Layers and operators in Lakota

Categories covering the expression of grammatical information such as aspect, negation, tense, mood, modality, etc., are crucial to the study of language universals. In this study, I will present an analysis of the syntax and semantics of these grammatical categories in Lakota within the Role and Reference Grammar framework (hereafter RRG) (Van Valin 1993, 2005; Van Valin and LaPolla 1997), a functional approach in which elements with a purely grammatical function are treated as  ́operators`. Many languages mark Aspect-TenseMood/Modality information (henceforth ATM) either morphologically or syntactically. Unlike most Native American languages, which exhibit an extremely complex verbal morphological system indicating this grammatical information, Lakota, a Siouan language with a mildly synthetic / partially agglutinative morphology, expresses information relating to ATM through enclitics, auxiliary verbs and adverbs, rather than by coding it through verbal affixes.


Introduction
The organisation of this paper is as follows: after a brief account of the most relevant morphosyntactic features exhibited by Lakota, Section 2 attempts to shed light on the distinction between lexical words, enclitics and affixes through evidence obtained in the study of this language. Section 3 introduces the notion of ´operator` and explores the ATM system in Lakota using RRG´s theory of operator system. After a description of each grammatical category, an analysis of the linear order exhibited by the Lakota operators with respect to the nucleus of the clause are analysed in Section 4, showing that this ordering reflects the scope relations between the grammatical categories conveyed by these operators. Finally, a summary of the most relevant findings obtained in this research concludes this paper. 1 Financial support for this research has been provided by the Spanish Ministry of Economy and Competitiveness (MINECO), FFI2011-29798-C02-01/FILO. I wish to thank Heiko Narrog for his valuable comments. the nominal phrases, although the latter may also occasionally mark a locative or instrumental adpositional case. As regards branching, Lakota is an example of a left-branching language owing to the fact that it tends to place dependents before heads, the only exception being the fact that adjectives follow nouns. Finally, Lakota can be classified as an active-stative language or a split intransitive language, since the only argument of an intransitive clause is sometimes marked in the same way as an agent of a transitive verb and sometimes in the same way as a patient.

Lexical items, enclitics, and affixes
Enclitics can be defined as morphemes expressing grammatical information and are syntactically independent but phonologically dependent on their host. Yet, enclitics in Lakota show a remarkable heterogeneity with respect to their morphological, phonological and lexical characteristics; it is therefore not easy to decide if postverbal elements are affixes, enclitics or lexical items, more specifically the auxiliary verbs. Firstly, most presumed enclitics in Lakota, like hÁŋ, pi, ktA, or šni, are very commonly written together with the preceding word, thus blurring the distinction between enclitic proper and suffix. Secondly, other elements that are normally considered enclitics, such as séčA, kéyA, láȟčA, huwó, sél, héči, yeló, kštó, ní, škhá or tkhá, as well as having syntactic independence, also show prosodic independence and, consequently, have their own stress. Finally, some other elements commonly referred to as enclitics, which appear in sentence-final position, such as séča, načhéčA, héčhA, iyéčhečA, kéyA, s´eléčheča/s´eléča, or škhé, are formally identical and semantially related to stative verbs, which leads us to think of them more as auxiliary verbs. To summarize, this confusion could be better explained in terms of grammaticalization (Klavans 1995), a process which means that a lexically independent item in a specific context loses the properties of a fully independent word over time and acquires the properties of a morphological morpheme. At any intermediate stage of this evolutionary process, the element in question can be considered as a clitic which, Kansas Working Papers in Linguistics, Vol. 36 (2015), 1-33 4 depending on its degree of grammaticalization, may resemble either a lexical word or a morphological affix, or even share a number of different characteristics with both of them.

Operators in Lakota
The existence of nine kinds of operator is recognized within RRG, namely aspect, negation (including nuclear negation and core/internal negation), directionals, event quantification, root modality, status (including the domain realis vs irrealis, external negation, and epistemic modality), tense, evidentials, and illocutionary force. Taking the study of Lakota enclitics made by De Reuse (1982) and Rood and Taylor (1996), an analysis of the different operators in this language is carried out below, category by category, in an order already determined by the result, namely from a relatively narrow scope to a relatively wide scope.

Aspect
Lakota makes a distinction between the two major aspectual categories, that is imperfective and perfective, by lexical, rather than morphological means. Thus, on the one hand, the presence of adverbs like tȟaŋníš 'already', eháŋtaŋ 'already', náka 'just' or léčheya/lečhála 'just now' marks the perfective aspect: (2 More recently it has been grammaticalized, becoming an enclitic marking duration or continuation of action (similar to the English suffix '-ing'), which may also be used with active verbs as well as with both animate and inanimate subjects: 'He is doing that.' (lit. 'He stands doing that.') In this example the active verb éčhuŋ 'do' is modified by the enclitic hÁŋ conveying the notion of continuative aspect suggestive of an action currently in progress. This evidence, then, confirms the strong tendency for progressives to derive from locative expressions as a cross-8 Lakota can also express continuous aspect through lexical means, that is, through the verbs yaŋká 'sit' and uŋ 'be, exist, remain': E.g. a) Čhéya-y-aŋké cry-3SG.ACT-sit 'She was crying.' (Boas and Deloria 1941: 104) b) A-Ø-phé-wa-úŋ STEM-3SG.STA-wait.for-1SG.ACT-be 'I am waiting for it.' (Buechel 1939: 282) As we can see, the embedded verb cannot be inflected for the subject. linguistic tendency (other lexical sources being motion verbs or auxiliary verbs meaning 'continue', 'hold' or 'keep on doing something (Heine and Kuteva 2002: 157-158 & 185-186)).
Finally, there is an enclitic la 'really, do so' that is used with both nouns and verbs to indicate affection or sympathy, hence it could be considered as an instance of intensive aspect: (8) Míš-eyá wa-škáte-la kte! me-too 1SG.ACT-play-really will 'I do so want to play it too!' (Rood and Taylor 1996: 473)

Negation
Negation is represented in Lakota by the enclitic šni and, like English, it can modify the nucleus, the core or the whole clause, leading then to three types of negation: nuclear, core (also narrow-scope or internal negation), and clausal negation (also wide-scope or external negation). The fact that these three types of negation are expressed using the same form, namely šni, makes it difficult to differentiate between them: (9) Čhaŋté-ma-wášte šni As can be observed in (9), in Lakota, the enclitic šni affects only the basic meaning of the predicate čhaŋtéwašte 'happy', not the participant 'I' or the clause as a whole, and is thus an example of nuclear negation 11 where the enclitic gives the predicate a negative meaning.
However, as we can see in (10) it is possible to negate one specific argument of the core: in this sentence, rather than 'I' or 'read', the enclitic šni negates the core argument wówapi 'book', hence it must be considered an instance of core negation. Example (11) also represents an instance of core negation since it affects the whole core, that is the argument-adjunct otȟúŋwahe-ta and the predicate yÁ 'go away from here', but not the optional peripheral adjunct (i.e. non-argument) ȟtálehaŋ 'yesterday', which is outside the core. Finally, in (12) we can see that the enclitic šni modifies the whole proposition, thereby constituting an example of clausal negation.

Directionals
Directionals express the directional orientation of the action itself or the movement of one of the participants in the action. Lakota realises this grammatical category mainly through the use of free words functioning as both adverbs and postpositions, such as tȟaŋkál ´outside`, mahél ´inside`, waŋkáta ´up`, khúta ´down`, ektá ´to, at, in`, etc. Dependent on their function, RRG is able to establish a distinction between nuclear directionals (13), that is, those directionals that modify the orientation of the action or the event itself without making reference to the 11 Another example of a construction involving nuclear negation could be one containing the enclitic kA 'rather, somewhat, kind of` which', which, according to Rood and Taylor (1996: 474), attenuates the verbal meaning: Eg. Hé Ø-wašté-ke (ye)ló DEIC 3SG.STA-good-rather DECL 'He certainly is a nice guy!' (lit. 'He is certainly not a nice person.') Kansas Working Papers in Linguistics, Vol. 36 (2015), 1-33 9 participants, and core directionals (14), namely those directionals that express the orientation or motion of the participants with reference to each other: The use of these affixes is not very widespread nowadays and it is perhaps indicative of an ancient synthetic way of expressing locatives that is gradually falling into disuse in favour of a more analytical way of using postpositions or adverbs.

Modality
RRG distinguishes between root modality and epistemic modality.

Status
The terms mood and modality have been used many times in studies of grammatical categories in overlapping ways. RRG does not use 'mood' as a theoretical term because it is a complex category whose composition in terms of more basic operators may vary crosslinguistically and, within this theoretical framework, it is considered important to keep these concepts distinct.
Thus, under the umbrella term 'mood ' Foley and Van Valin (1984: 213) include status, which in turn includes the expression of the realis vs irrealis distinction or 'grammatical mood' (i.e. indicative, subjunctive, etc.), external negation and epistemic modality or 'grammatical mood', and IF or 'speech act mood' (i.e. declarative, imperative, and interrogative).

Epistemic modality
As mentioned above, the set of grammatical distinctions termed 'epistemic modality', which specifies the speaker´s commitment to the truth of what is being related, is included in RRG´s

External negation
The Lakota enclitic šni can modify not only the nucleus or the core, but also the whole clause, leading then to an example of clausal, wide-scope, or external negation, which is analysed by RRG under the status operator: Unlike the example in (12), where the negative enclitic šni affected the whole clause, in (26) this element only affects the adjunct ȟtálehaŋ 'yesterday' but, as this peripheral element lies outside the core but inside the clause, it is also an instance of clausal negation. Ø-wašté kte načhéča 'He will probably be good.'

Evidentiality
The grammatical system for coding the source of information is commonly referred to as evidentials. Lakota reflects the different sources of information (e.g. hearsay, inference, conjuncture, or personal eyewitness) through the use of enclitics like škȟÁ 'it is said', or ké(yA) 20 'it is said':

Illocutionary force
The illocutionary force (henceforth IF) of an utterance reflects the speaker's intention when producing that utterance. This grammatical information is universal since all languages have ways of distinguishing statements, questions, and commands, whether by grammatical markers, intonation, or a combination of the two. In order to signal IF, Lakota uses a great number of enclitics, which vary according to the type of IF, the gender and number of the speaker, and the ending of the preceding word. The following chart shows the different markers used in Lakota to indicate the IF of an utterance: In order to express an informal question, especially when the questioner does not expect an answer or when the person being asked is not assumed to know the answer, -so (male speakers) and -se (female speakers) are used instead of -he. 22 Concerning the imperative IF, there is a difference regarding whether the command is addressed to one (singular) or more than one speaker (plural). In order to mark informal commands, -yetȟó (male speakers) and -nitȟó (female speakers) are used, rather than -yo and -ye. Furthermore, when the imperative conveys an entreaty rather than a command, both men and women use -ye.

Ordering of operators
Now that every kind of operator in Lakota has been presented, a reasonably detailed description of the mutual order between the elements conveying the ATM information will be given in this section of the paper by analysing the position occupied by these markers in relation to the nucleus.
This study is concerned with the study of the order of enclitics and auxiliary verbs, rather than adverbs. Adverbs expressing these grammatical meanings always occupy a pre-verbal position within the clause although this is not always the same as they can occur in three different positions : clause-initial position (e.g. takómni 'definitely'), preceding the subject, expressed syntactically through a dependent reference phrase, and verbal complex (e.g. ižéhaŋ 'often'), or before the verbal complex (e.g. lečhála 'just now'). Further research is needed, however, to establish whether the positioning of these lexical elements in Lakota responds to an established ordering principle or not. Although adverb ordering is indeed deserving of attention, I consider that it should definitely be considered separately.  1994 for Korean), have provided strong evidence in a variety of grammatical frameworks to confirm that relations between particular morpheme orders and (semantic or syntactic) scope are undoubtedly observable cross-linguistically. The data obtained with regard to Lakota shows that the order of these functional elements is governed by semantic scope and that the relationship between morpheme ordering and scope is captured elegantly by RRG´s proposal for ordering, which is based on scope in the sense that every operator is attached to a particular layer of the clausal structure.

Relationship between order and scope
RRG posits the existence of three groups of operator --nuclear, core and clausal --selected on the basis of the layer of the clause they modify. These three different groups of operator are represented in the operator projection, becoming a mirror image of the constituent projection, which in turn consists of the following layers: 1) the nucleus, containing the predicate; 2) the core, comprising the nucleus and its arguments; 3) the clause, formed by the core and any Regarding the linear ordering of these operators, RRG (Foley and Van Valin 1984;Van Valin 1993, 2005; Van Valin and LaPolla 1997) claims that there is a primary principle governing the relative order of these elements with reference to the nucleus and assumes that this ordering is a function of the semantic scope and works cross-linguistically. Thus, the nuclear operators must occur closest to the nucleus, the core operators farther from the nucleus than the former, but closer to it than the (sentential) clausal operators, which must be placed the farthest from the nucleus. This proposal resembles Hengeveld´s (1989Hengeveld´s ( , 1990, which also puts forward the idea that the order of operators within the multi-layered hierarchical model of the utterance proposed by Functional Grammar 23 (hereafter FG) reflects the scope relations between the grammatical categories conveyed by these operators. Furthermore, this ordering also seems to accord with Bybee´s (1985) Relevance Principle 24 , in which the ordering of grammatical morphemes is restricted by the relevance of their meaning to the semantics of the predicate. Thus, for example, the aspectual operator, which is related to the internal temporal structure of the event, must be placed the closest to the nucleus, whereas the illocutionary force operator, which identifies the nature of the speech act performed by the sentence, must be the outmost operator: ( the Clause since they both conceive of clause structure as layered. One difference between these two models could lie in the different nature of the clause structure, which is primarily semantic in FG and both semantic and syntactic in RRG. Another difference lies in the fact that, unlike FG, RRG does not consider that the operators are part of the layer. Finally, the order of categories put forward in both approaches is not exactly the same. 24 The basic idea behind morpheme ordering is shared both by RRG and Bybee. However, although the concepts 'scope' and 'relevance to the predicate' are related to morpheme ordering based on semantic information, they are not necessarily the same. This discussion is presented best in Cinque (2014) and Manova and Aronoff (2000).

21
operator is the left-most element and the clausal operator the right. Figure 2 below shows a template illustrating the linear ordering exhibited by the Lakota operators 26 : In (39) -(41) we can observe that core operators precede clausal operators in Lakota, since the enclitics expressing necessity, classified under modality, and event quantification occur closer to the nucleus than the enclitics marking epistemic modality, belonging to status, and IF.

PREDICATE-NUCLEAR-Number-Pronominal
Regarding the relative order of operators within each layer, the following examples include more than one operator belonging to the same layer. Thus, the sentence in (41) shows that the aspectual operator hÁŋ precedes nuclear negation: (42) Wa-čhéya-haŋ šni

ASP NEG
'I am not crying.' The enclitics la and kA, which express the speaker´s affection and an attenuation of the verbal meaning and could consequently also be considered to convey aspectual information (intensive aspect) and nuclear negation respectively, occur outside of hÁŋ (Taylor and Rood 1996: 473-474).
Kansas Working Papers in Linguistics, Vol. 36 (2015), 1-33 23 Unlike the ordering within nuclear operators, the positioning of core operators is not so evident. As we will see, although some core operators do not seem to have a fixed position, a tendency may exist whereby modality occurs closer to the nucleus than core negation, with the latter tending to precede event quantification (see example (56)  Regarding the linear ordering existing among the clausal operators, status seems to be the clausal operator appearing closest to the predicate, followed by evidentiality, with the IF operator occurring on the sentence periphery, as illustrated by the following example: (45) Ečháŋni wakȟáŋ-Ø-kičhi-yuzapi kta škȟé (ye)ló soon sacred-3.ACT-REC-marry-PL POT it.is.said DECL

STAT EVID IF
'It is said that they are going to get married soon.' As for the linear ordering among the different operators included under Status, the distinction between realis and irrealis seems to be the first clausal operator and external negation seems to precede epistemic modality:

Apparent conflicts
It is possible to find some constructions apparently in conflict with the principle governing the ordering of operators within a sentence. Firstly, we have constructions that include the enclitics kta/e héčha, kta iyéčheča, kta iyéčhetu or kta (iyéčheča/iyéchetu) tkȟá, manifesting deontic modality. A few sentences in which some postverbal elements deviate from the expected order are given below: 'We have to buy bread and sugar.' (Rood and Taylor 1976: 198) (50) Sakhíb uŋ-yíŋ kte iyéčhetu welo together 1.ACT-go.there POT must DECL

STAT MOD IF
'We must go together.' (Deloria 1932: 101) In (47) -(50) enclitics expressing obligation, namely héčha, iyéčheča and iyéčhetu, occur farther from the nucleus than the enclitic ktA, which has always been considered to mark the distinction realis vs irrealis. These combinations, in which a status operator precedes a core 27 Contrary-to-fact or counterfactual epistemic modality.
operator, are problematic, since this positioning appears to contradict the principle governing the linear ordering of operators, with a status operator (realis vs irrealis) being closer to the nucleus than a modality operator (obligation). Examples (47) and (48)  As regards examples (49) and (50), in accordance with the LLC (2011: 344), it could, in fact, be argued that the enclitic ktA functions as an element expressing volition. Consequently, the solution I suggest here is that, if the enclitic ktA is regarded as a core operator expressing volitive modality--also known as 'boulomaic' (Kiefer 1994(Kiefer : 2517 or 'bouletic' (Palmer 1986: 12)--, which is, in turn, considered a subcategory of deontic modality, and the enclitics héčha 'We have to buy bread and sugar.' (Rood and Taylor 1976: 198)  It is widely assumed that deontic modals modify the relation between the participant and the action and that epistemic modals are concerned with the speaker's judgment. According to the rules governing linear precedence, the modals should be ordered with respect to each other in terms of their semantic scope, with the deontic modals occurring closer to the verb than the epistemic modals. That is to say, the operator with a narrow semantic scope (deontic modality) precedes the operator with a wider semantic scope (epistemic modal). An attempt to account for the irregular ordering shown by the sequence kta okíhi in (52) could stem from the assumption that, as in many languages--like English for example--, where modal verbs like 'can' can express both root and epistemic modality, the operator okíhi used here could convey the idea of likelihood with two consecutive status operators. However, this possibility is probably untenable since there seems to be a clear-cut distinction in Lakota between root and epistemic modality so that none of the elements expressing modality is able to express both types of modal meaning.
A better way of analysing this anomalous ordering might involve the consideration of okíhi as an auxiliary verb, which can be inflected and also requires the preceding verb to be inflected, so that it seems plausible that the enclitic ktA could have scope over the first verb rather the second and that, consequently, the preceding verb, together with its arguments and operator, would constitute an embedded clause linked to the following verb okíhi 30 . Thus, the sequence kta okíhi would entail a present capacity for a future potentially realisable action and okíhi ktA a future capacity for an action obviously likely to take place in the future: The sentence in (53) would imply 'I think that now I am able to repair the car', whereas the example in (54) could be paraphrased by 'I think that in the future, maybe not now, I will be able to repair the car'.
Finally, as was mentioned above (pages 23-24) regarding the relative order between core negation and event quantification, although the enclitic šni normally precedes the enclitic s´a (55), despite regarding it as exceptional, my native consultants feel confident that it is grammatically correct to use them in a reversed order, namely s´a šni (56), and they argue that this change of order entails a slightly different interpretation: According to my native consultants, the difference between these two examples might conceivably lie in the scope of the negative enclitic šni. Thus, on the one hand, in (55) šni would only have scope over the predicate, but not over the enclitic s´a, leading to an interpretation of the sentence as 'Usually I don´t drive', which could be continued by '…, I ride a horse'. On the other hand, the example in (56) would imply that the element being negated is s´a, rather than the predicate, so that this sentence could be interpreted as 'I don´t usually drive', which could be followed by '…, I hardly ever drive' (see Cumberland 2005: 320 for an analogous example in Assiniboine).

Conclusion
In this paper the ATM functional domain in Lakota was examined using RRG´s theory of operator system. After describing each grammatical category, a comprehensive analysis of the linear order of the different operators in this language was then carried out. The findings obtained in the analysis of the linear ordering exhibited by the Lakota operators appear to validate RRG´s principle of linearity, since it conforms to the sequence nucleus > nuclear operators > core operators > clausal operators, in which operator ordering correlates with scope. There are, however, some constructions that seem to call this claim into question, especially those including the enclitics ktA and šni, which sometimes appear to be placed in an unexpected order when they are combined with other operators., It is particularly striking that the enclitic ktA, which is regarded as an irrealis marker (a clausal operator), normally precedes elements like héčha, iyéčheča, iyéčhetu, tkȟá, which serve to convey obligation, or okíhi, an auxiliary verb expressing deontic modality (both of them classified under modality).
It is also worthy of note that the enclitics šni and s´a are able to change position with respect to each other, thus affecting the scope of the negative operator and consequently its classification as either core or clausal negation. Nevertheless, after close examination, it seems plausible that the enclitic ktA might be used to designate volition as well as the realis vs irrealis distinction, allowing for its classification under modality or status. It is also worth mentioning that this analysis appears to confirm the fact that deontic and epistemic modality never converge in Lakota. Regarding the enclitic šni, it is also clear that, in Lakota, negation may have scope over different layers and, therefore, that šni is able to occupy different slots within the template. These findings emphasise the fact that some enclitics are more versatile than others, but also that maybe the ordering of operators could not be so strict as would be desirable.
Accordingly, these results also reveal the fact that the ordering of operators agrees with that put forward by Rood and Taylor (1996: 473), although the order of the enclitics ktA and šni is in fact freer than their template would suggest, since it is possible for them to express different grammatical meanings and, consequently, to have scope over different layers of the clause.