  A general principle of `causal duality' for physical systems, lying at the
base of representation theorems for both compound and evolving systems, is
proved; formally it is encoded in a quantaloidal setting. Other particular
examples of quantaloids and quantaloidal morphisms appear naturally within this
setting; as in the case of causal duality, they originate from primitive
physical reasonings on the lattices of properties of physical systems.
Furthermore, an essentially dynamical operational foundation for studying
physical systems is outlined; complementary as it is to the existing static
operational foundation, it leads to the natural axiomatization of `causal
duality' in operational quantum logic.
