  Causal modelling is a tool for generating causal explanations of observed
correlations and has led to a deeper understanding of correlations in quantum
networks. Existing frameworks for quantum causality tend to focus on acyclic
causal structures that are not fine-tuned i.e., where causal connections
between variables necessarily create correlations between them. However,
fine-tuned causal models (which permit causation without correlation) play a
crucial role in cryptography, and cyclic causal models can be used to model
physical processes involving feedback and may also be relevant in exotic
solutions of general relativity. Here we develop a causal modelling framework
capable of dealing with these general scenarios. The key feature of our
framework is that it allows operational and relativistic notions of causality
to be independently defined and for connections between them to be established
in a theory-independent manner. The framework first gives an operational way to
study causation that allows for cyclic, fine-tuned and non-classical causal
influences. We then consider how a causal model can be embedded in a space-time
structure (modelled as a partial order) and propose a compatibility condition
for ensuring that the embedded causal model does not allow signalling outside
the space-time future. We identify several distinct classes of causal loops
that can arise in our framework, showing that compatibility with a space-time
can rule out only some of them. We discuss conditions for preventing
superluminal signalling within arbitrary (and possibly cyclic) causal
structures and consider models of causation in post-quantum theories admitting
so-called jamming correlations. Finally, this work introduces the concept of a
"higher-order affects relation", which is useful for causal discovery in
fined-tuned causal models.
