Object Frameworks in Formal Contexts

  by   Martin Kovár, Marie Klimešová, Štěpán Křehlík

Abstract and usage:

The concept of a framework is derived from a slightly more general notion, formal context, which was introduced by B. Ganter and R. Wille at the end of the 70's as one of the key notions in Formal Concept Analysis. It is used in theoretical computer scince especially in connection with data representation and organization. Framework is an algebraic structure whose purpose is capturing the topological or topology-like structure of a system from its externally observed properties. Formally, framework is a special formal context whose incidence relation is the membership relation. The framework structure may be used, for example, for investigation of topological properties of certain causal structures, motivated by quantum gravity, interactions of particles, Feynman diagrams, information systems and databases as well as for classification of other mathematical objects, like dynamical systems.

Our experimental application Object 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 objects. 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 Object 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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