Order-consistent programs are cautiously monotonic

Some normal logic programs under the answer set (stable model) semantics lack the appealing property of "cautious monotonicity." That is, augmenting a program with one of its consequences may cause it to lose another of its consequences. The syntactic condition of "order-consistency" was shown by Fages to guarantee existence of an answer set. This note establishes that order-consistent programs are not only consistent, but cautiously monotonic. From this it follows that they are also "cumulative." That is, augmenting an order-consistent with some of its consequences does not alter its consequences. In fact, as we show, its answer sets remain unchanged.