Disjunctive attribute dependencies in formal concept analysis under the epistemic view of formal contexts

Abstract

This paper considers an epistemic interpretation of formal contexts, interpreting blank entries in the context matrix as absence of information, which is in agreement with the usual focus on the extraction of implications between attributes. After recalling non-classical connections induced by rough sets and possibility theory in formal concept analysis (FCA), and the standard theory of attribute implications in FCA, this paper presents the notion of disjunctive attribute implications, which reflect additional information that can be extracted from an epistemic context. We show that they can be computed like standard attribute implications from the complementary context. The paper also recalls the logic of classical attribute implications, relying on works pertaining to functional dependencies in database theory, and proposes a dual logic for disjunctive attribute implications. A method for extracting the latter kind of rules from a formal context is proposed, using a counterpart of pseudo-intents. Lastly, the paper outlines a generalization of both conjunctive and disjunctive attribute implications under the form of rules, with a conjunction of conditions in the body and a disjunction of conditions in the head, that hold in a formal context under the epistemic view.