Tales of ER and RE Syntax and Semantics

Abstract

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.