Abstract: To enhance the expressive power andthe declarative ability of a deductive database, various CWA (ClosedWorld Assumption)formalizations including the na?ve CWA, the generalized CWA and thecareful CWA are extended to multi-valued logics. The basic idea is toembed logic formulas into some polynomial ring. The extensions can beapplied in a uniform manner to any finitely multi-valued logics.Therefore they are also of computational significance.