Computing Implications with Negation from a Formal Context

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.