Relation Schemata vs. Relation Variables

In the context of an update, the predicate of a database along with the current database state determines the set of all /possible states/ that can become current. Integrity rules, which are implicitly or explicity specified as part of the database predicate, can be classified as either state constraints or transition constraints. State constraints define the set of all consistent database states; transition constraints determine whether or not a state change should be allowed. Given a set of consistent database states and the current state, one can derive a set of transitions, each containing what is different on a tuple by tuple basis between the current state and a proposed state (any one of the consistent states). A transition can be defined as a set of triples (r, t, t') where r is the name of a relation, t is a tuple from the current state, and t' is a tuple from the proposed state. t would be empty for an inserted tuple, t' would be empty for a deleted tuple, and neither would be empty for tuples corresponding in an update. From that set of transitions, only those that satisfy all transition constraints are /possible transitions/. The problem is that more than one transition can result in the same /possible state/ but that not all of those are /possible transitions/.

For instance, consider the following states for a relation describing people's marital status, and a transition constraint that says: Single people can't become Divorced:

Current                      Proposed
Jane Jones Married    Jane Jones Married
Jane Smith Single       Jane Smith Divorced

Should the proposed state be rejected? Or did Jane Jones get Divorced becoming Jane Smith at the same time that Jane Smith married Bob Jones? It is impossible to tell: not enough information has been provided.

Since a transition that violates a transition constraint can result in the same /possible state/ as a transition that doesn't, the notions of relational assignment and multiple assignment are broken: an update must be submitted as a transition or something equivalent, not just as sets of relation values, otherwise transition constraints cannot always be enforced. So, should Relation Variables be discarded in favor of Relation Schemata? Received on Sun Aug 20 2006 - 13:46:13 CDT