ion, whose properties led to a new kind of semantics [4]. In few words, in such a modal logics the modal connector, usually known as a ”necessity“ connector and represented as a square, could be translated as an ”abstraction“ operator, i.e. a sentence as ”2 P“ was understood as ”Abstractly P“. The corresponding semantics relied on a covering of the universe, and could not, except in particular cases, be translated as the standard ”possible world“ semantics of the most common modal logics. More recently, new trends in AI and data mining orient research towards linked data. The same formal notion of abstraction can be defined on graphs, and this leads to a way to extract closed patterns from graphs whose vertices are objects described in a FCA framework, therefore allowing to investigate attributed graphs [5]. Finally, recent work on data mining discuss closure operators on partially ordered pattern languages weaker than lattices, as the set of connected subgraphs of some graph, which leads to extend formal concept analysis beyond the lattice
structure still preserving a large part of the nice formal structures and results of
FCA[