Axiomatization of quantum logics (Q2365439)

The author introduces a system of probabilistically motivated axioms which make a couple \((L,{\mathcal S})\), where \(L\) is a \(\sigma\)-OMP and \({\mathcal S}\) is a convex full system of states, an orthomodular space. The aim of the paper is to obtain a characterization of the basic logic, the system of all closed subspaces of a real, complex, or quaternionic Hilbert space.