Logic programs are equivalent (that is, have the sameanswer sets). Strong equivalence is convenient for the study ofequivalent transformations of logic programs: one can prove that alocal change is correct without considering the whole program.Lifschitz, Pearce and Valverde showed that Heyting's logic ofhere-and-there can be used to characterize strong equivalence forlogic programs with nested expressions (which subsume thebetter-known extended disjunctive programs). This note considers asimpler, more direct characterization of strong equivalence for suchprograms, and shows that it can also be applied without modificationto the weight constraint programs of Niemelä and Simons. Thus, thischaracterization of strong equivalence is convenient for the studyof equivalent transformations of logic programs written in the inputlanguages of answer set programming systems dlv and SMODELS. The noteconcludes with a brief discussion of results that can be used toautomate reasoning about strong equivalence, including a novelencoding that reduces the problem of deciding the strong equivalenceof a pair of weight constraint programs to that of deciding theinconsistency of a weight constraint program.

Some normal logic programs under the answer set (or 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 program with some of its consequences does not alter its consequences. In fact, as we show, its answer sets remain unchanged.