A Categorical View on Algebraic Lattices in Formal Concept Analysis

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 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.Comment: 36 page

Using the Chu Construction for generalizing formal concept analysis

L. Antoni, I. P. Cabrera, S. Krajči, O. Krídlo, and M. Ojeda-Aciego. Using the Chu construction for generalizing formal concept analysis. In CLA 2015, pp. 147–158, Blaise Pascal University, LIMOS laboratory, Clermont-Ferrand, 2015El objetivo de este artículo es mostrar la conexión entre generalizaciones de Análisis de Conceptos Formales y la construcción de Chu sobre la categoría ChuCors de contextos formales y correspondencias de Chu. Todas las propiedades categóricas necesarias para la comprensión de los resultados de este trabajo como producto categórico, producto tensorial o propiedades de su bifuntor se presentan y demuestran. Finalmente, la generalización de Análisis de Conceptos Formales de segundo orden se representa por una categoría construida en términos de la Construcción de Chu

Formal Concept Analysis and Resolution in Algebraic Domains

We relate two formerly independent areas: Formal concept analysis and logic of domains. We will establish a correspondene between contextual attribute logic on formal contexts resp. concept lattices and a clausal logic on coherent algebraic cpos. We show how to identify the notion of formal concept in the domain theoretic setting. In particular, we show that a special instance of the resolution rule from the domain logic coincides with the concept closure operator from formal concept analysis. The results shed light on the use of contexts and domains for knowledge representation and reasoning purposes.Comment: 14 pages. We have rewritten the old version according to the suggestions of some referees. The results are the same. The presentation is completely differen