Answering complex First-Order Logical (FOL) queries on large-scale incomplete knowledge graphs (KGs) is an important yet challenging task. Recent advances embed logical queries and KG entities in the same space and conduct query answering via dense similarity search. However, most logical operators designed in previous studies do not satisfy the axiomatic system of classical logic, limiting their performance. Moreover, these logical operators are parameterized and thus require many complex FOL queries as training data, which are often arduous to collect or even inaccessible in most real-world KGs. We thus present FuzzQE, a fuzzy logic based logical query embedding framework for answering FOL queries over KGs. FuzzQE follows fuzzy logic to define logical operators in a principled and learning-free manner, where only entity and relation embeddings require learning. FuzzQE can further benefit from labeled complex logical queries for training. Extensive experiments on two benchmark datasets demonstrate that FuzzQE provides significantly better performance in answering FOL queries compared to state-of-the-art methods. In addition, FuzzQE trained with only KG link prediction can achieve comparable performance to those trained with extra complex query data.
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Beta Embeddings for Multi-Hop Logical Reasoning in Knowledge Graphs
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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- NSF-PAR ID:
- 10219020
- Date Published:
- Journal Name:
- Neural Information Processing Systems (NeurIPS)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Answering complex logical queries on large-scale incomplete knowledge graphs (KGs) is a fundamental yet challenging task. Recently, a promising approach to this problem has been to embed KG entities as well as the query into a vector space such that entities that answer the query are embedded close to the query. However, prior work models queries as single points in the vector space, which is problematic because a complex query represents a potentially large set of its answer entities, but it is unclear how such a set can be represented as a single point. Furthermore, prior work can only handle queries that use conjunctions (^) and existential quantifiers (9). Handling queries with logical disjunctions (_) remains an open problem. Here we propose QUERY2BOX, an embedding-based framework for reasoning over arbitrary queries with ^, _, and 9 operators in massive and incomplete KGs. Our main insight is that queries can be embedded as boxes (i.e., hyper-rectangles), where a set of points inside the box corresponds to a set of answer entities of the query. We show that conjunctions can be naturally represented as intersections of boxes and also prove a negative result that handling disjunctions would require embedding with dimension proportional to the number of KG entities. However, we show that by transforming queries into a Disjunctive Normal Form, QUERY2BOX is capable of handling arbitrary logical queries with ^, _, 9 in a scalable manner. We demonstrate the effectiveness of QUERY2BOX on three large KGs and show that QUERY2BOX achieves up to 25% relative improvement over the state of the art.more » « less
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Accepted Manuscript1.0
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