Quantum temporal logic and decoherence functionals in the histories approach to generalised quantum theory

We analyse and develop the recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell-Mann and Hartle for a generalised form of quantum theory based on the ideas of histories and decoherence functionals. Particular stress is placed on properties of the space of decoherence functionals, including one way in which certain global and topological properties of a classical system are reflected in a quantum history theory.