using the splitting set theorem of [ ]{}, if a top part of a split program is an [$\rm ASP^{\rm sc}$]{} program, then any answer set of the bottom part will give rise to at least one answer set of the full program—so for determining answer set existence, there would be no need to evaluate the top part.

On a more abstract level, one of the main criticisms of [$\rm ASP$]{} (being voiced especially in database theory) is that there are programs which do not admit any answer set (traditionally this has been considered a more serious problem than the related nondeterminism in the form of multiple answer sets, cf. ). From this perspective, programs which guarantee coherence (existence of an answer set) have been of interest for quite some time. In particular, if one considers a fixed program and a variable “database,” one arrives naturally at the class [$\rm ASP^{\rm sc}$]{} when requiring existence of an answer set. This also indicates that deciding super-coherence of programs is related to some problems from the area of equivalence checking in ASP [@Eiter05; @Eiter07; @Oetsch07b]. For instance, when deciding whether, for a given arbitrary program $P$, there is a uniformly equivalent definite 