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