## 2 Related Work  
The work related to this article encompasses three primary facets: transductive KGC, inductive KGC, and predicate inductive KGC. Transductive KGC represents a conventional reasoning task, with trained KGC models unable to engage in reasoning related to novel entities absent from the training set. By contrast, inductive KGC allows the reasoning model to handle new entities not seen during training, but falls short when dealing with novel predicates. Predicate inductive KGC demands that the reasoning model possess the capability to reason over both new entities and predicates. Our PDEC framework executes the predicate inductive KGC task, which involves decomposing polysemous predicates within the original predicate set to yield new, more rational predicates. As these three KGC tasks are progressively related and strongly correlated with PDEC, it becomes imperative for us to examine their associated literature. Compared with transductive KGC and inductive KGC, PDEC has performance advantages and unique capabilities in handling new predicates. Unlike existing models in the predicate inductive KGC realm, PDEC does not necessitate external information, instead solely relying on the analysis of the polysemy in the original predicate set to acquire reasoning capabilities for novel predicates. This approach, which is rooted in predicate decomposition, offers a more rational predicate set, thereby effectively enhancing the reasoning models' performance. Transductive KGC via KG embeddings.A number of works are proposed for KGC tasks using learnable embeddings for KG relations and entities. For example, in [1; 2; 3; 4; 13], they learn to map KG relations into vector space and predict links with scoring functions. NTN [14], on the other hand, parameterizes each relation into a neural network. In [15], the authors present a theoretical framework that highlights the capabilities of graph neural networks (GNNs) in embedding entities and relations within KGs and executing link prediction tasks. The paper [16] proposes a divide-search-combine algorithm, RelEns-DSC, to efficiently search relation-aware ensemble weights for KG embedding. Because these algorithms need to learn embeddings of entities and relations in the test set during the training process, they are generally only suitable for transductive KGC tasks and cannot be applied to scenarios where there are new predicates in the test set such as predicate decomposition. Inductive KGC.In recent years, inductive KG reasoning has gained increasing attention. This approach enables reasoning tasks to be performed in a bottom-up manner, focusing on the emergence of new entities. Methods such as ([17; 18]) have emphasized the importance of modeling emerging entities, while ([19]) has introduced rule-based attention weights and ([20]) has extended RotatE ([4]) to enhance inductive reasoning. Alternatively, some research has focused on conducting inductive KGC tasks through rule mining. Neural LP [7] and DRUM [8] have reduced the rule learning problem to algebraic operations on neural-embedding-based representations of a given KG. LogCo [21] combines logical reasoning with contrastive representations and extracts subgraphs and relational paths to achieve entity independence and addresses supervision deficiencies, achieving superior performance on inductive KG reasoning. The paper [22] proposes an adaptive propagation path learning method for GNN-based inductive KG reasoning, addressing the limitations of hand-designed paths and explosive growth of entities. Compared with these methods, we tackle a more challenging problem where predicates can be new instead of only some entities being new. Predicate inductive KGC.Predicate induction KGC is the latest development of inductive KGC (also known as entity induction KGC), which aims to enable KG reasoning models to perform KGC tasks on new predicate sets that do not exist in the training set. INGRAM [11] exhibits remarkable reasoning capabilities for novel predicates, enabling it to handle any new predicates.