  Bell non-local correlations cannot be naturally explained in a fixed causal
structure. This serves as a motivation for considering models where no global
assumption is made beyond logical consistency. The assumption of a fixed causal
order between a set of parties, together with free randomness, implies
device-independent inequalities --- just as the assumption of locality does. It
is known that local validity of quantum theory is consistent with violating
such inequalities. Moreover, for three parties or more, even the (stronger)
assumption of local classical probability theory plus logical consistency
allows for violating causal inequalities. Here, we show that a classical
environment (with which the parties interact), possibly containing loops, is
logically consistent if and only if whatever the involved parties do, there is
exactly one fixed-point, the latter being representable as a mixture of
deterministic fixed-points. We further show that the non-causal view allows for
a model of computation strictly more powerful than computation in a world of
fixed causal orders.
