Answer set programming (ASP) is a particularly useful approach for nonmonotonic reasoning in knowledge representation. In order to handle quantitative and qualitative reasoning, a number of different extensions of ASP have been invented, such as quantitative extensions LP^{MLN} and P-log, and qualitative extensions LPOD, and CR-Prolog2.

Although each of these formalisms introduced some new and unique concepts, we present reductions of each of these languages into the standard ASP language, which not only gives us an alternative insight into the semantics of these extensions in terms of the standard ASP language, but also shows that the standard ASP is capable of representing quantitative uncertainty and qualitative uncertainty. What's more, our translations yield a way to tune the semantics of LPOD and CR-Prolog2. Since the semantics of each formalism is represented in ASP rules, we can modify their semantics by modifying the corresponding ASP rules.

For future work, we plan to create a new formalism that is capable of representing quantitative and qualitative uncertainty at the same time. Since LPOD rules are simple and informative, we will first try to include quantitative preference into LPOD by adding the concept of weights, and tune the semantics of LPOD by modifying the translated standard ASP rules.