  One of the core assumptions in causal discovery is the faithfulness
assumption, i.e., assuming that independencies found in the data are due to
separations in the true causal graph. This assumption can, however, be violated
in many ways, including xor connections, deterministic functions or cancelling
paths. In this work, we propose a weaker assumption that we call $2$-adjacency
faithfulness. In contrast to adjacency faithfulness, which assumes that there
is no conditional independence between each pair of variables that are
connected in the causal graph, we only require no conditional independence
between a node and a subset of its Markov blanket that can contain up to two
nodes. Equivalently, we adapt orientation faithfulness to this setting. We
further propose a sound orientation rule for causal discovery that applies
under weaker assumptions. As a proof of concept, we derive a modified Grow and
Shrink algorithm that recovers the Markov blanket of a target node and prove
its correctness under strictly weaker assumptions than the standard
faithfulness assumption.
