Splitting a Logic Program

In many cases a logic program can be divided into two parts so that one of them the bottom part does not refer to the predicates de ned in the top part The bottom rules can be used then for the evaluation of the predicates that they de ne and the computed values can be used to sim plify the top de nitions We discuss this idea of splitting a program in the context of the answer set semantics The main theorem shows how com puting the answer sets for a program can be simpli ed when the program is split into parts The programs covered by the theorem may use both nega tion as failure and classical negation and their rules may have disjunctive heads The usefulness of the concept of splitting for the investigation of answer sets is illustrated by several applications First we show that a con servative extension theorem by Gelfond and Przymusinska and a theorem on the closed world assumption by Gelfond and Lifschitz are easy consequences of the splitting theorem Second locally strati ed programs are shown to have a simple characterization in terms of splitting The existence and uniqueness of an answer set for such a program can be easily derived from this characterization Third we relate the idea of splitting to the notion of order consistency