# Knowledge Reasoning via Jointly Modeling Knowledge Graphs and Soft Rules
###### Abstract
Therefore, we believe that rules are uncertain, but conclusions are deterministic in knowledge reasoning, as shown in Figure 1; each fact is only absolutely true or false. Previous methods associate each conclusion with a weight derived from the corresponding rule. In contrast, we propose inferring that all conclusions  
Figure 1: We propose a novel iterative knowledge reasoning framework that fuses logical rules into a knowledge graph embedding (KGE). Previous methods associate each conclusion with a weight derived from its corresponding rule. In contrast, our method can infer the true conclusion via jointly modeling the deterministic KG and uncertain soft rules. The facts in red are erroneous conclusions filtered out by our method. are true (e.g., ([PERSON], nationality, USA)) or not (e.g., ([PERSON], sister_of, [PERSON])) (the other fact, i.e., ([PERSON], gender, male), indicates that [PERSON] is not [PERSON]'s sister) by jointly modeling the deterministic KG and soft rules. Specifically, we first mine soft rules from the knowledge graph and then infer conclusions as candidate facts. Second, the KG, conclusions, and weighted rules are also used as resources to learn embeddings. Third, by defining deterministic conclusion loss, the conclusion labels are modeled as 0-1 variables, and the confidence loss of a rule is also used to constrain the conclusions. Finally, the embedding learning stage removes the noise in the candidate conclusions, and then the proper conclusions are added back to the original KG. The above steps are performed iteratively. We empirically evaluate the proposed method on public datasets from two real large-scale KGs: DBpedia and Freebase. The experimental results show that our method Iterlogic-E (Iterative using logic rule for reasoning and learning Embedding) achieves state-of-the-art results on multiple evaluation metrics. Compared to the state-of-the-art model, Iterlogic-E also achieves improvements of 2.7%/4.3% in mean reciprocal rank (MRR) and 2.0%/4.0% in HITS@1. In summary, our main contributions are as follows:  
* We propose a novel KGC method, Iterlogic-E, which jointly models logical rules and KGs in the framework of a KGE. Iterlogic-E combines the advantages of rules and embeddings in knowledge reasoning. Iterlogic-E models the conclusion labels as 0-1 variables and uses a confidence regularizer to eliminate the uncertain conclusions. * We propose a novel iterative learning paradigm that strikes a good balance between efficiency and scalability. Iterlogic-E not only densifies the KG but can also filters out incorrect conclusions. * Compared to traditional reasoning methods, Iterlogic-E offers better interpretability in determining conclusions. It not only knows why the conclusion holds but also knows which is true and which is false. * We empirically evaluate the performance of Iterlogic-E with the task of link prediction on multiple benchmark datasets. The experimental results demonstrate that Iterlogic-E can outperform other methods on multiple evaluation metrics. The qualitative analysis confirms that Iterlogic-E exhibits higher robustness for rules with varying confidence levels.