Properties of Answer Set Programming with Convex Generalized Atoms
  In recent years, Answer Set Programming (ASP), logic programming under the
stable model or answer set semantics, has seen several extensions by
generalizing the notion of an atom in these programs: be it aggregate atoms,
HEX atoms, generalized quantifiers, or abstract constraints, the idea is to
have more complicated satisfaction patterns in the lattice of Herbrand
interpretations than traditional, simple atoms. In this paper we refer to any
of these constructs as generalized atoms. Several semantics with differing
characteristics have been proposed for these extensions, rendering the big
picture somewhat blurry. In this paper, we analyze the class of programs that
have convex generalized atoms (originally proposed by Liu and Truszczynski in
[10]) in rule bodies and show that for this class many of the proposed
semantics coincide. This is an interesting result, since recently it has been
shown that this class is the precise complexity boundary for the FLP semantics.
We investigate whether similar results also hold for other semantics, and
discuss the implications of our findings.
