Translating Preferred Answer Set Programs to Propositional Logic

Abstract

We consider the problem of whether a given preferred answer set program can be reduced to a propositional formula. Research on this topic is of both theoretical and practical interests: on one hand, it will shed new insights to understand the expressive power of preferred answer set programs; on the other hand, it may also lead to efficient implementations for computing preferred answer sets of logic programs. In this paper, we focus on Brewka and Eiter's preferred answer set programs. We propose a translation from preferred answer set programs to propositional logic and show that there is one-to-one correspondence between the preferred answer sets of the program to the models of the resulting propositional theory. We then link this result to Brewka and Eiter's weakly preferred answer set semantics.