HEIGHT-TWO CONCEPT LATTICES: GRAPH DECOMPOSITION AND HORN AXIOMATIZABILITY

<div> We characterize subdirect formal contexts whose concept lattices are isomorphic to the lattices of height two, proving that this holds precisely when the context graph decomposes into disjoint complete bipartite components, equivalently when the incidence relation admits a partition-inducing multivalued functional representation, and when the clarified context relation is bijective. We also show that the class of context graphs whose concept lattices have height two forms a finitely axiomatizable universal Horn class. These results connect lattice structure, graph decomposition, and logical definability within Formal Concept Analysis. </div>