  Starting from certain causality conditions and a discrete form of general
covariance, we derive a very general family of classically stochastic,
sequential growth dynamics for causal sets. The resulting theories provide a
relatively accessible ``half way house'' to full quantum gravity that possibly
contains the latter's classical limit (general relativity). Because they can be
expressed in terms of state models for an assembly of Ising spins living on the
relations of the causal set, these theories also illustrate how
non-gravitational matter can arise dynamically from the causal set without
having to be built in at the fundamental level. Additionally, our results bring
into focus some interpretive issues of importance for causal set dynamics, and
for quantum gravity more generally.
