Jointly Embedding Knowledge Graphs and Logical Rules

Proceedings of the 2016 Conference on Empirical Methods in Natural Language Processing, pages 192–202, Austin, Texas, November 1-5, 2016. c⃝2016 Association for Computational Linguistics Jointly Embedding Knowledge Graphs and Logical Rules Shu Guo†‡, Quan Wang†‡∗, Lihong Wang§, Bin Wang†‡, Li Guo†‡ †Institute of Information Engineering, Chinese Academy of Sciences, Beijing 100093, China ‡University of Chinese Academy of Sciences, Beijing 100049, China {guoshu,wangquan,wangbin,guoli}@iie.ac.cn §National Computer Network Emergency Response Technical Team Coordination Center of China, Beijing 100029, China wlh@isc.org.cn Abstract Embedding knowledge graphs into continuous vector spaces has recently attracted increasing interest. Most existing methods perform the embedding task using only fact triples. Logi- cal rules, although containing rich background information, have not been well studied in this task. This paper proposes a novel method of jointly embedding knowledge graphs and log- ical rules. The key idea is to represent and model triples and rules in a unified framework. Specifically, triples are represented as atomic formulae and modeled by the translation as- sumption, while rules represented as complex formulae and modeled by t-norm fuzzy logic- s. Embedding then amounts to minimizing a global loss over both atomic and complex for- mulae. In this manner, we learn embeddings compatible not only with triples but also with rules, which will certainly be more predictive for knowledge acquisition and inference. We evaluate our method with link prediction and triple classification tasks. Experimental re- sults show that joint embedding brings signif- icant and consistent improvements over state- of-the-art methods. Particularly, it enhances the prediction of new facts which cannot even be directly inferred by pure logical inference, demonstrating the capability of our method to learn more predictive embeddings. 1 Introduction Knowledge graphs (KGs) provide rich structured in- formation and have become extremely useful re- sources for many NLP related applications like ∗Corresponding author: Quan Wang. word sense disambiguation (Wasserman-Pritsker et al., 2015) and information extraction (Hoffmann et al., 2011). A typical KG represents knowledge as multi-relational data, stored in triples of the for- m (head entity, relation, tail entity), e.g., (Paris, Capital-Of, France). Although powerful in representing structured data, the symbolic nature of such triples makes KGs, especially large-scale KGs, hard to manipulate. Recently, a promising approach, namely knowl- edge graph embedding, has been proposed and suc- cessfully applied to various KGs (Nickel et al., 2012; Socher et al., 2013; Bordes et al., 2014). The key idea is to embed components of a KG including en- tities and relations into a continuous vector space, so as to simplify the manipulation while preserving the inherent structure of the KG. The embeddings contain rich semantic information about entities and relations, and can significantly enhance knowledge acquisition and inference (Weston et al., 2013). Most existing methods perform the embedding task based solely on fact triples (Bordes et al., 2013; Wang et al., 2014; Nickel et al., 2016). The only re- quirement is that the learned embeddings should be compatible with those facts. While logical rules con- tain rich background information and are extreme- ly useful for knowledge acquisition and …

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