The logic decomposition of incompletely specified functions (ISFs) is studied. A theoretical support based on ternary algebras is provided. This support aims at the logic decomposition of ISFs. A partial order is defined on the ISFs determined by the definedness' of the functions, in which the completely specified functions are the maximal elements. The proposed methods aim at preserving the ISFs as undefined as possible during logic decomposition. Incompletely specified diagrams (IDDs) are proposed as a graph-based formalism to efficiently explore different decompositions.