Query model for object-oriented databases

A query language should be a part of any database system. While the relational model has a well defined underlying query model, the object-oriented database systems have been criticized for not having such a query model. One of the most challenging steps in the development of a theory for object-oriented databases is the definition of an object algebra. A formal object-oriented query model is described here in terms of an object algebra, at least as powerful as the relational algebra, by extending the latter in a consistent manner. Both the structure and the behavior of objects are handled. An operand and the output from a query in the object algebra are defined to have a pair of sets, a set of objects and a set of message expressions where a message expression is a valid sequence of messages. Hence the closure property is maintained in a natural way. In addition, it is proved that the output from a query has the characteristics of a class; hence the inheritance (sub/superclass) relationship between the operand(s) and the output from a query is derived. This way, the result of a query can be persistently placed in its proper place in the lattice.