  Knowledge graph reasoning, which aims at predicting the missing facts through
reasoning with the observed facts, is critical to many applications. Such a
problem has been widely explored by traditional logic rule-based approaches and
recent knowledge graph embedding methods. A principled logic rule-based
approach is the Markov Logic Network (MLN), which is able to leverage domain
knowledge with first-order logic and meanwhile handle their uncertainty.
However, the inference of MLNs is usually very difficult due to the complicated
graph structures. Different from MLNs, knowledge graph embedding methods (e.g.
TransE, DistMult) learn effective entity and relation embeddings for reasoning,
which are much more effective and efficient. However, they are unable to
leverage domain knowledge. In this paper, we propose the probabilistic Logic
Neural Network (pLogicNet), which combines the advantages of both methods. A
pLogicNet defines the joint distribution of all possible triplets by using a
Markov logic network with first-order logic, which can be efficiently optimized
with the variational EM algorithm. In the E-step, a knowledge graph embedding
model is used for inferring the missing triplets, while in the M-step, the
weights of logic rules are updated based on both the observed and predicted
triplets. Experiments on multiple knowledge graphs prove the effectiveness of
pLogicNet over many competitive baselines.
