A mathematical condition for a sublattice of a propositional system to represent a physical subsystem,with a physical interpretation

We display three equivalent conditions for a sublattice, isomorphic to aP, of the propositional systemP() of a quantum system to be the representation of a physical subsystem (see [1]). These conditions are valid for dim3. We prove that one of them is still necessary and sufficient if dim<3. A physical interpretation of this condition is given.Wetenschappelijke medewerkers bij het Interuniversitair Instituut voor Kernwetenschappen (in het kader van navorsingsprogramma 21 EN).