  The notion of an orthogonality space was recently rediscovered as an
effective means to characterise the essential properties of quantum logic. The
approach can be considered as minimalistic; solely the aspect of mutual
exclusiveness is taken into account. In fact, an orthogonality space is simply
a set endowed with a symmetric and irreflexive binary relation. If the rank is
at least $4$ and if a certain combinatorial condition holds, these relational
structures can be shown to give rise in a unique way to Hermitian spaces. In
this paper, we focus on the finite case. In particular, we investigate
orthogonality spaces of rank at most $3$.
