Extending the power of datalog recursion

Supporting aggregates in recursive logic rules represents a very important problem for Datalog. To solve this problem, we propose a simple extension, called Datalog^FS(Datalog extended with frequency support goals), that supports queries and reasoning about the number of distinct variable assignments satisfying given goals, or conjunctions of goals, in rules. This monotonic extension greatly enhances the power of Datalog, while preserving (i) its declarative semantics and (ii) its amenability to efficient implementation via differential fixpoint and other optimization techniques presented in the paper. Thus, Datalog^FSenables the efficient formulation of queries that could not be expressed efficiently or could not be expressed at all in Datalog with stratified negation and aggregates. In fact, using a generalized notion of multiplicity called frequency, we show that diffusion models and page rank computations can be easily expressed and efficiently implemented using Datalog^FS.