  The input language of the answer set solver clingo is based on the definition
of a stable model proposed by Paolo Ferraris. The semantics of the ASP-Core
language, developed by the ASP Standardization Working Group, uses the approach
to stable models due to Wolfgang Faber, Nicola Leone, and Gerald Pfeifer. The
two languages are based on different versions of the stable model semantics,
and the ASP-Core document requires, "for the sake of an uncontroversial
semantics," that programs avoid the use of recursion through aggregates. In
this paper we prove that the absence of recursion through aggregates does
indeed guarantee the equivalence between the two versions of the stable model
semantics, and show how that requirement can be relaxed without violating the
equivalence property. The paper is under consideration for publication in
Theory and Practice of Logic Programming.
