Attribute Implication Bases From Galois Connection Structures

Abstract

Modeling knowledge systems by determining relationships among key variables have been and currently is a fundamental and nontrivial challenge in real-world scenarios. Many approaches have been developed to reach this goal, but many of them are heuristic and require of alternative procedures to provide robust and tractable rules. With this significant aim, attribute implications were introduced in the mathematical framework of Formal Concept Analysis. In this paper, we will introduce a novel procedure to obtain relationships among variables from any dataset in which a Galois connection has been defined. In particular, we will be focused on the general multiadjoint framework, which is one of the most general approached in which a Galois connection have been considered, although the obtained results and methodology can also be used in other well-known approaches, such as in the residuated or heterogeneous frameworks.