Language is not logical. Logic uses language to express its concepts, but language itself is not logical.
Many folks insist on following the fallacy that a double negative makes a positive. However, while that phenomenon happens among speakers of English more often than it should, the truth is that only in mathematics does a double negative result in a positive. In speech, it serves only for emphasis. Moreover, in some languages -- French and Spanish, for example -- double negatives are required. "Ne ... pas" in French, or "No hay nada" (There is nothing) in Spanish. The English equivalent, "There ain't nothing," is frowned on not because of its mathematical contradiction, but because it's considered a "lower class" expression.
Otherwise, some may use the expression, "I am not unhappy," but that doesn't necessarily mean the speaker is in fact happy. Nor does it connote sadness. It could at best be construed as neutral, or accepting of a situation.
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