  In real-world phenomena which involve mutual influence or causal effects
between interconnected units, equilibrium states are typically represented with
cycles in graphical models. An expressive class of graphical models, relational
causal models, can represent and reason about complex dynamic systems
exhibiting such cycles or feedback loops. Existing cyclic causal discovery
algorithms for learning causal models from observational data assume that the
data instances are independent and identically distributed which makes them
unsuitable for relational causal models. At the same time, causal discovery
algorithms for relational causal models assume acyclicity. In this work, we
examine the necessary and sufficient conditions under which a constraint-based
relational causal discovery algorithm is sound and complete for cyclic
relational causal models. We introduce relational acyclification, an operation
specifically designed for relational models that enables reasoning about the
identifiability of cyclic relational causal models. We show that under the
assumptions of relational acyclification and $\sigma$-faithfulness, the
relational causal discovery algorithm RCD (Maier et al. 2013) is sound and
complete for cyclic models. We present experimental results to support our
claim.
