A monotonic extension for Horn-clauses and its significance in datalog's renaissance

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 fix-point 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 once negated goals are also allowed. Finally, the generalization of techniques such as seminaive fixpoint and magic sets, make possible the efficient implementation of Datalog^FS, i.e., Datalog with 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 Datalog^FS and a powerful Datalog^FS system is now being developed at UCLA.