Validating database updates

摘要

Individual facts in the real world are represented by tuples in database relations (instances), while universal (time-independent) facts are treated as semantic constraints regarding database relation schemata. One important role of these semantic constraints is their use as integrity constraints that must not be violated by update operations. Among these, static constraints are represented by assertions, which are extended relational calculi in which every tuple variable is bound over a relation, and become true in a consistent database. When an update has been made on a consistent database, it is necessary to ascertain if the updated database is still consistent. It can be done by evaluating all the assertions in the updated database, but this is very time consuming. If a given assertion is in one of some classes, it is possible to devise an efficient validation procedure, which before the update is actually applied determines if the update violates the given assertion. In many cases a simplified form can be found, by examining whose value the properness of the given update is determined. The existence of such an efficient procedure and simplified form depends on what class the given assertion belongs, and also on what type of the update is to be made on what relation. This paper presents a method of finding such a procedure and simplified form using several simple syntactical transformation rules regarding extended relational calculi. This method is based on several basic properties in prepositional logic and many-sorted predicate logic.