This paper investigates a consistent version cwaS Reiter’s closed world assumption cwa. It proves (cf. theorem 4.11) that for purely relational languages cwaS is ∀-complete with respect to minimal semantics, i.e. for every ∀-sentence φ and for every ∀-theory Σ, φ ∈ cwaS(Σ) iff Σ `min φ. Moreover, it relates cwaS to other known syntactic characterization of minimal semantics: Minker’s GCWA.