Yet Another Proof of the Strong Equivalence Between Propositional Theories and Logic Programs

Recently, the stable model semantics was extended to a more general syntax beyond the rule form. Cabalar and Ferraris, as well as Cabalar, Pearce, and Valverde, showed that any propositional theory under the stable model semantics can be turned into a logic program. In this note, we present yet another proof of this result. Unlike the other approaches that are based on the logic of hereand-there, our proof uses familiar properties of classical logic, and provides a different explanation of the reduction in terms of classical logic. Based on this idea, we present a prototype implementation of propositional theories under the stable model semantics by calling the answer set solver DLV. Using the same reduction idea, we also note that every first-order formula under the stable model semantics is strongly equivalent to a prenex normal form whose matrix has the form of a logic program.