Generalizing Level Ranking Constraints for Monotone and Convex Aggregates

In answer set programming (ASP), sets capture solutions to search problems of interest and thus the efficient computation is utmost importance. One viable implementation strategy provided by translation-based ASP where logic programs are translated into other KR formalisms such as Boolean satisfiability (SAT), SAT modulo theories (SMT), mixed-integer (MIP). Consequently, existing solvers can be harnessed for sets. Many translations rely on program completion level rankings minimality default negation properly. this work, we take ranking constraints reconsideration, aiming at their generalizations cover aggregate-based extensions in more systematic way. By applying a number transformations, rewritten general form that preserves structure monotone convex aggregates offers uniform basis incorporation ASP. The results open up new possibilities translators solver pipelines practice.