We generalize a theorem by François Fages that describes the relationship between the completion semantics and the answer set semantics for logic programs with negotiation as failure. The study of this relationship is important in connection with the emergence of answer set programming. Whenever the two semantics are equivalent, answer sets can be computed by a satisfiability solver, and the use of answer set solvers such as SMODELS and DLV is unnecessary. A logic programming representation of the blocks world due to Ilkka Niemelä is discussed as an example.
Lierler, Yuliya; Erdem, Esta; and Lifschitz, Vladimir, "Fages' Theorem and Answer Set Programming" (2000). Computer Science Faculty Proceedings & Presentations. 34.