# Property-Based Semantic Similarity Criteria to Evaluate the Overlaps of Schemas
## 4 Semantic Equivalence  
The evaluation criteria defined in the form of a set are introduced in the previous section. The next step is to compute them quantitatively. Taking \(Cov(A,B)\) as an example, in Formula (1), \(A\) and \(B\) are schemas, and \(A\cap B\) refers to the \"equivalent\" entity types. This section mainly describes the semantic equivalence of the entity types. Let us imagine several scenarios. Firstly, if all properties of two entity types are the same (semantically equivalent), then the two entity types are very likely to represent the same thing in the real world. Secondly, if two entity types in different schemas have the same individuals, they are similar in a certain way. The second situation is very common in life, as a person is likely to leave the same record in different databases. Additionally, these two individuals instantiate different entity types in the different schemas. Although we name the two entity types differently (in different schemas), the meanings of the two entity types are similar, at least for this person. It is rare to have two entity types to be 100% the same in the two schemas. If the similarity is high to a certain extent, they can be taken as equivalent entity types. The similarity of entity types lies in three levels. * Label level, such as polysemy, can be calculated by similarity at the language level. If the similarity between two entity types at the label level reaches a prescribed threshold, they can be directly considered as equivalent. * Property level, such as entity types with similar properties, for example, the entity types _student_ and _member_ in Figure 1. Although these two entity types are in different schemas, they have very similar properties, which shows that these two entity types are similar at the property level. Similarly, we should judge the similarity of different properties at the label level, such as properties _gender_ and _sex_, _ID_ and _student_ _ID_ in Figure 1 as representing the same meaning. If the similarity between two entity types at the property level reaches a prescribed threshold, it can be judged that the two entity types are equivalent. * Individual level, from the bottom up. Suppose _[PERSON]_ is an individual of entity type _student_ both in the database of the academic affairs office and an individual of entity type student in the database of the student union, as shown in Figure 1. It means that two different entity types correspond to the same individual, which shows that the entity type _student_ and the entity type _member_ are potentially similar (at least related). It might be rational to view the entity type _student_ and the entity type _member_ as the same from the different schemas. The following is the formal definition of entity type equivalence in the three aspects. **Definition 1**. : _Semantic Equivalence:_  
The semantic similarity of two entity types \(U\), \(V\) can be calculated with Formula (3). \[Sim_{s}(U,\ V)=\alpha Sim_{L}(U,\ V)+\beta Sim_{P}(U,\ V)+\gamma Sim_{I}(U,\ V) \tag{3}\]  
where  
\[Sim_{L}(U,\ V)=|\overline{U},\overline{V}|\]  
In which \(\overline{P}\) is the vector formed by the natural language labels of P and \(|\overline{U},\overline{V}|\) returns the semantic distance [39] of the two vectors;  
\[Sim_{P}(U,\ V)=\sum_{i,j}Sim_{L}\big{(}P_{u,i},\ P_{v,j}\big{)}\]  
where \(P_{u,i}\) and \(P_{v,j}\) are properties of \(U\) and \(V\), respectively,  
\[Sim_{I}(U,\ V)=\sum_{i,j}^{m,n}e\big{(}I_{u,i},\ I_{v,j}\big{)}\,/\,Min(m,\ n)\]  
where \(I_{u,i},\ I_{v,j}\) are among the \(m\), \(n\) individuals of \(U\), \(V\), respectively, and  
\[e\big{(}I_{u},\ I_{v}\big{)}=\left\{ \begin{array}{l}1,\text{if }I_{u}\text{ refers to the same individual as }I_{v},\\ 0,\text{otherwise.}\end{array} \right.\]  
Moreover, to compute Formula (3), the three factors take effects in the following conditions. \[(\alpha,\ \beta,\ \gamma)=\left\{