by   Martin Kovár, Alena Chernikava

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. The objects are called places and the attributes are collections of places connected by a possible presence of some physical object, e.g., a particle. The set of attributes is called a framology. The 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 or solutions of certain differential equations and their global properties. There are several possible and useful operations with a framework. One of them it is the construction of the dual framework. By our result [1] each framework arises as a dual if and only it is T₀ and for each framework, the first and the third duals are isomorphic. The framework duality may be naturally used for switching between the pointset and pointless approach in topology, since the places of the dual framework can be naturally interpreted as the abstract points of the original framework. Our experimental application Framework Duality Explorer checks if the original framework is correctly given by the input and then it generates the first three iterated duals of the given framework.