  We expect a theory of Quantum Gravity to be both probabilistic and have
indefinite causal structure. Indefinite causal structure poses particular
problems for theory formulation since many of the core ideas used in the usual
approaches to theory construction depend on having definite causal structure.
For example, the notion of a state across space evolving in time requires that
we have some definite causal structure so we can define a state on a space-like
hypersurface. We will see that many of these problems are mitigated if we are
able to formulate the theory in a "formalism local" (or F-local) fashion. A
formulation of a physical theory is said to be F-local if, in making
predictions for any given arbitrary space-time region, we need only refer to
mathematical objects pertaining to that region. This is a desirable property
both on the grounds of efficiency and since, if we have indefinite causal
structure, it is not clear how to select some other space-time region on which
our calculations may depend. The usual ways of formulating physical theories
(the time evolving state picture, the histories approach, and the local
equations approach) are not F-local.
  We set up a framework for probabilistic theories with indefinite causal
structure. This, the causaloid framework, is F-local. We describe how Quantum
Theory can be formulated in the causaloid framework (in an F-local fashion).
This provides yet another formulation of Quantum Theory. This formulation,
however, may be particularly relevant to the problem of finding a theory of
Quantum Gravity.
