On the evaluation of recursion in (deductive) database systems by efficient differential fixpoint iteration

Based on matured database technology the paper provides new insights into efficient ways to evaluate recursive deduction rules. We show how the forward-chaining approach to deduction can flexibly be married with goal-directed aspects of best/easiest-first strategies. From the natural fixpoint semantics of recursion we develop generally applicable differential iteration schemes that efficiently compute the fixpoint. Surprisingly the well-known Warshall-algorithm gets disclosed as a descendant of this class of algorithms. Performance measurements suggest the former as well as systolic Δ-algorithms with linear fixpoint equation as candidates for incorporating a transitive closure operator in databases. As a next important step towards integration of database technology and logic programming we suggest to profit from the standard features of concurrency control and transaction management by effectively using them for the synchronization of parallel deductions.