A topological representation of double Boolean lattices

Abstract

Boolean Concept Logic has been introduced by R. Wille as a mathematical theory based on Formal Concept Analysis. Concept lattices are extended with two new operations, negation and opposition which then lead to algebras of protoconcepts which are equationally equivalent to double Boolean algebras. In this paper, we provide a topological representation for double Boolean algebras based on the so-called DB-topological contexts. A double Boolean algebra is then represented as the algebra of clopen protoconcepts of some DB-topological context.