  We consider the incorporation of causal knowledge about the presence or
absence of (possibly indirect) causal relations into a causal model. Such
causal relations correspond to directed paths in a causal model. This type of
knowledge naturally arises from experimental data, among others. Specifically,
we consider the formalisms of Causal Bayesian Networks and Maximal Ancestral
Graphs and their Markov equivalence classes: Partially Directed Acyclic Graphs
and Partially Oriented Ancestral Graphs. We introduce sound and complete
procedures which are able to incorporate causal prior knowledge in such models.
In simulated experiments, we show that often considering even a few causal
facts leads to a significant number of new inferences. In a case study, we also
show how to use real experimental data to infer causal knowledge and
incorporate it into a real biological causal network. The code is available at
mensxmachina.org.
