FS-rules provide a powerful monotonic extension for Horn clauses that supports monotonic aggregates in recursion by reasoning on the multiplicity of occurrences satisfying existential goals. The least fixpoint semantics, and its equivalent least model semantics, hold for logic programs with FS-rules; moreover, generalized notions of stratification and stable models are easily derived when negated goals are allowed. Finally, the generalization of techniques such as seminaive fixpoint and magic sets, make possible the efficient implementation of DatalogFS, i.e., Datalog with rules with Frequency Support (FS-rules) and stratified negation. A large number of applications that could not be supported efficiently, or could not be expressed at all in stratified Datalog can now be easily expressed and efficiently supported in DatalogFS and a powerful DatalogFS system is now being developed at UCLA.

This paper describes the [Lscr ][Dscr ][Lscr ]++ system and the research advances that have enabled its design and development. We begin by discussing the new nonmonotonic and nondeterministic constructs that extend the functionality of the [Lscr ][Dscr ][Lscr ]++ language, while preserving its model-theoretic and fixpoint semantics. Then, we describe the execution model and the open architecture designed to support these new constructs and to facilitate the integration with existing DBMSs and applications. Finally, we describe the lessons learned by using [Lscr ][Dscr ][Lscr ]++ on various tested applications, such as middleware and datamining.