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

Using the Chu construction for generalizing formal concept analysis

Abstract. The goal of this paper is to show a connection between FCA generalisations and the Chu construction on the category ChuCors, the category of formal contexts and Chu correspondences. All needed categorical properties like categorical product, tensor product and its bifunctor properties are presented and proved. Finally, the second order generalisation of FCA is represented by a category built up in terms of the Chu construction

Proceedings of the 5th International Workshop "What can FCA do for Artificial Intelligence?", FCA4AI 2016(co-located with ECAI 2016, The Hague, Netherlands, August 30th 2016)

International audienceThese are the proceedings of the fifth edition of the FCA4AI workshop (http://www.fca4ai.hse.ru/). Formal Concept Analysis (FCA) is a mathematically well-founded theory aimed at data analysis and classification that can be used for many purposes, especially for Artificial Intelligence (AI) needs. The objective of the FCA4AI workshop is to investigate two main main issues: how can FCA support various AI activities (knowledge discovery, knowledge representation and reasoning, learning, data mining, NLP, information retrieval), and how can FCA be extended in order to help AI researchers to solve new and complex problems in their domain. Accordingly, topics of interest are related to the following: (i) Extensions of FCA for AI: pattern structures, projections, abstractions. (ii) Knowledge discovery based on FCA: classification, data mining, pattern mining, functional dependencies, biclustering, stability, visualization. (iii) Knowledge processing based on concept lattices: modeling, representation, reasoning. (iv) Application domains: natural language processing, information retrieval, recommendation, mining of web of data and of social networks, etc

Non-additive anonymous games

This paper introduces a class of non-additive anonymous games where agents are assumed to be uncertain (in the sense of Knight) about opponents’ strategies and about the initial distribution over players’ characteristics in the game. These uncertainties are modelled by non-additive measures or capacities. The Cournot-Nash equilibrium existence theorem is proven for this class of games. It is shown that the equilibrium distribution can be symmetrized under milder conditions than in the case of additive games. In particular, it is not required for the space characteristics to be atomless under capacities. The set-valued map of the Cournot-Nash equilibria is upper-semicontinuous as a function of initial beliefs of the players for non-additive anonymous games

Analysis of the transformation strain associated with the hexagonal-to-orthorhombic transition in Ti₃Sn

This review is dedicated to the analysis of the hexagonal-to-orthorhombic transition into Ti₃Sn. The place of martensitic transformation into broader category of displacive (diffusionless) transformations is shown from the point of view of a transformation strain associated with the transition. The transformation strain regarded to the transformation into Ti₃Sn was analyzed and the displacive shear-dominant (martensitic) origin of this transition was shown. The latter part of the work is dedicated to the comparison of the volume change and transformation temperature in Ti₃Sn with those into other materials undergoing martensitic transformation.Огляд присвячений аналізу перетворення із гексагональної в орторомбічну фазу в Ti₃Sn. Показано місце мартенситного перетворення в ширшій категорії бездифузійних перетворень з точки зору деформації перетворення. Деформація перетворення в Ti₃Sn проаналізована і зсувний (мартенситний) характер перетворення проілюстровано. Порівняно зміни об’єму та температури перетворення в Ti₃Sn з такими в інших матеріалах, що зазнають мартенситного перетворення.Обзор посвящен анализу превращения из гексагональной в орторомбическую фазу в Ti₃Sn. Показано место мартенситного превращения в более широкой категории бездиффузионных превращений с точки зрения деформации превращения. Деформация превращения в Ti₃Sn проанализирована и сдвиговый (мартенситный) характер превращения показан. Проведено сравнение изменения объема и температуры превращения в Ti₃Sn с этими характеристиками в других материалах, претерпевающих мартенситное превращение