Parameterized Splitting: A Simple Modification-Based Approach

In an important and much cited paper Vladimir Lifschitz and Hudson Turner have shown how, under certain conditions, logic programs under answer set semantics can be split into two disjoint parts, a “bottom” part and a “top” part. The bottom part can be evaluated independently of the top part. Results of the evaluation, i.e., answer sets of the bottom part, are then used to simplify the top part. To obtain answer sets of the original program one simply has to combine an answer set of the simplified top part with the answer set which was used to simplify this part. Similar splitting results were later proven for other nonmonotonic formalisms and also Dung style argumentation frameworks. In this paper we show how the conditions under which splitting is possible can be relaxed. The main idea is to modify also the bottom part before the evaluation takes place. Additional atoms are used to encode conditions on answer sets of the top part that need to be fulfilled. This way we can split in cases where proper splitting is not possible. We demonstrate this idea for argumentation frameworks and logic programs.