One of the fundamental problems in Artificial Intelligence is to perform complex multi-hop logical reasoning over the facts captured by a knowledge graph (KG). This problem is challenging, because KGs can be massive and incomplete. Recent approaches embed KG entities in a low dimensional space and then use these embeddings to find the answer entities. However, it has been an outstanding challenge of how to handle arbitrary first-order logic (FOL) queries as present methods are limited to only a subset of FOL operators. In particular, the negation operator is not supported. An additional limitation of present methods is also that they cannot naturally model uncertainty. Here, we present BETAE, a probabilistic embedding framework for answering arbitrary FOL queries over KGs. BETAE is the first method that can handle a complete set of first-order logical operations: conjunction (∧), disjunction (∨), and negation (¬). A key insight of BETAE is to use probabilistic distributions with bounded support, specifically the Beta distribution, and embed queries/entities as distributions, which as a consequence allows us to also faithfully model uncertainty. Logical operations are performed in the embedding space by neural operators over the probabilistic embeddings. We demonstrate the performance of BETAE on answering arbitrary FOL queries on three large, incomplete KGs. While being more general, BETAE also increases relative performance by up to 25.4% over the current state-of-the-art KG reasoning methods that can only handle conjunctive queries without negation.
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A Hybrid Model for Learning Embeddings and Logical Rules Simultaneously from Knowledge Graphs
The problem of knowledge graph (KG) reasoning has been widely explored by traditional rule-based systems and more recently by knowledge graph embedding methods. While logical rules can capture deterministic behavior in a KG, they are brittle and mining ones that infer facts beyond the known KG is challenging. Probabilistic embedding methods are effective in capturing global soft statistical tendencies and reasoning with them is computationally efficient. While embedding representations learned from rich training data are expressive, incompleteness and sparsity in real-world KGs can impact their effectiveness. We aim to leverage the complementary properties of both methods to develop a hybrid model that learns both high-quality rules and embeddings simultaneously. Our method uses a cross feedback paradigm wherein an embedding model is used to guide the search of a rule mining system to mine rules and infer new facts. These new facts are sampled and further used to refine the embedding model. Experiments on multiple benchmark datasets show the effectiveness of our method over other competitive standalone and hybrid baselines. We also show its efficacy in a sparse KG setting.
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- Award ID(s):
- 1918483
- NSF-PAR ID:
- 10327075
- Date Published:
- Journal Name:
- 2020 IEEE International Conference on Data Mining (ICDM)
- Page Range / eLocation ID:
- 1280 to 1285
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ICDM50108.2020.00164
