Classifiers, partitions, and measurements: Exploring the syntax and semantics of sortal classifiers

In many languages, measure terms like item and kilo, as in two items of furniture and two kilos of rice, can be used either to partition the nominal denotation into countable units, or to measure a denotation without inducing a partition. These two types of measurements are associated with two different syntactic structures: a partition-structure where the measure term forms a constituent with the noun independent of the numeral, and a measure-structure where the measure term forms a constituent with the numeral. Some researchers have claimed that in classifier languages, sortal classifiers are (most often) used in a partition-structure— hence the classifier forms a constituent with the noun independent of the numeral. In contrast, non-sortal classifiers (i.e., measure classifiers) are often used in a measure-structure— the classifier forms a constituent with the numeral and this constituent modifies the noun. Contrary to these claims, we demonstrate that in Ch’ol (Mayan) all classifiers, sortal and nonsortal alike, are used in a measure-structure independent of the types of readings that are available with respect to the measure term. As a result, the correlation between partitioned meanings and partition-structures is not universal. We review several diagnostics that support this claim. These diagnostics can be used as a template to test the constituency structure in other classifier languages.


Introduction
In this paper, we argue that in Ch'ol, the numeral and classifier together form a constituent, which is adjoined to the nP. We refer to this structure as a measure structure, for reasons that will become apparent in section 2. 1 Such a hypothesis is not without controversy. In previous work, Landman (2004), Rothstein (2009; and Li (2011) propose that classifiers appear in two different types of structures. According to them, socalled measured readings of measure terms and classifiers in English and Mandarin have the structure in (1). However, these authors argue for a different structure for so-called partitioned readings, shown in (2) below. (The terms measured and partitioned readings are discussed in section 2.) To understand these claims and how they relate to classifier languages, it is important to make a distinction between two types of classifiers: those that provide a unit of measurement (non-sortal or "measure" classifiers), and those that seem to rely on a natural "divided reference" inherent to the noun (sortal classifiers). 2 Non-sortal classifiers, such as the Ch'ol classifiers -chäjk' and -lojch', specify a vague or precise way of measuring and partitioning the nominal denotation, such as by drops or scoops, as reflected in the glosses in (3) and (4). 3 (3) ux-chäjk' ja' three-clf water 'three drops of water' (4) ux-lojch' ja' three-clf water 'three scoops of water' In contrast, sortal classifiers, like the Ch'ol classifiers -kojty and -p'ej in (5) and (6), cannot be so easily glossed. The classifier -kojty is used for counting four-legged things, but also chili peppers; -p'ej is used for spherical objects, but is also a generic or default classifier. 4 The partition/measurement that is relevant for counting tomatoes in (6a), for example, is completely different from the one that is relevant for counting beliefs in (6b).
(5) a. cha'-kojty mis two-clf cat 'two cats' b. cha'-kojty ich two-clf pepper 'two peppers' (6) a. cha'-p'ej koya' two-clf tomato 'two tomatoes' b. cha'-p'ej ñopbal two-clf belief 'two beliefs' Because they do not specify a unit of measurement, Li (2011) suggests that sortal classifiers are (almost always) used to communicate a partitioned reading and thus (almost always) appear as part of a partition structure, as in (2). 5 In contrast, we propose that all numeral classifier constructions in Ch'ol, sortal and non-sortal alike, whether used to convey a measured or partitioned reading, have the measure structure illustrated in (1) above. Thus, the correlation between partitioned meanings and partition structures is not universal. This analysis of Ch'ol has welcome consequences for the semantic composition of classifier phrases. As thoroughly discussed in Krifka (1995) and reviewed in Bale and Coon (2014), there are two possible semantics for sortal classifiers. They might function like the English terms item and piece, combining with their associate nouns to yield a set of minimal parts which can then combine with numerals. A version of this type of interpretation is given in (7), which is consistent with the partitioned structure in (2). 6 (7) {ab, ac, bc} Numeral meaning 'two' b, c, ab, ac, bc, abc} associated nP Alternatively, sortal classifiers may combine with numerals and together serve to restrict the denotation of a head noun, as shown in (8).
{ab, ac, bc} b, c, ab, ac, bc, abc} associated nP 5 Cheng & Sybesma (1999) argue for the this type of partition structure for classifier constructions more generally. Likewise Svenonius (2008) proposes a partition-like structure for all classifiers, modulo the labelling of syntactic nodes (the classifier is the head of a Unit phrase-UnitP-whose maximal projection is sister to D, whereas the numeral occupies the specifier position of this Unit phrase). 6 The exact details on how the measure term maps the associate noun to the set of atoms is not important for our purposes (see the discussions in Krifka 1995;Doetjes 1996;Chierchia 2010;Li 2011;Rothstein 2011;Li & Rothstein 2012, among others).
In such structures, the classifier could denote a measure function much like non-sortal classifiers. Importantly, this interpretation of sortal classifiers conveys a partitioned meaning even though the syntax is consistent with the measure structure in (1). The outline of this paper is as follows. In section 2, we review some of the syntactic and semantic distinctions among different types of measurement constructions in more wellstudied languages (English and Mandarin) in order to provide some background on the potential syntactic and semantic structures for interpreting Ch'ol classifiers. In section 3, we provide a broad overview of the grammatical nature of counting expressions in Ch'ol which will help in understanding the main sources of evidence presented in section 4. In section 4, we argue that classifier constructions in Ch'ol share a single syntactic structure, regardless of whether the classifier is sortal or non-sortal-specifically, we argue that the numeral and classifier together form a constituent which adjoins to a nominal phrase. It is our goal that the arguments we advance in section 4 will provide a template to investigate the syntactic status of sortal and non-sortal classifiers across a variety of different classifier languages to see if they differ critically from Ch'ol. In section 5, we discuss some empirical limitations when testing different types of readings in Ch'ol. Section 6 concludes.

Partitioning versus measuring
Before discussing Ch'ol, it is important to review some of the syntactic hypotheses surrounding measurement constructions in English. Such hypotheses will provide context for our discussion of the syntactic analysis of classifiers in Ch'ol. In English, there is evidence for a semantic and syntactic difference between measure terms that participate in a measurement, versus those that participate in a partition. Intuitively, a measurement involves the potential of dividing a nominal denotation into units like litres, grams, or seconds, without actually partitioning it (at least not in a contextually salient way). In contrast, when a noun is partitioned, the division of the nominal denotation is apparent, usually because there is a physical separation of "stuff/things" into "containers/objects". This contrast is best understood with an example. Take the English noun cups. The sentence in (9) is ambiguous. It can be understood as indicating that Mary put four separate cups on the table, each filled with water, or it can be understood as indicating that Mary put one container on the table filled with four cups-worth of water. The relevant contexts that can be used to establish the ambiguity are given in (9). 7 (9) Mary put four cups of water on the table. i. Context 1 (partition): Mary put four different cups on the table-each filled with water. ii. Context 2 (measure): Mary took a cup from the cupboard and filled it with water four times, each time dumping the water into a bowl. She then put the bowl on the table.
The former interpretation is a partitioned reading whereas the latter is a measured reading. The key difference here is that in contexts that support a measured reading, the contents being measured need not be spatially separated into different objects and furthermore there need not be more than one container that is used to make the measurement-for instance, the same cup can be used each time. In fact, in some contexts there need not be a measuring container at all-for example, the bowl could have lines on it that indicate when the contents have reached four cups-worth. In contrast, contexts that support a partitioned reading require that the contents be spatially separated into units and often that each unit is contained in its own separate container. The division of these readings into only two types is perhaps a little too coarse. As noted by Partee & Borschev (2012), container nouns like cup provide some evidence for a finer-grained distinction among partitioned and measured readings. For example, measured readings can be either ad hoc or based on a standard measure. 8 Similarly, there is some evidence for a reading that hovers between a partitioned and measured reading, sometimes called a concrete-portions reading. Such readings foreground the contents rather than the container, much like a measured reading, but require that the contents be physically partitioned, much like a partitioned reading (see Partee & Borschev 2012 for a discussion). 9 However, as we discuss in section 5, there are certain factors that limit the types of readings that are available and/or detectable when using Ch'ol classifier constructions. 10 Classifiers in Ch'ol tend to be used in contexts that support either an ad hoc measure reading or a containerless partitioned reading (i.e., partitioned readings where there is no physical container separate from the contents, as exemplified by the measure terms head, item and piece in head of cattle, item of clothing and piece of equipment). Terms that refer to standard measures or containers are represented as nouns, not classifiers (see section 5 for details). Thus, for the purposes of this paper, we will concentrate on the broad semantic and syntactic distinctions between measured and partitioned readings, mentioning finer-grained distinctions when it is relevant.
Terms that are predominantly used in contexts that support a measured reading include litres, grams, pounds, tonnes, inches, hours, and seconds. Examples of terms that are typically used in contexts that support a partitioned reading include items, pieces, baskets, buckets, and boxes. To some degree, all terms can be used to indicate either reading although some terms are more flexible than others, such as those that refer to containers like cups, teaspoons, and barrels. (10) Terms preferentially used in contexts that support a measured reading a. I put 500 grams of sugar in the pot. b. We observed ten seconds of silence.
(11) Terms preferentially used in contexts that support a partitioned reading a. I put four items of furniture in the hallway. b. I put four baskets of books in the hallway. 8 The ambiguity of such readings comes about when considering situations where a regular cup is used to measure water that is poured into a pot. In such cases, it can be both true and false to say There are three cups of water in the pot: false under a reading where cup is an agreed upon standard measure (i.e., the imperial cup); true where cup is treated as a contextually determined measure (i.e., three cups-worth of water as measured by the actual cup in the context of utterance). Partee & Borschev (2012) hypothesize a theoretical distinction between these two readings. Standard measure readings involve a lexical item that is stored as a measure function whereas ad hoc measure readings involve a lexical rule that converts container nouns into a measure function. 9 Such a reading is exhibited by sentences like Mary wants to drink those two glasses of milk, where the verb drink requires that its object be a liquid of some kind, but those two expresses and refers to the glasses that contain the liquid. It is critical to note that this reading is incompatible with contexts that typically support a measured reading. For example, the previous sentence is incoherent if the contents of the glasses are poured into a bowl and Mary wants to drink the milk out of the bowl. 10 It is important to note that the full range of readings is attested in Ch'ol. However some readings that critically rely on container terms involve the use of a default classifier with a container noun instead of a classifier that refers to the container.
(12) Terms without any preferential use a. I put four cups of water in the fridge. b. I put four teaspoons of sugar on the table. Landman (2004) and Rothstein (2009; propose that there is a syntactic distinction (and hence a syntactic ambiguity) that corresponds to the differences between the measured readings on the one hand, and the partitioned reading on the other. According to these authors, partitioned readings have a structure where the measure term is the syntactic head and the non-measure term is either a complement or a modifier, as shown in (13). 11 In contrast, measure readings are proposed to have a syntactic structure in which the noun denoting the thing being measured is the head, as shown in (14). The numeral and measure term form a constituent, here MP, that restricts the head noun.
(13) Partition reading DP As noted by Rothstein (2009;, the structures in (13) and (14) make different syntactic predictions. First, it is expected that the count-mass status of the DP will depend on which noun (the measure term or the non-measure term) is the head. In (13), the head noun is the measure term, which is count. In (14), however, the head noun is the non-measure term, which happens to be mass. Evidence from the distribution of much and many largely confirms this prediction. DPs that are typically used in contexts that support a partitioned meaning sound awkward when they follow much of but sound natural following many of, whereas the opposite holds for DPs that are typically used in contexts that support a measured reading. For example, in a context where the speaker is talking about a large amount of furniture stored in a single warehouse, the sentences in (15a) and (16b) are coherent whereas the ones in (15b) and (16a) sound distinctly odd. 11 There is variation in the literature as to whether the numeral is represented as a specifier of the phrase headed by the measure term, or as the head of its own projection, as shown here. The choice is not critical to our discussion below. There is also some variation in the literature as to whether the of term is a head of a prepositional phrase with a denotation equal to its complement nP or whether of is inserted for case reasons but is not a true P 0 head. Once again, the choice of analysis does not affect the discussion here.
(15) Partition Terms a. Many of the 300 items of furniture will be exported to India. b. #Much of the 300 items of furniture will be exported to India.
(16) Measure Terms a. #Many of the 300 tonnes of furniture will be exported to India. b. Much of the 300 tonnes of furniture will be exported to India.
The structures in (13) and (14) also make different predictions with respect to number agreement. It is well known that the number status of the subject DP is at least partly determined by number marking on the head noun. Considering this fact, the general structure in (13) predicts that number marking on the measure term should influence the form of the verb/auxiliary. In contrast, the general structure in (14) predicts that it should be the non-measure term that plays a role in agreement. The examples in (17) and (18) suggest that these predictions are on the right track.
(17) Measure terms a. The five minutes of silence we observed {was / ?were} appropriate. b. The 500 grams of sugar we added to the sauce {gives / ?give} it a sweet aftertaste.
(18) Partition terms a. The five boxes of equipment we loaded into the truck {were / # was} going to be shipped to Toronto. b. The 500 items of furniture that we bought at the flea-market {were / # was} in good condition.
In both (17) and (18), the non-measure term is singular and the measure term is plural. In contexts that support a measured reading-e.g., where the time-span of silence is contiguous (rather than 5 separate 1-minute intervals) and the sugar is measured in one big lump (rather than 500 separate 1-gram packets)-the sentences in (17) sound more natural with singular agreement. In contrast, in contexts that support a partitioned reading-e.g. where there are 5 separate boxes of equipment and 500 separate items of furniture-the sentences in (18) sound more natural with plural agreement. The syntactic structures in (13) and (14) can explain these preferences. 12 Given the behaviour of measure terms in English, a question arises about how classifiers are syntactically represented in languages like Mandarin and Ch'ol. Do DPs in such languages have a similar syntactic contrast between measured and partitioned readings? Li (2011) suggests that this is the case for Mandarin. He argues that sortal classifiers, which almost always convey a partitioned reading, are typically embedded in a partitioned syntax similar to (13). 13 In contrast, non-sortal classifiers, which are often used to convey a measured reading, are typically embedded in a measured syntax, similar to (14). For example, the phrase in (19) would have the syntactic structure in (21) when used to talk about five spatially separate eggs, whereas the phrase in (20) would have the 12 It remains an open question why plural agreement in (17) is more acceptable than singular agreement in (18). It could be that coercion of minutes and grams into a partitioned reading is easier than the coercion of items and boxes into a measured reading. The contrast between (17) and (18) nonetheless lend support to the idea that the measure term is the head of the partitioned reading whereas the non-measure term is the head of the measured reading. 13 A notable exception is when sortal classifiers are used to convey an estimation involving large round numbers. In such cases, Li (2011) argues that sortal classifiers convey a measured reading and are typically embedded in a measure syntax. syntactic structure in (22) As with English, there is some flexibility in terms of which type of reading the classifiers are used to convey-e.g., the phrase in (20) could be used to talk about three separate cups containing oil, in which case it would have the syntactic structure in (21)-however there is still a one-to-one correspondence between the reading that is conveyed and the syntactic structure that is employed, or so Li (2011) claims. The evidence in support of this analysis is based on the effect the subordinating particle de has on the readings when it appears between the classifier and noun (namely it forces a measured reading) and the effect that certain adjectival modifiers have on the readings when they appear between the numeral and classifier (namely they force a partitioned reading). 14 Contrary to Li's (2011) analysis of Mandarin, we argue below that all numeral classifier constructions in Ch'ol have the same syntactic structure, namely the measure structure in (22). We cannot assess classifier constructions in Ch'ol using the same type of syntactic diagnostics used in English or Mandarin. Unlike English measure terms, classifiers in Ch'ol are (with few exceptions, discussed in §4.2 below) not nouns and thus do not have any status in terms of nominal subcategorization (i.e., they cannot be singular/plural nor mass/count-in fact, at least on the surface, there does not appear to be a syntactic masscount distinction in Ch'ol). Unlike Mandarin, Ch'ol does not have a subordinating particle comparable to de nor does it allow adjectives to appear between numerals and classifiers. Nonetheless, other tests provide evidence that all classifiers in Ch'ol are embedded in a structure like the one in (22), which is more akin to the syntactic structure that underlies measured readings in English. However, Ch'ol allows for both measured and partitioned readings despite only having this type of structure.

Numerals and classifiers in Ch'ol
This section provides relevant background details about numerals and classifiers in Ch'ol, a Mayan language spoken by around 200,000 people in the state of Chiapas in southern Mexico. Unless otherwise noted, Ch'ol data presented here come from the third author, a speaker of the Tumbalá variety, as well as speakers consulted in the municipalities of Salto de Agua and Tila, Chiapas. Data appear from the two main dialects, Tila and Tumbalá; the dialects behave the same with respect to the core facts described here, with differences noted below. For overviews of Ch'ol grammar, see Vázquez Álvarez (2011) and Coon (2017a). We examine numerals in section 3.1 and then the origins of classifiers and productivity of the classifier system in section 3.2. Note that the grammatical overview in this section is intended to be broad in that it covers some relevant points about all types of classifier expressions in Ch'ol. In subsequent sections, we limit our focus to sortal classifiers, although we do discuss some historical and grammatical limitations on the types of readings that are available for other Ch'ol classifiers in section 5.

Ch'ol numerals
Numerals in counting expressions in Ch'ol obligatorily occur with a numeral classifier. As in other Mayan languages, the Ch'ol numerical system is vigesimal (base 20). Numerals 1-20 are shown in (23). As numerals never appear alone, numerals 1-19 are presented with the generic classifier -p'ej. 15

(23)
Ch'ol numerals (Arcos López 2009: 24) The numerals 20 and above involve roots in classifier position which refer to powers of 20 (i.e., measure classifiers), shown in the table in (24). We return to the formation of complex numerals in section 4; see also the appendix in Warkentin & Scott (1980). (24) Classifiers for multiples of 20 The base-20 roots in (24) fill the classifier position in the DP, as shown by the contrast in (25). In (25a), the numeral ux appears with the classifier -kojty for animals; in (25b), the numeral appears with the classifier -k'al for groups of twenty. That these occupy the same slot is shown by their inability to cooccur in (25c); the opposite ordering is ungrammatical as well. We return to this fact below.
Today most speakers, including many monolingual speakers, use Ch'ol numerals only up to six, as well as ten, twenty, forty, sixty, eighty, one hundred and four hundred (Vázquez Álvarez 2011). 16 Numerals that were historically borrowed from Spanish are used for higher numbers. While Ch'ol-based numerals obligatorily appear with a classifier in counting constructions, classifiers are impossible with numerals of Spanish origin (Bale & Coon 2014), as shown in (26).

Ch'ol classifiers
Numeral classifiers are found in a number of different Mayan languages, but the most robust systems are found in the Greater Tseltalan branch of the family, which includes Tseltal, Tsotsil, Chontal, Ch'orti', and Ch'ol (see e.g. Keller 1955;Berlin & Romney 1964;Berlin 1968;Fleck 1981). Arcos López (2009) identifies at least 180 classifiers in Ch'ol, though this is not an exhaustive list.
In closely-related Tseltal, Berlin & Romney (1964) identify 557 possible numeral classifiers. The table in (28), taken directly from Berlin & Romney (1964), provides an illustrative example of the richness of the system.  (28) raises questions about how speakers can acquire and use such systems. We discuss the formation of Ch'ol classifiers here, which will be relevant to their syntactic structures below. A small number of Ch'ol numeral classifiers have an unknown origin (Arcos López 2009). These include some of the more frequently used numeral classifiers, shown in (29).
(29) classifier used to count… -tyikil people -p'ej spherical things; generic classifier -k'ej round and flat things -ts'ijty long and skinny things While classifiers like those in (29) must simply be learned, the vast majority of numeral classifiers are formed from two main classes of roots: transitive roots and positional roots, discussed in turn below. 17 Richness in the verbal and positional domain thus translates directly to richness in the system of classifiers.

Classifiers from transitive roots
As in other Mayan languages, transitive and positional roots are CVC in form. Coon (2017b)-drawing on work in Yucatec Maya (Lois 2011)-argues that Ch'ol roots show templatic effects, comparable to the more well-studied "root-and-pattern" morphology in Semitic languages (e.g. McCarthy 1981). Both consonants of the CVC roots are fully specified, but suprasegmental vowel qualities are specified during the course of the derivation (see e.g. Arad 2003 on Hebrew). The forms in (30) and (31)  Transitive roots can be identified by their ability to appear underived in verbal constructions with two arguments (see e.g. Haviland 1994 for a discussion of root classes in Tsotsil). The roots above appear in transitive stem forms in (30a) and (31a) with a plain root vowel: kuch and jop. The transitive stem requires a harmonic vowel "status suffix" and appears with two arguments. In the passive forms in (30b) and (31b), the root appears with a lengthened and devoiced root vowel, represented in the orthography as CVjC (orthographic j = IPA [h]). 18 The stem requires the intransitive status suffix, -i, and now takes only a single internal argument.
Numeral classifiers may also be formed from these roots using the same CVjC form found in the intransitive (b) forms above. Examples of classifiers derived from transitive roots are shown in (32). Note that the internal argument of the transitive and unaccusative forms in (30) and (31) corresponds to the object being counted in the classifier constructions in (32).

Classifiers from positional roots
Numeral classifiers in Ch'ol are also derived from positional roots (discussed in detail in Arcos López 2009; see also Haviland 1981 on Tsotsil). Positional roots in Mayan languages form a distinct class, distinguishable in part by their semantic content (position, shape, surface quality, or physical state), but also by the special morphology used to form stems (England 1983;2001;Haviland 1994;Henderson 2016;Coon 2019). In Ch'ol, for example, positional roots form intransitive stative predicates with the suffix -Vl (the vowel is harmonic with the root vowel). As with transitive roots, the formation of numeral classifiers from positional roots is quite productive (though we have not systematically tested all roots): something that can be described as CVC-Vl can generally be counted with the classifier -CVjC. Examples with the positional roots pal 'clustered' and koty 'standing on four legs' are shown in (35) and (36) Though this process appears to be productive, some CVjC classifiers also have extended uses, not predictable from the meaning of the corresponding CVC root alone. For example, the classifier -kojty is derived from the positional root koty 'standing on four legs'. It can Bale et al: Classifiers, partitions, and measurements Art. 77, page 15 of 30 be predictably used to count four-legged animals such as cows, pigs, deer, and jaguars (38a). Beds, tables, and cars can also be counted with -kojty (38b). However, having four limbs is not necessary to be counted with -kojty, which is also used to count all animals regardless of the number of limbs: butterflies, snakes, chickens, birds, fish, or a dog with a missing leg (38c). The classifier -kojty is also used to count all chili peppers, regardless of shape (38d).
(38) a. cha'-kojty chityam two-clf pig 'two pigs' b. cha'-kojty wäyib two-clf bed 'two beds' c. cha'-kojty p'ejpem two-clf butterfly 'two butterflies' d. cha'-kojty ich two-clf pepper 'two peppers' In a similar vein, the classifier -tyejk is derived from the positional root tyek; roughly it is used to describe a configuration of organic things growing out of a sparsely-populated surface. Predictably, -tyejk may be used to count plants which are growing spaced apart, hairs sprouting out of an otherwise bald head, or several spaced-apart teeth (e.g. in a baby or an elderly person's mouth). For most elements, this configuration is important: -tyejk cannot be used to count teeth in a mouth full of teeth. However, -tyejk is also used to count all trees, regardless of their spacing. The relevance of position, shape, and configuration means that-just as in (34) abovea single noun may be counted with more than one classifier. Snakes are particularly good candidates for this type of productivity, as shown in (39).

Classifiers and Measured Structures
In this section, we provide syntactic and semantic evidence that all numeral classifier constructions in Ch'ol have the structure repeated in (40), corresponding to the measure structure, rather than the one repeated in (41), corresponding to the partition structure. As reviewed in section 2, Li (2011) hypothesizes that classifier languages have both types of structures, similar to English. Furthermore, the difference between the partition and measure structures generally corresponds with different semantic interpretations of sortal and non-sortal classifiers. In this section, we will mainly focus on sortal classifiers, since it is their status with respect to this type of hypothesis that we aim to challenge. Such classifiers include many of the underived classifiers mentioned at the beginning of section 3.2, namely -tyikil (for people), -p'ej (for spherical things and the generic classifier) and -ts'ijty (for long and skinny things). Also included are some of the classifiers derived from positional roots that have extended meanings that lie beyond the expected meaning related to such roots: for example, the classifier -kojty, which is derived from the root meaning 'standing on four legs' but used for non-four legged entities such as chili peppers, as well as the classifier -tyejk, which is derived from the root meaning 'growing out of sparsely populated surfaces' but which is used to pick out trees and larger tree-like plants no matter what arrangement they are in. Li (2011) argues that these kinds of classifiers are biased towards a partitioned meaning since they are not associated with a specific measure-the only exception being expressions of estimation. As mentioned in the introduction, the fact that sortal and non-sortal classifiers are used in the same types of structures regardless of whether they convey a measured or partitioned meaning (i.e., they are all used in measure structures) suggests that these structures should be associated with the same type of semantic entity (e.g., measure functions). Furthermore, such a structure implies that there does not exist a phrase-consisting only of the classifier and noun-that denotes a partition of the supremum of the nominal denotation. In other word, the syntactic structure is more in line with the compositional interpretation (42) rather than the one in (43).  Critically, the semantics in (42) can be used in contexts that support a partitioned meaning despite appearing in a syntactic structure that is isomorphic to the kinds of structures that convey a measured reading in languages like English and Mandarin. The measure function μ # maps groups to the number of objects/atoms in that group. Thus, it achieves the same result as counting the cardinality of a partition as shown by equivalencies of the topmost node in (42) and (43). In the rest of this section, we review some syntactic evidence that favours measured structures for all classifiers in Ch'ol and hence the type of semantic meaning for sortal classifiers represented in (42). In section 4.1 we argue that the [num+clf] behaves as a maximal projection. In section 4.2 we present evidence that the noun functions as the head of the phrase.

The numeral and classifier form a constituent
The first piece of evidence for the structure in (40) above is that the numeral and classifier form a single phonological word in Ch'ol. This fact can be easily accounted for under the measure structure in (40), in which the numeral and classifier are both inside the MP constituent. Previous work has accounted for this fact under the partition structure in (44) by proposing that the classifier head undergoes head movement to adjoin to the numeral (see Borer 2005). Some initial evidence in favour of the measure-structure approach-in which the [num+clf] is contained in a maximal projection excluding the nominal-comes from the formation of complex numerals. Recall from 3.1 above that Ch'ol's numerical system is base 20. To form numbers which are multiples of twenty, special classifiers denoting powers of twenty fill the classifier slot of the [num+clf] expression, as in (45).
(45) a. cha'-k'al two-clf.20 'forty ' (lit. two-20s) b. cha'-bajk' two-clf.400 'eight hundred' (lit. two-400s) These veintenas, or multiples of twenty, are important to the formation of more complex numerals, like those in (46). Numerals of each multiple of twenty belong to the next highest veintena, the bolded portion in the expressions below. For example, all numerals between 21 and 40 will contain cha '-k'al 'forty', as in (46a); numerals between 81 and 100 will contain jo '-k'al 'one hundred' in (46b), and so on.

c. jo'lujuñ-k'al i-cha'-bajk'
fifteen-clf.20 a3-two-clf.400 'seven hundred' (lit. fifteen-20s of the group of two-400s) Relevant for our purposes is that these forms clearly have an internal structure. In these complex expressions, the bolded veintena appears with 3rd person agreement ("Set A" in Mayanist terminology), normally found on possessed or relational nouns. 20 Though this system is not in current use by most Ch'ol speakers we have consulted, similar structures are reported in work on other languages in the family as well (e.g. Fleck 1981;Haviland 1981). While we do not elaborate on the structure of complex numeral expressions in Ch'ol, the important point is that the [num+clf] component can contain more material than a single word. We claim that this fact is best accounted for under a structure in which numerals and classifiers form an XP, rather than a single complex head. Evidence from juxtaposition corroborates the XP status of the [num+clf]. As discussed in Vázquez Álvarez (2011), there are no specific morphemes that indicate conjunction or disjunction in Ch'ol. Coordinate XPs are frequently juxtaposed, a possibility shown for [num+clf] phrases to express indefinite quantities in (47) Gil 1994 for similar arguments regarding Japanese). Basic word order in Ch'ol is described as VOS/VS (Coon 2010;Vázquez Álvarez 2011), but as in other Mayan 20 Ordinal numbers also appear obligatorily with 3rd person Set A possessive morphology, as in (i) (i) Tsa' chäm-i i-cha'-kojty-lel wakax.
pfv die-iv a3-two-clf-nml cow 'The second cow died.' Here and above, one might think of these "possessed" numeral stem forms as "belonging" to an abstract set of numbers, though we do not elaborate further on this here. languages, arguments may front to preverbal position for topic, focus, relativization, and wh-questions (see e.g. England 1991;Aissen 1992;Clemens & Coon 2018). An intransitive verb with a postverbal subject is shown in (48a); in (48b) the subject has fronted and a focus interpretation arises (indicated by italics in the translation). For example, the VS sentence in (48a) is an appropriate out-of-the-blue statement, while the subject-focus sentence in (48b) is an appropriate response to a question asking who arrived.
(48) a. Ta' jul-i-y-ob ux-tyikil x'ixik. pfv arrive-itv-ep-pl three-clf woman 'Three women arrived.' pfv arrive-itv-ep-pl 'Three women arrived.' (49), the numeral and classifier can be displaced as a unit independent of the noun (49a), but the numeral cannot be displaced without the classifier (49b). As might be expected, fronting the [num+clf] alone focuses the quantity; (49a) is an appropriate response to a question about how many women arrived, or to correct someone who erroneously claimed that only one woman arrived.

As shown in
. three pfv arrive-itv-ep-pl clf woman 'Three women arrived.' A similar example involving a wh-question is shown in (50) and (51). A transitive sentence with postverbal object is shown in (50a). In (50b) the entire DP has fronted to preverbal position. (50) Wh-question a. Ta' a-mäñ-ä cha'-p'ej alaxax. pfv a2-buy-tv two-clf orange 'You bought two oranges.' b. [ Jay-p'ej alaxax ] i ta' a-mäñ-ä ____ i ? how.many-clf orange pfv a2-buy-tv 'How many oranges did you buy?' The example in (51a) illustrates that jay-p'ej 'how many' can front independently of the noun; fronting jay without the classifier is ungrammatical, as in (51b).
(51) a. Jay-p'ej i ta' a-mäñ-ä [ ____ i alaxax ]? how.many-clf pfv a2-buy-tv orange 'How many oranges did you buy?' b. *Jay i ta' a-mäñ-ä [ ____ i p'ej alaxax ]? how.many pfv a2-buy-tv clf orange 'How many oranges did you buy?' The important point of these examples it not that it is impossible to separate the numeral and the classifier; given that the two form a phonological word and never appear as standalone morphemes, this fact is unsurprising. What is important is that the [num+clf] undergoes A′-fronting without the nP to a preverbal position occupied by other fronted XPs. The fact that [num+clf] is eligible for A'-movement provides strong support for its phrasal status.
Furthermore, this pattern shares properties with clear cases of extraction out of DPs elsewhere in Ch'ol. For example, as discussed in Coon (2009) (49) and (52), and transitive objects as in (51); see the discussion in Aissen 1996 andCoon 2009). Subextracting both possessors and the [num+clf] MP out of a transitive subject, as in (53b) and (54b), is ungrammatical.
[ Ux-tyikil xk'aläl-ob ] i ta' y-il-ä-y-ety ____ i . three-clf girl-pl pfv a3-see-tv-ep-b2 'Three girls saw you.' b. *Ux-tyikil i ta' y-il-ä-y-ety [ _____ i xk'aläl-ob ]. three-clf pfv a3-see-tv-ep-b2 girl-pl intended: 'Three girls saw you.' Taken together, the fact that (i) the [num+clf] may undergo A′-movement, and (ii) this A′-movement is subject to the same restrictions as other clear cases of A′-movement (i.e. subextraction of possessors), suggests that the [num+clf] forms an XP constituent independent of the noun. 21 Although we illustrated the movement restrictions and juxtaposition facts using sortal classifiers (since these are the more controversial classifiers with respect to the measure structure), it is important to note that these patterns hold for non-sortal classifiers as well. 22 For the sake of brevity, we forego the relevant examples (which can be obtained by direct substitution).

Evidence that the noun is a head and the MP is an adjunct
Having established that the [num+clf] forms an XP constituent-labeled MP in (40) above-we now turn to evidence that in the [MP noun] construction, the noun is the head and the MP is an adjunct. There are two sources of evidence. First, in constructions without numerals, it is clear that adjuncts modify the head noun in a DP. With respect to DPs with numerals and classifiers, only the noun can be modified by such adjuncts and not the classifier, even when the same root is used to form the classifier and noun. Second, there is a parallelism between adjectives and MPs, suggesting that they serve the same kind of syntactic and semantic function within a DP.

Modifying adjuncts and head nouns
Modification in Ch'ol provides evidence that the noun is the head in DPs that contain a measure phrase. In this section, we review some of the syntactic and semantic properties of Ch'ol modifiers discussed in Martínez Cruz (2007), before turning our attention to the relationship between nouns and measure phrases.
In Ch'ol, modifying adjuncts often appear with the relativizing clitic =bä, a borrowing from neighboring Zoquean languages (Zavala Maldonado 2007). Also, as in Zoque, Ch'ol modifiers with =bä may either precede or follow the head noun. We assume that the DP in (55a) has the structure in (55b), in which the modifier adjoins to the nP.
As Martínez Cruz notes, modification is a useful way to diagnose the head of the DP. Under our proposal, the [num+clf] in a classifier construction is an MP which adjoins to the nP. While most classifiers are derived from verbal or positional roots ( §3), a small number of nouns which denote measures-like p'ejty 'pot' and chikib 'basket'-may function either as nouns or as classifiers. 23 While both sentences in (56) below can be translated as 'one pot of eggs', p'ejty serves a different function in each.
(56) a. jum-p'ejty [ np tyumuty ] one-clf egg 'one pot of eggs' b. jum-p'ej [ np i-p'ejty-al tyumuty ] one-clf a3-pot-nml egg 'one pot of eggs' In (56a), -p'ejty is acting as a numeral classifier; under our proposed structure in (40) above, jump'ejty is an MP which adjoins to the nP tyumuty. In (56b), on the other hand, p'ejty is the head noun; the numeral appears with the default classifier -p'ej. Internal to the bracketed nP, tyumuty behaves like a possessor in following the possessee and triggering Set A possessive agreement ('egg's pot'/'pot of eggs').
As discussed in Martínez Cruz (2007), evidence that the bracketed strings in (56) indeed contain the nominal heads comes from modification. When a phrase-final modifier is added, it must be interpreted as modifying the head: in (57a) the eggs are broken, while in (57b), the pot itself is broken and nothing is asserted about the eggs (examples are from Martínez Cruz 2007: 29-30). The modifier can also precede the modified constituents in (58), resulting in the same interpretations as above. As predicted under our analysis, it cannot intervene between ip'ejtyal and tyumuty, as shown in (58c).

Modifying adjuncts and MPs
We claim that the MP is adjoined to the nP much like other modifiers, and we correctly predict the MP to share other behaviours with Ch'ol modifiers. First, given that nearly any lexical item in Ch'ol can serve as a stative predicate in what Mayanists call "non-verbal predicate" constructions, it is unsurprising that the [num+clf] may appear in initial predicate position as well. Examples of stative predicates involving the adjective kolem 'big', the derived modifier buchul 'seated', and the [num+clf] uxtyikil 'three (people)' are shown in (61).
Three-clf det woman-pl 'The women are (in a group of) three.' As with other modifiers, [num+clf] sequences may also appear with the relativizing clitic =bä (see Vázquez Álvarez 2011 for details). Bare adjectives in Ch'ol must appear in prenominal position in attributive constructions, as in (62a), unless they are suffixed with the relative clause clitic =bä, as in (62b), in which case they may either precede or follow the noun (see also the examples in (55) and (57) (63). (63) a. Ta' k-il-ä ux-tyikil x'ixik-ob. pvf a1-see-tv three-clf woman-pl 'I saw three women.' b. Ta' k-il-ä { ux-tyikil=bä } x'ixik { ux-tyikil=bä }. pvf a1-see-tv three-clf-rel woman three-clf-rel 'I saw three women.' (lit. 'I saw women that were three.') Again, given that [num+clf] sequences may serve as predicates, as in (61) above, these facts are unsurprising. Also as expected, the meaning of the MP construction is slightly different when it appears as a predicate within a =bä-marked relative clause as in (63b). For example, the sentence without the relative clitic in (63a) suitably describes a situation in which the speaker saw three woman either one at a time, or collectively. However, the sentence in (63b) best describes a context in which the women were grouped as three, such as in a situation in which a parade of people are walking by in groups of two, but then exceptionally a group of three women walk by.
Despite the slight difference in meaning (which is predicted given the contrast between numerals in predicate position versus modifying position even in English), numerals in combination with classifiers parallel adjectival modifiers like kolem 'big'. As demonstrated in (61), (62) and (63), both types of terms can appear as predicates, can directly modify a noun, and can modify a noun by serving as a predicate in a relative clause.

Summary
To summarize, in this section we defended the proposal that the [num+clf] sequence in Ch'ol classifier constructions forms a syntactic constituent (MP), which may undergo A′-movement and juxtaposition independently of the noun it modifies. The MP may also be complex, with its own internal syntax, as in the complex constructions for numerals above twenty. Furthermore, the classifier is not the head of the DP, as shown by the modification facts in the previous section. The type of classifier-sortal versus non-sortal-does not influence the type of syntactic construction it appears in. Furthermore, the syntactic similarity between the two types of classifiers suggests that compositionally, they should receive the same type of semantic treatment, namely that of being a measure function.
It is important to note that unlike English, there is no evidence that different readings (partitioned versus measured) are correlated with different syntactic structures. Except in exceptional circumstances involving estimation (see Li 2011), DPs with sortal classifiers cannot have a measured reading-for example, members of the denotation of the noun are necessarily contextually separated into concrete or abstract countable objects. DPs with non-sortal classifiers are generally associated with a measured reading. Thus, the correlation between partitioned readings and partition structures is not universal. In the next section, we discuss in more detail the availability of partitioned and measured adjective kolem 'big' in (62a). Derived modifiers, like buchul in (61b) and (55) above, as well as tyojp'em 'broken' in (57)-(58) above, always require the use of =bä. readings in Ch'ol, specifically focusing on some of the empirical limitations to making fine-grained distinctions.

Limits on assessing different types of classifier readings in Ch'ol
As described in section 3, there are only a small number of classifiers that are not derived from positional or transitive CVC roots. This puts certain limits on our ability to test for the range of different readings discussed in Rothstein (2011) and in Partee & Borschev (2012). There are three important limitations on classifier readings in Ch'ol: (i) classifiers in Ch'ol are generally not associated with "standard measures" in the sense described in Partee & Borschev (2012); (ii) measure terms associated with containers are generally not used as classifiers in Ch'ol; and (iii) because of the lack of container classifiers, it is difficult to assess whether some classifiers permit a partitioned reading or not.
The first limitation relates to how words for standard measurements became a part of Ch'ol. Current terms relating to standard measures-such as those associated with the English nouns litres, grams, cups and kilos-have been mainly borrowed from Spanish and function in Ch'ol as nouns, not as classifiers. In order to use such terms in counting expressions, they must appear in nominal position with the default classifier -p'ej attached to the numeral.

(64)
Ta' k-jap-ä cha'-*(p'ej) litro ja'. pfv a1-drink-tv two-clf litre water 'I drank two litres of water.' Another limitation of classifier readings in Ch'ol is that container readings are generally not associated with classifiers. This is not an inherent grammatical limitation but may be related to the way classifiers are derived from certain types of roots. As discussed in section 3.2 above, most of the classifiers in Ch'ol are derived from roots associated with either actions (transitive roots) or physical configurations (the positional roots). These roots in general do not denote concrete containers. As a representative example, consider the classifier -lujch which we glossed as ladle in the table in (33) above. This classifier is derived from the root luch which means 'to scoop up (liquid)'. It is important to highlight that the classifier is not derived from a noun that denotes or names a ladle. In fact, it might be more accurate to gloss the classifier as ladle-fuls or ladlings, as in two ladle-fuls of soup or two ladlings of soup. Such a gloss would more accurately reflect that the noun is being measured by the potential action rather than by the physical presence of a ladle.
Indeed, phrases like cha'-lujch ja' ('two ladles of water') can only be used to denoted and refer to the stuff being measured and cannot be used to refer to a physical object used to carry out the measurement. For example, cha'-lujch ja' is perfectly coherent when appearing in the object position of the verb meaning 'to drink', but sounds incoherent when appearing in the object position of the verb meaning 'to break', even when two physical ladles are present and the speaker broke both ladles.
The lack of container classifiers makes is difficult to test for some of the more subtle differences among partitioned, measured and concrete-container readings. This is the third limitation of assessing classifier readings in Ch'ol. Recall that a key aspect of diagnosing such readings was to take advantage of verbs that are sensitive to the subtle differences between a container and its contents. This is not possible if there is no container to distinguish from its contents.
For very similar reasons, it is also difficult to assess whether non-sortal classifiers permit a partitioned reading. To understand why, consider two different contexts that would render the sentence in (65a) above true. This sentence is true in a context where the speaker measures out two ladles worth of water into a bowl and drinks it. It is also true where there are two separate ladles with water in them and the speaker drinks all the water from both ladles (as long as the ladles are basically the same size). However, a measured reading could account for the truth of the sentence in both situations; in both contexts, the speaker is drinking two ladles worth of water. The truth conditions that account for measured readings are often broad enough to still be true in situations that typically support a partitioned reading.
To establish that there is a partitioned-reading with separate truth conditions, one either needs to take advantage of verbs that are sensitive to the differences between containers and contents (such as break versus drink, see Partee & Borschev 2012), take advantage of contrasts in number and nominal subcategorization (see Rothstein 2011), or use highly atypical contexts with very subtle judgment differences (see Rothstein's 2011 discussion of the English and Dutch measure term litre). The first strategy is generally not possible in Ch'ol since there is usually no contrast between a container named by a classifier and its contents-classifiers simply do not usually name containers. The second option is also not possible since Ch'ol does not mark contrasts in number nor in nominal subcategories in the same way that English does. The third is hard to implement in this case due to the difficulties of doing large-scale experimental tasks or tasks involving very subtle judgements in a non-university setting.
There is another option to detect partitioned readings with non-sortal classifiers, and this would be to test whether a sentence like (65a) is both true and false in a context where two ladles-worth of water were drunk from a bowl-true under a measured interpretation but false under a partitioned interpretation. (Note, speakers only report judging the sentence as true in such situations.) However, since the partitioned interpretation is so improbable with such constructions, not being able to detect an ambiguity might be due to the improbable nature of the reading rather than its impossibility.
Recall from the discussion in section 4.2 that for some speakers there are two nonsortal classifiers in Ch'ol that refer to containers and that are associated with nominal counterparts, namely -p'ejty ('pot') and -chikib ('basket'). However, the majority of Ch'ol speakers we consulted, including the third author, only permit these forms to function as nouns. Other work that reports on these classifiers (e.g., Martínez Cruz 2007) does not discuss them with respect to the availability of different types of readings. The two speakers we identified who accepted these forms as classifiers found it difficult to get a partitioned reading. For example, although the sentence in (66a) sounded natural, the one in (66b) was deemed questionable, although not completely unacceptable.
(66) a. Ta' k-jap-ä cha'-p'ejty ja'. pfv a1-drink-tv two-clf water 'I drank two pots of water.' Bale et al: Classifiers, partitions, and measurements Art. 77, page 27 of 30 b. ?Ta' k-tyop'-o cha'-p'ejty ja'. pfv a1-break-tv two-clf water 'I broke two pots of water.' To describe a situation where two pots were broken, the speakers preferred the sentences in (67), where p'ejty is part of a nominal expression and the default classifiers is affixed to the numeral.
(67) a. Ta' k-tyop'-o cha'-p'ej i-p'ejty-al ja'. pfv a1-break-tv two-clf a3-pot-nml water 'I broke two water-pots.' b. Ta' k-tyop'-o cha'-p'ej p'ejty ja'. pfv a1-break-tv two-clf pot water 'I broke two pots of water.' However, since so few speakers have been consulted and the judgments are rather subtle, more research needs to be done before making any firm conclusions about the availability of partitioned readings with non-sortal classifiers.

Conclusion
In this paper we explored the syntactic and semantic representation of classifiers in Ch'ol. We demonstrated that classifiers and numerals form a constituent that modifies the noun phrase. This same structure is used for both sortal and non-sortal classifiers, and furthermore seems to hold independent of different types of readings (measure versus partition readings). The syntactic similarities between these two types of classifiers suggest that they should also receive the same kind of semantic treatment, namely that of being a measure function (see Krifka 1995;Bale & Coon 2014).
Although our entire discussion has been limited to Ch'ol, there are consequences for the analysis of other languages. First, we have demonstrated that the correlation between partition readings and partitioned structures is not universal. Second, we have developed a framework of arguments that can be readily applied to other classifier languages. In particular, this paper provided a variety of syntactic diagnostics to help determine (i) whether classifiers and numerals form a constituent independent of the nouns they modify and (ii) whether the modified noun serves as the head of the nominal constituent.
In Ch'ol, sortal and non-sortal classifiers patterned in the exact same way: the classifier and numeral always formed a constituent that modified the noun and the noun was always the head of the larger nominal constituent. Future research should focus on whether classifier languages might differ in this respect. It is possible that, with these diagnostics, one could discover different classes of classifier languages in terms of how different types of readings and different types of classifiers correlate with different types of syntactic structures. Indeed, perhaps classifier languages form at least two distinct groups in this respect: those having both a partition and measure structure like Mandarin and those only having a measure structure like Ch'ol. Abbreviations a = "Set A" person marking (ergative, possessive), b = "Set B" person marking (absolutive), clf = numeral classifier, det = determiner, dtv = derived transitive verb suffix, ep = epenthetic insertion, ext = existential particle, ipfv = imperfective, itv = intransitive verb suffix, nml = nominal suffix, pass = passive, pfv = perfective, prep = preposition, rel = relative, sp = Spanish origin, stat = stative, tv = transitive verb suffix.