Bipolarity and opposition structures
A representation is bipolar as soon as it makes a distinction between positive and negative information, while also leaving room for the expression of an intermediate state of neutrality. There are several forms of bipolarity. In one of them, the two types of information have different origins. Bipolarity is found both in the representation of knowledge and preferences (in the latter case, what is really satisfactory is not complementary to what is rejected). It can also be found in argumentation or in machine learning.
Bipolarity, insisting on the contrast between the positive and negative aspects of information, maintains natural links with the square of oppositions, an essential scheme in classical or modal logic since Aristotle which has been generalized by Robert Blanché in one hexagon, and by the ADRIA team more recently in one cube of oppositions. It has thus been shown that this type of structure appears in a number of formalisms for the representation of knowledge and reasoning where the trichotomy (positive, neutral, negative) of bipolarity is at work. In particular, we have shown that areas such as argumentation, formal concept analysis, possibility theory and other theories of uncertainty, rough sets can be revisited in the light of opposition structures.
- Davide Ciucci, Didier Dubois, Henri Prade. Structures of Opposition in Fuzzy Rough Sets. Fundamenta Informaticae, IOS Press, Vol. 142 N. 1-4, p. 1-19, 2015. (pdf)
- Davide Ciucci, Didier Dubois, Henri Prade. Structures of opposition induced by relations – The Boolean and the gradual cases. Dans / In : Annals of Mathematics and Artificial Intelligence, Springer, Vol. 76 N. 3-4, p. 351-373, 2016. (pdf)
- Didier Dubois, Henri Prade. An introduction to bipolar representations of information and preference. Int. J. Intell. Syst. 23 (8), 866-877, 2008.
- Didier Dubois, Henri Prade. Modeling “and if possible” and “or at least”: Different forms of bipolarity in flexible querying. In : Flexible Approaches in Data, Information and Knowledge Management (O. Pivert, S. Zadrozny, eds.) Springer, 3-19, 2014.
- Didier Dubois, Henri Prade, Agnès Rico. The cube of opposition: A structure underlying many knowledge representation formalisms. Proc. 24th Int. Joint Conf. on Artificial Intelligence (IJCAI’15), Buenos Aires, 2933-2939, 2015