We constrain the antecedent sets such that only trees that correspond to the correct clustering can be built.
letÃ j denote the set of correct antecedents for a mention m j , or Aj = {m0} if mj has no correct antecedent {ai | COREF(ai, mj), ai ∈ Aj} otherwise that is, if mention m j is non-referential or the first mention of its cluster,Ã j contains only the document root.