by   Martin Kovár, Marie Klimešová, Štěpán Křehlík

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.