Properties of states in quantum logic

The role and properties of states from the point of view of various approaches amenable to quantum logic, are examined. In doing this, propositions, states and operations are alternatively, and sometimes jointly used as basic ingredients. Operations are mostly thought of as mappings of states. It is outlined how this basic mathematical structure, the atomic orthomodular lattice with the covering property can be activated on different, and alternative, grounds. Some pathologies, related to Gleason's theorem, of spin-1/2 systems are examined and the concomitant appearance of exceptional states which have no place in the Hilbert-space formulation are commented upon. (Auth.)