  Using a process-theoretic formalism, we introduce the notion of a
causal-inferential theory: a triple consisting of a theory of causal
influences, a theory of inferences (of both the Boolean and Bayesian
varieties), and a specification of how these interact. Recasting the notions of
operational and realist theories in this mold clarifies what a realist account
of an experiment offers beyond an operational account. It also yields a novel
characterization of the assumptions and implications of standard no-go theorems
for realist representations of operational quantum theory, namely, those based
on Bell's notion of locality and those based on generalized noncontextuality.
Moreover, our process-theoretic characterization of generalised
noncontextuality is shown to be implied by an even more natural principle which
we term Leibnizianity. Most strikingly, our framework offers a way forward in a
research program that seeks to circumvent these no-go results. Specifically, we
argue that if one can identify axioms for a realist causal-inferential theory
such that the notions of causation and inference can differ from their
conventional (classical) interpretations, then one has the means of defining an
intrinsically quantum notion of realism, and thereby a realist representation
of operational quantum theory that salvages the spirit of locality and of
noncontextuality.
