Modeling and Merging Database Schemas

We define a general model for database schemas which is basically functional and supports specialisation relationships. Despite it's simplicity, our model is very general and expressive, so that database schemas and instances arising from a number of other data models can be translated into the model. We define and investigate a representation for the observations that can be made by querying a database system, and, in particular, look at which observations are valid for a particular database schema, and when one observation implies the observability of another. We will also look at the correspondence between the instances of a database schema and the observations that can be made for the database. We then go on to look at the problem of schema merging: we define an ordering on schemas representing their informational content and define the merge of a collection of schemas to be the least schema with the informational content of all the schemas being merged. However we establish that one cannot, in general, find a meaningful binary merging operator which is associative, though we would clearly require this of any such operator. We rectify this situation by relaxing our definition of schemas, defining a class of weak schemas over which we can construct a satisfactory concept of merges. Further we define a method of constructing a canonical proper schema with the same informational content as a weak schema whenever possible, thus giving us an adequate definition of the merge of a collection of proper schemas whenever such a merge can exist. In addition we show that, if the schemas we are merging are translations from some other data model, our merging process "respects" the original data model.