A bisemilattice, which satisfies absorption law, is a lattice. Because various laws are led from the absorption law, it can be said that absorption law is comparatively strong law on bisemilattice. As relations between laws on bisemilattice are delicate, we considered them. Then, we tried the introduction of those laws in triple-semilattice. We show that a state is a little different from the case of bisemilattice.