On Answer Set Optimization Program

An answer set optimization (ASO) program is a pair (Pgen, Ppref). The generating program Pgen produces answer sets representing possible solutions. The preference program Ppref expresses user preferences. It induces a preference relation on the answer sets of Pgen based on the degree to which rules are satisfied. We proof that Brewka's ASO Program induces irrelevance problem. And we find out the reason for it. In order to eliminate irrelevance problem, we propose the new conceptε‐equivalence to redefine satisfaction degree of a preference rule in an answer set. Correspondingly, we define four types of preference relation between two answer sets. And we build a hierarchy structure on the answer sets to find out a new way to obtain the optimal model. With the help of new definition of satisfaction degree and new techniques to obtain optimal model, we demonstrate that irrelevance problem is eliminated.