Answering logical queries on knowledge graphs (KG) poses a significant challenge for machine reasoning. The primary obstacle in this task stems from the inherent incompleteness of KGs. Existing research has predominantly focused on addressing the issue of missing edges in KGs, thereby neglecting another aspect of incompleteness: the emergence of new entities. Furthermore, most of the existing methods tend to reason over each logical operator separately, rather than comprehensively analyzing the query as a whole during the reasoning process. In this paper, we propose a query-aware prompt-fused framework named Pro-QE, which could incorporate existing query embedding methods and address the embedding of emerging entities through contextual information aggregation. Additionally, a query prompt, which is generated by encoding the symbolic query, is introduced to gather information relevant to the query from a holistic perspective. To evaluate the efficacy of our model in the inductive setting, we introduce two new challenging benchmarks. Experimental results demonstrate that our model successfully handles the issue of unseen entities in logical queries. Furthermore, the ablation study confirms the efficacy of the aggregator and prompt components.

Knowledge graph (KG) completion aims to find out missing triples in a KG. Some tasks, such as link prediction and instance completion, have been proposed for KG completion. They are triple-level tasks with some elements in a missing triple given to predict the missing element of the triple. However, knowing some elements of the missing triple in advance is not always a realistic setting. In this paper, we propose a novel graph-level automatic KG completion task calledTriple Set Prediction (TSP)which assumes none of the elements in the missing triples is given. TSP is to predict a set of missing triples given a set of known triples. To properly and accurately evaluate this new task, we propose 4 evaluation metrics including 3 classification metrics and 1 ranking metric, considering both the partial-open-world and the closed-world assumptions. Furthermore, to tackle the huge candidate triples for prediction, we propose a novel and efficient subgraph-based method GPHT that can predict the triple set fast. To fairly compare the TSP results, we also propose two types of methods RuleTensor-TSP and KGE-TSP applying the existing rule- and embedding-based methods for TSP as baselines. During experiments, we evaluate the proposed methods on two datasets extracted from Wikidata following the relation-similarity partial-open-world assumption proposed by us, and also create a complete family data set to evaluate TSP results following the closed-world assumption. Results prove that the methods can successfully generate a set of missing triples and achieve reasonable scores on the new task, and GPHTperforms better than the baselines with significantly shorter prediction time.

Rule mining is an effective approach for reasoning over knowledge graph (KG). Existing works mainly concentrate on mining rules. However, there might be several rules that could be applied for reasoning for one relation, and how to select appropriate rules for completion of different triples has not been discussed. In this paper, we propose to take the context information into consideration, which helps select suitable rules for the inference tasks. Based on this idea, we propose a transformer-based rule mining approach, Ruleformer. It consists of two blocks: 1) an encoder extracting the context information from subgraph of head entities with modified attention mechanism, and 2) a decoder which aggregates the subgraph information from the encoder output and generates the probability of relations for each step of reasoning. The basic idea behind Ruleformer is regarding rule mining process as a sequence to sequence task. To make the subgraph a sequence input to the encoder and retain the graph structure, we devise a relational attention mechanism in Transformer. The experiment results show the necessity of considering these information in rule mining task and the effectiveness of our model.

Answering complex queries over knowledge graphs (KG) is an important yet challenging task because of the KG incompleteness issue and cascading errors during reasoning. Recent query embedding (QE) approaches embed the entities and relations in a KG and the first-order logic (FOL) queries into a low dimensional space, making the query can be answered by dense similarity searching. However, previous works mainly concentrate on the target answers, ignoring intermediate entities' usefulness, which is essential for relieving the cascading error problem in logical query answering. In addition, these methods are usually designed with their own geometric or distributional embeddings to handle logical operators like union, intersection, and negation, with the sacrifice of the accuracy of the basic operator -- projection, and they could not absorb other embedding methods to their models. In this work, we propose a Neural and Symbolic Entangled framework (ENeSy) for complex query answering, which enables the neural and symbolic reasoning to enhance each other to alleviate the cascading error and KG incompleteness. The projection operator in ENeSy could be any embedding method with the capability of link prediction, and the other FOL operators are handled without parameters. With both neural and symbolic reasoning results contained, ENeSy answers queries in ensembles. We evaluate ENeSy on complex query answering benchmarks, and ENeSy achieves the state-of-the-art, especially in the setting of training model only with the link prediction task.