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Abstract: Natural languages may contain words for conjunction, disjunction, and negated disjunction (and, or, and nor), but no word for negated conjunction (there is no "nand"). The explanation of this observation calls for the study of semantic universals. We introduce a system of rules for context update, in which assertion and denial are different types of update. We give rules for how assertion and denial of a sentence interact with the main logical operator in the sentence. We show that only conjunction, disjunction, and negated disjunction are definabile by the update rules. (If time permits, we will give the analogous explanation for the quantifiers.) The upshot is this: there are only a few ways to update the context by asserting or denying a sentence, and the only logical operators that can be expressed in the lexicon of a natural language are those whose meaning can be characterized by update rules.