An Inference System for Exhaustive Generation of Mixed and Purely Negative Implications from Purely Positive Ones

The objective of this article is to study the problem of generating implications with negation when only a set of purely positive implications related to a formal context K = (G,M, I) is provided. To that end, we define a sound and complete inference system which includes a characterization of implications whose left-hand side is a key in the context K|K representing the apposition of the context K and its complementary K.

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