Complexity of 2-ASP(Q) Programs with Weak Constraints

A new arXiv paper (2605.27338) investigates 2-ASP(Q)^w, a fragment of ASP(Q) that extends Answer Set Programming with quantifiers and weak constraints. This class can express optimization problems up to Delta_3^P. The study provides a complete complexity characterization for main computational tasks, including previously unaddressed cases. On the practical side, the authors introduce novel strategies for computing optimal quantified answer sets in the Casper system using a Counterexample-Guided Abstraction Refinement (CEGAR) technique. Experimental evaluation on hard benchmarks shows effectiveness.