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

Recently, the stable model semantics was extended to the syntax of arbitrary propositional formulas, which are beyond the traditional 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 here-and-there, our proof uses familiar properties of classical logic. Based on this idea, we present a prototype implementation for computing stable models of propositional theories using the answer set solver DLV. 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.