th International Joint Conference on Artificial Intelligence (IJCAI 2015), 25 July 2015 - 31 July 2015 (Buenos Aires, Argentina).

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Abstract

The square of opposition is a structure involving two involutive negations and relating quantified statements, invented in Aristotle time. Rediscovered in the second half of the XXth century, and advocated as being of interest for understanding conceptual structures and solving problems in paraconsistent logics, the square of opposition has been recently completed into a cube, which corresponds to the introduction of a third negation. Such a cube can be encountered in very different knowledge representation formalisms, such as modal logic, possibility theory in its all-or-nothing version, formal concept analysis, rough set theory and abstract argumentation. After restating these results in a unified perspective, the paper proposes a graded extension of the cube and shows that several qualitative, as well as quantitative formalisms, such as Sugeno integrals used in multiple criteria aggregation and qualitative decision theory, or yet belief functions and Choquet integrals, are amenable to transformations that form graded cubes of opposition. This discovery leads to a new perspective on many knowledge representation formalisms, laying bare their underlying common features. The cube of opposition exhibits fruitful parallelisms between different formalisms, which leads to highlight some missing components present in one formalism and currently absent from another.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Thanks to AAAI editor. The definitive version is available at http://www.aaai.org/ocs/index.php/IJCAI/IJCAI15/paper/view/11355
Audience (conference):International conference proceedings
Uncontrolled Keywords:
Institution:French research institutions > Centre National de la Recherche Scientifique - CNRS (FRANCE)
Université de Toulouse > Institut National Polytechnique de Toulouse - INPT (FRANCE)
Université de Toulouse > Université Toulouse III - Paul Sabatier - UPS (FRANCE)
Université de Toulouse > Université Toulouse - Jean Jaurès - UT2J (FRANCE)
Université de Toulouse > Université Toulouse 1 Capitole - UT1 (FRANCE)
Other partners > Université Claude Bernard-Lyon I - UCBL (FRANCE)
Other partners > Université Lumière-Lyon 2 (FRANCE)
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Deposited By: IRIT IRIT
Deposited On:02 Mar 2016 13:09

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