# Property-Based Semantic Similarity Criteria to Evaluate the Overlaps of Schemas
## 3 Problem Definition  
As is shown in the related work, it is vital to evaluate the overlaps of schemas to reuse high-quality knowledge graphs. The concepts of coverage and flexibility should be defined in the perspective of properties in a computable way. Since the concept of knowledge graphs came into being and was developed, there have been the emergence of many domain-specific and cross-domain knowledge graphs. However, most of these knowledge graphs are constructed from scratch, with the disadvantage of \"built once, used once\". On the one hand, this consumes too much time and energy for each case; on the other hand, it leads to high probability of conflicts in the interactions among the multiple applications based on different knowledge graphs. Therefore, it is more practical to reuse than to build a new knowledge graph.  
After we recognize the importance of knowledge graph reuse, two important issues are worth thinking about.  
* What kind of knowledge graph can I reuse to solve my need? This leads to the introduction of the schema-level knowledge graph.
* How to determine if an existing knowledge graph is suitable for use? This asks for a quantitative evaluation method.  
A knowledge graph can be regarded from the schema level (with the classes and properties) and the data level (with the individuals). Once we have constructed a schema for a knowledge graph, it can be populated via different sets of individuals. Such knowledge graphs with individuals are difficult to reuse [36], but the schema itself can be reused rather easily. Common sense knowledge graphs such as Schema.org, DBpedia, etc. contain many high-quality schemas with uniform specifications. When constructing a new knowledge graph, it will save energy and avoid conflicts if we can reuse these existing high-quality schemas effectively. Now the question is to determine whether an existing schema is suitable to reuse. The first step is to determine the entity types and the properties in the **query** (short for competency query [37]) provided by users. The next step is to choose an existing schema that can cover most of the entity types and properties. In this process, the key is to measure overlaps of the schema onto the query to determine whether the schema selected is suitable.  
Coverage and flexibility are evaluation criteria used to measure the overlaps of schemas. Coverage focuses on the overlaps of one schema on another, while flexibility focuses on the redundancy after one schema covers another. Suppose there are two schemas, \(A\) and \(B\). The calculation formula defined in the form of a set in Formulas (1) and (2) is abbreviated as \(Cov(A,B)\) and \(Flx(A,B)\). Note that the two parameters \(A\), \(B\) are ordered. It means that the coverage degree of schema \(A\) over \(B\) is not equal to the coverage degree of schema \(B\) over \(A\). In the experiment in Section 5, we use these two criteria to measure the overlapping effect between the query [38], the schema and the datasets.  
At present, the definitions are based on set theory. \(Cov(A,B)\) is the ratio of the part of schema \(A\) that covers \(B\) (\(A\cap B\)) divided by schema \(B\). \(Flx(A,B)\) is the ratio of the part of schema \(A\) that does not cover \(B\) (\(A-B\)) divided by schema \(A\). Neither criterion is symmetric.  
\[Cov(A,B) =\frac{A\cap\ B}{B} \tag{1}\] \[Flx(A,B) =\frac{A-B}{A} \tag{2}\]  
In Formula (1), \"\(A\cap B\)\" represents the \"same\" part of \(A\) and \(B\) and \"\(A-B\)\" in Formula (2) represents the part of \(A\) that is different from \(B\), that is, the part of \(A\) not covered by \(B\). However, it is not obvious that \(A\) and \(B\) are schemas that are not classical sets. To compute quantitatively the two criteria, the equivalence of entity types in the schema should be well defined.