Models of the axiomatic theory associated with the lattice of subspaces of a finite-dimensional Hilbert space

It is shown that we can associate with the latticeL of subspaces of a separable Hilbert space an axiomatic theory in sentential logic that reflects some of the basic properties of the simplest types of experimental reports in quantum mechanics. It is also shown that every collection of mutually nonorthogonal elements ofL determines a model of the axioms and that, if the Hilbert space is finite dimensional, every model is determined this way.