Optimization problems on posets with regard to formal concept analysis

In Formal Concept Analysis (FCA), cover- and packing problems occur naturally as an equivalent formulation of the problem to determine the order 2-dimension and breadth of a complete lattice. Furthermore, isolation- and blocking problems provide bounds for these parameters w.r.t. the tensor product of complete lattices.This article introduces an abstract framework based on posets to treat the above mentioned optimization problems in a unified manner. From that point of view, connections to other areas of mathematics, where such optimization problems frequently occur, and the area of FCA emerge. It might even be possible that solutions to the four problems can be pulled to FCA or, vice versa, to push out solutions to the FCA cases to other areas of mathematics.