From the perspective of data integration, we have two ontologies from different sources as the input of QUEST. Before continuing, we define some notation for simplicity. 

1. Two ontologies (or schemas) are A and B. 

2. map(A, B): defines a set of mapping rules between A and B, which depict relationships of elements or structures in A with those in B. These rules also define conflicts happened during the matching or merging. 

3. comb(A, B): gives the integrated view of both A and B. Mapping rules may be merged in this integrated representation. 

4. tran(A): converts the ontology/schema A into the graphic representation of QUEST.

5. tran(R): integrates the mapping rule R into the graphic representation of QUEST.

Three cases are considered when the data integration of A and B is concerned:

1) A + B + map(A, B) --> comb(A, B) --> tran(comb(A, B))

The two ontologies A and B are matched based on some algorithm and mapping rules are generated as well. All of these are merged into one single integrated view comb(A, B). 

Therefore, QUEST model is obtained through translating the integrated view comb(A, B). 

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