The Acquisition of Logical Connectives in Child Mandarin

Abstract

This study investigates 2–5-year-old Mandarin-speaking children’s interpretation of the disjunction word huozhe (‘or’) in two positions in ruguo (‘if’)-conditional statements, i.e., in the antecedent clause versus in the consequent clause. The findings from three experiments show that the meanings children assign to disjunction and to ruguo-conditionals conform closely to the meanings that are assigned to the corresponding logical connectives in classical logic. Experiment 1 demonstrates that children assign an inclusive-or interpretation to disjunction in both the antecedent clause and in the consequent clause of conditional statements, whereas adults assign an exclusive-or interpretation to disjunction when it appears in the consequent clause of conditional statements. The findings of Experiment 2 provide evidence of children’s adherence to a putative semantic universal—that disjunction licenses a conjunctive entailment in the antecedent clause of conditional statements, but not in the consequent clause. It is shown in Experiment 3, moreover, that children’s knowledge doesn’t stem from their mistaking disjunction as conjunction. Because the logical meanings of connectives emerge early in the course of language acquisition, and without decisive evidence from the adult input, these findings suggest that children draw upon an innate logical vocabulary at the initial stages of language acquisition.

Notes

1. ¹Negative statements of the form ¬ (A ∨ B) offers another way to distinguish between inclusive-or and exclusive-or. As Jennings (2001) points out, if disjunction is exclusive-or, then statement (1) will be true if Lydia brought both cake and ice cream to the party. However, to our knowledge, no evidence has been reported in the literature demonstrating that children or adults make such critical judgments that are expected if disjunction is exclusive-or.

2. ²There are cases where conditional statements are not strictly downward entailing (see Heim 1984; Kadmon & Landman 1993; von Fintel 1999). We will set aside these cases for the purposes of the present article.

3. ³The truth conditions of disjunction in the consequent clause are “disjunctive.” To see why, notice that when disjunction appears in the consequent clause, as in If A then (B or C), it is logically equivalent to Not-A or (B or C). This, in turn, is logically equivalent to (Not-A or B) or (Not-A or C). Hence, the following “disjunctive” inference is valid when disjunction appears in the consequent clause: If A then (B or C)⇒ If A then B or If A then C.

4. ⁴For further discussion about downward entailment as a “core” universal property that raises special challenges for the usage-based account, see e.g., Crain & Pietroski 2002; Crain, Gualmini & Pietroski 2005; Crain, Thornton & Khlentzos 2009; Crain, Khlentzos & Thornton 2010. See also Su, Zhou & Crain 2012 for a view from Mandarin Chinese.

5. ⁵This one of de Morgan’s laws applies only if negation takes scope over disjunction. When disjunction appears in simple negative sentences, languages are partitioned into two groups (Crain & Thornton 2013; Goro & Akiba 2004; Notley et al. 2012; Szabolcsi 2002). In languages like Hungarian, Japanese, Chinese, Russian, Serbo-Croatian, Slovak, and Polish, disjunction takes scope over local negation. In languages like English, German, French, Greek, Romanian, Bulgarian, and Korean, negation takes scope over disjunction.

6. ⁶It is well documented that when required to judge a conditional statement with a false antecedent (which is logically true, despite the truth value of the consequent), subjects often gave a negative response of “false,” or replied with “can’t tell” when this kind of indeterminate response option was available (e.g., Braine & Rumain 1983; O’Brien 1987). This is because when the antecedent is false, the subjects are required to judge the whole conditional sentence based on an assertion that is not relevant to the content of the consequent, which violates the Principle of Cooperation (Grice 1975, 1989; Jackson 1987; Noveck et al. 1991).

7. ⁷From the view of logic, a conditional is true when its antecedent is false (no matter whether the consequent is true or false). It follows that on the exclusive-or interpretation (which made the antecedent false), sentence (9) remained true in both the situations in which Mickey Mouse received a reward (which made the consequent true) and when he didn’t receive a reward (which made the consequent false). However, in our study, when the antecedent was false, almost all the 32 child subjects in the final sample (98% of the time) and the 28 adult subjects (97% of the time) decided not to reward the characters. There were 4 children who always decided to reward the characters following all of the puppet’s predictions, but their data were eliminated from the final analysis for two reasons. First, for the purpose of the present study, we need to distinguish between the subjects’ interpretations of inclusive-or versus exclusive-or based on their observable behaviors. It becomes ideal if the subjects could make a distinction in their judgments of the truth or falsity of the antecedent clause, by providing positive or negative responses. Second, we were not sure about the reasons behind children’s consistently affirmative replies (Crain & Thornton 1998).

8. ⁸Scalar implicatures become operational only when the listener knows that the speaker has the accurate knowledge of the information strength of an alternative set of scalar expressions being used in the conversational context, where the speaker is supposed to choose the most informative statement. In situations of uncertainty, e.g., when or appears in a prediction or a bet or other future events, the listener knows that the speaker does not have an accurate knowledge about the situations being described, and the speaker is not supposed to know the truth values of alternative expressions containing scalar terms like or and and. Consequently, the speaker is not supposed to compare their information strength or to select the most informative sentence. In this case, the speaker’s choice of or doesn’t implicate the denial of the alternative expression, i.e., ‘not both A and B.’ In this way, situations of uncertainty discourage the triggering of scalar implicatures and enable the interpretation of scalar terms like or to follow their basic meanings such as inclusive-or (Chierchia et al. 1998; Crain, Gualmini & Meroni 2000; see Horn 1972, 1989).

9. ⁹Of course, if children interpreted the disjunction word huozhe to mean the conjunction word he, then they would also be expected to accept the test sentences in the TT condition. This possibility is dealt with in Experiment 3.

10. ¹⁰We did not include the TF/FT condition in Session 2 because this would make the sentences infelicitous in the description mode. Specifically, the inference from A alone or B alone to a disjunctive statement (A or B) makes the sentence an instance of Weakening (a.k.a. Disjunction Introduction). It is well known that language users find instances of Weakening to be pragmatically odd when describing past events (Grice 1975; Horn 1989). For example, in a situation in which the elephant that jumped over the fence received an apple, it is pragmatically odd to use the description If the elephant jumped over the fence, then he got a pear or an apple. The pragmatic infelicity of Weakening is circumvented in situations of uncertainty, such as when describing future events in prediction mode (for further discussion, see Crain 2012; Crain & Khlentzos 2008, 2010). In this study, we tested the TF/FT condition in the antecedent clause in Session 1 and again in the consequent clause in Experiment 3; both were presented in prediction mode, thus making the TF/FT condition felicitous for testing.

11. ¹¹An additional precaution was taken to remove a possible order effect. For half of the test sentences, the sentences were false in virtue of the first disjunct, and for the other half, the test sentences were false because of the second disjunct.

12. ¹²A reviewer proposed an alternative account of the subjects’ rejection of test sentences like (11) If a pony moves a corn or a sausage, then he will get a gold coin, when disjunction appeared in the antecedent clause of ruguo-conditionals. Specifically, a conditional is falsified when the antecedent is true and the consequent is false. In our design, the antecedent clause was true across conditions in Experiment 2 to ensure that it was felicitous for the subjects to judge the truth value of the whole conditional statement (see Footnote 6). So, children could reject (11), for example, by noticing that the consequent was falsified when the two ponies that moved sausages didn’t receive gold coins. We cannot adjudicate between our account and the one proposed by the reviewer.

13. ¹³To remove possible order effect, one of the three test sentences with huozhe in the consequent clause was true in virtue of the first disjunct, and the other two test sentences were true because of the second disjunct.