Affiliations: Université du Québec en Outaouais, Département d'informatique et d'ingénierie, 101, rue St-Jean Bosco, Gatineau (Québec), J8X 3X7 Canada, Rokia.missaoui@uqo.ca | LIMOS - CNRS UMR 6158, Université Blaise Pascal, Complexe scientifique des Cézeaux, 63 177 Aubičre Cedex – France, nourine@isima.fr | LIRIS - CNRS UMR 5208, INSA Lyon, 7 av, Jean Capelle, 69 621 Villeurbanne Cedex France, yoan.renaud@gmail.com
Note: [] We acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC). Address for correspondence: Département d'informatique et d'ingénierie, Université du Québec en Outaouais, 101, rue St-Jean Bosco, Gatineau (Québec), Canada J8X 3X7
Note: [] We are grateful to the French National Research Agency (ANR) for the funding of the DAG project. All the authors express their gratitude to the Guest Editors and the anonymous reviewers for their help and useful suggestions.
Note: [] Address for correspondence: Département d'informatique et d'ingénierie, Université du Québec en Outaouais, 101, rue St-Jean Bosco, Gatineau (Québec), Canada J8X 3X7
Abstract: The objective of this article is to define an approach towards generating implications with (or without) negation when only a formal context K = (G, M, I) is provided. To that end, we define a two-step procedure which first (i) computes implications whose premise is a key in the context K | $\tilde{\rm K}$ representing the apposition of the context K and its complementary $\tilde{\rm K}$ with attributes in $\tilde{\rm M}$ (negative attributes), and then (ii) uses an inference axiom we have defined to produce the whole set of implications.
Keywords: Formal concept analysis, implication, negation, key, inference system
