Attribute Frameworks in Formal Contexts

  by   Martin Kovár, Marie Klimešová, Štěpán Křehlík

Abstract and usage:

Formal context is one of the key notions in Formal Concept Analysis. It is motivated by idea of concetrating the information of various types at one algebraic structure. Especially it is used in connection with data representation and organization. Framework is a formal context whose incidence relation is the membership relation. The objects are called places and the attributes are collections of places connected, for instance, by a possible presence of some physical object. The set of attributes is called a framology. Both structures may be used for representation of information and data of various type, including the properties of other mathematical objects, like dynamical systems. However, the framework representation is sometimes more natural, especially for structures having some spatial or topological character.

Our experimental application Attribute Frameworks checks if the formal context is correctly given by the input and then it calculates the framework associated with the formal context on the set of its attributes. A source of inspiration for this application is the joint research of the first author with his former student, A. Chernikava during her (already finished) doctoral study. The coauthors, M. Klimešová and Š. Křeklík are current doctoral students of the Department of Mathematics.


The set of objects:

The set of attributes:

The incidence relation:


The object framework:

The set of places:

The abstract points and their simplified notation:


The application Attribute Frameworks is written in Java powered by Wolfram webMathematica 3.1. The application is hosted at the server of the Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology. The results representing its theoretical background were presented by the authors on several scientific conferences as an integral part of their research. In case of interest in more detail, see [1] or contact the authors. For research and scientific activities the software is available free of charge. In all other cases, please contact RNDr. M. Novák, Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Technická 8, 616 00 Brno, phone: +420 5 4114 3135. Acknowledgement: FEKT-S-14/2200 "Reprezentace řešení dynamických systémů, numerické algoritmy řešení"

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