Learning First Order Logic Embeddings via Matrix Factorization
Many complex reasoning tasks in Artificial Intelligence (including relation extraction, knowledge base completion, and information integration) can be formulated as inference problems using a probabilistic first order logic. However, due to the discrete nature of logical facts and predicates, it is challenging to generalize symbolic representations and represent first order logic formulas in probabilistic relational models. In this work, we take a rather radical approach: we aim at learning continuous low dimensional embeddings for first order logic from scratch. In particular, we first consider a structural gradient based structure learning approach to generate plausible inference formulas from facts; then, we build grounded proof graphs using background facts, training examples, and these inference formulas. To learn embeddings for formulas, we map the training examples into the rows of a binary matrix, and inference formulas into the columns. Using a scalable matrix factorization approach, we then learn the latent continuous representations of examples and logical formulas via a low rank approximation method. In experiments, we demonstrate the effectiveness of reasoning with first order logic embeddings by comparing with several state of the art baselines on two datasets in the task of knowledge base completion.
IJCAI