We first skim some background problems associated to model theory. Then, we develop the notion of sustained models.
Sustained models coincide with partial stable models.
On the basis of sustained models, we develop a semantics of database integrity. Conventional semantics are two-valued and hence do not explicitly consider states that neither satisfy nor violate integrity. In a sense, they are biased, by either paying more attention to satisfaction than to violation, or vice-versa, independent of any application. Our semantics is three-valued and not biased. Four cases of integrity satisfaction and violation are identified.