3.1 Excluded idiomatic uses

Before I discuss the results of the corpus study, let me briefly note that there are a number of frequent idiomatic uses of some of the Polish PQs, which I have excluded from the analysis. ⁶ For instance, the noun cząstka is polysemous. Apart from the relevant quantifier meaning, i.e., ‘part’, it can also mean ‘particle’, as used in physics to refer to an extremely small constituent of matter. To make things even more complex, there are in fact two quantifier senses of cząstka (‘part₂’). The one I will not analyze here is just a diminutive form derived from część (‘part₁’), which often appears modified by the adjectives mała and niewielka (both ‘small’). Its meaning can be paraphrased simply as ‘small part/portion’. The other two expressions derived by the suffix -k-, i.e., ćwiartka and połówka, also have additional lexicalized meanings, namely ‘0.25 l bottle of liquor’ and ‘0.5 l bottle of liquor’, respectively. Moreover, in sports commentary ćwiartka and połówka are sometimes used instead of much more common kwarta and połowa in reference to phases of a game, as in basketball and football. In addition, ćwierć is ambiguous between a PQ meaning and a name of an old measure unit of capacity for dry commodities, especially grain. ⁷

The meanings mentioned above are interesting cases of lexicalization and closer investigation might shed some light on the process of how quantifier meanings can be utilized in the process of word formation. However, given space limitations in the following sections, I will simply ignore them and focus only on the relevant PQ meanings introduced already in Section 1.

3.2 Numerals and measure terms

The first finding regards the distribution of Polish PQs with respect to expressions that do not designate individuals, but rather abstract objects such as degrees and numbers. If all apparently synonymous PQs were semantic expressions of the same type, one would expect that they all should be either compatible or incompatible with such expressions. Yet, there is an asymmetry. Out of all of the examined PQs only two, namely ćwierć (‘quarter₁’) and pół (‘half₁’), can and frequently do co-occur with numeral phrases and measure terms. ⁸ Some representative examples from the NCP corpus are given in (19) and (20), respectively.

Crucially, replacing ćwierć (‘quarter₁’) and pół (‘half₁’) in constructions with numerals and measure terms with other PQs results in unacceptability. For instance, the use of PQs derived by the suffix -k- is infelicitous, as illustrated in (21a). Likewise, połowa (‘half₂’), część (‘part₁’) and większość (‘most’) are incompatible with numeral and measure phrases, see (21b), (22a) and (22b), respectively.

Given the contrasts demonstrated above, the asymmetry between ćwierć (‘quarter₁’) and pół (‘half₁’), on one hand, and the corresponding PQs ćwiartka (‘quarter₂’) and połowa (‘half₂’) and połówka (‘half₃’), on the other, is remarkable. Different distribution suggests that, despite the apparent synonymy, in fact there is a non-trivial difference in the meaning of these expressions. Specifically, only ćwierć (‘quarter₁’) and pół (‘half₁’) can operate on abstract degree/number structures. This means that in order to capture the distinction in question a mechanism distinguishing between proportional quantification in the domain of individuals and in the domain of degrees/numbers is required.

3.3 Approximative modifiers

Another aspect in which particular types of Polish PQs differ, concerns the possibility to co-occur with approximatives such as niemal (‘nearly’) and prawie (‘almost’). It turns out that the distribution of such modifiers is restricted and they are attested only with ćwierć (‘quarter₁’), pół (‘half₁’), połowa (‘half₂’) and większość (‘most’), see (23).

On the other hand, partitives with część (‘part₁’), cząstka (‘part₂’), ćwiartka (‘quarter₂’) and połówka (‘half₃’) modified by approximatives are unattested in the NCP corpus. Moreover, attempts to construct felicitous examples do not give positive results, see (24). And though there seems to be a detectable contrast between sentences such as (24a) and (24b), on the one hand, and (24c) and (24d), on the other, the latter are still judged as somewhat strange. In any case, constructions with approximatives and the PQs in questions are degraded at best.

From the facts that natural occurrences of część (‘part₁’), cząstka (‘part₂’), ćwiartka (‘quarter₂’) and połówka (‘half₃’) are not attested in the NCP and the weirdness of the examples in (24), I conclude that these PQs are incompatible with approximative modifiers, while other Polish PQs are compatible with such expressions. At the same time, given the slight difference in judgments between (24a–b), on the one hand, and (24c–d), on the other, it is possible that the source of the incompatibility in the two cases is not the same. Hence, to account for the contrasts, one needs to identify what semantic features are necessary for the felicitous interaction with the meaning of approximatives.

3.4 Cumulative predicates

Corpus data reveals also that various types of Polish PQs differ with respect to the compatibility with cumulative predicates such as mass nouns and plurals. While część (‘part₁’), połowa (‘half₂’) and większość (‘most’) take such expressions as their complements in partitive constructions, the other quantifiers do not. For instance, (25) and (26) give some of many corpus examples of constructions with plurals and mass nouns, respectively. All of them are ordinary well-formed Polish sentences.

On the other hand, cząstka (‘part₂’), ćwierć (‘quarter₁’), ćwiartka (‘quarter₂’), pół (‘half₁’) and połówka (‘half₃’) appear to be incompatible with mass nouns and plurals. Such combinations either do not occur in the NCP or occur only marginally and can be classified as noise. ⁹ Furthermore, the awkwardness of the sentences in (27) and (28) illustrates their infelicity with plurals and mass terms, respectively.

Importantly, the constraint on plurals does not seem to be syntactic, but rather due to a semantic restriction. In fact, in the NCP one can find examples of partitives with PQs derived with the suffix -k- taking pluralia tantum as their complements, as in (29). Crucially, however, in such constructions pluralia tantum are interpreted as referring to singular objects and not to pluralities. For instance, in (29a) the genitive form of the plurale tantum noun usta (‘mouth’) cannot be understood as designating a collection of mouths. Probably, an even better example is given in (29b) since in Polish the proper name for Hungary, namely Węgry, is a plural form lacking a singular counterpart.

Based on the data discussed in this section, I conclude that ćwierć (‘quarter₁’), pół (‘half₁’) as well as PQs derived by the suffix -k- can only combine with predicates denoting sets of singular objects, whereas other Polish PQs are also compatible with mass terms and plurals. Under standard assumptions about proportional quantification, this contrast is somewhat unexpected. Therefore, a proper treatment of Polish PQs has to involve a notion that would capture the distinction between part-whole structures of singular entities, on the one hand, and that of pluralities and masses, on the other, and explain why the semantics of certain PQs is sensitive to this distinction, whereas the semantics of others is not.

3.5 Collocations

The final piece of corpus-based evidence concerns frequent collocations of the examined PQs. Using the NCP collocator based on the PELCRA search engine, one can determine what nominal expressions follow immediately a given lemma in the corpus sample most frequently. ¹⁰ In this section, I briefly discuss most common complements of Polish PQs, as attested in the NCP. ¹¹

As already mentioned in Section 3.2, ćwierć (‘quarter₁’) and pół (‘half₁’) most frequently co-occur with numerals and measure words designating units of time, volume, length, etc. Though such expressions form the absolute majority of the partitive constructions headed by ćwierć (‘quarter₁’) and pół (‘half₁’), other relatively frequent collocators include several container nouns as well as nouns denoting solid objects. ¹²

On the other hand, część (‘part₁’), połowa (‘half₁’) and większość (‘most’) frequently combine with various types of common nouns including concrete count nouns, abstract nouns, group nouns and mass nouns. Though all of those PQs can combine with both singulars and plurals, as demonstrated in Section 3.4, część (‘part₁’) seems to more often select for singulars, połowa (‘half₂’) appears to be more or less neutral with this respect and większość (‘most’) strongly prefers plurals. ¹³

Finally, as already discussed in Section 3.4, PQs derived by the suffix -k- are only compatible with singular count nouns. Most frequently, they co-occur with nouns denoting solid objects with an internal structure composed of identifiable segments. According to the NCP collocator, the relevant uses of cząstka (‘part₂’), ćwiartka (‘quarter₂’) and połówka (‘half₃’) most often combine with countable food terms. ¹⁴ Another class of expressions these PQs frequently co-occur with are nouns denoting solid artifacts. ¹⁵ What all those nouns seem to have in common is that they denote physical entities such that one can easily divide (or imagine diving them) into compact pieces. ¹⁶

To conclude, the collocation study revealed that ćwierć (‘quarter₁’) and pół (‘half₁’) primarily combine with expressions denoting degrees and numbers. PQs derived with the suffix -k- select for singular count concrete NPs, whereas część (‘part₁’), połowa (‘half₁’) and większość (‘most’) can co-occur with various types of nominals. In the next section, I will discuss two more respects in which Polish PQs differ from each other. Specifically, I will examine properties related to the internal structure of parts denoted by partitives with singular count NPs.

4.1 Spatial integrity

Wągiel (2018, 2019) observed that the Polish PQ połówka (‘half₃’) has a property of imposing a remarkable constraint on the part-whole structure of entities in the denotation of the entire partitive. In particular, połówka (‘half₃’) restricts the relevant set by designating only those parts of a whole that constitute 50% of its volume and form a spatially contiguous object. In other words, it excludes arbitrary sums of portions of matter, which do not form a topologically compact configuration.

To illustrate the effect described above, let us consider the three sentences in (30), which differ only with respect to whether pół, połowa or połówka (all ‘half’) have been used in the partitive. At first glance, they seem to be utterly synonymous, but closer examination reveals that they differ in a non-trivial way. (30a) and (30b) would be true in both scenarios schematically depicted in Figs 1 and 2, where the dashed lines indicate 50% of the volume of the apple eaten by Marysia. Such weak truth conditions differ significantly compared to (30c), which would be true in a scenario represented in Fig. 1, but false in a scenario illustrated in Fig. 2. Wągiel (2018, 2019) proposes that this is because for an entity to count as połówka jabłka (‘a half of the apple’), it needs to be perceived as a compact integrated portion of matter that can be individuated as an object in its own right. Since the spatial configuration in Fig. 2 does not facilitate such conceptualization, (30c) is infelicitous in that scenario.

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Contiguous half

Citation: Acta Linguistica Academica 69, 1; 10.1556/2062.2022.00449

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Discontiguous half

Citation: Acta Linguistica Academica 69, 1; 10.1556/2062.2022.00449

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The same contrast also holds between the basic quantifier ćwierć (‘quarter₁’) and the derived form ćwiartka (‘quarter₂’). While the former imposes no topological restrictions on entities in the denotation of the partitive construction, the latter patterns with połówka (‘half₃’) in that it requires a part constituting 25% of a whole to be perceived as an integrated object that comes in one piece. For instance, (31a) would be true if Marysia simply ate 25% of the watermelon, whereas (31b) requires the portion eaten by Marysia to form an integrated piece.

Finally, the PQs część (‘part₁’) and cząstka (‘part₂’) display the same semantic behavior as discussed above. For instance, (32a) would be true if Marysia ate any portion of the orange irrespective of the fact whether it formed a contiguous or a discontiguous part. On the other hand, (32b) would be true only in a situation when an integrated part, i.e., an orange segment, was eaten by Marysia.

The data discussed in this section provides strong evidence that Polish PQs derived by the suffix -k- restrict the denotation of the entire partitive construction to include only those parts that have a particular topological make-up. Specifically, they denote sets of portions of an entity that are perceived as constituting contiguous integrated parts of a whole.

4.2 Physical and abstract objects

Another data set concerns a class of nouns that systematically have (at least) two senses. Nouns such as bank can simultaneously refer to a concrete physical entity, e.g., a building, and to some abstract object, e.g., an institution. To illustrate this, let us consider the classical examples from the literature on co-predication in (33) (e.g., Pustejovsky 1995; Gotham 2017). The subject DP in (33a) designates a physical volume and its informational content at the same time. Likewise, the noun school can be used to simultaneously refer to a building and an educational community, see (33b), whereas lunch can mean both food and an eventuality of eating that food, as in (33c).

The phenomenon is cross-linguistically widespread and it is also attested in Polish. For instance, a good example of the noun in question is książka (‘book’). As evidenced by (34a), it can simultaneously designate an informational object, i.e., the content authored by Olga Tokarczuk, and a physical entity, i.e., a volume that is lying on the table. Similarly, posiłek (‘meal’) in (34c) refers to both a physical object, i.e., cooked food, and an event of eating.

Before I investigate the behavior of nouns such as książka (‘book’) and posiłek (‘meal’) in proportional partitives in Polish, let us discuss a seemingly different, yet pertinent construction in Hungarian.

6.1 Degree semantics

In Section 3.2, I demonstrated that only the morphologically simplex PQs ćwierć (‘quarter₁’) and pół (‘half₁) can combine with numerals and measure terms, recall (19)–(22). This fact calls for distinguishing typally between expressions that can operate on degree structures and those that cannot. Therefore, following a long tradition dating back at least to Cresswell (1976), I assume an ontology with degrees. Degrees are elements of totally ordered sets called scales (e.g., von Stechow 1984; Heim 1985; Kennedy 1997). Here, I take degrees to be points on a scale, i.e., abstract objects of the primitive type d, rather than intervals of a scale (as proposed, e.g., by Schwarzschild & Wilkinson 2002). Such points can be ordered along different dimensions giving rise to various types of scales, e.g., a scale of height, a scale of weight, etc. I also assume that numerals make reference to degrees on a cardinality scale.

6.2 Mereotopology

The second set of assumptions I adopt in order to derive the typology of PQs in Polish concerns the way parts relate to a whole and to each other. Since Link (1983), mainstream accounts of the meaning of nominal expressions have been grounded in mereology. As such, they distinguish between singular entities and sums thereof, i.e., pluralities. Typically, the two are associated via the parthood relation ⊑, which relates parts and wholes formed from the parts. This allows to model part-whole relations in various linguistic expressions including plurals and conjunctions. Consequently, the mereological enterprise has proved very successful and led to a number of influential theories extending our understanding of nominal semantics (e.g., Krifka 1989; Landman 2000; Champollion 2017 to name just a few).

However, one drawback of such a purely mereological approach is that it reduces a whole to the mere sum of its parts, and thus neglects the arrangement of parts within the part-whole structure. And yet, as discussed in Section 4.1, the data concerning the spatial integrity inference triggered by Polish PQs derived by the suffix -k-, demonstrated in (30c), (31b) and (32b), call for a framework that would allow for distinguishing between arbitrary sums and structured configurations of entities.

6.3 Partitivity

Following Barker (1998), I model the part-of relation in terms of mereological proper parthood (⊏). ¹⁸ Though it is typically postulated that in English partitive constructions this relation is expressed by the preposition of, cross-linguistically there are various ways in which it can be encoded, e.g., via case marking (de Hoop 2003). Therefore, I propose an abstract element part introducing ⊏, as defined in (51), which can be expressed by various formal exponents. For the purpose of this paper, I will assume that part is encoded in Polish PQs themselves as part of their semantics.

Another assumption concerns the so-called Partitive Constraint (Jackendoff 1977). According to the semantic explanation of this restriction, the embedded DP in the partitive construction needs to be entity-denoting, i.e., either definite or specific (de Hoop 1997). I assume the standard maximization plus uniqueness (max) and choice function (cf) treatment for definiteness (cf. Sharvy 1980) and specificity (cf. Reinhart 1997), respectively. In both cases, the denotation of the NP is turned into type e. While in languages such as English max and cf are overtly marked, Polish lacks articles, and thus they are often covert.

Given the assumptions above, the interpretation of the partitive construction in Polish is as provided in (52). Of course, depending on a particular PQ the structure can be augmented with some additional semantic information concerning, e.g., the ratio of the quantity of a part compared to that of a whole.

With every tool in place, let us now move on to derive the differences in the meaning of the Polish PQs under discussion.

7.1 Class 1: Inherent measures

Let us start with the semantics for Class 1 PQs in Tables 1 and 2 represented by ćwierć (‘quarter₁’) and pół (‘half₁’). I propose that underlyingly they are simply measures that can combine either with degree- or entity-denoting expressions. Due to this underspecificity they are the only PQs in Polish that can take measure words and numerals as their complements, recall Section 3.2. In such a case, the entire partitive construction denotes a set of degrees which can be then shifted to type d, if needed. For instance, the phrases ćwierć tony (‘quarter of a tonne’) and pół miliona (‘half a million’) get the interpretations in (53a) and (53b), respectively.

Importantly, however, due to their underspecified status, Class 1 PQs can also combine with entity-denoting nouns provided that they are not cumulative predicates, recall Section 3.4. This restricted distribution can be explained by postulating that ćwierć (‘quarter₁’) and pół (‘half₁’) introduce a special restriction concerning the type of part-whole structures they can combine with. In particular, let us assume that singular count nouns denote sets of mssc individuals (Grimm 2012), i.e., entities conceptualized as integrated objects, as in (54).

Then, the distribution of Class 1 PQs can be captured by proposing that they encode an mssc presupposition, which would allow them to combine only with nominals referring to singular individuals. The measure function μ in (55a) and (55b) yields 25% and 50% of the volume of such an object, respectively.

To conclude, Class 1 PQs are inherent measures. When they combine with a degree-denoting expression, they simply give a measure of that degree. On the other hand, in entity-denoting constructions, they require their arguments to refer to singular objects.

7.2 Classes 2 and 3: Part designators

Classes 2 and 3 differ from Class 1 in that połowa (‘half₂’), większość (‘most’) and część (‘part₁’) simply designate parts within an encoded part-whole structure of an entity denoted by the embedded DP, irrespective of the fact whether it is a singular or a plural individual. As such, they introduce no topological constraints concerning nominal denotations they combine with, and thus are compatible with count singulars, plurals and mass nouns. At the same time, the fact that they take only entity-denoting arguments explains why they do not co-occur with numerals and measure terms.

The contextually conditioned μ measures in terms of volume when applied to a singular object and in terms of number of objects when applied to a plurality. The formulae in (56) and (57) give denotations of partitives with plural DPs, where μ measures in terms of cardinality.

The proposed semantic properties of Classes 2 and 3 discussed above account for most of their distribution and semantic behavior. However, as discussed in Section 6.1.4, the two types of PQs differ with respect to their (in)compatibility with approximative modifiers such as prawie (‘almost’) and niemal (‘nearly’).

7.3 Distinguishing between Classes 2 and 3: Scalar alternatives

The crucial difference between Class 2 PQs and część (‘part₁’) is that the latter is semantically simpler. Unlike other PQs, it merely encodes parthood and introduces no specific information regarding what exact proportion of a whole a given part constitutes, compare (56) and (57). As a result, partitives headed by część (‘part₁’) are true of any (proper) part of an entity denoted by the embedded DP, be it a plurality or a singularity. ¹⁹ Consequently, the closest alternatives for (58a) and (58b) are that no students passed the exam and that no part of the watermelon got spoiled. But those alternatives are false, and thus the meaning of the approximative modifier cannot be applied.

As a result of the semantic incompatibility of Class 3 with approximative modifiers, the composition fails, and thus sentences such as (58a) and (58b) are infelicitous.

7.4 Class 4: Object forgers

The last class, Class 4, consists of the PQs derived by the suffix -k- cząstka (‘part₂’), ćwiartka (‘quarter₂’) and połówka (‘half₃’), which both presuppose and assert the mssc semantics. Similar to Class 1 PQs, via an mssc presupposition they require that a DP they combine with denotes a singular object. This explains their restricted distribution, in particular the incompatibility with cumulative predicates. Yet, what distinguishes Class 4 from all other PQs in Polish is that they also assert that parts in the set denoted by the entire partitive are mssc individuals, i.e., entities conceptualized as integrated objects, recall Section 4.

I propose that the semantic effects of Class 4 PQs are due to a special mereotopological partitioning operation encoded in their semantics. Specifically, mssc _part in (50) restricts the denotation of the entire partitive to a set of non-overlapping integrated proper parts of the relevant entity (see Wągiel 2018). This explains spatial integrity effects as well as forcing physical object interpretations discussed in Section 4. Arguably, mssc _part is introduced by the suffix -k- which would also explain Class 4's derivational uniformity.

Finally, the reason why Class 4 PQs are incompatibile with approximative modifiers is simply because there are no scalar alternatives involved to begin with, and thus there is no ‘close by’ alternative approximative modifier could evaluate. This is because partitives headed by PQs derived by the suffix -k- denote sets of parts of an object that are integrated entities themselves and as such they are conceptualized as independent objects rather than a quantity of matter.

While (60a) is an ordinary felicitous Polish sentence, (60b) is at least degraded because the entity denoted by the partitive construction połówka arbuza (‘a half of the watermelon’) is not viewed as a plurality of material parts whose volume makes up 50% of the whole but more like an object in its own right. This makes it similar to infelicitous examples such as (60c). ²⁰

Class 4 provides interesting evidence for the relevance of the notion of integrity in natural language. I conclude that the interaction of the proposed scalar and mereotopological properties allows us to derive the typology of Polish PQs given in Tables 1 and 2.