  The stable model semantics had been recently generalized to non-Herbrand
structures by several works, which provides a unified framework and solid
logical foundations for answer set programming. This paper focuses on the
expressiveness of normal and disjunctive programs under the general stable
model semantics. A translation from disjunctive programs to normal programs is
proposed for infinite structures. Over finite structures, some disjunctive
programs are proved to be intranslatable to normal programs if the arities of
auxiliary predicates and functions are bounded in a certain way. The
equivalence of the expressiveness of normal programs and disjunctive programs
over arbitrary structures is also shown to coincide with that over finite
structures, and coincide with whether NP is closed under complement. Moreover,
to capture the exact expressiveness, some intertranslatability results between
logic program classes and fragments of second-order logic are obtained.
