A representation of continuous domains via relationally approximable concepts in a generalized framework of formal concept analysis

Abstract

In this paper, in order to realize a representation of continuous domains, the notions of relationally consistent F-augmented contexts and relationally approximable concepts are introduced, which provides a generalized framework of formal concept analysis. We also introduce the notion of F-approximable mappings which serves as the morphism between relationally consistent F-augmented contexts. The main result is that the category of relationally consistent F-augmented contexts is equivalent to that of continuous domains with Scott continuous maps being morphisms. This provides a new approach to concretely representing continuous domains and demonstrates the efficiency of formal concept analysis in representing some important partially ordered structures.