by   Martin Kovár, Marie Klimešová, Štěpán Křehlík

Formal context is an structure 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 for various purposes, but 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 formal context whose incidence relation is the membership relation. These structures may be used, for example, for investigation of properties of various mathematical objects, including topological properties of causal structures, databases or information and dynamical systems. The generalized distance of two structures of the same type is an important characteristic of their mutual similarity.

Our experimental application Attribute Generalized Metrics checks if the formal context is correctly given by the input and then it calculates the tables of three modifications of the generalized distance between the attributes of the given formal context. The calcullation is based on the properties of the framework associated with the formal context on the set of its attributes. The notion of a generalized distance is inspired by the notion of partial metrics due to S. Matthews. A source of inspiration of this application is also the joint research of the first author with his former student, A. Chernikava during her doctoral study. The coauthors, M. Klimešová and Š. Křeklík are the current doctoral students of the Department of Mathematics.