DENSITY CONDITIONS FOR QUANTUM PROPOSITIONS

As has already been pointed out by Birkhoff and von Neumann, quantum l ogic can be formulated in terms of projective geometry. In three-dimen sional Hilbert space, elementary logical propositions are associated w ith one-dimensional subspaces, corresponding to points of the projecti ve plane. It is shown that, starting with three such propositions corr esponding to some basis {u,v,w}, successive application of the binary logical operation (x,y)-->(x boolean OR y)(perpendicular to) generates a set of elementary propositions which is countable infinite and dens e in the projective plane if and only if no vector of the basis {u,v,w } is orthogonal to the other ones. (C) 1996 American Institute of Phys ics.