Mario Alviano, Javier Romero Davila, Torsten H. Schaub

• Declarative languages for knowledge representation and reasoning provide constructs to define preference relations over the set of possible interpretations, so that preferred models represent optimal solutions of the encoded problem. We introduce the notion of approximation for replacing preference relations with stronger preference relations, that is, relations comparing more pairs of interpretations. Our aim is to accelerate the computation of a non-empty subset of the optimal solutions by means of highly specialized algorithms. We implement our approach in Answer Set Programming (ASP), where problems involving quantitative and qualitative preference relations can be addressed by ASPRIN, implementing a generic optimization algorithm. Unlike this, chains of approximations allow us to reduce several preference relations to the preference relations associated with ASP’s native weak constraints and heuristic directives. In this way, ASPRIN can now take advantage of several highly optimized algorithms implemented by ASP solvers forDeclarative languages for knowledge representation and reasoning provide constructs to define preference relations over the set of possible interpretations, so that preferred models represent optimal solutions of the encoded problem. We introduce the notion of approximation for replacing preference relations with stronger preference relations, that is, relations comparing more pairs of interpretations. Our aim is to accelerate the computation of a non-empty subset of the optimal solutions by means of highly specialized algorithms. We implement our approach in Answer Set Programming (ASP), where problems involving quantitative and qualitative preference relations can be addressed by ASPRIN, implementing a generic optimization algorithm. Unlike this, chains of approximations allow us to reduce several preference relations to the preference relations associated with ASP’s native weak constraints and heuristic directives. In this way, ASPRIN can now take advantage of several highly optimized algorithms implemented by ASP solvers for computing optimal solutions…