Integrity checking in deductive databases : an exposition

Relational systems are extended in several ways. We consider extensions with rules and integrity constraints to so-called deductive databases. There are several problems in handling these rules and constraints. One problem is to check, in an efficient way, the integrity of a deductive database when an insertion or deletion is made. There exist several integrity maintenance methods. All these methods avoid a full check of the integrity constraints in order to keep them efficient. Therefore, the database is supposed to be consistent before a transaction is made. We take a look at one of the most efficient methods proposed by Bry, Decker and Manthey. They determine from the updates, rules and constraints and without accessing the fact base the so called update constraints which have to be checked in the updated database. These constraints are instantiations of the constraints that are relevant to the update. Although this method is more efficient than other ones, it is still susceptible of improvement. Our goal in this article was to show by some well-chosen examples that in some regards the proposed method is still very inefficient. By these examples it becomes clear where the inefficiencies come from; they were not mentioned in the article of Bry, Manthey and Decker. INTEGRITY CHECKING IN DEDUCTIVE DATABASES; AN EXPOSITION §O INTRODUcnON:REIATIONAL DATAB~ RULES, IN1EGRITY CONSTRAINTS, DEDUCTIVE DATABASES, INTEGRITY ENFORCEMENT Most commercially available database systems are based on the relational database model. In this relational model facts are stored in tables. Tables contain explicit data. A relational database management system (RDBMS) takes care of fast retrieval of information from a database. Besides explicit information tables also contain implicit information. In conventional relational systems the derivation of implicit from explicit information is left to the user. There is a growing need to delegate such derivations to the system. We can do this by extending a relational database with deductive rules. In that case, we speak of a deductive database. On the basis of the next example, consisting of a PARENT-table and a GRANDFATHER-table, we shall illustrate the extensions mentioned above of a conventional RDBMS.l) PARENT-table I NAME II AGE II FATHER II MOTHER I ALEX 15 CARL JANE JANE ? PETER LUCY JACOB 38 PETER LUCY CARL 41 LEON ANNE LEON ? JACK ? GRANDFATHER-table I NAME II GRANDFATHER I ALEX LEON ALEX PETER LEON JACK Besides storing facts, there is a great need to store general knowledge about the universe of discourse in the database. Both rules and integrity constraints represent such knowledge.