Disjunction, negation and universal quantification in universal grammar

This present study investigated the interpretations that are assigned by English- and Mandarin-speaking adults to complex sentences with three logical expressions. For example, one of the test sentences in both languages contained the combination of negation, a universal quantifier and the word for disjunction. Other sentences replaced the universal quantifier (‘every’) by an existential quantifier (‘some’). In different conditions, the position of the disjunction word was varied in order to evaluate the logical equivalence between negative sentences with a universal quantifier and ones with an existential quantifier (e.g., ‘not every…or…’ versus ‘some…not…or…’). The findings confirmed to the expectation of classical logic in both languages. First, both English- and Mandarin-speaking adults were found to license one interpretation of the disjunction word in one position of the test sentences, but another interpretation when the disjunction word appeared in a different position. Second, the anticipated logical equivalences between negated universally quantified statements and negated existentially quantified statements were found in both languages. The cross-linguistic convergence between logic and language stands in contrast to previous research which observed cross-linguistic differences in the interpretation of disjunction in simple negative sentences.