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To enhance the expressive power and the declarative ability of a rndeductive database, various CWA (Closed World Assumption) formalizations inrncluding the naive CWA, the generalized CWA and the careful CWA are extended to rnmulti-valued logics. The basic idea is to embed logic formulas into some polynomial rnring. The extensions can be applied in a uniform manner to any finitely multi-valued rnlogics. Therefore they are also of computational significance.