On the Dedekind–MacNeille completion and formal concept analysis based on multilattices

Abstract

The Dedekind–MacNeille completion of a poset P can be seen as the least complete lattice containing P. In this work, we analyze some results concerning the use of this completion within the framework of Formal Concept Analysis in terms of the poset of concepts associated with a Galois connection between posets. Specifically, we show an interesting property of the Dedekind–MacNeille completion, in that the completion of the concept poset of a Galois connection between posets coincides with the concept lattice of the Galois connection extended to the corresponding completions. Moreover, we study the specific case when P has multilattice structure and state and prove the corresponding representation theorem.