# SFCA: A Scalable Formal Concepts Driven Architecture for Multi-Field Knowledge Graph Completion
## 1 Introduction
### Motivation  
After analyzing the dilemmas involved in fetching external information, we meet three puzzles. What kind of concept can be defined as commonsense concepts? Which part of the commonsense concept provides valuable information in the KGC model? Is it possible to refine a concept from data to instead commonsense concept? The essence of the commonsense concept is summarized in many instances by human cognition. Thus, we try to explore new metaphysical 'concepts' from the latent space of KGs. Inspired by data mining theories, we argue that formal concepts with lattice structures are similar to ontologies with tree structures and can guide instance knowledge in KGC tasks. Thus, we use formal concepts to represent a concept, including entities and relations subset of KG. Figure 1a shows a schematic diagram of the ontology and concept lattice structure. In light of the definition of formal concept analysis in data mining, a formal concept is an idea or category defined by a concrete or specific set of rules, guidelines, or properties. Extending to KGs, formal concepts can be treated as an ensemble of two sets. One is its extension to denote entity sets. The other is its intention to represent latent relations of entities. For the first set, our identification of instance membership in formal concepts relies on the formal concept's instance set. By comparing the source instances and instances in the formal concept instances collection to judge whether this instance belongs to the formal concept. As shown in Figure 1b, In the lower part of the figure, diamonds represent formal concepts, and the squares and the rectangles to the right of the diamond, respectively, represent the objects and properties that make up the formal concept. The source of formal concepts is shown in the upper part of the figure. Specifically, huskies can be recognized as an instance in the formal concept of the \"Dog\" and an instance in the formal concept of the \"Sled Dog\" since it is contained in the instances collection of \"Dog\" and \"Sled Dog\" in formal concepts (The three names of \"Dog\", \"Herding Dog\" and \"Sled Dog\" are matched by ourselves according to the instance set an attribute set of formal concept, formal concepts themselves have no names, but the individual elements of instance sets and property sets have their names). For the second set, formal concepts involve potential information of instances concepts, including possible properties (According to the different attributes of the instance, we can find the different formal concepts corresponding to the instance that are more focused on a certain attribute in meaning). For example, BorderCollies, in this instance, hide the attribute of \"Hunting\" and the attribute of \"Herding\", which are respectively contained in the formal concept of \"Dog\" and the formal concept of \"Herding Dog\". Figure 1: (**a**) A schematic diagram of ontology structure and concept lattice structure. (**b**) Examples of Correspondence between instances and formal concepts and sources of formal concepts. This sparked our interest in exploring the role of formal concepts in KGC research. Formal concepts can be found from the binary relations between known instances and attributes and exactly corresponds to the entity and relation in KG. For example, in a triplet SPO, P can be regarded as an attribute of S, and S can be regarded as an instance with the P property, from which we can naturally mine the formal concept in KG. In this work, we apply formal concepts, such as metaphysical structural information, to enhance the KGE model for the KGC task. Compared with commonsense concepts, formal concepts have the following advantages:  
1. Formal concepts can be efficient and automatically generated, while commonsense concepts require expensive manual annotation. The formal concept is derived from the KG itself and belongs to the information of the KGs. On the contrary, the commonsense concept must be manually annotated for information outside the KG. 2.