An Example for Metamodeling Syntax and Semantics of Two Languages, their Transformation, and a Correctness Criterion

We study a metamodel for the Entity Relationship (ER) and the Relational data model. We do this by describing the syntax of the ER data model by introducing classes for ER schemata, entities, and relationships. We also describe the semantics of the ER data model by introducing classes for ER states, instances, and links. The connection between syntax and semantics is established by associations explaining that syntactical objects are interpreted by corresponding semantical objects. Analogously we do this for the Relational data model. Finally, we give a metamodel for the transformation of ER schemata into Relational database schemata. By characterizing the syntax and semantics of the languages to be transformed and also the transformation itself within the same (meta-)modeling language we are able to include equivalence criteria on the syntactical and on the semantical level for the transformation. In particular, we show that the semantical equivalence criterion requires that the ER states and the corresponding Relational states bear the same information.