## 2 KG Inference Method Framework Integrating Logical Rules and Embedded Learning  
Assembly process KG construction refers to the process of transforming heterogeneous assembly process data into a structured KG. This process can be decomposed into two types of tasks: natural language processing tasks and knowledge inference tasks. Therein, knowledge inference tasks consist of knowledge judgment, entity completion and relation completion, which are significantly crucial for assembly process KG construction. In the process of assembly process KG construction, in addition to the entity and relation semantic information, entity type information is an important factor to reflect the difference between entities and mapping relation. Therefore, assembly process KG inference considering entity type is an effective way to improve the accuracy of assembly process KG inference and fast construction of assembly process KG. In this paper, proposed KG inference method for KG construction, whose framework is shown in Figure 1, comprehensively considers the semantic information of entity, relationand entity type. The method framework is divided into three layers: data sampling layer, model construction layer and tasks application layer. In the data sampling layer, several data dictionaries and logical rules are constructed according to KG information. Subsequently, the vectorization of entity, relation and entity type is realized according to these data dictionaries and word2 vec model. In the model construction layer, embedded learning model is constructed based on the vectorization above, and the logic rules of vectorization are embedded in the embedded learning model to guide the training direction. In the tasks application layer, the optimized model is trained for different KG inference tasks. For knowledge judgment task, the optimized model is trained while considering the constraint of logic rules. For entity completion task, the optimized model is trained using positive and negative samples generated by entity and entity type replacement. For relation completion task, the optimized model is also trained with positive and negative samples, which are generated by relation replacement. Classical KG adopts the entity, relation and fact approach, and a fact is represented by a triplet <_head entity_, _relation, tail entity_>. Aiming at the problem that the triplet form cannot effectively express entity type information required for assembly process KG inference, this paper introduces entity type information including head entity type and tail entity type. In that, a fact in assembly process KG could be represented by three triplets:  
\[AK=\left\{ \begin{array}{c}<\textit{head entity},\ \textit{relation},\ \textit{tail entity}>\\ <\textit{head entity}.\ \textit{whose type is},\ \textit{head entity type}>\\ <\textit{tail entity}.\ \textit{whose type is},\ \textit{tail entity type}>\end{array} \right. \tag{1}\]  
where \(AK\) represents some fact of assembly process KG. To circumvent the problem of increased computational complexity caused by multiple triplets, this paper constructs a  
Figure 1: Inference method integrating logical rules and embedded learning and application. quintuple containing entity, relation and entity type to express assembly process knowledge, which is defined as follows:  
\[AK=(h,r,t,ht,tt) \tag{2}\]  
where \(h\) is the head entity, \(r\) is the relation, \(t\) is the tail entity, \(ht\) is the head entity type, and \(tt\) is the tail entity type. In this paper, problem models are constructed for KG inference tasks such as knowledge judgment, entity and relation completion. The knowledge judgment task in assembly process KG inference is to determine whether a quintuple is true. For example, determine whether the quintuple _<borehole, next operation, repair, operation, operation>_ is true, that is, whether there is a sequential relation between 'borehole' step and'repair' step. In this regard, a knowledge decision problem model is constructed:  
\[