John Gluckman and Margit Bowler

The expression of modality in Logoori

Open Access
De Gruyter Mouton | Published online: January 20, 2021

Abstract

This study presents a theoretically informed description of the expression of modality in Logoori (Luyia; Bantu). We document verbal and non-verbal modal expressions in Logoori, and show how these expressions fit into proposed typologies of modal systems (Kratzer, Angelika. 1981. The notional category of modality. In Hans-Jurgen Eikmeyer & Hannes Rieser (eds.), Words, worlds, and contexts: New approaches in word semantics, 38–74. Berlin: Mouton de Gruyter, Kratzer, Angelika. 1991. Modality. In Armin von Stechow & Dieter Wunderlich (eds.), Semantics: An international handbook of contemporary research, 639–650. Berlin: Mouton de Gruyter; van der Auwera, Johan & Vladimir Plungian. 1998. Modality’s semantic map. Linguistic Typology 2. 79–124. https://doi.org/10.1515/lity.1998.2.1.79; Nauze, Fabrice. 2008. Modality in typological perspective. Amsterdam: Institute for Logic, Language, and Computation PhD thesis). We show that Logoori’s modal system raises some interesting questions regarding the typology and theoretical analysis of modality and its relationship to other kinds of meaning. Our study contributes to the nascent but growing research on modal systems cross linguistically by adding data from an understudied Bantu language.

Abstract in Loogori

Kuloma sia linyalika na lidemadema, kya kulanganga “imiima” (“modality”), gavoleka mu Lulogooli. Lulogooli ni lulimi lwa ihiri ya avaluhya, na lumolomwa mu vivala vya imugwi wa Afrika. Ulusuma ilu lunduta kutula ku zisaabu na lilekanya lya uvuhandiki na uvwimiridzu vwa imiima. Kulangama sia livugirirana lya tsingulu (“force”) na lifunya (“flavor”) kutula ku Kratzer, Angelika. 1981. The notional category of modality. In Hans-Jurgen Eikmeyer & Hannes Rieser (eds.), Words, worlds, and contexts: New approaches in word semantics, 38–74. Berlin: Mouton de Gruyter, Kratzer, Angelika. 1991. Modality. In Armin von Stechow & Dieter Wunderlich (eds.), Semantics: An international handbook of contemporary research, 639–650. Berlin: Mouton de Gruyter limannywa mu Lulogooli, na kuviika imiima djia Lulogooli mu vugeri vwa imiima djia tsinyimi tsya lilova. Misingi minene djia likaladasi yili ni: (a) Amang’ana gamannya imiima djia amakuva ga Lulogooli gamannya mativuli manyingi. Mala gaveye na luvera na imiima na khandi si gaveye navwo dave. Yagandi gavuula he, ni mativuli galiha gavoyong’ana na imiima gya amang’ana (henza Bowler na Gluckman. To appear. Gradability across grammatical domains. Linguistic Variation); na (b) imiima mu Lulogooli gyavukanya mugati mwa imiima msi mwa umundu (“participant-internal”) na imiima ikyova wa mundu (“participant-external”) sia Nauze, Fabrice. 2008. Modality in typological perspective. Amsterdam: Institute for Logic, Language, and Computation PhD thesis na Auwera, Johan & Vladimir Plungian. 1998. Modality’s semantic map. Linguistic Typology 2. 79–124. https://doi.org/10.1515/lity.1998.2.1.79 vaahandika. Mu goosi ndio, likaladasi lyetu limeda ku igasi ineneha imannya imiima mu tsinyimi tsya Avaafrika (Kawalya, Deo, Gilles-Maurice de Schryver, & Koen Bostoen. 2019. A corpus-driven study of the expression of necessity in Luganda (Bantu JE15). Southern African Linguistics and Language Studies 37. 361–381).

1 Introduction

This article provides a theoretically informed description of modality in Logoori (Bantu, JE 41, rag), a Luyia language spoken in East Africa, primarily in Kenya.[1] Logoori is also known as Maragoli, Llogoori, Logooli, and Luragooli, among other names. Conceptually speaking, modals are used to talk about what is possible or necessary, rather than what is real. We show examples of some basic modal expressions in English in (1); the relevant modal elements are underlined.

(1)
a.
Mary might be at home.
b.
Mary must be at home.

Cross-linguistic research has revealed a great deal of variation in how modal categories are grammaticalized (Bybee et al. 1994; Deal 2011; Matthewson et al. 2007; Nauze 2008; Vander Klok 2013; van der Auwera and Plungian 1998, among others). However, from a typological standpoint, the modal systems of African languages are relatively under-described. This article therefore works towards addressing this descriptive gap, and contributes to our overall body of typological literature on modality.

The Logoori modal system is of linguistic interest for several reasons. First, Logoori verbal modals have a synchronic “double life” as both modal and lexical (i.e., main, non-modal) verbs. Second, Logoori displays what we believe is a previously undescribed connection between the expression of strong necessity modality and scalar (including spatial) thresholds (discussed in Section 4.5). Third, the Logoori modal system is of typological interest in that it makes some categorial distinctions that are not commonly grammaticized in other languages, namely, the distinction between “participant-internal” and “participant-external” modality (Nauze 2008; van der Auwera and Plungian 1998; discussed in Section 2.2). We otherwise find confirmation of some previously observed cross-linguistically robust patterns e.g., Logoori modals are fixed for Kratzerian force, but vary in flavor.[2]

Our primary focus is on the Logoori verbal modals, though we will also briefly discuss some non-verbal modal markers. We primarily aim for descriptive adequacy. While our goal is theoretically informed description, we will not attempt to formalize any of the notions discussed below. That said, it is not possible to talk about modal categories without presupposing some basic theoretical concepts. We therefore begin by summarizing previous literature on formal and typological approaches to modality in Section 2. This will frame our own discussion of the Logoori data. We discuss our fieldwork methodology and data presentation in Section 2.4, and provide our data in Sections 3, 4, and 5 on possibility, strong necessity, and weak necessity modality, respectively. In Section 6, we conclude and discuss our findings.

2 Existing categorizations of modal systems

In this section, we briefly review two proposed categorizations of modal systems. We discuss Kratzer’s (1981, 1991) highly influential theory of modality in Section 2.1. Kratzer distinguishes between modal “force” and “flavor,” which we show in Sections 3, 4, and 5 are relevant distinctions in Logoori. In Section 2.2, we discuss van der Auwera and Plungian (1998) and Nauze (2008)’s proposed modal typologies, focusing particularly on their distinction between “participant-internal” and “participant-external” modality. In our presentation of the Logoori data, we show that this distinction is relevant in capturing some morphosyntactic facts about the Logoori modals. We present our Logoori modal data in Sections 3, 4, and 5 roughly according to the modal classification proposed by Nauze (2008) (following van der Auwera and Plungian 1998). In Section 2.4, we discuss how we collected the data in this paper.

2.1 Kratzerian modal force and flavor

Conceptually speaking, the English modal elements might and must in (2) differ with respect to the “strength” of the speaker’s belief in the proposition “Mary is at home right now.” (Hence-forth, we will refer to the proposition embedded under a modal as the scope proposition.)

(2)
a.
It’s the weekend. Sometimes Mary stays at home on the weekend, sometimes she goes to the park or the farmer’s market, so … Mary might be at home right now.
b.
Mary always drives her car to and from work. It’s 7pm on a work day, and I see that her car is parked in front of her house, so … Mary must be at home right now.

Might in (2a) conveys that the speaker believes that it is a possibility that Mary is at home. Must in (2b) conveys that for all the speaker knows (based on e.g. her perception of Mary’s car in front of her house), the speaker is certain that Mary is at home (i.e., the speaker believes it is necessarily true that Mary is at home). Kratzer (1981, 1991 describes might and must as differing in modal force. In the broadest strokes, Kratzer distinguishes between what she calls “existential force” modals like might and “universal force” modals like must.[3]

In addition to encoding a distinction in force, modals can also encode a distinction in what Kratzer terms modal flavor. This describes the kind of facts that speakers use to evaluate a modal. Given the contexts provided in (2), might and must convey that the speaker is using their knowledge of the world to reason about the truth of the scope proposition. In Kratzerian terminology, these are instances of epistemic modality. However, there are other ways to reason about hypothetical situations. We can reason about possibilities and necessities with respect to laws (deontic modality), goals (goal-oriented modality, also called teleological modality), or with respect to the circumstances of the world (circumstantial modality). We show an example of a deontic possibility modal may in (3a), a goal-oriented possibility modal can in (3b), and a circumstantial possibility modal can in (3c).[4]

(3)
a.
Deontic modality:
You may go to the bathroom.
b.
Goal-oriented modality:
You can take a bus to the airport.
c.
Circumstantial modality:
Now that you’ve bought the ingredients, you can make donuts.

Under a Kratzerian theory of modality, modals can therefore vary along two axes: force and flavor.[5] Cross-linguistic work has shown that languages can vary with respect to whether or not their modals are lexically specified for force and/or flavor. Some languages’ modals only mark force (English; von Fintel 2006), whereas others only mark flavor (St’át’imcets; Rullmann et al. 2008).[6] Others are argued to be underspecified for both force and flavor (Washo; Bochnak 2015), or mark both force and flavor (Paciran Javanese; Vander Klok 2014). In this paper, we show that Logoori modals pattern roughly like English in that they are marked for force and unmarked for flavor. However, as we show, certain morphosyntactic configurations are only compatible with certain modal flavors.

2.2 Participant-internal and participant-external modality

The Kratzerian concepts of modal force and flavor in Section 2.1 are central to contemporary semantic theories of modality. However, it is possible to categorize modal data like (1)-(3) in different ways. One of our goals in this paper is to bring together theoretical ideas and typological ideas about how to describe modal data.

We categorize the Logoori data according to participant-internal versus participant-external modality, following classifications proposed in the typological literature by van der Auwera and Plungian (1998) and Nauze (2008), among others. Like Kratzer (1981, 1991, these authors assume a category of epistemic modality as shown in (2) (i.e., modal reasoning that is based on the speaker’s knowledge about the world). These authors then divide the rest of the modal space into what they term participant-internal and participant-external modality.[7]

Participant-internal (PI) modality refers to possibilities or necessities that are “internal” to some participant in the event. PI possibility modality therefore expresses an ability or capability of some event participant. van der Auwera and Plungian (1998) define PI ability as including things like physical ability, learned ability, disposition, or know-how, as in (4a). Similarly, PI necessity expresses the internal needs or requirements of an event participant; this typically refers to their bodily or physical needs, as in (4b).

(4)
a.
PI ability:
(Because he took swimming lessons), Boris can swim.
b.
PI necessity:
(Because he stayed up all night), Boris needs to sleep now.

Participant-external (PE) modality refers to circumstances external to an event participant that make the state of affairs possible or necessary. Examples of such external circumstances include legal necessity or permission, obligation, and teleological (i.e., goal-oriented) requirements (van der Auwera and Plungian 1998). PE modality includes the Kratzerian categories of deontic and goal-oriented modality. Deontic modality involves reasoning with respect to laws or rules, whereas goal-oriented modality involves reasoning with respect to the external requirements on how to achieve a goal. Both categories are therefore inherently PE.

(5)
a.
PE ability:
(Now that the pool is open), Boris can swim.
b.
PE necessity:
(Because his mom told him so), Boris needs to sleep now.

A point of clarification is in order about our use of the term “circumstantial” below. We use this term in the Kratzerian sense to refer to any modals that quantify over a circumstantial modal base, where circumstantial modal bases contain propositions describing the circumstances of the actual world. In typological studies, the term “circumstantial” is often (though not exclusively) associated with PE modality (van der Auwera and Plungian 1998). However, PI modals can also use Kratzerian circumstantial modal bases. In these contexts, the propositions in the modal base describe the circumstances intrinsic to an individual (e.g., the facts of their life, or the physical properties of an object), or how the circumstances of the world affect the internal abilities or needs of an individual (Davis et al. 2009; Nauze 2008; Portner 2009).[8]

The contexts provided in Vander Klok (2014), which we used to guide our elicitations, presuppose a Kratzerian model of modality and therefore include PI contexts in the category of circumstantial modality. For transparency in the source literature (in particular, Vander Klok 2014), we will continue to use this terminology. We refer the reader to the informed discussion in Narrog (2012) for comparison of modal categories and terminology.

2.3 Weak necessity

Finally, we include weak necessity modality in our study. In (6), the weak necessity modal should conveys that the speaker’s belief regarding the proposition “Mary is at home” falls between it being possibly true and necessarily true. The speaker’s expressed belief in the proposition is therefore “weaker” than if they had used a necessity modal, but “stronger” than if they had used a possibility modal.[9]

(6)
It’s 7pm on a work day. Mary isn’t at the office right now, and she typically goes straight home after work, so … Mary should be at home right now.

The inclusion of weak necessity in our study is important for two reasons. First, weak necessity is often omitted from typological studies of modality, and is therefore not as well understood from a typological perspective. Its omission is perhaps due to the second reason, which is that strategies for marking weak necessity seem to vary widely cross-linguistically and can involve morphosyntactic strategies that are not used elsewhere in a language’s modal system (cf. von Fintel and Iatridou 2008’s study of weak necessity in Romance languages). We show in Section 5 that Logoori has a marker of weak necessity, and that it exhibits exceptional behavior compared to the rest of the modal system.

We thus follow Nauze (2008) in making a tripartite distinction between PI, PE, and epistemic modal categories. Nauze (2008) does not include weak necessity modality in his classification system; we therefore supplement his system with a weak necessity category. The modal categories that we assume are shown in Table 1.

Table 1:

Modal classifications from Nauze (2008), modified to include weak necessity.

Participant internal Participant-external Epistemic
Deontic Goal-oriented
Ability Permission Possibility Possibility
Weak need Weak obligation Weak necessity Weak necessity
Need Obligation Strong necessity Strong necessity

2.4 Data presentation

We collected our Logoori data following a modified version of Vander Klok’s (2014) modal fieldwork questionnaire.[10] The questionnaire assumes the distinctions made by Kratzer (1991, 1981, as discussed in Section 2.1. It probes whether Kratzerian modal forces and flavors are lexically specified in the language of study, and if so, how. Vander Klok’s (2014) questionnaire does not explicitly distinguish between PI and PE modality; we supplemented the questionnaire with our own contexts to specifically target this distinction.

In the following sections, we present the Logoori data first divided according to distinctions in Kratzerian modal force (possibility, strong necessity, and weak necessity). We then subdivide each of these three sections according to Nauze’s (2008) modal classifications (PI, PE, and epistemic modality). We label each example in these subsections with the Kratzerian modal flavor it expresses (e.g., examples in the PE sections are labeled for deontic or goal-oriented modality). Our data is therefore presented according to classifications that are relevant to both the theoretical and typological literatures. Our intent in doing so is to make our data accessible to both theoretical and typological audiences.

When we discuss the Logoori verbal modals in isolation, we present them in their infinitival form.[11] We noted in Section 1 that the Logoori verbal modals have modal as well as lexical uses. We therefore give underspecified interlinear glosses in our examples, since they are compatible with more than one meaning. We summarize these modal and lexical uses in Table 2. In the following sections, we informally discuss the semantic connection between the modal and lexical meanings of each verbal modal in turn.

Table 2:

Summary of the modal and lexical uses of the Logoori verbal modal stems.

Verbal modal stem Modal use Lexical use Gloss
-nyal- Possibility ‘to manage (to do sth.)’ nyal
-eny- (Weak) necessity ‘to want’ eny
-dok- Strong necessity ‘to arrive,’ ‘to reach’ dok

We distinguish between two possible morphosyntactic forms for each verbal modal: a plain form and an impersonal form. (The terms “plain” and “impersonal” do not have theoretical significance.) With the exception of kudoka ‘to arrive,’ plain forms host subject agreement with the noun class or person/number of their subject. Conversely, impersonal forms like (7) are generally identified by the presence of one of the two “expletive” subject agreement markers, noun class 6 ga- or noun class 9 e-.[12]

(7)
ga-nyal-ek-a Sira a-sad-a li-gena
6sm-nyal-ac-fv 1.Sira 1sm-lift-fv 5-rock
‘It’s possible that Sira lift the rock.’[13]

Impersonal forms of kunyala ‘to manage (to do sth.)’ and kwenya ‘to want’ can also be identified by the presence of the anticausative suffix -Vk (for which see Gluckman and Bowler 2016a) and the optional appearance of the reciprocal marker -an (for which see Gluckman 2019). The occurrence of -Vk and -an in impersonal forms is well-known in the Bantuist literature (Seidl and Dimitriadis 2003).

In addition to impersonal forms like (7), we also observe impersonal uses of verbal modals with non-expletive subjects, as in (8). The verbal modal kunyala ‘to manage (to do sth.)’ has been detransitivized, but still appears with a lexical (i.e., non-expletive) subject. We still refer to examples like (8) as impersonal forms due to the presence of -Vk.[14]

(8)
sasa Imali a-nyal-ek-a a-roomb-a ma-ndazi
now 1.Imali 1sm-nyal-ac-fv 1sm-make-fv 6-mandazi
‘Now Imali can make mandazi.’

We summarize the morphological differences between the plain and impersonal forms of each verbal modal in Table 3. In the following sections, we discuss the characteristics and interpretation of the plain and impersonal forms of each verbal modal in turn.

Table 3:

Plain and impersonal forms of the Logoori verbal modals.

Verbal modal Plain form Impersonal form Modal use
nyal -nyal- -nyal-ek(-an)- Possibility
eny -eny- -eny-ek(-an)- (Weak) necessity
dok kudoka -dok(-an)- Necessity

3 Ability and possibility modality

All flavors of ability/possibility modality can be expressed using the predicate kunyala. In its plain form, kunyala does not grammaticalize any distinction between PI possibility, PE possibility, and epistemic possibility; the modal flavor is solely determined by the context in which it occurs. However, speakers can force a non-PI modal interpretation of kunyala by using the impersonal form of the verb, as described in Section 2.4. We give examples of both plain and impersonal forms of kunyala in (9).

(9)
a.
Plain form:
Sira a-nyal-a ku-sad-a li-gena
1.Sira 1sm-nyal-fv 15-lift-fv 5-rock
‘Sira can lift the rock.’
b.
Impersonal form:
ga-nyal-ek-a Sira a-sad-a li-gena
6sm-nyal-ac-fv 1.Sira 1sm-lift-fv 5-rock
‘It’s possible that Sira lift the rock.’

In its plain use in (9a), kunyala hosts a prefix marking the person/number of the subject or the noun class. The embedded verb occurs in an infinitival form; i.e., it hosts the noun class 15 prefix ku- and the final vowel -a. In its impersonal use in (9b), kunyala hosts the anticausative suffix -Vk, and may optionally occur with the reciprocal marker -an. Kunyala must also occur with one of the two expletive subject agreement markers, class 6 ga- or class 9 e-. The embedded verb in the impersonal form may appear in any tense/mood/aspect depending on contextual and lexico-semantic factors.

3.1 Participant-internal possibility modality

PI possibility modality expresses an ability or capability that is attributed to someone or something, typically the subject of the sentence. For instance, kunyala is used in (10) to express that Sira has the internal ability (i.e., the physical capability) of lifting the rock. In Kratzerian terms, PI possibility modality is a kind of circumstantial modality, where the circumstances of the subject (i.e., his or her properties) are considered.[15]

(10)
Circumstantial possibility context: Sira is quite old now, but he is still strong. His children are scared that he will hurt his back if he does any intense labor, so they told him that he is forbidden to lift heavy things. But one day Sira’s friend Maina asked to help him in the field, because Maina knows Sira is still strong. So when Maina saw a large rock that had to be moved, he asked Sira straightaway for help (but he didn’t tell Sira’s children!). Maina knew that:
Sira a-nyal-a ku-sad-a li-gena
1.Sira 1sm-nyal-fv 15-lift-fv 5-rock
‘Sira can lift that rock.’
(11)
Circumstantial possibility context: The matatus have a limit of 13 people by law. But the drivers don’t care, and stop for more than 13 people. Also, the matatus are bigger than you think.
ma-tatu ga-nyal-a ku-geeng-a ava-andu ishirini
6-matatu 6sm-nyal-fv 15-walk-fv 2-person twenty
‘Matatus can carry 20 people.’

The impersonal form of kunyala is infelicitous in a PI possibility context, as in (12). We show in Section 3.2 that PI possibility differs from PE possibility in this respect.

(12)
Circumstantial possibility context: Sira is quite old now, but he is still strong. His children are scared that he will hurt his back if he does any intense labor, so they told him that he is forbidden to lift heavy things. But one day Sira’s friend Maina asked to help him in the field, because Maina knows Sira is still strong. So when Maina saw a large rock that had to be moved, he asked Sira straightaway for help (but he didn’t tell Sira’s children!). Maina knew that:
# ga-nyal-ek-a ndee Sira a-sad-a li-gena
6sm-nyal-ac-fv that 1.Sira 1sm-lift-fv 5-rock
‘It’s possible that Sira lift the rock.’

3.2 Participant-external possibility modality

PE possibility modality encompasses both deontic and goal-oriented Kratzerian modal flavors. Deontic possibility modality expresses permission: it indicates that the scope proposition is possible, according to some participant-external body of laws or rules. (13)-(15) show examples of kunyala expressing deontic possibility.

(13)
Deontic possibility context: According to the rules of the hospital, only family members are allowed to enter the patient’s room during visiting hours. You came to visit your sister, but it was after visiting hours. However, the nurse gives you permission to see her, anyway. She says:
u-nyal-a ku-zi-a mu
2sg-nyal-fv 15-go-fv in
‘You may go in.’
(14)
Deontic possibility context: Kageha’s parents are very strict, but they realize that she is getting older and needs more space. They know that Kageha has not ever dated someone yet, but they know that she likes this one guy from school. They decide that now that she is getting older and is more responsible:
Kageha a-nyal-a ku-vol-iz-a
1.Kageha 1sm-nyal-fv 15-see-caus-fv
‘Kageha may go on a date.’

It is possible to force a non-PI reading of kunyala by explicitly stating that the subject does not have the internal ability to carry out the scope proposition, as in (15). In this context, Maina lacks the learned ability of how to swim. While Maina has (participant-external) permission to swim, he does not have the (participant-internal) ability to swim.

(15)
Deontic possibility context: Maina’s teacher told his class that they are allowed to go swimming, but Maina doesn’t want to because he cannot swim!
Maina a-nyal-a ku-zi-a ku-erem-a netare si a-many-i
1.Maina 1sm-nyal-fv 15-go-fv 5-swim-fv but neg 1sm-know-fv
sia ku-erem-a daave
how 15-swim-fv neg
‘Maina can go swimming, but he doesn’t know how.’

Goal-oriented possibility modality expresses what means are possible with respect to achieving a goal. Since these means are external to the participant, goal-oriented modality is also subsumed within the category of PE modality. Kunyala is also compatible with this modal flavor; it does not grammatically distinguish between deontic and goal-oriented modality. In (16), kunyala expresses that it is possible to take a matatu in order to achieve the goal of going to the market.

(16)
Goal-oriented possibility context: Your friend Sira wants to get some fruit at the market. There are many ways to go there, so you tell him:
ni-w-eny-a u-zi-e mu li-sogooni, u-nyal-a ku-vogor-a li-tatu
if-2sg-eny-fv 2sg-go-sbjv in 5-market 2sg-nyal-fv 15-take-fv 5-matatu
‘If you want to go to the market, you can take a matatu.’

Speakers can use the impersonal form of kunyala to express PE possibility modality, as in (17)-(18). This contrasts with (12), in which we showed that the impersonal form of kunyala cannot express PI modality. We take the felicity of impersonal kunyala in PE modal contexts, and the infelicity of impersonal kunyala in PI modal contexts, to support the distinction between PI and PE modal categories made in the typological literature.

(17)
Deontic possibility context: According to the rules of the hospital, only family members are allowed to enter the patient’s room during visiting hours. You came to visit your sister, but it was after visiting hours. However, the nurse gives you permission to see her, anyway. She says:
ga-nyal-ek-a u-zi-a mu
6sm-nyal-ac-fv 2sg-go-fv in
‘It’s possible to go in.’[16]
(18)
Goal-oriented possibility context: Your friend Sira wants to get some fruit at the market. There are many ways to go there, so you tell him:
ni-w-eny-a u-zi-e mu li-sogooni, ga-nyal-ek-a u-vogor-a
if-2sg-eny-sbjv 2sg-go-fv in 5-market 6sm-nyal-ac-fv 2sg-take-fv
li-tatu
5-matatu
‘If you want to go to the market, it’s possible to take a matatu.’

3.3 Epistemic possibility modality

Epistemic possibility modality indicates that according to the speaker’s knowledge of the world, they believe that it is possible that the scope proposition is true. In (19), kunyala expresses that Kageha believes that it is possible that the proposition “The professor will come to class” is true. In this context, coming to class is not a learned or inherent ability of the professor, so (19) is not an instance of PI modality. The professor coming to class is also not something that is permitted by laws or rules, so (19) is not an instance of PE (deontic) modality. Rather, the truth of (19) is evaluated relative to Kageha’s knowledge of the world. We show additional examples of kunyala being used to express epistemic possibility in (20)-(21).

(19)
Epistemic possibility context: Kageha’s professor is not dependable. The students never know if he’s going to come to give the lecture or not. Today, it’s time to start class and the students are waiting again.
Profesa a-nyal-a ku-za mu ki-lasi karono
1.professor 1sm-nyal-fv 15-come in 7-class today
‘The professor might come to class today.’
(20)
Epistemic possibility context: Sira’s parents told him that he is not allowed to go to see his friend in Nairobi because it is too far away. You heard that Sira is leaving Kisumu next week, but you don’t know where he is going. Sira is a daring type of guy that often does things that he is not permitted to do. You think:
Sira a-nyal-a ku-zi-a Nairobi
1.Sira 1sm-nyal-fv 15-go-fv 9.Nairobi
‘Sira might go to Nairobi.’
(21)
Epistemic possibility context: The police are looking for Sira, and they’ve been given a tip that he might be in one of the countries neighboring Kenya. They say:
Sira a-nyal-a ku-v-a e-Buganda
1.Sira 1sm-nyal-fv 15-cop-fv 9-Uganda
‘Sira might be in Uganda.’[17]

Speakers can also use the impersonal form of kunyala to express epistemic possibility, as in (22). Epistemic possibility and PE possibility therefore pattern together in this respect, to the exclusion of PI possibility.

(22)
Epistemic possibility context: The police in Kisumu are looking for Sira, and they’ve been given a tip that he’s traveled to one of the other major cities in Kenya. Therefore, they say:
ga-nyal-ek-an-a ndee Sira a-zi-i Nairobi
6sm-nyal-ac-recp-fv that 1.Sira 1sm-go-fv 9.Nairobi
‘It’s possible that Sira went to Nairobi.’

3.4 Non-verbal expression of possibility modality

In addition to kunyala, Logoori has two modal adverbs that express epistemic possibility. The adverbs haondi and fwana strictly express epistemic possibility; they are incompatible with PI and PE possibility contexts. These adverbs can occur at various points in the clause. However, they typically occur sentence-initially or immediately preceding the verb, as in (23).[18] In these non-verbal modal constructions, the main verb is fully marked for subject agreement and tense/aspect.

(23)
Epistemic possibility context: The police in Kisumu are looking for Sira, and they’ve been given a tip that he’s traveled to one of the other major cities in Kenya. Therefore, they say:
(haondi/fwana) Sira (haondi/fwana) y-a-zi-a Nairobi
maybe 1.Sira maybe 1sm-pst-go-fv 9.Nairobi
‘Maybe Sira went to Nairobi.’

There are no adverbial strategies for encoding PI or PE ability/possibility. These meanings may only be expressed by using some form of kunyala.

3.5 Lexical usage of kunyala

In addition to its modal usage, kunyala also has a lexical usage of ‘to manage (to do something).’

(24)
Sira a-nyal-i ku-niing-a e-baasi
1.Sira 1sm-nyal-fv 15-catch-fv 9-bus
‘Sira managed to catch the bus.’

Though both the lexical and modal uses appear in syntactically similar contexts, i.e., as modal auxiliaries with an infinitival complement, there are two ways of distinguishing the lexical use from the modal use. First, the lexical use of kunyala differs morphologically from the modal use in that the verb is marked for tense; in (24), kunyala is marked for past tense (in part) through the final vowel -i.[19]

The second way that the lexical use differs from the modal use is in the associated actuality entailment (terminology from Bhatt 1999). In (24), it must be the case that Sira actually caught the bus. It is infelicitous to follow (24) with the continuation “… But he didn’t get on the bus.” The modal use does not have this actuality entailment, and is compatible with a context in which Sira has not caught the bus (“Sira was able to catch the bus, but decided to walk instead.”) This is consistent with the generalization that possibility modals describe what is possibly true in the actual world, and not what is true, and it supports our description of (24) as non-modal.

The connection between possibility modality and the lexical items meaning ‘to manage’ has been previously observed (Bhatt 1999; van der Auwera and Plungian 1998), and so in this respect, the dual usage of Logoori kunyala is unsurprising. According to Bhatt (1999), possibility modality is derived from ‘to manage’; the modal meaning is derived from the lexical verb ‘to manage’ in combination with a generic operator that is used in generic statements like Dogs bark.[20]

Interestingly, we find evidence substantiating Bhatt’s (1999) claims in the Logoori data. Generic statements in Logoori, like modal expressions with kunyala, do not involve tense morphology.[21] Verbs in generic statements like (25a) are unmarked for tense, as signaled by the final vowel -a and the lack of tone and/or overt tense morphology, which may appear either between the subject markers and the stem and/or as part of the final vowel. These contrast with episodic statements like (25b), which are marked for tense/aspect.

(25)
a.
Generic
zi-mbwa zi-rok-a
10-dog 10sm-bark-fv
‘Dogs bark.’
b.
Episodic
zi-mbwa zi-rok-áa
10-dog 10sm-bark-prs
‘The dogs bark/are barking.’

This morphological distinction can be used to distinguish modal vs. lexical uses of kunyala: modal uses are incompatible with tense marking, whereas lexical uses are compatible with tense marking like other main verbs. As shown in (26), both plain and impersonal modal uses of kunyala are ungrammatical in combination with tense marking.[22] We take this data to suggest that modal uses of kunyala have combined with a generic operator, in some cases blocking the realization of tense morphology.

(26)
a.
Plain modal use:
Sira a-nyal-a ku-sad-a li-gena
1.Sira 1sm-nyal-fv 15-lift-fv 5-rock
‘Sira can lift the rock.’
b.
Impersonal modal use:
ga-nyal-ek-a/*ga-nyal-ek-áa ndee Sira a-sad-áa li-gena
6sm-nyal-ac-fv/6sm-nyal-ac-pres that 1.Sira 1sm-lift-prs 5-rock
‘It’s possible that Sira lift/is lifting the rock.’
c.
Lexical use:
Sira a-nyal-áa ku-sad-a li-gena
1.Sira 1sm-nyal-prs 15-lift-fv 5-rock
‘Sira manages/is managing to lift the rock.’

Statements of past possibility (as in English John might/could have gone to Nairobi (but he went to Cairo)) are expressed using a nominalized form of kunyala in combination with a past tense marked copula. (27) expresses that it was possible at some time prior to the utterance time for Sira to catch the bus; i.e., Sira had the ability to catch the bus at some past time. (27) is diagnosed as an expression of past possibility rather than an expression of past tense ‘to manage’ due to the fact that no actuality entailment arises, i.e., it is felicitous to follow (27) with the continuation “… but he didn’t get on the bus.”

(27)
Sira y-a-r-i na vu-nyala vu-a ku-niing-a e-basi
1.Sira 1sm-pst-cop-fv with 14-ability 14-asso 15-catch-fv 9-bus
‘Sira was able to catch the bus.’ (Literally: Sira had the ability to catch the bus.’)

4 Necessity modality

There are a number of productive strategies for expressing necessity modality in Logoori. The most common strategy is to use some form of the predicate kudoka in combination with a main verb that is marked for the subjunctive mood. PI necessity modality can also be expressed using the predicate kwenya, which is otherwise primarily a marker of weak necessity (Section 5).

Like kunyala, kudoka can occur in both plain and impersonal forms. Kudoka is unique among the three Logoori verbal modals in that it occurs as an infinitive in its plain use in (28), hosting noun class 15 subject agreement.[23] This infinitival use is invariant and does not change, regardless of the noun class or person/number of the subject. As we show in (29), (modal uses of) kudoka cannot take individual subject arguments and do not take infinitival clauses as internal arguments. In its infinitival use, kudoka solely marks necessity modality; it does not grammaticalize any distinction between PI necessity, PE necessity, or epistemic necessity.

(28)
Plain (infinitival) use:
ku-dok-a Sira a-zi-e
15-dok-fv 1.Sira 1sm-go-sbjv
‘Sira must go.’
(29)
*Sira a-dok-i ku-zi-a Nairobi
1.Sira 1sm-dok-fv 15-go-fv 9.Nairobi

Impersonal uses of kudoka, like kunyala, require agreement with noun class 6 ga- or 9 e-, with associated differences in interpretation (Gluckman and Bowler 2016b).[24] Impersonal uses of kudoka differ from kunyala in that impersonal kudoka cannot occur with the detransitivizing suffix -Vk and requires the reciprocal marker -an. Impersonal kudoka also patterns differently in that it can fully inflect for tense/aspect.

(30)
Impersonal use:
ga-dok-an-a Sira a-zi-e
6sm-dok-recp-fv 1.Sira 1sm-go-sbjv
‘It’s necessary that Sira go.’

4.1 Participant-internal necessity

PI necessity modality expresses a need that is internal to or relative to a particular individual/entity, typically the subject. Statements of PI necessity typically refer to the subject’s bodily or physical needs, as in (31)-(32). The “circumstances affect the actions available to a volitional individual” (Portner 2009: 135).[25] In (31), the circumstances of the world are such that the speaker now feels the urge to urinate. In (32), the circumstances of the world are such that the speaker feels the urge to sneeze.

(31)
Circumstantial necessity context: You are on a bus to Nairobi. You have not had a chance to go to the toilet for 6 hours, and your bladder is full. You text your friend:
ku-dok-a inz-inyaal-e
15-dok-fv 1sg-urinate-sbjv
‘I have to pee.’
(32)
Circumstantial necessity context: You feel the need to sneeze. You say:
ku-dok-a inzi-ashiamul-e
15-dok-fv 1sg-sneeze-sbjv
‘I have to sneeze.’

The impersonal form of kudoka can be used to express PI necessity, though this is less common. (33) shows a rare use of impersonal kudoka in a PI necessity context. Some speakers find such sentences awkward and prefer PE readings with the impersonal form.

(33)
Circumstantial necessity context: There’s a fire in the house, and so Sira gathers his family and says:
ga-dok-an-a ku-zi-e
6sm-dok-recp-fv 1pl-go-sbjv
‘We have to leave.’

PI necessity is the only modal category that can be expressed using more than one modal verb. PI necessity can also be expressed using plain forms of the predicate kwenya, which is primarily a marker of weak necessity (Section 5). However, in its plain form, kwenya can express ‘to want’ or ‘to need [to do something].’ We take the latter to be a marker of PI strong necessity (cf. van der Auwera and Plungian 1998).

Our consultants give both plain kwenya and kudoka in response to PI strong necessity contexts like (34), with individual speakers providing both options in different elicitation sessions. We take this data to show that their meanings overlap.

(34)
Circumstantial strong necessity context: In the middle of a conversation, you feel a sneeze coming on. You say:
a. m-veel-a n-eny-a inz-ashiamul-e
1om-excuse-fv 1sg-eny-fv 1sg-sneeze-sbjv
‘Excuse me, I need to sneeze.’
b. m-veel-a ku-dok-a inz-ashiamul-e
1om-excuse-fv 15-dok-fv 1sg-sneeze-sbjv
‘Excuse me, I need to sneeze.’

The determining factor between whether kwenya or kudoka is used is whether the subject has a desire about the scope proposition, i.e., whether the modal flavor is bouletic. Kwenya is used in PI strong necessity contexts when a desire is attributed to the subject about the scope proposition (35) (i.e., bouletic contexts), while kudoka is used when the subject does not have a desire about the scope proposition (36) (i.e., non-bouletic contexts).[26]

(35)
Circumstantial (bouletic) necessity context. Sira loves sweet things, and can’t help himself when he sees a tasty treat.
a. #ki-bari ki-aar-i ki-nyooru saamu e-duk-an-i Sira
7-cake 7sm-cop-fv 7-sweet enough 9sm-dok-recp-fv 1.Sira
a-ki-li-e
1sm-7om-eat-sbjv
‘The cake was so sweet, Sira was required to eat it.’
b. ki-bari ki-aar-i ki-nyooru saamu Sira y-eny-a
7-cake 7sm-cop-fv 7-sweet enough 1.Sira 1sm-eny-fv
a-ki-li-e
1sm-7om-eat-sbjv
‘The cake was so sweet, Sira needed to eat it.’
(36)
Circumstantial (non-bouletic) necessity context: Sira cries whenever he cuts onions, even though he hates crying and does not want to cry.
a. chigera Sira a-kar-i ki-tunguru e-duk-an-i ndee
because 1.Sira 1sm-cut-fv 7-onion 9sm-dok-recp-fv that
a-le-e
1sm-cry-sbjv
‘Because Sira cut an onion, he had to cry.’
b. #chigera Sira a-kar-i ki-tunguru y-eny-a a-le-e
because 1.Sira 1sm-cut-fv 7-onion 1sm-eny-fv 1sm-cry-sbjv
‘Because Sira cut an onion, he needs to cry.’

A reviewer points out that the reader may infer from the discussion above that we treat PI necessity modality as being compatible only with animate subjects. This is not the case. We show in (37) that sentences with inanimate subjects are also felicitous in PI contexts. However, the felicity of animate subjects differs between kudoka and kwenya; since inanimate subjects cannot have a desire about the scope proposition, only kudoka can be used.[27]

(37)
Circumstantial (non-bouletic) necessity context: You have an old car. Because it is old:
a. ga-duk-an-a mu-doga gu-v-e na ama-guta
6sm-dok-recp-fv 3-car 3sm-cop-sbjv with 6-oil
‘The car needs to have oil.’
b. #mu-doga gu-eny-a gu-v-e na ama-guta
3-car 3sm-eny-fv 3sm-cop-sbjv with 6-oil
‘The car needs to have oil.’

We attribute the contrast in (35)-(37) to the lexical meaning of plain kwenya, ‘to want.’ (We discuss the lexical uses of kwenya in Section 5.4.) The data in (35)-(36) are consistent with the assumption that (i) want is a universal quantifier over possible worlds (that are compatible with the subject’s desires), and (ii) that necessity modality is gradable (Lewis 1973; Kratzer 1981; Lassiter 2017). We suggest that the ‘to want’ and ‘to need’ meanings of plain kwenya reflect different modal forces and constant modal flavor (i.e., circumstantial bouletic).[28] It could be the case that the scope proposition is true in all of the worlds compatible with the subject’s desires (translated as ‘to need’); alternatively, the scope proposition could be true in just at least one of the worlds (translated as ‘to want’). The variable modal force associated with plain kwenya-expressions is therefore unsurprising on its ‘to want’ reading.

4.2 Participant-external necessity

PE necessity modality encompasses both Kratzerian flavors of deontic and goal-oriented necessity. Kudoka, like kunyala, does not grammatically distinguish between these two flavors. Both are expressed using either the plain or impersonal forms of kudoka.

Statements of deontic necessity express a requirement that is imposed by some (speaker-external) body of laws or rules. In the context in (38), the hospital rules are such that patients must have a hospital ID card to be seen by a doctor. This PE necessity can be expressed by either the plain or impersonal forms of kudoka. We give additional instances of kudoka expressing deontic necessity in (39)-(40).

(38)
Deontic necessity context: When Sira went to the hospital, he was confused at first because he tried to get a doctor’s appointment, but he couldn’t! The lady at the information desk explained that he didn’t yet have a hospital ID card, and if you don’t have one you can’t be a patient there. This is because the regulations at the hospital state:
a. ava-rwaye ku-dok-a va-v-e na ki-baande ki-a
2-patient 15-dok-fv 2sm-cop-sbjv with 7-card 7-asso
ki-vitale ku-ror-a mu-ahi
7-identity 15-see-fv 1-doctor
‘Patients must have a hospital ID to see a doctor.’
b. ga-dok-an-a ndee ava-rwaye va-v-e na
6sm-dok-recp-fv that 2-patient 2sm-cop-sbjv with
ki-baande ki-a ki-vitale ku-ror-a mu-ahi
7-card 7-asso 7-identity 15-see-fv 1-doctor
‘It’s necessary that patients have a hospital ID to see a doctor.’
(39)
Deontic necessity context: In Kenya, the law states that when you ride a motor bike:
ku-dok-a w-evek-e i-gudwe
15-dok-fv 2sg-wear-sbjv 9-helmet
‘You must wear a helmet.’
(40)
Deontic necessity context: You are going to visit your friend in the hospital. When you enter into the hospital, you stop at the information desk to inquire what room your friend is in. But the woman at the information desk tells you that you can’t visit your friend now because it’s already 8pm! She says, “I’m sorry, the hospital regulations say that:
ava-geni ku-dok-a va-zi-e i-saa kumi na mbili
2-visitor 15-dok-fv 2sm-go-sbjv 9-hour ten and two
‘Visitors must leave at 6pm.’

Statements of goal-oriented necessity express what means are necessary in order to achieve a goal. For example, in the context in (41), Ingwe must beat Gor Mahia in order to advance in the tournament. We show in (41) that kudoka can occur in either its plain or impersonal form to express this meaning.

(41)
Goal-oriented necessity context: AFC Leopards (Ingwe) are playing in a tournament. In order to advance:[29]
a. ku-dok-a Ingwe va-leg-e Gor Mahia
15-dok-fv 9.Ingwe 2sm-beat-fv 9.Gor Mahia
‘Ingwe must beat Gor Mahia.
b. ga-dok-an-a Ingwe va-leg-e Gor Mahia
6sm-dok-recp-fv 9.Ingwe 2sm-beat-fv 9.Gor Mahia
‘Ingwe must beat Gor Mahia.
(42)
Goal-oriented necessity context: There is only one flight a day from Nairobi to Vihiga. So, if you want to fly to Vihiga today:
ni-w-eny-a u-vorok-e mpaka Vihiga karono ku-dok-a
if-2sg-want-fv 2sg-fly-sbjv until 9.Vihiga today 15-dok-fv
u-niin-e ndege e-ye
2SG-take-sbjv 9.flight 9-dem
‘If you want to fly to Vihiga, you have to take this plane.’

When kudoka is used to express necessity modality, the main verb is obligatorily marked for subjunctive mood by the verbal suffix -e. Interestingly, we find that subjunctive mood—without the inclusion of kudoka, or any other additional morphology—may express necessity modality on its own.[30] This subjunctive-only strategy is only compatible with PE readings. We show in (43)-(44) that subjunctive-marked verbs are compatible with both deontic and goal-oriented flavors of PE modality. For example, in (43), Khufu brushing his teeth is a necessity according to Sira, i.e., an individual that is external to Khufu himself.

(43)
Deontic necessity context: Sira is going out for the evening, and Imali is going to baby-sit his son Khufu. Sira tells Imali:
Khufu a-kor-e mi-ino ni-a-ta-gon-a
1.Khufu 1sm-brush-sbjv 4-tooth comp-1sm-irr-sleep-fv
‘Khufu has to brush his teeth before he sleeps.’
(44)
Goal-oriented necessity context: There’s only ever one flight per day to Kisumu. Therefore, if you want to fly to Kisumu today:
u-niiny-e ndege e-ye
2sg-take-sbjv 9.plane 9-dem
‘You have to take this flight.’

The subjunctive strategy may not be used to express PI or epistemic necessity, as in (45)-(46), respectively. The subjunctive is also ungrammatical in imperatives, as in (47b); this example is ungrammatical despite the fact that the command is being given by an “external” individual.

(45)
Circumstantial necessity context: You feel the need to pee.
#inz-inyal-e
1sg-urinate-sbjv
Intended: ‘I have to pee.’
(46)
Epistemic necessity context: It’s 3pm on a Tuesday, therefore:
#Sira a-v-e ku gaasi
1.Sira 1sm-cop-sbjv at work
Intended: ‘Sira must be at work.’
(47)
Imperative:
a. vogor-a maaze
take-imp 6.water
‘Take the water!’
b. *vogor-e maaze
take-sbjv 6.water
Intended: ‘Take the water!’

We speculate that the ungrammaticality of examples like (47b) reflects that imperative and subjunctive mood markers are in complementary distribution.

Finally, we note one other marginal strategy for expression of PE necessity. Plain kwenya is felicitous in PE contexts when the modal base is expressed as a lexical subject in the matrix clause. In (48), the subject of kwenya is maragoo ‘law.’ Constructions like (48) are unique to kwenya; they are unavailable with either kunyala or kudoka.

(48)
Participant-external necessity context: The laws in Kenya are very strict: If you ride a motorbike, you have to wear a helmet.
ma-ragoo ga-eny-a w-ivek-e i-gudwa
6-law 6sm-eny-fv 2sg-wear-sbjv 9-helmet
‘The law requires you to wear a helmet.’ (i.e. ‘The law wants you to wear a helmet.’)
(49)
Participant-external necessity context: During rush hour, it can be difficult to get to the market. If you want to get there in a reasonable amount of time, you need to take a bodaboda.
zi-barabara zi-eny-a Sira a-nin-e e-bodaboda
10-road 10sm-eny-fv 1.Sira 1sm-take-sbjv 9-bodaboda
‘The roads require Sira to take a bodaboda (to get to the market).’[31]

These should most likely be treated as cases of metonymy, though we leave the issue open for now.

4.3 Epistemic necessity

Epistemic necessity modality expresses that according to the speaker’s knowledge of the world, they believe that the scope proposition is necessarily true. In (50), Kageha uses her knowledge that people use umbrellas when it is raining, and that if an umbrella is wet it is most likely due to rain, to reason from her observation of wet umbrellas to the conclusion that it must be raining outside. We give additional examples of kudoka expressing epistemic necessity in (51)-(52).

(50)
Epistemic necessity context: Kageha is in the library. She sees that the people who are coming into the library are carrying wet umbrellas, and that their clothes are wet. She also knows that it is currently the rainy season. Kageha thinks:
ku-dok-a i-mbula e-v-e ni-e-kub-ang-a
15-dok-fv 9-rain 9sm-cop-sbjv comp-9sm-beat-prog-fv
‘It must be raining.’ (Literally: ‘The rain must be beating.’)
(51)
Epistemic necessity context: Sira routinely has coffee at Imali’s coffee shop every day. Even if he’s sick, he doesn’t miss a day! It’s not obligatory for Sira; he just really likes the coffee shop and goes for coffee there all the time. It’s coffee time now, so:
Sira ku-dok-a a-v-e ni-a-v-e mu li-duka li-a
1.Sira 15-dok-fv 1sm-cop-sbjv comp-1sm-cop-sbjv in 5-shop 5-asso
Imali li-a e-kahaua
1.Imali 5-asso 9-coffee
‘Sira must be at Imali’s coffee shop.’
(52)
Epistemic necessity context: You know that Imali goes to the market every day after work, even though she is not required to. Right now, you wonder where Imali is. You check the clock: it’s 6pm. Therefore:
Imali ku-dok-a a-v-e ni-a-v-e mu li-sogooni
1.Imali 15-dok-fv 1sm-cop-sbjv comp-1sm-cop-sbjv in 5-market
‘Imali must be at the market.’

Only the infinitival form of kudoka can be used to express epistemic necessity; the impersonal form of kudoka is incompatible with this meaning, as shown in (53). Kudoka contrasts in this respect with kunyala, which is able to express epistemic possibility in its impersonal use (Section 3.3).

(53)
Epistemic necessity context: Kageha is in the library. She sees that the people who are coming into the library are carrying wet umbrellas, and that their clothes are wet. She also knows that it is currently the rainy season. Kageha thinks:
#ga-dok-an-a i-mbula e-v-e ni-e-kub-ang-a
6sm-dok-recp-fv 9-rain 9sm-cop-sbjv comp-9sm-beat-prog-fv
‘It’s necessary that it rain.’ (Literally: ‘It’s necessary that the rain be beating.’)

4.4 Non-verbal expression of necessity modality

There are two non-verbal strategies for expressing necessity modality in Logoori: the words mpaka and lazima, as in (54). Note that in both of the examples in (54), the verb must bear the subjunctive mood marker. We therefore do not treat these words as simple adverbs, since they stand in some sort of selectional relationship with the main verb. Nor do we treat them as auxiliary verbs, since they cannot bear any inflectional morphology, and can appear in front of the subject, which is a position barred for other auxiliary elements.

(54)
a.
mpaka Sira a-zi-e Nairobi
until 1.Sira 1sm-go-sbjv 9.Nairobi
‘Sira must go to Nairobi.’
b.
lazima Sira a-zi-e Nairobi
must 1.Sira 1sm-go-sbjv 9.Nairobi
‘Sira must go to Nairobi.’

Both of these words are likely borrowed from Swahili. Swahili also uses lazima to express necessity modality of all flavors; it has therefore likely been directly borrowed into Logoori as a modal element.[32]Mpaka has two uses in Swahili: first, as a prepositional element meaning ‘until’ or ‘towards,’ and second, as a nominal meaning ‘border.’ Logoori mpaka is also used as a preposition meaning ‘until’/‘towards,’ but it lacks the latter nominal use. We show an example of the prepositional use of Logoori mpaka in (55).[33]

(55)
n-tum-i Sira mpaka Nairobi
1sg-send-fv 1.Sira until 9.Nairobi
‘I sent Sira up until Nairobi.’[34]

Both mpaka and lazima may be used for PE and epistemic necessity, but neither are felicitous in PI contexts as they are judged to be “too strong” by our consultants.

We draw two hypotheses from these observations. First, given kudoka’s relative “weakness” in comparison with mpaka and lazima, we hypothesize that Logoori speakers may have borrowed mpaka and lazima from Swahili in order to fill a lexical gap expressing “absolute” necessity. Second, kudoka’s relative weakness compared to mpaka and lazima may provide evidence for an analysis of Logoori modality as gradable, rather than categorical, i.e., reflecting a binary choice of existential versus universal quantification. (See Bowler and Gluckman 2019; To appear for extended discussion of what it means to model modality as gradable in Logoori.)

4.5 Lexical usage of kudoka

The verb kudoka also has a lexical use, meaning ‘to arrive’ or ‘to reach.’ Lexical uses of kudoka differ from modal uses of kudoka in that the verb hosts tense/aspect marking and is predicated of an individual, i.e., it hosts subject agreement marking reflecting the person/number/noun class of its subject. We show examples of lexical uses of this verb in (56). These examples are unambiguous and do not express any (obvious) modal meaning.

(56)
a.
Sira a-dok-i
1.Sira 1sm-dok-fv
‘Sira arrived.’
b.
Sira a-dok-i Nairobi
1.Sira 1sm-dok-fv 9.Nairobi
‘Sira reached Nairobi.’

This dual use of kudoka raises questions regarding the semantic relationship between necessity modality and ‘to arrive’/‘to reach.’ Bowler and Gluckman (2019; To appear) propose a semantics for kudoka that can unify its modal and non-modal uses.[35] In brief, it is proposed that the non-modal meaning is basic. They argue that both modal and lexical meanings of kudoka involve reaching some contextually defined threshhold. In its lexical use in (56), this threshhold is one of location; i.e., the meaning of (56b) is that the location of Sira reached or passed a locational threshhold that “counts as” being in Nairobi. In its modal use in (28), the threshhold is more abstract and is one of goodness according to contextually supplied laws/rules/likelihood. (28) expresses that the proposition “Sira goes” meets or exceeds this modal threshhold. The existence of parallel data with the prepositional element mpaka as in Section 4.4 suggests that the link between necessity modality and reaching a threshhold/boundary is a robust generalization and is not simply an accidental polysemy associated with kudoka.[36]

5 Weak necessity

Weak necessity modality, like strong necessity modality, expresses some obligation or requirement. However, in expressions of weak necessity modality, the source of the obligation or requirement is relative to something “less strict” than in instances of strong necessity modality. For example, a weak necessity modal might be interpreted relative to someone’s personal preferences about how the world should be, as opposed to how the law states that the world must be. In English, weak necessity is expressed using should.

Weak necessity is expressed in Logoori using impersonal forms of the predicate kwenya, diagnosed by the presence of the anticausative suffix -Vk (see discussion in Section 2.4). We use tests from Vander Klok and Hohaus (2020) (following Rubinstein to appear) to verify that impersonal kwenya is a marker of weak necessity.

First, we show in (57) that impersonal kwenya is not a marker of strong necessity. In this example, the speaker asserts that the scope proposition is a weak necessity using impersonal kwenya, and denies that it is a strong necessity using kudoka. If impersonal kwenya were a marker of strong necessity, this example would be infelicitous.

(57)
a.
Sira y-eny-ek-a a-zi-e yeengo, kari ndio ku-dok-a
1.Sira 1sm-eny-ac-fv 1sm-go-sbjv 9.home in.fact 15-dok-fv
a-zi-e
1sm-go-sbjv
‘Sira should go home; in fact, he must go.’
b.
#ku-dok-a Sira a-zi-e yeengo, kari ndio y-eny-ek-a
15-dok-fv 1.Sira 1sm-go-sbjv 9.home in.fact 1sm-eny-ac-fv
a-zi-e
1sm-go-sbjv
‘Sira must go home; in fact, he should go.’

Second, we show that impersonal kwenya is not a marker of possibility. The conjunction of contradictory propositions is felicitous when they combine with the possibility modal kunyala, as in (58a). However, the conjunction of contradictory propositions is infelicitous when they combine with impersonal kwenya, as in (58b). This is predicted if it makes a stronger modal claim than possibility.

(58)
a.
Sira a-nyal-a ku-v-a e-Buganda na a-nyal-a
1.Sira 1sm-nyal-fv 15-cop-fv 9-Uganda and 1sm-nyal-fv
ku-v-a Kenya
15-cop-fv 9.Kenya
‘Sira might be in Uganda and he might be in Kenya.’
b.
#Sira y-eny-ek-a a-v-e e-Buganda na y-eny-ek-a
1.Sira 1sm-eny-ac-fv 1sm-cop-sbjv 9-Uganda and 1sm-eny-fv
a-v-e Kenya
1sm-cop-sbjv 9.Kenya
‘Sira should be inside and he should be outside.’

Kwenya differs from the other verbal modals in that its plain and impersonal forms reflect a contrast in modal strength. Only impersonal uses of kwenya express weak necessity; plain uses of kwenya are compatible with strong necessity.

In its impersonal form, kwenya hosts the anticausative suffix -Vk; and noun class 6 or 9 agreement marking if there is no lexical subject; it can also optionally host the reciprocal suffix -an. The impersonal form of kwenya combines with a subjunctive clause, diagnosed by the presence of subjunctive marking -e on the embedded verb. Kwenya and kudoka pattern together in this respect to the exclusion of kunyala, which does not subcategorize for a subjunctive clause. Unlike kunyala, impersonal forms of kwenya inflect for tense/aspect. The examples in (57)-(58) demonstrate impersonal form of kwenya with a raised subject (see discussion in footnote 14).

Plain forms of kwenya are only found in participant-internal contexts, and differ from impersonal kwenya-expressions in two main ways. First, they express strong necessity rather than weak necessity (see discussion in Section 4.1). Second, they are ambiguous between modal and nonmodal interpretations; non-modal uses of kwenya mean ‘to want’ or ‘to be about to [do something].’[37] We provide an example of plain kwenya in (59); note the availability of the strong necessity modal meaning (translated as ‘to need [to do something]’) as well as the non-modal meanings in (59b)-(59c). We discuss plain uses of kwenya at length in Section 5.1 and Section 5.4.

(59)
Plain use:
Sira y-eny-a ku-li-a ma-barabandi
1.Sira 1sm-eny-fv 15-eat-fv 6-loquat
a. ‘Sira needs to eat loquats.’
b. ‘Sira is about to eat loquats.’
c. ‘Sira wants to eat loquats.’

Unlike kudoka, kwenya may not express modal meaning in its class 15 infinitival form, as in (60).

(60)
(Ungrammatical) infinitival use:
*ku-eny-a Sira a-zi-e Nairobi
15-eny-fv 1.Sira 1sm-go-sbjv 9.Nairobi
Intended: ‘Sira should go to Nairobi.’

We have not found any non-verbal strategies for expressing weak necessity modality in Logoori, unlike possibility and necessity modality (Section 3.4 and Section 4.4, respectively).

5.1 Participant-internal weak necessity

PI weak necessity modality expresses a desire or requirement that is internal to or relative to an individual/entity, typically the subject. Like the PI necessity data in Section 4.1, expressions of PI weak necessity typically refer to the subject’s bodily or physical needs. In theory, expressions of PI weak necessity make a weaker claim about the subject’s desires than PI strong necessity.

PI weak necessity is expressed in Logoori using the impersonal form of kwenya, as in (61a); note that for PI weak necessity, the impersonal form must have a lexical (raised) subject. Impersonal constructions with expletive subjects are infelicitous in PI weak necessity contexts, as in (61b). (See Section 2.4 for discussion of copy-raising and hyper-raising, particularly footnote 14.) This is the only context in which the presence/absence of a lexical subject with the impersonal form matters for the modal category. In (61a), the speaker expresses that the internal needs of their body are such that they should pee.

(61)
Circumstantial weak necessity context: This is going to be a long bus ride, therefore:
a. ni-n-la-niin-a e-basi nzi-eny-ek-a nzi-nyal-e
comp-1sg-fut-board-fv 9-bus 1sg-eny-ac-fv 1sm-urinate-sbjv
‘Before getting on this bus, I should pee.’
b. #ni-n-la-niin-a e-basi ga-eny-ek-a nzi-nyal-e
comp-1sg-fut-board-fv 9-bus 6sg-eny-ac-fv 1sm-urinate-sbjv
‘Before getting on this bus, it should be that I pee.’

Recall from Section 4.1 that expressions of PI (strong) necessity use different markers depending on whether the subject has a desire about the scope proposition: plain kwenya is used if the subject desires the scope proposition, otherwise kudoka is used. This dichotomy does not appear to extend to weak necessity contexts. PI weak necessity is always expressed using the impersonal form of kwenya regardless of whether or not the subject has a desire about the scope proposition. This is demonstrated in (62) and (63); the latter has an inanimate subject (cf. (37)).

(62)
Circumstantial weak necessity context (non-bouletic): This is going to be a long busride, but the bathrooms at the station are gross, so:
nd-eny-ek-a nzi-nyaal-i netare si n-eny-a daave
1sm-eny-ac-fv 1sm-urinate-sbjv but neg 1sm-eny-fv neg
‘I should pee, but I don’t want to.’
(63)
Circumstantial weak necessity context (inanimate subject, non-bouletic): It’s been a year since the car was last tuned up, so:
mu-doga gu-eny-ek-an-a gu-v-e na ama-guta
3-car 3sm-eny-ac-recp-fv 3sm-cop-sbjv with 6-oil
‘The car should have oil.’

As we illustrate in the next sections, both PE and epistemic weak necessity are consistently expressed with impersonal forms of kwenya. This contrasts with the other two verbal modals, kudoka and kunyala, for which the plain and impersonal forms do not correlate with a difference in modal strength.

In sum, Logoori PI weak necessity modality presents a number of interesting descriptive challenges. While many of these issues are specific to Logoori, we believe that part of the problem stems from an inherent, language-independent issue concerning PI weak necessity modality. This category seems to inherently overlap with the subject’s desires (when the subject is animate). For example, in (61a), the context can also be interpreted as being that the speaker has the desire to pee before getting on the bus in order to avoid an uncomfortable bus ride. Similarly, in (34a), the context can be interpreted as the speaker wanting to sneeze for body-internal reasons. As a result, it is difficult to distinguish PI weak necessity from bouletic modality in general—if in fact such a distinction exists at all.

Furthermore, in English (the metalanguage used for our elicitations), one can suppress the bouletic reading of should by explicitly stating that the subject does not desire the scope proposition, as in (62). However, we find that in such examples, a deontic reading of English should arises. As we will show in Section 5.2, deontic (PE) weak necessity readings are unavailable when kwenya occurs in its plain form. The use of English as a metalanguage therefore stymies our ability to elicit non-bouletic PI weak necessity modality in Logoori, since enforcing a non-bouletic reading gives rise to a deontic reading of our English prompt.

5.2 Participant-external weak necessity

PE weak necessity encompasses both deontic and goal-oriented flavors of weak necessity modality. Kwenya does not grammatically distinguish between these two modal flavors. Both are expressed using the impersonal form of kwenya; its plain form is infelicitous in PE contexts, as in example (64b).

Deontic weak necessity modality expresses a weak desire or requirement of some speaker-external body of laws or rules. In (64), these rules are the social expectation that someone should ask permission before borrowing someone’s things.

(64)
Deontic weak necessity context: Sira wants to go to town but he doesn’t have a bike. He wants to borrow his brother’s bike, and he thinks that he could do so without his brother knowing, but:
a. ga-eny-ek-a Sira a-sav-e amu-aavo
6sm-want-ac-fv 1.Sira 1sm-ask-sbjv 1-brother
‘It should be that Sira asks his brother.’
b. #Sira y-eny-a a-sav-e amu-aavo
1.Sira 1sm-eny-fv 1sm-ask-sbjv 1-brother
‘Sira wants/needs to ask his brother.’
c. Sira y-eny-ek-a a-sav-e amu-aavo
‘1.Sira 1sm-eny-ac-fv 1sm-ask-sbjv 1-brother
‘Sira should ask his brother.’
(65)
Deontic weak necessity context: There is a movie playing in Nairobi tonight, but Sira isn’t sure if he wants to see it. His best friend Maina texts him saying, “Please come to the movie, I really want to go with you!” To be a good friend to Maina:
a. ga-eny-ek-an-a Sira a-zi-e mu e-sinema
6sm-eny-ac-recp-fv 1.Sira 1sm-go-sbjv in 9-cinema
‘It should be that Sira goes to the movie.’
b. #Sira y-eny-a a-zi-e mu e-sinema
1.Sira 1sm-eny-fv 1sm-go-sbjv in 9-cinema
‘Sira wants/needs to go to the movie.’

Goal-oriented weak necessity expresses what means should ideally be used in order to achieve a goal. In (66a), kwenya expresses that in order to get the best groceries, Sira should ideally go to the market in the east. Only impersonal forms of kwenya are felicitous in PE contexts when both clauses share the same subject. Plain uses are infelicitous, as shown in (66b).

(66)
Goal-oriented weak necessity context: There are three markets close to where Maina is staying in Nairobi. Sira tells him that the market to the east is the cheapest, the market to the west is the most expensive, and the market to the south has the fewest vendors. The eastern market is the best. So according to Sira, to get the best groceries:
a. ga-eny-ek-an-a Maina a-zi-e mu li-sogooni
6sm-eny-ac-recp-fv 1.Maina 1sm-go-sbjv in 5-market
li-v-e e-vogwe
5sm-cop-sbjv 9-east
‘It should be that Maina go to the market to the east.’
b. #Maina y-eny-a a-zi-e mu li-sogooni
1.Maina 1sm-eny-sbjv 1sm-go-sbjv in 5-market
li-v-e 9-east
5sm-cop-sbjv e-vogwe
‘Maina wants/needs to go to the market to the east.’
c. Maina y-eny-ek-a a-zi-e mu li-sogooni
1.Maina 1sm-eny-ac-fv 1sm-go-sbjv in 5-market
li-v-e e-vogwe
5sm-cop-sbjv 9-east
‘Maina should go to the market to the east.’

5.3 Epistemic weak necessity

Epistemic weak necessity modality expresses that according to the speaker’s knowledge of the world, they believe that the scope proposition ought to be true. In the context in (67), the speaker reasons based on their knowledge of the skill of the Portuguese football team and their current statistics and the relative skill of the Hungarian football team and their current statistics, et cetera, to express their belief that it ought to be the case that Portugal wins the match.

(67)
Epistemic weak necessity context: Portugal is playing Hungary in a football match. Because you follow football, you know that Portugal is a better team, so you say:
a. ga-eny-ek-an-a Portugal i-goot-e Hungary
6sm-eny-ac-recp-fv 9.Portugal 9sm-beat-sbjv 9.Hungary
‘It should be that Portugal beats Hungary.’
b. Portugal y-eny-ek-an-a i-goot-e Hungary
9.Portugal 9sm-eny-ac-recp-fv 9sm-beat-sbjv 9.Hungary
‘Portugal should beat Hungary.’

Epistemic weak necessity modality may only be expressed using impersonal forms of kwenya (either with subject raising or without). Plain uses of kwenya are infelicitous in epistemic contexts, as shown in (68b).

(68)
Epistemic weak necessity context: Sira works everyday. But you know that his mother sometimes comes to town to visit, and when she does, he doesn’t go to work. You’re pretty sure that his mother hasn’t come to town, so when someone asks you where Sira is, you say:
a. ga-eny-ek-an-a Sira a-v-e ni-a-v-e ku
6sm-eny-ac-recp-fv 1.Sira 1sm-cop-sbjv comp-1sm-cop-sbjv at
e-gaasi
9-work
‘It should be that Sira is at work.’
b. #Sira y-eny-a a-v-e ni-a-v-e ku e-gaasi
1.Sira 1sm-eny-fv 1sm-cop-sbjv comp-1sm-cop-sbjv at 9-work
‘Sira wants/needs to be at work.’

5.4 Lexical usage of kwenya

When it is used as a lexical verb, kwenya hosts both subject agreement marking and tense/aspect marking. Lexical uses of kwenya are morphologically identical to plain modal uses of kwenya, as in (34a). Plain kwenya-expressions are therefore unique among the three Logoori verbal modals in that they are ambiguous between modal and non-modal meanings.

We show an instance of kwenya being used to mean ‘to want’ in (69), and ‘to be about to [do sth.]’ (among other readings) in (70). Examples (69) and (70) differ only with respect to the internal argument of the verb. In (69), it combines with a nominal, whereas in (70), it combines with an infinitival clause. When kwenya takes a nominal internal argument, as in (69), only its ‘to want’ reading is available.

(69)
Sira y-eny-a ma-barabandi
1Sira 1sm-eny-fv 6-loquat
‘Sira wants loquats.’
(70)
Plain use with embedded infinitival clause:
Sira y-eny-a ku-li-a ma-barabandi
1Sira 1sm-eny-fv 15-eat-fv 6-loquat
a. ‘Sira is about to eat loquats.’
b. ‘Sira wants to eat loquats.’
c. ‘Sira needs to eat loquats.’

There is variation in the kind of embedded clause that kwenya can combine with. The embedded clause can be infinitival, as in (70), or subjunctive, as in (71). When the embedded clause is infinitival, there is a three-way ambiguity between its modal and two non-modal meanings, as in (70). When the embedded clause is subjunctive, as in (71), its ‘to be about to [do sth.]’ meaning is absent.

(71)
Plain use with embedded subjunctive clause:
Sira y-eny-a y-inyal-e
1.Sira 1sm-eny-fv 1sm-urinate-sbjv
a. ‘Sira wants to pee.’
b. ‘Sira needs to pee.’

We note that bouletic modality (i.e., modality concerning wishes and desires) is often excluded from modal typologies (van der Auwera and Plungian 1998). However, the data on kwenya suggests that this particular flavor of modality plays a major role in the modal system of Logoori, and deserves future in-depth study. The Logoori data also offers a counter example to the typological pattern proposed by von Fintel and Iatridou (2008) that weak necessity modality is often marked by a necessity modal plus counterfactual morphology.

We conclude by summarizing the morphosyntax and uses of each Logoori verbal modal.

6 Conclusion

Logoori’s modal system presents a number of interesting data points for typological and theoretical consideration. Typologically, we find confirmation of a number of known patterns. First, Logoori modal expressions generally have fixed Kratzerian force and variable flavor (as found in English and German; Kratzer 1991). However, we identify one modal element, kwenya, which can express both strong and weak necessity and multiple modal flavors. Such variation is interesting from a theoretical viewpoint because we find that the difference in strength correlates with a difference in valency of the verb: the detransitivized form of kwenya (i.e., the impersonal form) may only express weak necessity, while the transitive form (i.e., the plain form) may only express strong necessity.[38]

Second, our study has implications for our understanding of participant-internal modality. We find that the expression of PI modality depends on a number of factors, including: (i) whether the modal stem bears detransitivizing morphology; (ii) whether there is a lexical subject; (iii) whether the lexical subject is animate; and (iv) what the modal strength is. For instance, with PI ability, we find that PI modality is incompatible with impersonal forms of kunyala—though we also note that the plain form does not uniquely pick out PI modality; it expresses PE and epistemic modality as well. (Strong) PI necessity is uniquely marked only when the flavor is also bouletic and hence the subject is animate; inanimate objects cannot have desires. In this case, the plain form of kwenya plus a subjunctive embedded predicate expresses the concept of “needing.” Otherwise, PI necessity can be marked with an impersonal or plain form of kudoka. Weak necessity PI modality, like PI ability modality, requires that the modal verb have a lexical subject; though again, this particular structure does not uniquely distinguish PI weak necessity.

We believe that this complex set of facts is significant for two reasons. First, Logoori illustrates that PI modality lies somewhat outside of the “normal” strategies for modal marking. There is no dedicated morpheme or syntactic strategy for PI modality; rather, the meaning arises from an array of factors, including context. It is unsurprising that PI modality often requires a lexical subject, since this modal category is often subject-oriented (cf. Palmer 2001), though we also note that PI (strong) necessity is compatible with impersonal forms of the verb (cf. example (33)). Second, PI modality is rarely addressed in theoretical discussions of modality (though see Portner 2009; Vander Klok 2013). However, we believe Logoori suggests a more nuanced theoretical view of this particular modal category needs to be provided, in particular how it is, and is not, related to other modal categories and (morpho-)syntactic processes.

The Logoori data additionally supports a prediction by Nauze (2008) (following van der Auwera and Plungian 1998 and van der Auwera et al. 2005; see also Narrog 2012) regarding the distribution of modal meanings in languages that grammatically mark PI and PE modality. Nauze predicts that there should not be any single modal element that expresses “non-contiguous” categories in Table 1. For example, there should not be any element that expresses both PI modality and epistemic modality. This is because PE modality intervenes between the two categories in his classification, making them non-contiguous. This prediction is upheld in Logoori, and has implications for the (diachronic and synchronic) relationships between modal categories.

A particularly interesting and important result of our study is the discovery that all Logoori verbal modals also have non-modal uses. We believe it is likely that the modal meanings of the Logoori verbs arose secondarily, as a byproduct of their lexical meanings (see the “modal maps” in Bybee et al. 1994; van der Auwera and Plungian 1998; and van der Auwera et al. 2009). The observation that modal markers can be multi-functional is not new—indeed, it is not even a new observation for Bantu languages (Devos 2008, Bostoen et al. 2012; Mberamihigo 2014; Kawalya 2017; Kawalya et al. 2018, Kawalya et al. 2019).[39] Modal markers are well known to be historically and synchronically related to non-modal elements cross-linguistically. The observations about these polysemies therefore raise familiar questions about the connections between modal meaning and non-modal meaning, and how these connections can be formally modeled, both diachronically and synchronically. For instance, it may be that certain markers “gain” a modal meaning over time by taking on meanings in particular contexts. Alternatively, it may be that lexical items are sufficiently bleached of meaning so that they are compatible with more than one context. Or it may be that the markers retain their core lexical meanings, but that the language otherwise restructures to admit the markers in more than one context (perhaps by losing a previous modal marker).

Finally, our study demonstrates the importance of (morpho-)syntax in the distribution and meaning of modal elements. Each modal verb in Logoori has two forms: plain and impersonal; however, the availability of these forms to express each modal category is different for each verb. In Table 4, we summarize the morphosyntax and uses of each Logoori verbal modal.[40] The reader should keep in mind that the plain and impersonal forms are not homogeneous across the verbal modals. The plain forms of kunyala and kwenya take lexical subjects, inflecting for subject agreement, while the plain form of kudoka is the infinitive. The plain forms of kwenya and kunyala additionally differ in that the latter does not inflect for tense/aspect in its modal use. The impersonal forms of kwenya and kunyala require the anticausative suffix, while the impersonal form of kudoka does not appear with the anticausative. In sum, Table 4 shows that each verbal modal has two forms, and that their distributions are distinct.

Table 4:

Distribution of plain and impersonal forms across modal categories.

Modal use Participant-internal Participant-external Epistemic
nyal ability/possibility plain/*impersonal plain/impersonal plain/impersonal
dok necessity plain/impersonal plain/impersonal plain/*impersonal
eny (weak) necessity plain/impersonal *plain/impersonal41 *plain/impersonal

The difference between the plain and impersonal forms is most striking in the comparison of epistemic modality across forces. Both forms are allowed for epistemic possibility. However, only the plain form is allowed for epistemic necessity, and only the impersonal form is allowed for epistemic weak necessity. We take this to be strong evidence that modal categories have both semantic and syntactic implications. We are hopeful that a closer inspection of these differences will reveal deeper connections between modality and syntactic structure.

We hope this study will contribute to the nascent program of documenting modal expressions in Eastern Africa (cf. Botne 1997; Devos 2008; Bostoen et al. 2012; Kawalya et al. 2019), and to the body of cross-linguistic typological literature on modality. Logoori provides evidence for novel connections between lexical and modal categories, and enriches our understanding of the typological variation found in modal expressions.

Abbreviations

We use the following abbreviations in this paper: 1/2/3/…: noun classes

ac

anticausative

asso

associative

caus

causative

comp

complementizer

cop

copula

dem

demonstrative

fut

future

fv

final vowel

imp

imperative

irr

irrealis

neg

negative

om

object marker

pass

passive

pst

past

prs

present

prog

progressive

recp

reciprocal

sbjv

subjunctive

sg/pl

singular/plural

sm

subject marker

Acknowledgment

We would like to thank our wonderful Logoori consultants for teaching us so much about their language; thank you to Mwabeni Indire, Bernard Lavussa, Walter Kigali, and Bernard Chahilu.

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Published Online: 2021-01-20
Published in Print: 2020-10-06

© 2021 John Gluckman and Margit Bowler, published by De Gruyter, Berlin/Boston

This work is licensed under the Creative Commons Attribution 4.0 International License.