  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.
