A cover analysis of the plural classifier in Hmong

.title[
# A cover analysis of the plural classifier in Hmong
]
.subtitle[
## Goethe University Frankfurt (SuB30)
]
.author[
### Quartz Colvin (they/them)
]
.institute[
### Rutgers University
]
.date[
### 2025-09-24
]

---

# Introduction

- In this presentation, I show that Hmong *cov* is a plural classifier that generates a set of subsets (a **cover**).

- Classifiers in White Hmong (Hmong-Mien) typically give rise to definite readings via a null ι determiner in the absence of an indefinite article.

---

# Introduction

### Research questions for broader project

1. What are the individual meanings of *ib*, *tus*, and *cov*?

- ***ib***: indefinite article
  
  - ***tus***: general singular classifier
  
  - ***cov***: general plural classifier 
  
--

2. How do the indefinite article *ib* and the classifiers *tus* and *cov* combine to give us the correct meanings for the possible DP configurations in Hmong?

**Investigating this made me realize that Hmong's plural classifier is really interesting...**

(So is the indefinite article, but that's not the focus for today!)
---

# Introduction

1. Introduction

2. Hmong background

3. Literature

4. Hmong data

5. Proposal

6. Discussion & Implications

7. Conclusion

---

# Hmong background

---

# Hmong background

### Morphosyntax

- strict SVO word order

- analytical morphology

- no case or grammatical gender distinction

---

# Hmong background

### Semantics

- no definite article

- bare classifier phrases are definite

- bare nouns are only grammatical as kinds

(1) **tsov** ntxaus ntxaus ntshai

(1) tiger intensifier REDUP fear

(1) *"Tigers are dangerous."*

---

# Hmong background

### Phonology

- monosyllabic CV words **(no consonant codas!)**

### Romanized Popular Alphabet (RPA)

- the final letter of the written word corresponds to a ***tone***!

- White Hmong has 7 tones:
  - high rising (***-b***) 
  - high falling (***-j***)
  - mid (***unmarked***)
  - low (***-s***)
  - mid-rising (***-v***)
  - low-falling creaky (***-m***)
  - high-falling breathy (***-g***)

---

West Hmongic branch

~4.5 million speakers

Diaspora communities in the US speak **White Hmong** and **Green Hmong** and are mainly from Laos, Thailand or Vietnam

---

# Hmong background

### The consultants

- All data and discussion are based on elicitation on Zoom with **Ying** (35) and in person with **Keng** (25), two (sibling!) White Hmong speakers who were raised in Wisconsin (WI).

- neither speaker can read or write Hmong, and education was in English

- **Keng:** White Hmong, English, high school German

- **Ying:** White Hmong, English, high school Japanese

- Keng was born in WI and Ying immigrated to the US from Laos at age 4

- One parent is Green Hmong heritage, but both parents speak White Hmong primarily

---

# Hmong data

---

# Hmong data

## Singular DPs

(1) Keng see CLF dog

(1) *"Keng sees the dog."*

(3) Keng pom **ib tus aub**

(1) Keng see INDEF CLF dog

(1) *"Keng sees a/some dog."* 
]

(3) ***ib tus aub*** can refer to any one of the dogs in the context 
]

---

# Hmong data

## Plural DPs

(1) Keng see CLF dog

(1) *"Keng sees (all) the dogs."*

(5) Keng pom **ib** **cov** **aub**

(1) Keng see INDEF CLF dog

(1) *"Keng sees (some of) the dogs."*
]

(5) ***ib cov aub*** can refer to any subgroup of the dogs in the context

]

---

# Literature

---

# Literature

## Hmong-specific

- there is minimal semantic work on Hmong and previous discussion of classifiers is brief, descriptive, and focused on classifier choice (Bisang 1993)

- some work on bare classifier phrases in Hmong being definite (Simpson 2008; Simpson 2011; Simpson et. al 2015)

- note that this is mainly syntactic work

- **that's about it!**

---

# Literature

## Mereology (Link 1983)

**Mereology:** the study of parthood

- The operator **⊕ ** allows us to put individuals together to form "collections" and their formal object is called a SUM

- a SUM is an **individual, not a set**
  
  - another word for a SUM is a fusion

Lattice structures are inherent in **mereological predicate logic**

- particularly, they are join-semilattices (*discussed on next slide*)

---

# Literature

## Mereology (Link 1983)

**Join-semilattice:** is a partially ordered set in which all pairs have a join

- the **join** of a subset *S* of a partially ordered set *P* is the **supremum** of *S* (*V S*)

- **supremum:** the smallest number that is greater than or equal to every element in the set
  
  - it *doesn't* need to be an element of the set
  
  - it always exists for a set that is bounded above and is unique when it exists

---

# Literature

## Mereology (linguistic example)

- this is an example of a mereological structure with three atomic entities (*m, l, and p*)

- we can see it's a join-semilattice!

- keep this mereological structure in mind

- *the details of certain types of lattices will be mostly irrelevant to understanding the rest of the talk*

]

- Coppock & Champollion (2023: 410)

]

---

# Proposal (White Hmong)

---

# Proposal

### The two DP structures with ***cov***...

---

# Proposal

- Recall bare N is type *e*

- We can say the lexical contribution of *cov* is to convert a type *e* bare noun (a kind) into a property *e,t* (Chierchia 1998) and generate a **cover**

- A **cover**  generates a set of subsets of entities that fit the noun’s descriptive content in the context

---

# Proposal

### Formal definition (Schwarzschild 1996)

- **Cov** is a set of subsets of A
  
  - Every member of A belongs to some set in **Cov**
  
  - ∅ is not in **Cov**
  
  - **Cov***(A) = ℘(A), without ∅
]

- \{\{c1 &oplus; c2 &oplus; c3\},

- {c1 &oplus; c2}, {c1 &oplus; c3}, {c2 &oplus; c3},

- \{c1\}, \{c2\}, \{c3\}\}
  
  - *cups = ℘(cup), without ∅*
]

the classifier *cov* and the concept being **cov** is a coincidence...

---

# Proposal

**Returning to Hmong,**

- *cov* generates a cover of things in the relevant situation context that are of the property *P*, where *P* corresponds to the NP

(8) [[*cov*]]*M,g* = λP.λx.x ∈ **Cov**(P)

- compare with the singular classifier *tus*, which doesn't generate a cover

(9) [[*tus*]]*M,g* = λP.λx.[P(x) ∧ AT(x)]

**Classifiers in Hmong**

- *cov* doesn’t operate over kinds and instead operates over properties

- there is an "up" operator (following Chierchia 1998) coupled with the *cov* denotation to show that *P* must be a property by the time *cov* combines with the noun, though this operator is not explicitly shown in my denotations

- now, at the ClfP level of the structures, we have a property type (*e,t*)

---

# Proposal

### *The* determiners: iota

- there are two relevant D options: ι, a **null determiner** which gives a definite reading, and *ib*, which gives a very non-specific indefinite reading.

- the following formulation of ι is what I use here (Jenks 2018)

(10) [[ι]] = λP : ∃!x[P(x)].ιx[P(x)]

---

# Proposal

### *A* determiner: *ib*

- the indefinite article *ib*, is primarily a choice function indefinite (Winter 1997) rather than simply an existential quantifier

(11) [[*ib*]]*M,g* = λP. *f**cf* (λy.P(y) = 1)

- the choice functional analysis for *ib* more clearly explains the fact that Hmong indefinite *ib cov* DPs have a non-specific meaning and they select a random subset from the cover generated by *cov*

- *ib* has a primary function of choosing a subset from the set of options in the context

- the DP structures are built via standard functional application, we see a micro-case of ***antipresupposition***

---

# Proposal

### Antipresupposition

Antipresupposition ***"imposes the condition that the interlocutors not take the truth of a certain proposition for granted"*** (Percus 2006)

Must be visible at the DP level since it takes the semantics of the determiner (iota or *ib*) into account

***ib cov aub*** vs *iota* ***cov aub***?

- In *ib cov aub*, the choice function does not select the largest entity; otherwise, the definite (null) ι would be the determiner chosen for the utterance instead of *ib*

This antipresupposition yields the non-singular and non-maximal entities as the pragmatically sound options when *ib cov aub* is uttered

---

# Proposal (contexts)

---

# Contexts

Instead of cups, which the mereology example in the literature review used, we'll use a context of three dogs: **Apollo, Copper** and **Mars**

(1) (a.) *tus aub* = A

(1) (b.) *ib tus aub* = A or M or C

- **(12a)** definite via iota
  
- **(12b)** nonspecific via choice function *ib*
]

]

---

# Contexts

(13) *AUB**C*: \{Apollo,Mars,Copper\}

(1) (a.) *cov aub* = AMC

(1) (b.) *ib cov aub* = AMC or AM or AC or CM or A or M or C

(1) (c.) *ib cov aub* = AM or AC or CM (**via antipresupposition!**)

- **(13a)** definite and maximal via iota determiner
  
- **(13b)** semantically, all entities are options 
  
- **(13c)** pragmatically, only the non-maximal and non-atomic entities are good options

---

# Discussion & Implications

---

# Discussion & Implications

- **First,** the only defining characteristic of a classifier in Hmong (and likely other Chinese-type languages) is to convert a kind into a property.

- I have not applied this analysis to any languages with optional classifiers, so I'm unsure about how much this can extend to those languages.

- **Second,** we expect plural classifiers in any language to have this cover property, *so long as* the classifier is the sole morphological contributor to the plurality of the noun phrase.

- Mandarin? Maybe?

- **Third,** this may be able to extend to other languages with interactions between plurality and (in)definiteness

- Persian object DPs, for example!

---

# Discussion & Implications: Mandarin

## What about Mandarin?

- This is an interesting prediction for **Mandarin**, which has also been said to have a plural classifier ***xie*** (Wu 2019).

- It’s not clear without more thorough investigation whether indefinite ***xie*** phrases are compatible with this Hmong analysis because we would first need to establish:

- that the word for 'one’ ***yi*** is a choice function indefinite 
  
  - that ***xie*** is a plural classifier

---

# Discussion & Implications: Persian

## What about Persian DOM? (Jasbi 2016)

Plural marking, (in)definiteness and (accusative) case interactions

- not a classifier language, at least in the same way that HMong or Chinese are, so this could be a new way to look at the **cover** concept in natural language

- certain configurations have the same **maximal** versus **nonmaximal** readings that Hmong conveyed with the choice function indefinite article and **cover** classifier!

**Two indefinite morphemes**

*ye* = indefinite determiner

*-i* = indefinite suffix

---

# Discussion & Implications: Persian DOM

(1) *"book"* or *"books"*

(15) ketāb-o

(1) book-ACC

(1) *"the book"* (unique; atomic)

(16) ye ketāb

(1) one book

(1) *"a book"* (~~specific~~, sg. indef.)
]

(17) ye ketāb-o

(1) one book-ACC

(1) *"a book"* (specific, sg. indef.)

(18) ketāb-ā-ro

(1) book-PL-ACC

(1) *"the books"* (maximal)

(19) ye ketāb-ā-i

(1) one book-PL-INDEF

(1) *"some books"* (~~maximal~~)
]

---

# Discussion & Implications: Persian

(1) one book

(1) *"a book"* (~~specific~~,sg.indef.)

(21) ketāb-**ā**-ro

(1) book-PL-ACC

(1) *"the books"* (maximal)

(22) **ye** ketāb-**ā**-i

(1) one book-PL-INDEF

(1) *"some books"* (~~maximal~~)
]

(1)

= *cov aub*

(1)

= *ib cov aub*

]

---

# Discussion & Implications: Persian

### ***ye*** (one) may have similar choice functional semantics to *ib*

### ***ā*** (plural morpheme) may have a cover-generating property like *cov*

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# Conclusion

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# Conclusion

- My analysis is unique in that it explains definiteness facts as well as the number facts of definite and indefinite uses of *cov*.

- This may extend to other classifier languages with a general plural classifier!

- It may also extend any other language with interactions between (at least) plural morphology and (in)definiteness.

---

# Cov aub 😄

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# References 1

*Basic analysis: Sequence convergence (1)*. Mathematics and Such. (2012, November 17). https://mathstrek.blog/2012/11/09/basic-analysis-sequence-convergence-1/)

Bisang, W. 1993 . ‘Classifiers, quantifiers and class nouns in Hmong’, *Studies in Language* 17 : 1–
51.

Chierchia, Gennaro. 1998. Reference to kinds across language. *Natural Language Semantics*
6:339–405.

Chierchia, Gennaro. 1997. Partitives, Reference to Kinds and Semantic Variation. *SALT VII*, 73-98. Cornell University. Ithaca, NY.

Coppock, Elizabeth & Champollion, Lucas. 2023. *Invitation to Formal Semantics.* Manuscript.

Elbourne, Paul D. 2005. On the acquisition of Principle B. Linguistic Inquiry 36:333–366

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# References 2

Jasbi, M. (2016). Three types of indefinites in Persian: Simple, Complex, and Antidefinite. In Mary Moroney, Carol-Rose Little, Dan Burgdorf, and Jacob Collard, (Eds.), *Proceedings of Semantics and Linguistic Theory* 26, (pp. 244-263). Ithaca, NY: CLC Publications. https://doi.org/10.3765/salt.v26i0.3807

Jenks, Peter. 2018. Articulated definiteness without articles. Linguistic Inquiry 49:501–536.

Link, G. (1983). The logical analysis of plurals and mass terms: A latticetheoretical approach. In Bauerle, R., Schwarze, C., and von Stechow,  A., editors, *Meaning, Use, and Interpretation of Language*, pages 303–23.  Mouton de Gruyter Berlin.

Percus, O. 2006. "Antipresuppositions." In A. Ueyama(ed.), Theoretical and Empirical Studies of Reference and Anaphora: Toward the establishment of generative grammar as an empirical science, Report of the Grant-in-Aid for Scientific Research (B), Project No. 15320052, Japan Society for the Promotion of Science, 52-73.

Schwarzschild. 1996. *Pluralities*, Springer.

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# References 3

Semilattices, lattices and complete lattices there’s nothing quite so ﬁne. (n.d.). https://www.math.hawaii.edu/~jb/math618/os2uh_17.pdf

Simpson. 2008. "Classifiers and DP Structure in South Asia" in The oxford handbook of comparative
syntax. Cinque, G., & Kayne, R. S. (Eds.). Oxford University Press, Incorporated. Created from
rutgers-ebooks on 2025-02-17 20:33:03.

Simpson et. al. 2011. Bare classifiers and definiteness. *Studies in Language* 35:1 (2011), 168–193. doi
10.1075/sl.35.1.10sim

Winter, Y. 1997. Choice Functions and the Scopal Semantics of Indefinites. Linguistics and Philosophy 20, 399–467. https://doi.org/10.1023/A:1005354323136

Wu, Yi-Chi. 2019. Plural Classifier xie and Grammatical Number in Mandarin Chinese. *Berkeley Papers in Formal Linguistics* 2(1).

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# Thank you! Questions? Comments?

### contact: quartz.colvin@rutgers.edu