  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.
