I introduce a formal language called the language of informational independence (IL-language, for short) that extends an ordinary first-order language in a natural way. This language is interpreted in terms of semantical games of imperfect information. In this language, one can define two negations: (i) strong or dual negation, and (ii) weak or contradictory negation. The latter negation, unlike the former, can occur only sentence-initially. Then I argue that, to a certain extent, the two negations match the distinction existing in natural languages between sentential and constituent negation. As a corollary, I derive the fact that there are no mechanical rules for forming the contradictory negation of an English sentence.