Foundations of Semantic Subsumption in Deductive Databases

Gerhard Köstler

Foundations of Semantic Subsumption in Deductive Databases

Dissertation, University of Augsburg.
1st Examiner: Prof. Dr. W. Kießling
2nd Examiner: Prof. Dr. B. Möller
erschienen 07/1995


Deductive databases improve the expressive power of conventional database systems by coupling the logic programming paradigm with relational databases. The increase of the expressive power, however, implies the integration of high-level mechanisms to specify semantic knowledge controlling the deduction process.

This thesis examines the theoretical foundations of user-supplied semantic subsumption. Semantic subsumption can be characterized as logic programming with declarative deletion and introduces a restricted but efficient form of non-monotonic reasoning into deductive databases. The user specifies preferences on the program results at a meta level, expressing that some results of a Datalog program are more desirable than other ones. By a new fixpoint iteration scheme, called fixpoint iteration with subsumption, subsumed tuples are discarded from the program evaluation on the fly. The result of this evaluation is a subsumption fixpoint that contains only the best facts of the conventional program fixpoint (w.r.t. the user-supplied semantic subsumption). It is shown that the subsumption fixpoint can be computed efficiently by a differential iteration scheme called delta-iteration with subsumption.

Two classes of Datalog programs are examined in more detail: programs that are monotonic w.r.t. semantic subsumption as a whole and programs that are stratified w.r.t. the subsumption.

This thesis also describes the Datalog_S database language that permits a unified syntactic representation of Datalog programs and the user-supplied subsumption orderings. It is shown that the monotonicity of a wide class of Datalog_S programs is decidable at compile time and that the magic-set optimization can be applied to this class.

The feasibility of semantic subsumption in deductive databases and the practical applicability of this programming methodology are exemplified by applications from various areas. It is especially demonstrated that many aggregations can be expressed by this paradigm giving them intuitive semantics.