THE EXHAUSTIVE PARTICLE = ok IN HILL MARI AND BEYOND

. The paper examines the semantics and distribution of the polyfunc-tional Hill Mari focus particle =ok . We describe two interpretations of =ok possible on a wide range of hosts: the exhaustive use and the counteradditive use; besides, we consider several uses that are only possible with a lexically or semantically conditioned set of entities. We argue that =ok falls into a class of devices with not-at-issue exhaustive inferences, along with the English it -cleft and some other cross-linguistic counterparts. We discuss the implications that the Hill Mari data have for the typology of this class of constructions: Hill Mari =ok suggests that discourse givenness of the denotation of the focus constituent is an important dimension along which such elements vary across languages. Besides, in this paper we draw an areal comparison of the Hill Mari =ok with its counterparts in the Volga-Kama languages: Meadow Mari, Chuvash, Tatar, Bashkir, and Udmurt. Although the origin and the general set of readings are the same, the syntactic behavior of =ok ’s counterparts varies significantly.


Introduction
This paper examines the semantics and distribution of the Hill Mari focus particle =ok.It is illustrated by (1): (1) sedӛndon=ok vot jӛlmӛ-žӛ-m=ät because_of_that=EMPH here language-POSS.3SG-ACC=ADDlitÍeratur-ž -m=at jarat-kt-en mošt-en (Mikrjakovo corpus) literature-POSS.3SG-ACC=ADDlove-CAUS-CVB be_able-PRF[3SG] 'It is because of that that she was able to make everyone love both language and literature.' (1) is a natural example taken from a monologue.The main topic of this monologue is a schoolteacher.In this example, the particle attaches to the word sedӛndon 'because of that' and can be translated into English by means of an it-cleft.However, there are other occurrences of =ok which can hardly be translated with an it-cleft.Those are going to be demonstrated later.
The particle =ok is polyfunctional, which means that it is hardly possible to ascribe each and every token of =ok exactly the same semantics.In some cases, -ok is clearly lexically or semantically conditioned; several interpretations only arise with a closed set of entities.Short surveys of the semantics of =ok are contained in (Кашкин, Сидорова, Мордашова, Гарейшина, Учитель 2018; Козлов 2017).The particle =ok, as well as its counterparts in the Volga-Kama languages, will be hereafter glossed as EMPH.
The objective of this paper is threefold.First, we are going to describe the polyfunctionality of the Hill Mari focus particle =ok.We will argue that this particle falls into a class of devices with not-at-issue exhaustive inferences, along with the English it-cleft and some other cross-linguistic counterparts.
Second, we are going to discuss the implications that the Hill Mari data have for the typology of this class of constructions.Hill Mari =ok suggests that the discourse givenness of the denotation of the focus constituent is an important dimension along which such elements vary across languages.
The third objective of the paper has to do with the diachrony of =ok.Hill Mari =ok is a loan from some Turkic language of the Volga-Kama area (presumably Chuvash); particles similar to it both in form and function are attested in several other languages of the area, including Finno-Ugric as well as Turkic.The historical relationship between =ok and its counterparts in the Volga-Kama languages is traced by Zakirova (Закирова 2023).In this paper, we draw an areal comparison of the Hill Mari =ok with its counterparts in the Volga-Kama area: Meadow Mari, Chuvash, Tatar, Bashkir, and Udmurt particles.Meadow Mari data come from the authors' fieldwork in the village of Pri volžskij (Mari El Republic), Chuvash data from Maloe Karačkino1 (Chuvash Republic), and Udmurt data from Šamardan (Udmurt Republic). 2atar data were obtained from native speakers living in Moscow, Kazan (Republic of Tatarstan), and Volžsk (Mari El Republic) and represent different dialects.For Bashkir, we have preliminary elicited data from one speaker of a Southern Bashkir dialect, from which Bashkir seems to pattern with Tatar.Besides elicitation, various grammar descriptions were consulted, namely Пенгитов 1961;Галкин 1964;Alhoniemi 1993;Саваткова 2002  Our Hill Mari data come from two sources.The first is the authors' own fieldwork in the villages of Mikrjakovo and Sosnovoje in the west of the Gornomarijskij Region, Republic of Mari El, Russia, which includes both a database of elicited examples and occurrences of =ok in the collected texts (Mikrjakovo corpus).The second is a corpus of texts coming from another variety of Hill Mari, spoken in the village of Kuznetsovo (Gornomarijskij Region, Republic of Mari El, Russia) and in nearby settlements (http://hillmari-exp.tilda.ws/corpus).Although it should be kept in mind that there might be dialectal differences between those two sources, we are unaware of any such differences that are actually relevant for the purposes of the current paper.Our main argument is based on the elicited and textual data from the Mikrjakovo variety.
Before we proceed to describe the functions of =ok, we will make a few methodological notes.As expected of a focus particle, in all its functions =ok conveys a fairly abstract meaning, which is closely related to the pragmatics of the utterance and its position in the rhetorical structure of discourse.Therefore, it poses a challenge when studied in the field by the usual means of elicitation.Our main method was to construct minimal pairs of sentences that only differed by =ok and to present them to our consultants, asking them to explain the semantic or pragmatic difference between the two.The metalanguage of elicitation was Russian, in which all of the consultants were fluent.
Sometimes our consultants tried to describe prototypical circumstances in which an utterance with =ok would be felicitous.In most cases, however, they just translated =ok with different Russian lexical items: in one group of cases it was 'imenno', in another group 'we, towe, opqtx' were interchangeably used.Russian imenno is best translated into English by means of an it-cleft, towe is an additive particle parallel to English also, opqtx is fairly equivalent to again, and we has no good translational equivalent; we assume that its semantic contribution to a Russian sentence is roughly equal to what we describe as the counteradditive reading of =ok in Section 3.1 (see also Paducheva 1987;Падучева 2018).As the meanings conveyed by those Russian words are quite abstract themselves, often the speakers failed to provide any additional comments on the specific meaning they intended to convey when choosing these Russian equivalents.
A logical step to further capture the actual semantic impact of =ok was to study its distribution, combining it with other operators and running various diagnostics in order to test a number of possible hypotheses about its meaning.However, the starting point of our discussion will be to assume that =ok has two main readings that first emerged during the elicitation process: one more or less corresponding to Russian imenno and the other corresponding to Russian we, towe, and opqtx.Later, we will see if these two sets of contexts where =ok is used form a natural class.
The two aforementioned readings are lexically unconditioned, i. e., they are available for =ok attached to an open class of expressions (with some exceptions).However, there are yet other readings, surfacing in a narrower set of contexts.Descriptively, they only arise in combination with a certain class of words or morphemes restricted semantically or lexically: for example, a peculiar reading of =ok arises when the particle is attached to universal and existential quantifiers.
The structure of this paper is as follows.Section 2 provides some background information on Hill Mari syntax and the particle =ok.Section 3 introduces two major readings that =ok can have: counteradditive and exhaustive.Section 4 is dedicated to the interpretations of =ok that arise with lexically or semantically restricted classes of hosts, such as quantifiers or spatial expressions.In Section 5 we look at =ok from an areal perspective and compare possible uses of =ok with the behavior of its counterparts in the Volga-Kama languages.In addition, we consider a typological parallel of =ok from the East Caucasian family.Section 6 is a short conclusion.

=ok: background information
Hill Mari is spoken by approximately 20,000 speakers in the west of the Republic of Mari El.It is arguably one of the Finno-Ugric languages that have undergone the heaviest contact influence from Turkic (Johanson 2000;Helimski 2003;Agyagási 2012); during its history, it has been in extensive contact with Chuvash and Tatar.It has many borrowings from Chuvash, including not only lexical, but also functional items, e.g.case markers (Федотов 1990).
Like other Hill Mari focus particles, =ok is a clitic which almost always attaches to the word that bears the pitch accent (in most cases, it is the focus of the clause).Usually, it is the sole focus constituent of the clause.

Interpretations of =ok
In this section, we discuss two different interpretations of =ok: counteradditive (Section 3.1) and emphatic (Section 3.2).Then in Section 3.3 we show that these two are, indeed, distinct interpretations.
To describe the contribution of the particle to the semantics of the utterance, we use Roothean Alternative semantics for focus (Rooth 1992).In a nutshell, it implies that focus invokes a set of alternative propositions: for example, the utterance (5a) would have alternatives of the kind (5b).
(5) a. Al wears RED boots b. {Al wears green boots; Al wears black boots; …} The set of focus alternatives explains the dependency between the main pitch accent of the utterance (red in 5a) and the context in which the utterance may be felicitously produced.For every utterance, the context should provide an antecedent that is either a member of its focus alternative set (for example, (5a) can be a correction of the statement Al wears black boots) or a question such that its potential answers are the focus alternatives (for (5a), such question would be What kind of boots does John wear?) The latter option connects the theory of focus with the theory of discource structure.Even in cases in which there are no explicit questions, coherent discourse can be viewed as structured with a hierarchy of Q u e s t i o n s U n d e r D i s c u s s i o n (QUDs; Roberts 2012) that have to be resolved.For example, in a discourse like Even if I don't see his face, I can recognize Al by his boots.Al wears RED boots the question What kind of boots does Al wear?, despite not been explicitly posed, is a natural question to ask after the first utterance.Thus, focus can be viewed as marking the question under discussion.
In such a framework, focus particles can be viewed as contributing some additional information about the set of alternatives.When it is necessary to say something about the connection between the focus particle and the focus of the clause, the latter is called the semantic associate of the particle.In our examples, the associate will in most cases be the phonological host of the particle.4

Counteradditive interpretation
Typologically, one of the broadest and most well-studied types of focus particles is a d d i t i v e (König 1991; Gast, van der Auwera 2011).We will dub the most frequent interpretation of =ok c o u n t e r a d d i t i v e.This term is meant to reflect the fact that a counteradditive focus particle is licensed, in general, by the same discourse context as an additive particle, but is placed on a different constituent than an additive particle is, or would have been, placed.Here we imply the literal, spatial meaning of the Latin preposition contra 'face-to-face; opposite '. 5   To give the reader a first impression of what uses we are going now to describe, we will consider example ( 6): 'MASHA works in the field, and MASHA looks after the children, too.'Such sentences can be translated into English by means of an utterance with an additive focus particle (such as also, too, as well, etc.).However, there is one important difference: the associate of the particle (which is also its syntactic sister) is the repeated constituent, not the newly introduced one.Compare the English example in ( 7), where the associate of also is, by a common assumption, the focus constituent of the clause, i. e., the newly introduced verbal phrase.(7) {Masha works in the field,} Masha also [looks after the children] FOC .
At least at the first glance, =ok restricts the possible context of the use of an utterance in a fashion close to that of the additive particles.Additive focus particles are said to convey an additive presupposition: (8) John also painted [the wall] FOC → 'There is some X, other than the wall, such that John painted X.' However, if we were to translate (8) into Hill Mari, =ok would attach to John rather than to the wall -it is for that reason that we dub this use of =ok counteradditive: (9) stenä-m džon=ok čiält-en (elicited) wall-ACC J.=EMPH paint-PRF[3SG] 'It was John who also painted the wall' {and he also painted something else} Hill Mari also possesses a genuine additive focus particle =at, which behaves in a more predictable fashion, attaching to the newly introduced material.Thus, =at and =ok often co-exist in the same sentence, albeit being attached to different constituents.Compare (10), which is a version of ( 6): 'MASHA works in the field, and MASHA looks after the children, too.'For such sentence as (9), there thus exists a paradigm of three variants.Their propositional meaning is roughly the same: all of them share a common at-issue component 'John painted the wall' and a presupposition 'There is something else that John painted'.However, the utterances (11a-c) differ as to in which discourse context they are to be used.The most immediate question under discussion in (11a) is "Who painted the wall?", and in (11b) "What did John paint?" or "What did John do?" (in the latter case, we have a marked word order with a leftdislocated focus).As for (11c), it can be felicitous under both QUDs.
As well as in the case of additive particles, this presupposition is anaphoric.(11a-c) would seem weird if pronounced out of the blue; they require a preceding utterance such as John painted the floor.More generally, we can say that to host a counteradditive =ok an utterance should have some parallel antecedent utterance, provided (or at least entailed) by discourse context.
Let us take two parallel utterances, each having a pair of contrasting entities: The values [α], [β], [γ] and [δ] can be all distinct, as in (13): floor-ACC I paint-PRF-1SG U2. [stenä-m] FOC [džon] FOC čiält-en (elicited) wall-ACC J. paint-PRF[3SG] 'I painted the floor, and John painted the wall.'However, the value of both [γ] and [δ] can coincide with [α] or [β].In this case, the coinciding constituent carries counteradditive =ok.In other words, counteradditive =ok requires an antecedent utterance that should contain (a) a constituent which is identical to the =ok-marked constituent (John in (11a-c)) but also (b) some material that is different from what there is in the prejacent of =ok (e.g. the floor).
We will make this generalization more explicit arguing that an utterance with =ok should be able to partially resolve a QUD (question under discussion; see Roberts 2012) that is expressible as a multiple wh-question.So, such an utterance has to have either two (or perhaps more) foci or a contrastive topic and a focus (we will assume Büring's (2003;2014)  The Y-value of (18) would be the set {people used to P in the hut | P is a household activity}.The semantic contribution of =ok would be intro-ducing a presupposition that there is some other household activity that the speaker used to perform in the large hearth in the hut.This presupposition holds, since immediately before this sentence the speaker spoke about how beer was brewed in this very place (the large hearth in the hut).
There are also cases in which the host of =ok is the only accent-carrying constituent of the clause: (19) doesn't have any pitch-marked constituents (e. g. foci or contrastive topics) other than the DO, which hosts =ok.Then its Y-value is calculated with respect to some covert non-contrastive topic.Hill Mari is a pro-drop language, and ( 19) contains a null subject pronoun.This yields the interpretation (19a), in which the Y-value is {He chose you; Al chose you; Ben chose you; etc.}; accordingly, the antecedent utterance He chose you makes (19a) felicitous.The Y-value can be calculated with respect to some other covert topic, i. e. a null situation indexical ('this time' / 'in this situation').This would lead to the interpretation (19b), in which the antecedent utterance can be something of the kind Last time, I chose you.
The counteradditive reading of =ok often surfaces with demonstratives.Being attached to a demonstrative pronoun, it yields an interpretation roughly translatable as 'the same': The difference between regular 'this'-readings and particle-based 'the same'readings of the demonstrative can be explained by the above interpretation rule for counteradditive =ok.While 'this'-demonstratives just pick up a salient antecedent individual, 'the same'-demonstratives require that it be contained in an antecedent utterance that partially resolves the same QUD as the current one.hut-in one.ADD neg.EX that-ILL=EMPH that-ILL S. go-PRF[3SG] 'There is nobody in the summer kitchen.Serjoža went there.'In ( 23), the overarching QUD may be something like 'Who is going to be where in the near future?'.Sub-QUDs aiming at partial resolving of the overarching QUD are 'Where are you now going to be?', 'Where is Serjoža now going to be? ',etc. Conversely,in (24), unlike in ( 23), there hardly can be a QUD for which both the prejacent utterance 'Seryozha went to the summer kitchen' and the antecedent utterance 'There is nobody in the summer kitchen' are relevant.

Exhaustive interpretation
Another salient interpretation of =ok is the exhaustive, or the emphatic identity interpretation.The label "emphatic identity" was introduced by König (1991) to describe the semantic impact of such particles as German eben or gerade: ( In general, when discussing the semantics of emphatic identity particles, König (1991) follows the previously proposed analyses of English it-clefts, to which he believes the emphatic identity particles to be semantic equivalents.An English it-cleft is exemplified in ( 33): (33) It was me who he chose.
The semantics and pragmatics of English it-clefts have been vastly discussed (Atlas, Levinson 1981;Horn 1981;Velleman, Beaver, Destruel, Bumford, Onea, Coppock 2012).As it is known since Atlas, Levinson 1981, English it-clefts introduce an e x h a u s t i v i t y not-at-issue component (we will follow Atlas and Levinson in taking it to be a presupposition).It-clefts presuppose that no relevant focus alternative except for the prejacent is true.König takes his "emphatic identity" particles to make more or less the same semantic contribution that it-clefts do, the main difference being that it-clefts form a specialized construction and emphatic identity particles form the same syntactic category as the much-studied only and even.Erlewine and New (2021) give a finegrained semantic analysis of a particle in Burmese that has a "cleft-like" interpretation.Among other linguistic phenomena that have been claimed to contain an exhaustivity presupposition, Hungarian preverbal foci (Szabolcsi 1981;É. Kiss 1998)  We can impressionistically state that German (31), Russian (32) and English ( 33) examples involve emphasis.Our Hill Mari consultants, too, often reported that in cases such as ( 34) and ( 35) =ok is used to emphasize the meaning of the word it is attached to.However, we believe that the notion of emphasis per se is too vague to be lexically encoded.For it-clefts at least, this notion has been successfully reduced to a simpler one, namely that of exhaustivity.For the Hill Mari =ok we suggest that the "emphatic" interpretation boils down to two semantic ingredients, exhaustivity and givenness.

Exhaustivity
Velleman, Beaver, Destruel, Bumford, Onea and Coppock (2012) formulate the exhaustivity presupposition introduced by English it-clefts as follows: (36) "No true answer to the QUD is strictly stronger than p", where p is the prejacent of the cleft.
Note that the QUD determines the focus alternatives: the relevant focus alternatives are a subset of the possible answers to the QUD.Thus, (36) states that among relevant focus alternatives only the prejacent (or, possibly, also other answers entailed by the prejacent) is true.
This presupposition holds for =ok: (37) cannot be continued by an utterance stating that there is something else on the table without making a contradiction: Intended: 'It is a cup that is there on the table.And there is also a pancake.' As is predictable for an exhaustifying device, on no condition does =ok combine with the additive particle =at: 'I wanted to make a pie, but I only managed to make pancakes.'

Givenness
Apart from the exhaustivity inference, the reading of =ok that we dub e x h a u s t i v e in fact includes one more semantic ingredient, namely g i v e n n e s s o f a s s o c i a t e.An interesting and underinvestigated topic in the typology of focus-associated items is which devices have an additional givenness component and which do not.Consider, for example, the Russian imenno.For the utterance with imenno to be successful, the referent should be already introduced in discourse (Козлов 2020).( 40a), an answer to an out-of-the blue question, is infelicitous, while a pre-mentioning of Vasja makes именно felicitous.Russian speakers differ in preferring the options (40b) and (40c).
( Examples (43 a, b), parallel to English (41), are another illustration of the fact that givenness of the associate is a necessary condition on the exhaustive use of =ok.(43a) is infelicitous, as the context does not contain any mentioning of students.(43b), however, is felicitous, as the utterance containing =ok appears in the discussion of the abilities of contemporary students.Note that the referent of the NP that hosts =ok ('some student') is not discourse-given but the denotation of the noun is: students have to be mentioned in the preceding context.(43) a. {Nobody was able to prove this theorem for years} # studÍent=ok tidӛ-m dokazaj-en student=EMPH this-ACC prove-PRF[3SG] 'Intended: 'It was some student that proved that.' b. {Nowadays students can be stunning.For example, you know that nobody was able to prove this theorem for years} studÍent=ok tidӛ-m dokazaj-en student=EMPH this-ACC prove-PRF[3SG] 'It was some student that proved that.' Simonenko and Carlier (2020) propose the following definition of givenness (based on earlier definitions in Schwarzschild 1999 and Kučerová 2012): (44) A constituent C of an utterance u in a context c (in Stalnaker's sense) interpreted with respect to a situation s is considered g i v e n if c entails the non-emptiness of the extension of C in s. (Simonenko, Carlier 2020 : 205).
What is important in Simonenko and Carlier's definition is that givenness, under their view, should be defined not only with respect to contexts, but also with respect to situations (understood in the vein of Kratzer 2007).For example, it is very likely that the speaker of (43a) believes that the extension of the Hill Mari word studÍent is non-empty, i. e. that students, generally, do exist.However, to be g i v e n according to (43) means more: the context entails that the situation under discussion contains a non-empty set of students.This is why (43a) is bad in an out-of-the-blue context but felicitous, if the context contains a discussion of students.For example, it can be uttered in a discussion of how brilliant modern students are.
Not only denotations of constituents, but the entire proposition can be construed as given, as is the case in a special subclass of exhaustive readings known as v e r u m f o c u s readings.Verum focus can be defined as a type of focus which presupposes only two alternatives: the prejacent and its negation (although some data call for a more complicated definition, cf.Höhle 1992).
come-PRF[3SG]=EMPH 'Eventually / after all, Vasja DID come.' Focus alternatives for (45) are as follows: {Vasja came, Vasja did not come}.As in previous cases, =ok states that the prejacent alternative is true, and others are not.In (45), focus alternatives are mutually contradicting, so the exhaustivity presupposition of =ok is vacuous.We claim that in (45), the focus associate of =ok is the whole proposition; consequently, the whole proposition should be discourse-given.It brings about the 'after all' component of meaning: (45) is felicitous if Vasja's coming was already discussed, and now it is asserted that it eventually took place.

Two readings or just one?
We have examined two major interpretations of =ok: counteradditive and exhaustive.However, it might not be immediately clear that the distinctness of the two readings is linguistically real rather than, for example, being merely an epiphenomenon of the study's methodology.Originally, the hypothesis of =ok having two main readings came to the authors' mind during fieldwork, as the speakers offered different Russian words to convey the semantic contribution of =ok (Russian particles we and opqtx for counteradditive, imenno for exhaustive).Could it be possible that what appears to be two readings are actually manifestations of one single reading, simply translated into Russian by different means in different cases?Remember that one of the necessary conditions on the usage of counteradditive =ok is that its host is repeated in a salient antecedent utterance that answers the same QUD as the given utterance.This sounds somewhat similar to the givenness requirement of the exhaustive =ok.
At first glance, there are contexts where it seems to be a natural descriptive choice to assume that both readings are available: (46) klovoj-m=ok aj r-en-äm blue-ACC=EMPH choose-PRF-1SG 1. {I was offered a blue cup or a red cup.I thought for a while, because I liked both.Finally,} 'it was the blue one that I chose.' (Exhaustive reading) 2. {Mary chose the blue cup.-What about you? -} 'I also chose the blue cup.' (Counteradditive reading) However, since the two interpretations of the particle are quite close to each other, there may arise a doubt that we are really dealing with two distinct interpretations rather than two different imprecise translations of a single interpretation.In what follows, we are going to provide additional evidence that the two readings are indeed distinct.The point is that they have different syntactic distribution.
There are certain syntactic contexts, where only the exhaustive reading is available.For example, only exhaustive reading is possible when the particle attaches to a finite verb (47).Counteradditive reading, while logically possible, is illicit (48a).A grammatical means to express the same idea is (48b), where =ok attaches to tenge 'so, in this fashion', a demonstrative pronoun denoting manner, to yield the sense 'in the same fashion, similarly'.These facts fit into a general tendency for focus particles to disprefer verbs as hosts (Forker 2015; Branan, Erlewine 2022).However, what interests us is the asymmetry between the two readings.If counteradditive and exhaustive interpretations were in fact the same interpretation, simply translated by native speakers into the meta-language in different ways, we would not expect this difference in distribution.This is the reason why on the descriptive level, we choose to speak of two distinct major interpretations.Note that we do not make any deeper commitments: for now, we remain agnostic about whether we have to postulate two different lexical entries for those two interpretations.The two distinct interpretations might arise via interaction of the single meaning of the particle with some other elements of syntactic structure.

Summary
In this section, we have presented two readings of =ok that we dub counteradditive and exhaustive.The counteradditive interpretation can be translated with English also or too, but has a different distribution, surfacing on the repeated rather than on the new constituent.The exhaustive interpretation boils down to the inferences of exhaustivity and discource-givenness of the focus associate.While the first interpretation is not available when the particle attaches to finite verbs, the second one is, which shows that the two interpretations are indeed distinct.

Lexically-conditioned uses
Finally, there are some uses of =ok that do not fall into the categories outlined above.For both counteradditive and exhaustive versions of =ok, there are distributional restrictions, but they still can attach to an open class of associates.For the readings we list below, it is not the case: those readings are only available with a restricted set of associates, defined lexically or semantically.In what follows, we discuss lexically-conditioned uses of =ok with quantifiers (Section 4.1), spatial expressions (Section 4.2), similative constructions (Section 4.3), caritives (Section 4.4), and contrastive topics (Section 4.5).

=ok with quantifiers
One of such lexically-conditioned functions of =ok arises when the particle is attached to quantifier phrases, in particular universal and existential quantifiers.We would describe the function of =ok in such contexts as domain-widening.
Domain widening is a pragmatic effect that is well-attested for negative polarity and free choice any (Kadmon, Landman 1993; Krifka 1995) and similar elements in the worlds' languages.In natural languages, quantification over the whole universum of entities is extremely rare; more often the domain of quantification is pragmatically restricted in one way or another.We may utter a sentence like Every person in the village knows Mary even if there are 50 villagers, and exactly 48 of them know Mary, the other two being elderly women who never leave their homes and so have had no opportunity to meet Mary.What we mean uttering this sentence is in fact something like 'Every person in the village who ever meets any people at all knows Mary'.Note, however, that if it is known that there are two old ladies not yet acquainted with Mary in the village, the utterance Every single person in the village knows Mary feels less felicitous.
One of the most widespread views of any and its likes is that such items are existential quantifiers equipped with a sort of pragmatic rule: their domain of quantification is wider than the prototypical domain which can be provided by the context.It is illustrated by the minimal pairs of the following kind: (49) a.A fork will do.
b. Any fork will do.
(49b), unlike (49a), stresses the fact that some conditions in question can be satisfied not only by a default kind of fork (e. g. a steel fork), but also by a non-default kind of fork (e. g. a plastic fork).The precise source of this inference is irrelevant to our present goals.We claim that while any is an existential quantifier that carries a hard-wired domain widening inference, =ok can attach to different quantifiers, adding this inference: According to what the teacher in (51) thinks, the pupil overestimates the complexity of the task.He believes that he could do nothing that would have counted as "something relevant", i. e., a meaningful contribution.The advice of the teacher widens the domain of existential quantification: now some easier things, e. g. solving the easiest bits or even copying the task onto the sheet count as "something relevant".
This function is also attested with universal quantifiers.A universal statement with a widened domain is more informative than one with a standard, nonwidened domain.The speakers often try to express the semantic contribution of =ok in Russian, using reduplicated universal quantifiers: vse-vse [ALL.NOM.PL ALL.NOM.PL], kawdyj-prekawdyj [every.M.NOM.SG.-SUPERL.every.M.NOM.SG].In English, this interpretation is best rendered by expressions such as every single X or every bloody X.  52a) and (53b) from (53a) is reduced tolerance for exceptions.We take the function of the particle in (52b) to be essentially the same as in (53b): the domain of quantification (i.e. the set of which the universal statement holds) is widened so that fewer exceptions remain outside the domain.
This reading of =ok also arises with negative universal quantifiers: Finally, the same function is attested with wh-words.In Hill Mari, wh-questions with the particle =ok attached to the wh-words are infelicitous when uttered out of the blue.The speakers report that the particle signals some difficulty or perplexity on the part of the speaker with respect to how the question might be answered.So =ok is infelicitous in (56a) but is fine in ( 56b What is going on in (56a, b) and (57a, b) is roughly the following: the speaker has a pragmatic presupposition that within the "standard" set of alternatives, no answer to the question is true, e. g., no standard kind of a copybook suits the addressee in (56a, b), no person from some relevant set of people can help the addressee in (57a, b).However, we may be able to find the answer if we consider a widened set of alternatives, i. e. weird kinds of copybooks, or unusual people.

=ok with spatial expressions
=ok attaches to DPs in locative cases and to spatial PPs, indicating greater precision in identifying the location.
Look at (58a).This sentence means that the house in question would be quite close to a person who would turn a certain corner.(58b), in its turn, means that the house in question is the first or the second of the houses behind the corner.(58) a. tӛdӛ-n pört-šӛ [ povorot paštek] PP that-GEN house-POSS.3SGturn behind 'His house is behind the corner.' The Exhaustive Particle -ok in Hill Mari...

b. tӛdӛ-n pört-šӛ [ povorot paštek]
PP =ok that-GEN house-POSS.3SGturn behind=EMPH 'His house is just behind the corner.'A similar interpretation arises in (59).(59a) means that the picture should be placed in some area on the wall above the table.In (59b), the area is interpreted to be narrower: deviation to the left or to the right is tolerated to a lesser extent.( 59 Informally, this function of =ok can be described as zooming in.The meaning of küšän 'above' has two components, referring to the position of an object on the vertical axis (in the upper part of the wall divided by the plane of the table) and on the horizontal axis.In respect to the latter, we may accept a coarsegrained partition of the space of the wall, noticing only three principally different alternatives: 'to the left of the table', 'above the table' and 'to the right of the table' (Figure 1).However, in some cases, we may need a finer-grained partition, where 'above the table' would refer to a smaller region of space lying around the vertical line going through the center of the table (Figure 2).
Arguably, this function of =ok can be described as similar to the previous one.Zooming in means considering more alternatives that would have been overlooked without it: we take into account not only the most salient alternatives, but also the less salient ones.

=ok with similative constructions
With similative constructions, =ok also indicates a greater degree of precision.Consider (60a) and (60b) (the latter is taken from a text).The semantic import of =ok can be compared to that of English just: (60) a. é seé roža-na tože mӛÉ n gaÉ n-em, ätÍä-žӛ gaÉ n S.-POSS.1PLalso I like-POSS.1SGfather-POSS.3SGlike 'Our Serjoža is like me, like his father.'In (61), =ok again helps us to zoom in.If we classify people's heights into classes of comparison, we may do so with different degrees of precision.If we assume a more coarse-grained classification, two people's heights may be counted as equal, but in a finer-grained classification they may still belong to different classes.An utterance with =ok implies that the two people's heights belong to the same comparison class even under a classification which is fine-grained enough.

=ok with caritives
In Hill Mari, caritive meaning ('without') is usually expressed with one of the following markers: caritive case -de or a complex construction consisting of two postpositions gӛc pasna 'without', lit.'from except'.Both constructions attach =ok with a peculiar interpretation that does not have any parallels in other uses of =ok, namely scalar additive interpretation.Possible context: {Don't call Vasja, as he would only interfere and to nothing.}In (63a), Vasja would be a welcome help, but the roof can be repaired even without him.( 63b) is a positive answer: without Vasja the task won't be fulfilled, but with Vasja, it will.In this context, =ok cannot be attached to the caritive: (63c) is pragmatically odd and only possible if the speaker considers Vasja an additional problem, who can only hinder the process.
The contribution of =ok in (62, 63) is one that we haven't encountered yet, namely additive.In particular, it presupposes that some other salient focus alternative is true.As the caritive constituent is focused, in each case two salient alternatives are 'without Vasja' and 'with Vasja'. In (63a), presupposing the 'with' alternative is pragmatically coherent, but in (63c), it yields a contradiction (supposing that we consider Vasja to be a welcome help): a. 'I'll manage to do everything with Vasja' presupposed 'I'll manage to do everything without Vasja' asserted c. 'I won't manage to do everything with Vasja' presupposed 'I won't manage to do everything without Vasja' asserted.
(c) is only felicitous in a context where we would be able to accommodate the necessary presupposition, i. e. Vasja is an obstacle rather than a welcome help -for example, if he would only interfere and do nothing.This is indeed the case, according to our speakers' comments.
Apart from functioning as a caritive case marker on nouns, -de also attaches to verbal stems and forms negative converbs (V-de 'without doing V').The scalar additive interpretation arises with converbial -de as well.

=ok with contrastive topics
Hill Mari has a way of morphological marking of contrastive topics by third person possessive, which is not obligatory but very frequent in natural discourse.Arguably, the semantics of the third person possessive does not come down to contrastive topicality (Плешак, Хомченкова 2019).Rather, instances of contrastive topic simply fall into another natural class, presumably defined by membership in a discourse-given set (see Simonenko 2014 for Meadow Mari).However, contrastive topic instances of 3rd person possessive are quite frequent, and it is those instances that can attach =ok.
Contrastive topics bear a not-at-issue component quite similar to exhaustivity (on the nature of this component, see Büring 2014).Consider English example (66): (66) [This pear] CT , I will have for my breakfast.
(66) is felicitous in a context, where (a) besides the pear, there is one or several items (another pear or an apple), and (b) the fate of being eaten for breakfast awaits only the pear in question, while other items are going to be preserved.This not-at-issue component is often strengthened by the exhaustive presupposition introduced by =ok: We argue that in this case, =ok bears its regular exhaustive interpretation.
A common pragmatic function of the combination of third person possessive and =ok is fixing the scope of negation.While Hill Mari has constituent negation, another strategy can be employed instead: the constituent that is to be negated is contrastively topicalized, and the negated verb bears a verum focus accent.It is exemplified in ( 68 A translation of ( 68) reflecting the information structure of the original sentence more accurately would be 'As for often, the going-home event cannot be characterized with this frequency'.The contrastive topic in (68) presumes a set of discourse questions of the following kind: (i) 'Did we go home often?' (ii) 'Did we go home once a month?(iii) 'Did we go home regularly?' (iv) 'Did we go home sometimes?' (68) is a negative answer to (i).But, just as it was the case in ( 66), (68) implies that this kind of answer is only true for (i) but not for (ii)-(iv).There are only two possible answers for general questions such as (ii-iv), namely posi tive and negative.So, contrastive topic in (68) entails that questions (ii)-(iv) have positive answers.This is why (68) has the following resulting interpretation: 'We did go home, but not regularly.' In a similar vein, (69) has an interpretation 'She does speak Mari, but not very well': 'She speaks {Mari} not very well.'

Lexically or semantically-conditioned functions: summary
In this section, we have listed several lexically-conditioned functions of =ok.It is by no means an exhaustive list.We did not discuss, e.g., =ok with imperatives, with converbs and other temporal expressions, or in combination with the word lač 'only, exclusively'.However, it is clear that several relatively frequent uses that we have outlined already give the impression of a complicated network of readings.
The readings arising with quantifiers, spatial expressions and similative constructions are clearly quite close to each other: in those cases, =ok denotes what we have informally dubbed as zooming in.In the case of quantifiers, we enlarge the domain of quantification, including less salient instances.Spatial expressions and similative constructions do not involve quantification, but in these cases, an utterance with =ok also considers more alternatives than the utterance without =ok.However, it remains to be seen whether there can be done a compositional analysis explaining the semantic contribution of =ok in the aforementioned cases and its inability to appear in some other contexts.For example, =ok cannot mean something like 'precisely' in combination with numerals: (70) kok edem=ok tol-n-t two person=EMPH come-PRF-3PL 1. 'It's two people that came' (exhaustive) 2. 'Again, two people came' (counteradditive) 3. # Exactly two people came.

The Hill Mari =ok in an areal-typological perspective
Linguistic theory has two principally different ways to explain complex phenomena, and in particular, tricky polysemy patterns.One is internal analysis of meaning, which can show that what seems a handful of diverse functions has a non-trivial common core or, perhaps, is in fact multiple manifestations of a single function (for an example see Coppock, Beaver 2014).Another one is considering the external history of the phenomena: its many complications may be due not to some or another internal logic, but due to a series of unconnected events in the history of language.For example, Grossman and Polis (2017) discuss one case of adposition borrowing from Greek into Coptic, which shows that disjoint functions on the semantic map can be borrowed apparently independently from each other, thus forming a typologically unexpected polyfunctionality pattern.
As we have already said, an important fact about =ok is that it is a loanword into Hill Mari from Turkic, and Hill Mari is by no means the only language that borrowed this particle.Let us now put =ok into an areal perspective.Hill Mari belongs to the Volga-Kama Sprachbund along with, at least, Chuvash, Tatar, Bashkir (< Turkic), Meadow Mari and Udmurt (< Finno-Ugric).As more peripheral members, Mordvinic and Komi languages (< Finno-Ugric) are also included in the Volga-Kama Sprachbund (Johanson 2000;Helimski 2003).
The Volga-Kama languages share a considerable number of common features in morphology, syntax and lexicon (Beke 1914(Beke -1915;;Серебренников 1960;Johanson 2000;Helimski 2003;Agyagási 2012).One property of interest for us shared by the core members of the Sprachbund is the presence of exhaustive particles cognate to =ok.Table 1 provides data on the distribution of these particles across the languages of the Sprachbund.
The particles listed in Table 1 all go back to the same source, namely to the Proto-Turkic *=ok.Its earliest appearance in texts dates back to the Old Turkic period, i.e. to manuscripts attributed to the 7 th -13 th centuries (Erdal 2004 : 342): (71) Old Turkic maytri bodisavt ol=ok oron-ta olor-up...

Maitreya bodhisattva that=EMPH place-LOC sit-CVB '
The bodhisattva Maitreya sat down in that very place…'.

Table 1 Cognates of the Hill Mari particle =ok in the Volga-Kama languages
In Turkic languages of the area reflexes of *=ok are inherited from the protolanguage, whereas in Finno-Ugric languages the corresponding particles are considered by several researchers to be borrowings from Chuvash (Wichmann 1903 : 37;Galkin 1964 : 183-184;Wichmann, Korhonen, Uotila 1987 : 65;Fedo tov 1990 : 119).This is supported by the distribution of these particles in the Turkic and Finno-Ugric languages: none of the Uralic languages outside the Volga-Kama area feature counteradditive particles phonologically similar to =ok, including Komi-Permyak and Komi-Zyrian, which are close relatives of Udmurt. 8n the other hand, reflexes of =ok are present in many Turkic languages outside the Volga-Kama area: Altai, Baraba Tatar, Kazakh, Kyrghyz, Kumyk, Nogay, Tofalar, Uzbek, Uighur, Khakas, Shor (Şahin 2009; Закирова 2019).
The two major readings described for the Hill Mari =ok, counteradditive and exhaustive, are available for cognates of =ok in most Volga-Kama languages.However, the details of semantics and syntax of counterparts of =ok differ significantly across the area.For example, while Chuvash, Hill and Meadow Mari and Udmurt allow for a counteradditive reading of the particle on all types of NPs, e.g. ( 72), in Tatar and Bashkir =uk/=ük is very rare on NPs and is conditioned by some factors that require further investigation.For example, the Tatar counterpart of the example (72) is ungrammatical (73), however, =uk/=ük seems to be licit in ( 74 Intended meaning: 'Mary works in the garden and she also babysits.' (74) Tatar kem klč belän kil-ä, klč-tan=uk ül-ä who sword with come-PRS.3SGsword-ABL=EMPH die-PRS.3SG'Who comes with a sword, will die by the sword.' The counteradditive reading of demonstratives (Dem) marked by counterparts of =ok is possible in all languages considered; however, here again Tatar and Bashkir differ from the rest of the Volga-Kama Sprachbund.In all languages considered, adnominal modifiers precede nouns (N).However, while in Chuvash, Hill and Meadow Mari, and Udmurt the particle attaches to the noun (Dem N=ok) (75), in Tatar and Bashkir it follows the demonstrative pronoun ( 76 Our findings corroborate the claim that the availability of being hosted by a finite verb is a relevant parameter.We have shown in Section 2 that in Hill Mari, the exhaustive reading is, and the counteradditive reading is not licit on finite verbs.This is a generalization that holds across the Volga-Kama Sprachbund.On verbs, cognates of =ok behave differently from other types of constituents: in the Volga-Kama languages counteradditive readings of =ok are ruled out (81-82), although they are possible at least in one Turkic language outside of the Volga-Kama area, namely Khakas (83).In Khakas, the particle =ox has counteradditive interpretation (83a), which is available on finite verbs as well ( 83b Table 2 shows that the uses of cognates of =ok in Chuvash, Udmurt and Mari are similar, while Tatar and Bashkir pattern differently.This can be interpreted in at least three ways.
The first possibility is that Chuvash is conservative, and Tatar and Bashkir innovative.If this is the case, at the Proto-Turkic stage =ok had approximately the repertoire of uses that it now has in Chuvash and in the Finno-Ugric languages of the area.In Tatar and Bashkir, on the other hand, the use of =ok has declined.
The second possibility is that Tatar and Bashkir are closer to the Proto-Turkic state, while in Chuvash =ok became much more productive and was transferred into the Finno-Ugric languages of the area with the whole range of its contexts.
Finally, it may be the case that the proto-language had a range of contexts different from both Chuvash and the Kipchak languages of the area.While we do not have access to Proto-Turkic, at least written records in Old Turkic and Chagatai are available.Although we have not conducted a full-fledged study of the matter, a brief search in grammars of these languages already yields promising results.Erdal's Old Turkic grammar ( 2004) contains examples of a verum focus reading on verb (86).Another example from Chagatai grammar (Щербак 1962) illustrates an exhaustive reading of =ok on an NP.(86) Old Turkic öl-ür-täči=k=ök die-CAUS-PTCP.FUT=EMPH=EMPH 'He will really kill us.' (Erdal 2004 : 343) On the other hand, we can see from (71) that in Old Turkic =ok attached directly to the demonstrative and not to the right edge of the DP.Thus, the situation in the Proto-Turkic could have been different both from Chuvash and Kipchak, but at least Chuvash was not unique in having uses of =ok shown in Table 2.We can thus conclude that at least some uses of =ok were lost in Tatar and Bashkir.
The fact that all languages of the Volga-Kama Sprachbund share the restriction against the counteradditive reading of the exhaustive particle on verbs may be interpreted as an areal feature, as the use of a cognate particle is found in Khakas.On the other hand, as we pointed out above, there is a crosslinguistic tendency for languages to restrict the use of focus particles on verbs.So we can consider the counteradditive use in Khakas as a typological rarum.
We would like to mention one more use of =ok that is absent in Hill Mari but is important for =ok's counterparts in the Volga-Kama region.Finno-Ugric languages of the Volga-Kama area express standard negation via analytic construction with a negative auxiliary that agrees with the subject and a connega tive form of the verb.Udmurt =ik and Meadow Mari =ak can cliticize to the negative auxiliary and have scalar additive interpretation: (87) Particles ambiguous between exhaustive and scalar additive interpretation, the latter available only in presence of negation, are attested cross-linguistically (see Erlewine, New 2021 for an analysis of a Burmese focus particle, with a review of cases of a similar polysemy attested worldwide).While Hill Mari =ok does not have the scalar additive reading on negated verbs, it may have been there on some earlier stage.Remember that Hill Mari =ok can have scalar additive interpretation with caritive constructions and negative converbs.This might be a remnant of a wider scalar additive function under negation that disappeared in Hill Mari but is preserved in other Volga-Kama languages.
In general, at least some puzzles about syntax and semantics of Hill Mari =ok may be explained if we understand an areal distribution of the features of =ok's counterparts in Volga-Kama languages, both in synchrony and diachrony.Georgieva, Salzmann and Weisser (2020) develop a structural account within the framework of Distributed Morphology to explain the morpheme order in Mari verbal complex.While this is a good example of a language-internal (or biocognitive in terms of Haspelmath 2021) explanation, we would like to propose a language-external explanation to a group of facts of a similar kind.
As we have pointed out, in Hill Mari, =ok can be attached to finite verbs.When the verb is negated, =ok attaches not to the negative auxiliary, but to the connegative verb form (or, in other words, appears on the right edge of the whole negative construction): (91) a-k tol=ok There might be an internal syntactic explanation for this fact, but at least not an obvious one: both =at and =ok have wide scope with respect to negation, and apart from this peculiar fact, the syntax of =at and =ok is quite similar.On the other hand, the history of language interaction readily provides an external explanation.While =ok is a loan, =at has a Finno-Ugric origin.Note that =at behaves in a more expected way (if a marker modifies a construction, it is expected to be hosted on the head of the construction rather than on its dependents, cf.Zwicky 1985): it is the behaviour of =ok that is deviating and needs an explanation.We tentatively propose the following one: =ok is a clitic that attaches to multiple types of hosts.However, it has probably been borrowed not as a separate lexical item, but by way of calquing certain Chuvash constructions where it was present.Chuvash has no negative auxiliaries: it expresses negation by means of a bound morpheme.Thus, the only possible place for the emphatic clitic is to the right of the verbal form.(93) Chuvash vəl kil-mest=ex he come-neg.NPST.3SG=EMPH'He is not coming, eventually.' We propose that the whole pattern was copied into Hill Mari from Chuvash along with the matter borrowing of the particle.The Chuvash synthetic verb form was replaced with Hill Mari analytic construction with a negative auxiliary, but the original position of the particle on the right edge of the construction was retained.
Finally, we would like to mention that the colexification pattern typical of =ok and its counterparts is by no means restricted by the Volga-Kama Sprachbund.Particles with a similar distribution are found at least in one branch of the East Caucasian family, namely in the Avar-Ando-Tsez branch, cf.Avar =go, Andi =gu, Karata =da, Tsez =tow etc.The different uses of the Avar =go and its diachrony have been described in detail in Forker 2015.Particles of this type are labeled by the author as intensifying particles, which emphasizes the functional similarity of these particles to SELF-intensifiers (König, Gast 2006).Forker (2015) provides a semantic map based on the data of Avar, Bagvalal, Hinuq and Hunzib, which includes the following functions: identity, reflexive, scalar additive, contrast & emphasis, derivation of indefinite pronouns.While it is not immediately clear how to map some of those functions onto Hill Mari, in general the colexification pattern looks quite similar.Thus, the polysemy pattern exhibited by =ok seems to be cross-linguistically recurrent not only within the borders of the Volga-Kama Sprachbund, but also beyond it.

Conclusion
In this paper, we have described some of the uses that the Hill Mari particle =ok has.We have shown that its two major readings are c o u n t e r a d d it i v e and e x h a u s t i v e.For the counteradditive reading, we have proposed a semantic analysis that captures its similarity to additive particles but highlights the difference, namely that counteradditive particles attach to the repeated constituent and not a newly introduced one.As for the exhaustive reading, we showed that it boils down to a combination of exhaustivity and givenness.We argued that the two readings are distinct by comparing the possible hosts for both readings: whereas the counteradditive reading is impossible if the particle attaches to the verb, the exhaustive reading is possible with =ok on verbs and surfaces as a verum focus reading.
Besides counteradditive and exhaustive, =ok has numerous other readings, that only surface in combination with a certain type of hosts, restricted lexically or semantically.We described several of them, specifically focusing on the interaction between the host and the particle =ok, and concluded that for quantifiers, spatial expressions, and similative constructions, the semantic effect of =ok may be described as "zooming-in": =ok signals that a wider range of alternatives should be considered, including the less salient ones.With caritive constructions, the contribution of =ok is scalar additive; this reading of =ok is not found in other contexts in Hill Mari but is prominent under negation in other languages of the area.Moreover, =ok attaches to constituents marked for contrastive topic; this construction is particularly frequent as a means to express constituent negation.We propose that in this use, the contribution of =ok is exhaustive.
Finally, we have put =ok into an areal perspective.We have compared the two major uses of =ok in the Volga-Kama languages and found that Chuvash, Hill and Meadow Mari, and Udmurt pattern rather similarly: they allow the same counteradditive and exhaustive interpretations on NPs and adverbs but only the exhaustive interpretation (verum focus) on verbs.This, however, is not a trivial restriction, as another Turkic language, Khakas, allows for a counteradditive reading on verbs.
One point where variation is observed is negated verbs.In all Finno-Ugric languages of the area, counterparts of =ok attach to the negative auxiliary with a scalar additive interpretation.In Hill Mari, however, =ok attaches to the lexical verb.We propose an external, contact-based explanation for this phenomenon.

Figure 1 .
Figure 1.A coarse-grained partition of the space of the wall: 'to the left of thetable' vs. 'above the table' vs. 'to the right of the table'.

table' vs. 'above the table' vs. 'to the right of the table'. Figure 2. A finer-grained partition of the space of the wall: 'right above the table' vs. all other alternatives.
The first-aid post is a wooden old house, there also… in the yard of the first-aid post, again…' [there is a barn].

Table 2 Readings of =ok on different hosts across the Volga-Kama Sprachbund
The Exhaustive Particle -ok in Hill Mari...The contexts of use and the readings of =ok's counterparts are summarized in Table2: The examples below illustrate counteradditive (94), verum focus (95), and scalar additive under negation (96) readings from Andi (< Avar-Andic < East Caucasian).
F-come=REP this-F forest-INTER person=EMPH M-reach-FUT.NEG dʒahan_daman-no (Magomedova, Alisultanova 2010) hell-SUP.LAT 'In the forest, she came to the place where not even one person has stepped foot.'