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 structures underlying quantum logics

A Hilbert space $H$ induces a formal context, the Hilbert formal context $\overline H$, whose associated concept lattice is isomorphic to the lattice of closed subspaces of $H$. This set of closed subspaces, denoted $\mathcal C(H)$, is important in the development of quantum logic and, as an algebraic structure, corresponds to a so-called ``propositional system'', that is, a complete, atomistic, orthomodular lattice which satisfies the covering law. In this paper, we continue with our study of the Chu construction by introducing the Chu correspondences between Hilbert contexts, and showing that the category of Propositional Systems, PropSys, is equivalent to the category of $\text{ChuCors}_{\mathcal H}$ of Chu correspondences between Hilbert contextsUniversidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

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

Relational Galois connections between transitive fuzzy digraphs

Fuzzy-directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems. In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering