2-ASP(Q)^w can express optimization problems up to Delta_3^P complexity, and the CEGAR-based approach in Casper makes solving these problems practical despite their theoretical hardness.
This paper extends Answer Set Programming with quantifiers and weak constraints, creating a system called 2-ASP(Q)^w that can solve complex optimization problems. The authors prove how hard these problems are to solve theoretically, then build practical software using a refinement technique that gradually improves solutions by learning from counterexamples.