Strong attribute implications in data with unknown information

This work presents an extension of the classical framework of Formal Concept Analysis (FCA) to incorporate the treatment of unknown information. In particular, we introduce a new kind of implication, called strong implication, which holds in a formal context with unknown information and still holds when unknown information becomes known regardless of the value of this new information. We further explore the construction of several axiomatic systems for reasoning with this new kind of implication and prove that all the axiomatic systems presented are equivalent, sound, and complete.