A direct approach to representing algebraic domains by formal contexts

Abstract

This paper is to establish closer links between domain theory and Formal Concept Analysis (FCA). We propose the notion of an optimised concept for a formal context, which has some properties similar to an intent. With the tool of optimised concepts, we show that the class of formal contexts has directly corresponded with algebraic domains. Meanwhile, two subclasses of formal contexts are identified to characterize algebraic L-domains and Scott domains. As an application, we resolve the open problem of how to reconstruct bounded complete continuous domains in the languages of attribute continuous contexts. Finally, we extend our presentation of algebraic domains to a categorical equivalence.