Continual knowledge graph embedding (CKGE) has gained wide attention for managing dynamic knowledge graphs (KGs), which are continuously updated with new facts. Unlike traditional methods designed for static KGs, CKGE enables incremental updates to KG embeddings to accommodate new facts while retaining previously learned knowledge. Despite these advancements, current CKGE studies and benchmarks primarily focus on handling the increasing scale of data while overlooking changes in graph patterns. These changes, altering the graph structure of KGs, are referred to as pattern shifts in this paper. Pattern shifts frequently arise as new facts are added, introducing significant challenges to the stability and adaptability of CKGE methods. To address this gap, we introduce a suite of novel and challenging benchmarks, called PS-CKGE, specifically designed to evaluate CKGE methods under pattern shifts, where logic rules are utilized to capture and manage structural changes in dynamic KGs. Through these benchmarks, we comprehensively evaluate current CKGE methods in terms of their overall performance, resistance to catastrophic forgetting, and adaptability to new knowledge. The results show that pattern shifts not only exacerbate their risk of catastrophic forgetting but also impair their adaptability, usually with greater performance degradation over triples associated with more significant changes.

Knowledge Graph (KG) reasoning aims to predict missing entities in incomplete triples, which requires adequate structural information to derive accurate embeddings. However, KGs in the real world are not as dense as the idealized benchmarks, where sparse graph structures restrict the comprehensive structural information for superior performance. Although the logical semantics in KGs shows its potential in alleviating the impact of structural sparsity, there still exist some challenges. The deficient supervision and the semantic gap of logic make it difficult to introduce logical semantics in sparse KG reasoning. To this end, we propose a novel KG reasoning approach LoLLM injecting logic with the supervised information supplied by the Large Language Model (LLM), which is proved to be effective in evaluating and scoring. Firstly, LoLLM derives structural embeddings employing a graph convolutional network (GCN) with relation-aware and triple-aware attention. LoLLM secondly constructs reasoning paths instantiated from the first-order logic rules extracted from sparse KGs, and injects the logical semantics by a designed LLM-enhanced tuning strategy. We propose a textual loss (TL) and a logical loss (LL) in the optimization and obtain logical tuning embeddings of KG in this process. Finally, LoLLM fuses structural embeddings from the GCN and logical tuning embeddings from the LLM-enhanced tuning for scoring and incomplete triple prediction. Extensive experiments on two sparse KGs and a benchmark show that LoLLM outperforms state-of-the-art structure-based and Language Model (LM)-augmented baselines. Moreover, the logic rules with corresponding confidences provide explicit explanations as an interpretable paradigm.

Embedding symbolic logical formulas into a low-dimensional continuous space provides an effective way for the Neural-Symbolic system. However, current studies are all constrained by the syntactic structure modeling and fail to preserve intrinsic semantics. To this end, we propose a novel model of Contrastive Graph Representations (ConGR) for logical formulas embedding. Firstly, it introduces a densely connected graph convolutional network (GCN) with an attention mechanism to process syntax parsing graphs of formulas. Secondly, the contrastive instances for each anchor formula are generated by the transformation under the guidance of logical properties. Two types of contrast, global-local and global-global, are carried out to refine formula embeddings with semantic information. Extensive experiments demonstrate that ConGR obtains superior performance against state-of-the-art baselines.

Relation prediction in knowledge graphs (KGs) aims at predicting missing relations in incomplete triples, whereas the dominant paradigm by KG embeddings has a limitation to predict the relation between unseen entities. This situation is called an inductive setting, which is more common in the real-world scenario. To handle this issue, implicit symbolic rules have shown great potential in capturing the inductive capability. However, it is still challenging to obtain precise representations of logic rules from KGs. The argument variability and predicate non-commutativity in symbolic rule integration make the modeling of component symbols difficult. To this end, we propose a novel inductive relation prediction model named SymRITa with a logic transformer integrating rules. SymRITa firstly extracts the subgraph, whose embeddings are captured by a graph network. Meanwhile, symbolic rule graphs in the subgraph can be generated. Then, the symbolic rules are modeled by a proposed logic transformer. Specifically, the input format based on the subgraph-based embeddings is to focus on the argument variability in symbolic rules. In addition, a conjunction attention mechanism in the logic transformer can resolve predicate non-commutativity in the symbolic rule integration process. Finally, the subgraph-based and symbol-based embeddings obtained from the previous steps are combined for the training regime, and prediction results as well as rules explaining the reasoning process are explicitly output. Extensive experiments on twelve inductive datasets show that SymRITa achieves outstanding effectiveness compared to state-of-the-art inductive baselines. Moreover, the logic rules with corresponding confidences provide an interpretable paradigm.

Commonsense knowledge graphs (CKGs) store massive commonsense knowledge as triples whose nodes consist of free-form texts. CKG reasoning aims to predict missing nodes in incomplete commonsense triples, which is challenging as it requires more accurate embeddings for reasoning. Compared to conventional knowledge graphs (KGs), CKGs have deficient structural information due to their sparsity and contain nodes indistinguishable due to the conceptual diversity. These issues limit the performance of previous reasoning methods, because they face difficulties obtaining precise CKG representations. To address these issues, we propose a context-aware CKG reasoning framework with path-guided explanations, named CoRPe. Firstly, CoRPe constructs context sentences based on the target commonsense triple using designed templates. The context captures reasoning paths instantiated from the first-order logic. Secondly, to improve CKG representations, CoRPe injects context semantics and employs a context-augmented tuning strategy on a pre-trained language model (PLM) via a synergistic optimization. Finally, CoRPe embeds structural information using a graph convolutional network (GCN) and associates the textual semantics for joint scoring. Extensive experiments on two CKGs show that CoRPe outperforms state-of-the-art KG and CKG reasoning baselines in terms of embedding and reasoning performance. Furthermore, the interpretability of CoRPe is reflected in the implicit logic during reasoning.

Currently, the non-transparent computing process of deep learning has become a significant reason hindering its further development. The Neural-Symbolic (NS) system formed by integrating logic rules into neural networks has attracted increasing attention owing to its direct interpretability. Embedding symbolic logical formulas into a low-dimensional continuous space provides an effective way for the NS system. However, current studies are all constrained by the modeling ability for its syntactic structure and fail to preserve the intrinsic semantics in embeddings, which causes poor performance on downstream reasoning tasks. To this end, this paper proposes a novel method ofContrastiveGraphRepresentations (ConGR) for logical formulas embedding. First, to improve the modeling ability for the syntactic structure, ConGR introduces a densely connected graph convolutional network (GCN) with an attention mechanism to process syntax parsing graphs of formulas. In this way, discriminative local and global embeddings of formulas are obtained at the syntax level. Second, the contrastive instances (positive or negative) for each anchor formula are generated by the transformation under the guidance of logical properties. To preserve semantic information, two types of contrast, global-local and global-global, are carried out to refine formula embeddings. Extensive experiments demonstrate that ConGR obtains superior performance against state-of-the-art baselines on entailment checking and premise selection datasets.

Relation prediction on knowledge graphs (KGs) aims to infer missing valid triples from observed ones. Although this task has been deeply studied, most previous studies are limited to the transductive setting and cannot handle emerging entities. Actually, the inductive setting is closer to real-life scenarios because it allows entities in the testing phase to be unseen during training. However, it is challenging to precisely conduct inductive relation prediction as there exists requirements of entity-independent relation modeling and discrete logical reasoning for interoperability. To this end, we propose a novel model ConGLR to incorporate context graph with logical reasoning. Firstly, the enclosing subgraph w.r.t. target head and tail entities are extracted and initialized by the double radius labeling. And then the context graph involving relational paths, relations and entities is introduced. Secondly, two graph convolutional networks (GCNs) with the information interaction of entities and relations are carried out to process the subgraph and context graph respectively. Considering the influence of different edges and target relations, we introduce edge-aware and relation-aware attention mechanisms for the subgraph GCN. Finally, by treating the relational path as rule body and target relation as rule head, we integrate neural calculating and logical reasoning to obtain inductive scores. And to focus on the specific modeling goals of each module, the stop-gradient is utilized in the information interaction between context graph and subgraph GCNs in the training process. In this way, ConGLR satisfies two inductive requirements at the same time. Extensive experiments demonstrate that ConGLR obtains outstanding performance against state-of-the-art baselines on twelve inductive dataset versions of three common KGs.

Machine reading comprehension has aroused wide concerns, since it explores the potential of model for text understanding. To further equip the machine with the reasoning capability, the challenging task of logical reasoning is proposed. Previous works on logical reasoning have proposed some strategies to extract the logical units from different aspects. However, there still remains a challenge to model the long distance dependency among the logical units. Also, it is demanding to uncover the logical structures of the text and further fuse the discrete logic to the continuous text embedding. To tackle the above issues, we propose an end-to-end model Logiformer which utilizes a two-branch graph transformer network for logical reasoning of text. Firstly, we introduce different extraction strategies to split the text into two sets of logical units, and construct the logical graph and the syntax graph respectively. The logical graph models the causal relations for the logical branch while the syntax graph captures the co-occurrence relations for the syntax branch. Secondly, to model the long distance dependency, the node sequence from each graph is fed into the fully connected graph transformer structures. The two adjacent matrices are viewed as the attention biases for the graph transformer layers, which map the discrete logical structures to the continuous text embedding space. Thirdly, a dynamic gate mechanism and a question-aware self-attention module are introduced before the answer prediction to update the features. The reasoning process provides the interpretability by employing the logical units, which are consistent with human cognition. The experimental results show the superiority of our model, which outperforms the state-of-the-art single model on two logical reasoning benchmarks.

Coreference resolution aims at recognizing different forms in a document which refer to the same entity in the real world. Although many models have been proposed and achieved success, there still exist some challenges. Recent models that use recurrent neural networks to obtain mention representations ignore dependencies between spans and their proceeding distant spans, which will lead to predicted clusters that are locally consistent but globally inconsistent. In addition, these models are trained only by maximizing the marginal likelihood of gold antecedent spans from coreference clusters, which will make some gold mentions undetectable and cause unsatisfactory coreference results. To address these challenges, we propose a neural coreference resolution model. It employs mutual attention to take into account the dependencies between spans and their proceeding spans directly (use attention mechanism to capture global information between spans and their proceeding spans). And our model is trained by jointly optimizing mention clustering and imbalanced mention detection, which enables it to detect more gold mentions in a document to make more accurate coreference decisions. Experimental results on the CoNLL-2012 English dataset show that our model can detect the most gold mentions and achieve the state-of-the-art coreference performance compared with baselines.