  Relational data in its most basic form is a static collection of known facts.
However, by learning to infer and deduct additional information and structure,
we can massively increase the usefulness of the underlying data. One common
form of inferential reasoning in knowledge bases is implication discovery.
Here, by learning when one relation implies another, we can extend our
knowledge representation. There are several existing models for relational
implication, however we argue they are motivated but not principled. To this
end, we define a formal probabilistic model of relational implication. By using
estimators based on the empirical distribution of our dataset, we demonstrate
that our model outperforms existing approaches. While previous work achieves a
best score of 0.7812 AUC on an evaluatory dataset, our ProbE model improves
this to 0.7915. Furthermore, we demonstrate that our model can be improved
substantially through the use of link prediction models and dense latent
representations of the underlying argument and relations. This variant, denoted
ProbL, improves the state of the art on our evaluation dataset to 0.8143. In
addition to developing a new framework and providing novel scores of relational
implication, we provide two pragmatic resources to assist future research.
First, we motivate and develop an improved crowd framework for constructing
labelled datasets of relational implication. Using this, we reannotate and make
public a dataset comprised of 17,848 instances of labelled relational
implication. We demonstrate that precision (as evaluated by expert consensus
with the crowd labels) on the resulting dataset improves from 53% to 95%.
