Formal Topology, Chu Space and Approximable Concept

Within Martin-Lőf type theory ([4]), G. Sambin initiated the intuitionistic formal topology which includes Scott algebraic domain theory as a special case (unary formal topology)([7]). In [6], he introduced the notions of (algebraic) information base and translation, and proved the equivalence between the category of (algebraic) information bases and the category of (algebraic) Scott domains. In [1], B. Ganter, R. Wille initiated formal concept analysis, which is an order-theoretical analysis of scientific data. Concept is one of the main notions and tools. Zhang considered a special form of Chu space, and introduced the notion of approximable concept in [3, 9, 10], which is a generalization of concept. These are two “parallel worlds”. In this paper, we introduce the notion of (new) information base, and investigate the relations between points of an information base and approximable concepts of a Chu space; the translations and context morphisms.