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 dim 3. 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).