Tales of ER and RE Syntax and Semantics

This paper explains how four model transformations between database models work: (1) An ER (Entity-Relationship) database schema is transformed into a collection of ER database states, (2) a RE (Relational) database schema into a collection of RE database states, (3) an ER database schema into a RE database schema, and (4) a collection of ER database states into a collection of RE database states. These four separate transformations may be viewed as a single transformation between the ER datamodel and the RE datamodel. The schemas are regarded as determining the syntax of the datamodels, and the set of associated states is regarded as being the semantics of the datamodels, because the states associate meaning with the schemas. When one usually considers database models, one formally only treats syntactical aspects, i.e., schemas, and handles the semantics merely informally. Our approach allows to formally handle syntax and semantics of database models and their transformation within a single and uniform framework. The approach thus allows to precisely describe properties of the datamodels and properties of the transformation. The method behind our approach is to divide a language into a syntax and semantics part and to describe a transformation between two languages as a direction-neutral affair. Formal properties of the languages to be transformed and formal properties of the transformation are described uniformly. Transformation properties can be properties regarding syntax and semantics. The method can be applied not only to database languages but to transformations between common computer science languages.