Affiliations: Institut AIFB, Universität Karlsruhe, Karlsruhe,
Germany. E-mail: {hitzler,kroetzsch}@aifb.uni-karlsruhe.de | Department of Electrical Engineering and Computer
Science, Case Western Reserve University, Cleveland, Ohio, USA.
E-mail: eqz@eecs.case.edu
Abstract: Formal concept analysis has grown from a new branch of the
mathematical field of lattice theory to a widely recognized tool in Computer
Science and elsewhere. In order to fully benefit from this theory, we believe
that it can be enriched with notions such as approximation by computation or
representability. The latter are commonly studied in denotational semantics and
domain theory and captured most prominently by the notion of algebraicity, e.g.
of lattices. In this paper, we explore the notion of algebraicity in formal
concept analysis from a category-theoretical perspective. To this end, we build
on the notion of approximable concept with a suitable category and show that
the latter is equivalent to the category of algebraic lattices. At the same
time, the paper provides a relatively comprehensive account of the
representation theory of algebraic lattices in the framework of Stone duality,
relating well-known structures such as Scott information systems with further
formalisms from logic, topology, domains and lattice theory.
Keywords: Algebraic lattice, Formal concept analysis, Domain theory, Stone duality, Category theory
