Representation of Concrete Logics and Concrete Generalized Orthomodular Posets

In the present paper, we deal with the question when an effect algebra, resp. a generalized effect algebra, can be represented in the projection lattice of a Hilbert space. We show that such representability is closely related to the existence of a rich set of two-valued and Jauch–Piron states, resp. generalized two-valued and Jauch–Piron states.AMS Classification: Primary 81Q10, Secondary 03G12.