# Measuring the Inferential Values of Relations in Knowledge Graphs
###### Abstract  
Knowledge graphs, as an important research direction in artificial intelligence, have been widely applied in many fields and tasks. The relations in knowledge graphs have explicit semantics and play a crucial role in knowledge completion and reasoning. Correctly measuring the inferential value of relations and identifying important relations in a knowledge graph can effectively improve the effectiveness of knowledge graphs in reasoning tasks. However, the existing methods primarily consider the connectivity and structural characteristics of relations, but neglect the semantics and the mutual influence of relations in reasoning tasks. This leads to truly valuable relations being difficult to fully utilize in long-chain reasoning. To address this problem, this work, inspired by information entropy and uncertainty-measurement methods in knowledge bases, proposes a method called Relation Importance Measurement based on Information Entropy (RIMIE) to measure the inferential value of relations in knowledge graphs. RIMIE considers the semantics of relations and the role of relations in reasoning. Specifically, based on the values of relations in logical chains, RIMIE partitions the logical sample set into multiple equivalence classes, and generates a knowledge structure for each relation. Correspondingly, to effectively measure the inferential values of relations in knowledge graphs, the concept of _relation entropy_ is proposed, and it is calculated according to the knowledge structures. Finally, to objectively assess the effectiveness of RIMIE, a group of experiments are conducted, which compare the influences of the relations selected according to RIMIE and other patterns on the triple classifications by knowledge graph representation learning. The experimental results confirm what is claimed above. knowledge graph; information entropy; relation entropy; inferential value +
Footnote †: journal: _Algorithms_  
0000-0001-5000-5000-5000]X. Zhang  
0000-0001-5000  
to the correct answer. If such biases are placed in a longer chain of reasoning, in which each step affects subsequent reasoning, noises will be constantly amplified and the reasoning result will seriously deviate from the correct answers. It can be considered that different relations have different influences on the reasoning process, and identifying the inferential value of relations is conducive to the acquisition of inference answers. In fact, as a kind of specific information carrier with knowledge semantics, the relations in knowledge graphs have uneven information values which have uneven impact on reasoning. As shown in Figure 1, the relation \"plays for\" connects player entities to club entities and describes key knowledge information about the player's work, significantly affecting the completeness of knowledge graphs. On the other hand, the relation \"birthday\" describes personal information about a player and contains less critical information on the player's work. Therefore, when an inference path is selected, it is essential to seriously consider the semantic characteristics and significance of different relations. However, most current multi-step reasoning approaches overlook this aspect. In this study, we believe that for long-chain logical reasoning, it is crucial to properly evaluate and identify the inferential values of different relations, which will contribute to completing the knowledge graph and improving its performance in downstream tasks. A closely related issue for the inferential value of relations in knowledge graphs is the importance metric of relations. Most current methods of measuring relation importance focus on the topological features of graphs, using metrics such as the degree of relation or the degrees of tied nodes on a relation [2; 3]. These methods primarily consider the connectivity and structural characteristics of relations, but neglect the semantics and the mutual influence of relations in reasoning tasks. And thus, they cannot solve the problem of long-chain logical reasoning discussed above.