Abstract
We propose a class of programs, called modularly stratified programs that have several attractive properties. Modular stratification generalizes stratification and local stratification, while allowing programs that are not expressible by stratified programs. For modularly stratified programs the well-founded semantics coincides with the stable model semantics, and makes every ground literal true or false. Modularly stratified programs are all weakly stratified, but the converse is false. Unlike some weakly stratified programs, modularly stratified programs can be evaluated in a subgoal-at-a-time fashion. We demonstrate a technique for rewriting a modularly stratified program for bottom-up evaluation and extend this rewriting to include magic-set techniques. The rewritten program, when evaluated bottom-up, gives the same answers as the well-founded semantics. We discuss extending modular stratification to other operators such as set-grouping and aggregation that have traditionally been stratified to prevent semantic difficulties.
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