A Model-Theoretic Approach to A-not-A Questions in Chinese

Jianxin Wu

(University of Maryland)

The A-not-A question exhibits some intriguing, but hitherto unnoticed, properties. Unlike the yes/no question which can be formed out of any declarative sentence, the A-not-A question has a number of restrictions: it is not compatible with (a) a quantified NP in subject position, (b) a modal adverb, (c) a focus particle, as shown by examples (1, 2, 3). The paper attempts to provide a model-theoretic account for this array of facts.

Following Higginbotham (1993) that a question is a nonempty and exhaustive partition of the possible states of affairs into mutually exclusive but jointly exhaustive cells, I propose that an A-not-A question partitions the possible states into two mutally exclusive but jointly exhaustive cells: the contradictory, under the assumption that the negative element in an A-not-A question, one assigns a choice function to it to pick one of the cells as true and dismiss the other as false. This assignment of a choice function does not cause any problem for the A-not-A questions having referential NP's, such as names, demonstratives and pronouns, in subject position, because mapping a single entity onto the A and not-A sets yields exactly two mutually exclusive but jointly exhaustive cells, as required.

The interpretive problem posed by ta quantified expression in subject position of an A-not-A question is that a quantifier denotes a set of sets, and as such, the partition might yield more than two cells. Given a model having two memebers in it, three cells may obtain as a result : (a) both members belong to the A set (positive cell), (b) both belong to the not-A set (negative cell); (c) one belongs to the A set, the other to the not-A set (mixed cell). In the (c) case where the set memebers are split, no true answer can be given when a subject is a universal quantifier, or a negative existential quantifier, because neither the affirmative answer nor its negative one would be true. The problem is reversed when a subject is an existential quantifier : both the affirmative and negative answers would be true (tautology). Thus, they, in one way or another, block the assignment of a choice function.

Adopting possible worlds semantics, Itake an adverb of necessity and of possibility to have a universal and an existential quantification over relevant possible worlds, respectively. So, the interpretive problem with the modalized A-not-A question is explained is explained in an analogous fashion. Given a modelhaving tworelevant worlds for evaluation, three cells may results : a proposition can be true in (a) both worlds, (b) either one of the worlds, (c) neither. If situation (b) happens to hold, then neither the affirmative answer nor its negative one would be true for an A-not-A question with an adverb of neccsity; conversely, both the affirmative and negative answers would be true for an A-not-A question with an adverb of possibility.

Following Rooth (1992), I treat a focused expression as introducing a set of alternatives. To see where the problem lies for the focused A-not-A question, I first analyze a focused yes/not question like hiyou Zhanggsan Pao ma? (only Zhangsan runs ?) and its negative counterpart hiyou Zhangsan bu pao ma ?(only Zhangsan does not run ?) as follows : The former is a partition of the possible states into at least two cells, with Zhangsan being always a member of the runner set in any cell yielded; the same is true for the latter, but with Zhangsan being always a member of the non-runner set. What it means is : thge proposition Zhangsan pao (Zhangsan runs) is presupposed in the former and its negative counterpart in the latter. The problem with the corresponding focused A-not-A question is that it requires these two contradictory presuppositions to be simultaneously true, which is logically impossible.

An apparent counterexample to the proposal made here is : forming an "A-not-A question" by reduplicating the copula shi, instead of a main verb, will render those otherwise unacceptable sentences acceptable, as shown by examples (4, 5, 6). I argue that the negative element in this special type of 'A-not-A questions" is sentential, therefore scoping over a quantified expression, which is responsible for not causing the interpretive problem under discussion when more than two cells are generated. Given the model cited earlier, the affirmative answer to question (4a) covers the positive cell; the negative answer covers the mixed cell. These two cells are mutually exclusive in that if one is false the other must be true. The requirement of joint exhaustiveness can be met by extending the negative answer to cover the negative cell via implicature cancellation. The analysis of the similar sort is applicable for the rest of good sentences (4, 5, 6)

EXAMPLES

(1) a. ? meigeren dou pao bu pao ?

everyone all run-not-run

does everyone run or not run ?

b.*you ren pao bu pao ?

someone run-not-run

Does someone run or not run ?

c. * mei you ren pao bu pao ?

no body run-not-run

Does nobody run or not run ?

(2) *Zhangsan yiding/keneng pao by pao ?

Zhangsan necessarily/possibly run-not-run ?

Zhangsan will necessarily/possibly run or not run ?

(3) *Zhi you Zhangsan qu bu qu xuexiao ?

only have Zhangsan go-not-go to school

Lit. Does only Zhangsan go to school or not ?

(4) a. shi-bu-shi meigeren dou pao ?

be-not-be everyone all run ?

Is it the case or not that everyone runs ?

b. shi-bu-shi you ren pao ?

be-not-be someone run/not run ?

Is it the case or not that someone runs ?

c. shi-bu-shi mei ren pao ?

be-not-be no one run

Is it the case or not that someone runs ?

(5) Zhangsan shi-bu-shi yiding/keneng pao ?

Zhangsan be-not-be necessarily/possibly runs ?

Is it true that Zhangsan necessarily/possibly runs ?

(6) shi-bu-shi zhi you Zhangsan ?

be-not-be only have Zhangsan run

Is it true that only Zhangsan run ?