{"type":"ScholarlyArticle","title":"Learning First-Order Logic Embeddings via Matrix Factorization","authors":[{"name":"William Yang Wang","slug":"william-yang-wang","given":"William Yang","family":"Wang","affiliation":""},{"name":"William W. Cohen","slug":"william-w-cohen","given":"William W.","family":"Cohen","affiliation":""}],"abstract":"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.","doi":null,"url":"https://ijcai.org/proceedings/2016/304","pdf":"https://ijcai.org/proceedings/2016/0304.pdf","markdown":"https://ijcai.org/proceedings/2016/304.md","bibtex":"https://ijcai.org/proceedings/2016/bibtex/304","volume":{"slug":"2016","title":"Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2016","url":"https://ijcai.org/proceedings/2016/","year":2016,"location":"New York, NY, USA","dates":"9–15 July 2016","editors":"Subbarao Kambhampati","isbn":"978-1-57735-770-4; 978-1-57735-771-1","publisher":"AAAI Press / International Joint Conferences on Artificial Intelligence","doi_prefix":""},"section":null,"track":"","number":304,"pages":{"first":2132,"last":2137},"keywords":[],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}