ON CONTEXT PATTERNS ASSOCIATED WITH CONCEPT LATTICES

In this paper, we consider the following reconstruction problem: Given two ordered sets (G, less than or equal to) and (M, less than or equal to) representing join- and meet-irreducible elements, respectively together with three relations J, sic, sic on G X M modelling comparability (g less than or equal to m) and maximal noncomparability with respect to g (g not less than or equal to m, but g less than or equal to m*) and with respect to m (g not less than or equal to m, but g less than or equal to m*). We determine necessary and sufficient conditions for the existence of a finite lattice L and injections alpha: G --> J(L) and beta: M --> M(L) such that the given order relations and the abstract relations coincide with the one induced by the lattice L.