Is Language Logical? A Study Of Disjunction Scope Parameters.pdf

The meaning of English sentences involving negation and disjunction, such as "I don't like apples or pears," can be paraphrased as "I dislike both apples and pears." This is because negation and disjunction in English follow the rules of formal logic, specifically De Morgan's Law, which states that ¬(P ∨ Q) ⇔ (¬P) ∧ (¬Q). This is also true for French, as exemplified in the sentence "Je n'aime pas les pommes ou les poires," which means "I don't like apples or pears."

However, languages like Mandarin and Japanese present a challenge to this view, as they appear to assign a disjunctive meaning to negative sentences involving a disjunction, rather than the conjunctive entailment. One plausible way to analyze this is to argue that the disjunctor in languages like Japanese is a positive polarity item, which must take wider scope than the sentential negation. This would mean that the meaning of a sentence like "Butasan-wa ninjin ka piiman-wo tabe-nakat-ta" would be equivalent to (¬P) ∨ (¬Q), rather than (¬P) ∧ (¬Q).

Research has shown that children under the age of 6 fail to assign a disjunctive reading to the disjunctor in negative sentences, and instead apply the natural language default, i.e. De Morgan's Law. However, as children get older, they begin to realize that the disjunctor is a positive polarity item, and start to assign the disjunctive reading.

A study was conducted with 55 French native speaker monolingual learners, aged 4.3-6.2, to test the hypothesis that focus allows for a disambiguation of negative sentences containing disjunctions. The results showed that children in the control group assigned an adultlike conjunctive entailment reading 97% of the time, while children in the test group showed a significant increase in disjunctive readings when focus was introduced. The results also showed an intragroup age effect, with older children being more likely to adopt a disjunctive reading when focus was introduced.

The study's results support the hypothesis that focus allows for a disambiguation of negative sentences containing disjunctions, and explain why formal logic rules can be violated in language. The study also suggests that the participants were able to give a reading violating the rules of logic presumably the first time they had ever been given the option to, and very likely while they had never heard such a reading from adult-language.