Weak necessity without weak possibility: The composition of modal strength distinctions in Javanese

This paper investigates the semantics of the suffix -NE in Javanese (Austronesian; Indonesia), bringing to light new findings to bear on the composition of modal strength distinctions. In a transparent manner, this functional morpheme derives weak necessity modals from strong necessity modals, but cannot attach to possibility modals to derive weak possibility. Javanese thereby takes a different compositional route to weak necessity than most Indo-European languages, which lexicalise modal strength distinctions or rely on counterfactual morphology. We propose a new type of domain restriction analysis for weak necessity to capture both the defining properties of weak necessity as well as the restriction in Javanese to only necessity modals. Specifically, we propose that -NE requires quantification over a nonempty subset of a minimal witness set for the original quantification. The Javanese data thus show that weak necessity is not a unified phenomenon across languages, and our analysis contributes to a model of crosslinguistic variation concerning the relationship between gradability and modality, and the semantics of weak modal strength.


Introduction
The expression of modality in natural language can be descriptively characterised by three dimensions of meaning: modal force (necessity versus possibility), modal flavour (e.g., epistemic versus root), and modal strength (strong versus weak). The larger research question behind this paper is the composition of modal strength distinctions across languages. For English, such a difference in the strength of necessity is perceived in comparing ought and must, which (1) picks up on. (1) Employees must wash their hands. Non-employees really ought to wash their hands, too.
(von Fintel & Iatridou 2008: p. 115) Languages appear to rely on two strategies to weaken a necessity modal (von Fintel & Iatridou 2008): They might lexicalise this weak necessity meaning (like present-day English) or derive weak necessity modals from their strong counterparts using counterfactual morphology (like French). Yet, beyond von Fintel & Iatridou (2008), there has been little crosslinguistic research on modal strength.
In this paper, we discuss original fieldwork data from Javanese (Austronesian, Malayo-Polynesian; Indonesia), which uses yet another strategy: The language has a dedicated functional morpheme, -NE, which combines with a strong necessity modal to derive a weak one. An example is in (2). 1 The language is thus morphologically and compositionally maximally transparent in deriving weak necessity modality. However, the change in modal strength is restricted to strong necessity: -NE cannot occur with possibility modals to derive weak possibility, as demonstrated in (3) av.swim (Int.) 'There is a slight possibility that I can swim. ' We propose an analysis that follows some of the guiding ideas of von Fintel & Iatridou (2008) and Rubinstein (2012Rubinstein ( , 2014, who propose to model weak necessity as quantification over a subset of the favoured worlds. We pursue a different compositional implementation of these ideas, however, to derive weak necessity without weak possibility: -NE encodes universal quantification over a non-empty subset of a minimal witness set for the quantifier it attaches to. Necessity modal expressions only have one witness set, the set of favoured worlds. Minimal witness sets for possibility modal expressions are singleton sets, and thus do not make available any subsets that meet the requirements, hence the unacceptability of -NE with possibility modals. The paper is organised as follows: In Section 2, we discuss the crosslinguistic literature and approaches to deriving weak modal strength, focusing on domain restriction and degree-based analyses of weak necessity. Section 3 discusses our methodology, and provides some background on the language, including the modal system of Javanese as spoken in Paciran, an East Javanese variety. Section 4 constitutes the empirical core of the paper: It presents the data on how Javanese -NE derives weak necessity (but not weak possibility), and is otherwise not counterfactual morphology. Section 5 spells out the domain restriction analysis we propose and shows how this analysis also captures the distributional restrictions of -NE. In this section, we also revisit the existing approaches, showing that the Javanese data present problems for existing domain restriction approaches as well as for degree-based approaches to weak necessity. Section 6 concludes, and Section 7 outlines some directions for further research, both within Malayo-Polynesian linguistics and crosslinguistically.

Modal strength distinctions
We first provide in Section 2.1 the background on the approach to modality in general that is used in this paper, and then hone in on weak necessity and how to define it in Section 2.2. In Section 2.3, we then introduce two different approaches to weak modal strength, domain restriction approaches and degree approaches. We conclude with a discussion of the little research there is on weak modal strength across languages in Section 2.4.

The quantificational analysis of modality
Our starting point is a quantificational analysis of modality in English (for recent overviews, see Portner 2009, Hacquard 2011, Matthewson 2016. Under this analysis, there are at least two dimensions to modal meaning, modal force and modal flavour. Possibility modals like English can existentially quantify over possible worlds, while necessity modals like English must universally quantify over possible worlds. English thus lexically differentiates between these two types of modal force. The domain of quantification in English is restricted both lexically and contextually, giving rise to what we perceive as distinct flavours. Under the view developed in Kratzer 1977Kratzer , 1978Kratzer , 1981Kratzer , 1991 and subsequent work, the domain restriction is composed in a step-wise fashion from an accessibility relation and an ordering source, as illustrated in Figure 1. A contextually provided (and potentially lexically restricted) accessibility relation allows us to select an initial subset of the set of possible worlds (Steps 1 and 2), say the worlds compatible with what the speaker knows under an epistemic reading. From this set, we select as the domain of quantification those worlds which are ranked highest with respect to a contextually provided ordering source (Steps 3 and 4). 2 We follow von Fintel & Iatridou (2008: p. 177) in referring to these worlds as the "favoured worlds".

Figure 1
Composing modal quantification domains 2 Unlike Lewis (1973Lewis ( , 1981 and Kratzer (1981Kratzer ( , 1991 we assume for simplicity that there are such worlds (see also Stalnaker 1984). For a recent critical discussion of this limit assumption, see Kaufmann 2017. As one reviewer correctly points out, the visualisation in Figure 1 and the definition to follow in (6) assume that the ordering relation induces a strict ordering of worlds, rather than just a pre-order. This is ultimately a presentational choice. We would also like to thank one of our editors, Magdalena Kaufmann, for discussion relating to this choice and its consequences.
The ordering source, represented as order in (5), is a contextually provided function that assigns to the world of evaluation a set of propositions that are used to define a strict order > on the set of accessible worlds, provided by the relational accessibility function, represented as access in the LF structure above. A world is ranked higher than a world ′ with respect to a set of propositions if and only if the propositions ′ makes true form a subset of the propositions makes true, as in (6). A maximality operator, best, defined in (7), selects the best worlds from the accessible worlds with respect to the ordering source. Quantification is over the best of the accessible worlds, the favoured worlds.
For any set of worlds ∈ ⟨ , ⟩ and set of propositions ∈ ⟨⟨ , ⟩, ⟩ : (see also von Fintel & Heim 2011: p. 61, no. (107)) 3 We opt here for syntactically representing worlds as well as the accessibility relation and ordering source. The actual world @ is syntactically represented in the highest layer of the clause, following ideas in Kusumoto 1999Kusumoto , 2005. We assume that binding constraints require that the accessibility relation and the ordering source are interpreted relative to the same world (see also Percus 2000, Keshet 2008 (Bochnak 2015). Gitksan (Tsimshianic; Canada) exhibits variable force with epistemic flavours (Peterson 2010, Matthewson 2013. Nez Perce (Penutian, United States) also exhibits variable force effects (Deal 2011). It is important to note, though, that in all of these languages, the observed variability does not translate to an underspecification of the quantificational force in the lexical entry of those modal expressions. Rather, these modals have been analysed as encoding either existential or universal quantification, and variable force is due to pragmatic effects. Previewing some of the discussion in Section 3.3, the modal system of Javanese lexicalises force distinctions, and all modal markers exhibit restrictions as to the flavours they allow (Vander Klok 2012.

Weak modal strength
The semantics outlined in the previous section, however, does not yet capture that possibility and necessity are in principle gradable notions, and that both necessity and possibility modal expressions appear to exhibit strength distinctions. Present-day English, for instance, lexicalises ought or should apart from must. Intuitively, the modal claim in (8a) is somehow weaker than the modal claim in (8b). Similar intuitions -but admittedly more subtle -are also reported for could as opposed to can in (9). 4 Although these strength distinctions, and in particular weak necessity modality, have only more re-cently become the focus of a more sustained research effort, they have been featured in both the philosophical and linguistic literature. 5 (8) a. Mary {ought to/ should} attend the meeting. b. Mary must attend the meeting.
(9) a. It could be dangerous to cycle in the city. b. It can be dangerous to cycle in the city.
Setting weak possibility aside for a moment, what characterises weak necessity? And how can we reliably identify weak modal strength in a fieldwork setting? We follow here a definition by Rubinstein (2020), who proposes to characterise weak necessity as in (10). We use this working definition in Section 4 to identify weak necessity modality in Javanese. (Note that this definition crucially relies on the existence of modal force distinctions in a language.) (10) A modal word is a weak necessity modal if (i) to (iii) hold, for any proposition .
(i) The conjunction of ( ) and (¬ ) is a contradiction.
(ii) There is a necessity modal such that ( ) entails ( ).
(iii) There is a possibility modal such that ( ) entails ( ).
The first part of the definition establishes that a weak necessity modal behaves like a necessity modal, but not like a possibility modal: Only possibility modals allow the conjunction of two mutually exclusive propositions, see (11a) below. English should and must pattern alike when it comes to the conjunction of mutually exclusive propositions: The resulting sentences are contradictory, when the domain restriction is kept constant, as is shown in (11b) and (11c).
The latter two parts of the definition establish that weak necessity is different from both necessity and possibility modals using entailment (see also Jones & Pörn 1986). Thus, in (12), if it is true that Jordan must stay inside, then is it also true that Jordan should stay inside, but not vice versa. And similarly, if it is true that Jordan should stay inside, then is it also true that Jordan may stay inside, but not vice versa.
(12) Context: It is raining cats and dogs. Jordan's mom is worried about him getting sick. She tells her partner: Jordan must stay inside.
⇝ Jordan should stay inside. ⇝ Jordan may stay inside.
These entailment relations also show up in the scalar implicature that weak necessity modals may give rise to: I ought to help the poor in (13) gives rise to the implicature that the strong necessity modal claim is false. As shown in (13a) to (13c) from Silk (2019: p. 23), this implicature may be cancelled, reinforced or suspended. 6 (13) I ought to help the poor.
a. In fact, I must.
[ cancellation ] b. But I don't have to.
[ reinforcement ] c. Maybe I have to.

Two approaches to modal strength distinctions
We review here what we consider to be the two most prominent lines of approaches to weak modal strength, the domain restriction approach (most 6 Silk (2019) however ultimately rejects that for any proposition , must p entails ought p, and ought p entails may p, at the very least under the epistemic reading. See also Yalcin 2016 for discussion of whether weak necessity should and ought even allow for true epistemic readings in the first place.
12:8 notably, von Fintel & Iatridou 2008, Rubinstein 2012, and the degreebased approach (notably, Lassiter 2011, Portner & Rubinstein 2016. 7 We end up adopting a new variant of a domain restriction approach for Javanese weak necessity modality, which we present in Section 5. Domain restriction approaches. The idea behind domain restriction approaches to weak necessity modality is quite simple, despite differences in the technical implementation (for an overview, see Rubinstein 2020). As von Fintel & Iatridou (2008: p. 118) put it for weak necessity modals: "What makes them weaker semantically is that they have a smaller domain of quantification: Strong necessity modals say that the prejacent is true in all of the favoured worlds, while weak necessity modals say that the prejacent is true in all of the very best (by some additional measure) among the favoured worlds." We present an implementation of such a domain restriction approach in (14) and (15)  The weak necessity modal in (14) here has one more argument slot than a strong necessity modal to accommodate the additional ordering source, 7 But see also footnote 5 on page 7 for further references. 12:9 represented as order2 in the Logical Form. Just like the accessibility relation and the primary ordering relation, the content of this restriction will be determined by the utterance context (discussed further below). The set of favoured worlds is then re-ranked according to this additional ordering source, and the highest ranked worlds are selected as the domain of quantification. Building on Figure 1, we can then visualise the internal composition of the quantification domain of a weak necessity modal as in Figure 2, with an additional round of the ranking and selection process (Steps 5 and 6), resulting in a subset of the domain of quantification that the primary ordering source would derive.

Figure 2
Composing quantification domains for weak modality While intuitively appealing, the literature has identified two major challenges for domain restriction approaches, one conceptual, the other empirical: Conceptually challenging is the question of how to distinguish the accessible worlds and the ordering relation from the additional restriction (see also Silk 2019): "The success of the domain restriction approach to weak necessity depends on an ability to make finer-grained distinctions than are standardly assumed …" (Rubinstein 2012: p. 39). Put differently, can the sets of worlds that may serve as the domain of quantification for a weak necessity modal also serve as the domain of quantification for a strong necessity modal in certain contexts? For instance, a proposition that serves to restrict the set of accessible worlds for a weak necessity modal could just as well be part of the propositions from which we derive the set of accessible worlds for a strong necessity modal, as spelled out in (16) under the assumption of an empty ordering source. As a result, quantification would be over the 12:10 Weak necessity without weak possibility same set of worlds irrespective of the strength of the modal (Rubinstein 2012: pp. 39-48). (16) Assume access 1 ( * )= 1 ∩ 2 ∩ 3 as well as access 2 ( * )= 1 ∩ 2 and restrict( * )= 3 .
Then, access 1 ( * )=access 2 ( * ) ∩ restrict( * ). Rubinstein (2012Rubinstein ( , 2014 proposes that English weak necessity modals like ought and should (at least under their deontic interpretation) lexically specify that the additional domain restriction is derived from the set of propositions that are negotiable: "…strong necessities are necessities relative to non-negotiable priorities, while weak necessities are necessities relative to negotiable priorities -raised and promoted by an opinionated individual. … A priority is negotiable if it is not assumed that all members of a relevant group of individuals take it for granted." (Rubinstein 2014: p. 537) This analysis is motivated by examples such as (17). Unlike the context in (17a), the context in (17b) does not appear to license a strong necessity claim because "…it is not taken for granted that considerations of lawful conduct apply in the case of illegally employed workers. In contrast, such considerations are presupposed to guide the actions of those affiliated with a respectable university. Thus, moving to a conversation in which there is no commitment to the crucial priority appears to affect the choice of necessity modal." (Rubinstein 2012: p. 52 (i) She should get health insurance.
(ii) #She has to get health insurance. (Rubinstein 2012: p. 52, no. (40)) Another example that brings out this intuition is (18). As Rubinstein (2014) discusses, if uttered by an accountant with the company that is known for their integrity, we get an inference that other company officials might not be as committed to obeying the law. Uttered by a manager, we might infer that they are contemplating tax evasion. Rubinstein (2014: p. 538) writes that, in both cases, "… the tax law is portrayed as a negotiable ideal for some discourse participant, and in both cases the speaker is opinionated about the best course of action in the situation: he or she draws attention to an ideal and is taken to be promoting it."

(18) [Preparing a company's tax report.]
We should report all of our revenue. (Rubinstein 2014: p. 538, no. (45)) Rubinstein (2012Rubinstein ( , 2014 implements this idea as a selectional restriction on the additional ordering source that weak necessity modals combine with (and thus as a definedness condition). Recourse to negotiability as a defining feature of weak necessity modality does address the conceptual worries of what characterises the additional domain restriction that brings about the weakening in the strength of the modal. Negotiability and speaker commitment however also feature in degree-based approaches (in particular Portner & Rubinstein 2016) as well as in Silk 2019, to which we will return in a moment. Before we do, let us review an empirical worry regarding domain restriction approaches.
Even though the existing research literature on modal strength distinctions almost exclusively focuses on weak necessity, possibility, too, may be perceived as a gradable notion and thus exhibit strength differences  Weak necessity without weak possibility ière 1981, Kratzer 1991, Lassiter 2011, Klecha 2014. In English, this is particularly visible when we consider adjectival and nominal expressions of modality, as in (19) and (20), but recall (9) from Section 2.2 as well.
(19) a. It is barely possible to climb Mount Everest without oxygen. b. It is easily possible to climb Mount Toby. (Kratzer 1991: p. 643, no. (18)) (20) a. There is a good possibility that Michl is the murderer. b. There is a slight possibility that Michl is the murderer. (Kratzer 1991: p. 643, no. (19)) (9) a. It could be dangerous to cycle in the city. b. It can be dangerous to cycle in the city.
Domain restriction approaches are not amenable to an analysis of weak possibility (see also Silk 2019: pp. 16-17): If we were indeed to assume that weak modal strength is about acknowledging the negotiability of a set of propositions that are used to derive the favoured worlds, this type of possibility modal expression should in fact be stronger than its plain counterpart, contrary to our intuitions about can as opposed to could. 8 More specifically, for any proposition and any two sets of favoured worlds and ′ , where ′ ⊂ , there is a world ∈ ′ such that ( ) = 1 logically entails that there is a world ∈ such that ( ) = 1, but not vice versa. We will see that in Javanese, however, the morphology used to weaken a necessity modal, when used on a possibility modal, neither results in the strengthening predicted under the domain restriction approach nor in the weakening actually observed for English, but rather in unacceptability, as previewed above in (3).
Degree-based approaches. Weak modal strength has more recently also been discussed as one facet of a more general phenomenon, that of the gradability of modal expressions and their acceptability in comparison constructions (Villalta 2008, Yalcin 2010, Lassiter 2011 a. I need to go on vacation more than I need to finish this work. (Solt 2015: p. 20, no. (18)) b. It is just as likely that Barbara will win as it is that Alice will win. (Portner & Rubinstein 2016: p. 257 (23a) and establish a relation between an entity and a measurement degree; at their core is a measurement function like height. In the unmarked positive case in (22a), the degree argument is closed off by a covert operator like (23b), which relates the maximal degree to which an entity has some property to a contextually salient standard (for further discussion, see von Stechow 1984, Fults 2006, Kennedy 2007. The resulting interpretation is in (23c). Other degree operators include the comparative (encoding the greater-than relation) and the equative (encoding the greater-than-or-equal relation).
The maximal degree to which Martina is tall exceeds the contextual standard for tallness.' Extending this analysis to weak necessity modals like should will assign them a semantics under which they relate propositions to degrees, as in (24). Suggestions as to the underlying scale that the measure function in (24) operates on include measures of probability of achieving a certain outcome (Finlay 2009(Finlay , 2010, of utility with respect to a certain goal (Lassiter 2011, but see 12:14 Weak necessity without weak possibility Lassiter 2017), and of compatibility with the speaker's negotiable priorities (Portner & Rubinstein 2016).
Generalising across the different proposals, the example in (25) says that the addressee calling Barbara is ranked higher on the underlying scale than the addressee calling Alice, and can be analysed in a structurally parallel fashion to any other clausal comparative.
(25) Weak necessity comparatives a. You should call Barbara more than (you should call) Alice. (Portner & Rubinstein 2016: p. 257 c. Clausal comparative operator: Degree-based approaches vary in their analysis of the unmarked case (that is, of plain should), and more specifically in their assumptions as to the standard of the comparison in this case. Like Klecha (2014), Portner & Rubinstein (2016: p. 276) assume that a covert Positive operator will close off the degree argument just as in (23) above, and relate it to a contextually provided standard for negotiable necessity, as sketched in (26) and (27). In contrast, Villalta (2008) assumes that comparison is with a set of alternative propositions in the context and proposes a null operator that is essentially a superlative (see also Finlay 2009Finlay , 2010. We sketch an implementation of such an analysis in  (27) Unmarked weak necessity as Positive: a. Covert operator: Unmarked weak necessity as superlative: a. Covert operator: While we won't discuss the differences between these two approaches in detail here, note that (27) allows for higher ranked propositions in the context and will be true if calling Barbara is an acceptable or good enough alternative. The truth conditions in (28) exclude this option, and require that the prejacent be higher ranked than all contextually salient alternative propositions. Compared to domain restriction approaches, degree-based approaches to weak modal strength are attractive because they allow for a uniform analysis of comparison constructions, modal or not, and predict gradable necessity as well as possibility. Previewing some more of our findings for Javanese, however, necessity modal expressions suffixed by -NE (even though adverbial) are unacceptable in comparison constructions, and we will not pursue a degreebased analysis. The data from Javanese thus point to potentially interesting variation in the composition of weak modal strength across languages.

The crosslinguistic picture
From von Fintel & Iatridou (2008)'s informal survey of nine languages spoken in Eurasia, 9 there emerge two strategies for linguistically encoding weak necessity (see also Rubinstein 2014): Under the first strategy, weak necessity is lexicalised, as in the case of ought or should in English (even though it is a result of grammaticalisation in this case). Under the second strategy, a strong necessity modal receives a weak interpretation when combined with the morphology also used to mark counterfactuality. We find this strategy in French, for instance, as shown in (29). Here, the necessity modal devoir is in the conditional mood (le mode conditionnel), which crucially is also used in the consequent of a counterfactual conditional like (30) (18)) The two strategies are not mutually exclusive, however: Present-day Dutch (Indo-European, Germanic) appears to have lexicalised a weak necessity modal, horen, as exemplified in (31). Weak necessity may additionally be expressed with the help of conditional zou, as in (32). As is the case with counterfactual morphology in French, zou also appears in the consequent of counterfactual conditionals like (33) (30)) von Fintel & Iatridou (2008: p. 126) conclude "…that it is a crosslinguistically stable fact that the meaning of OUGHT can be conveyed with counterfactual morphology on a strong necessity modal." Note that this conclusion is phrased as a possibility rather than a necessity statement, and von Fintel & Iatridou (2008: p. 124) are careful to point out that they "…are not claiming that all the world's weak necessity modals are formed by counterfactual marking on strong necessity modals." The two strategies, counterfactual marking and lexicalisation, are thus not mutually exclusive, and may very well not be exhaustive. We would expect there to potentially be other strategies to weaken the strength of a modal across languages.
For the languages that von Fintel & Iatridou (2008) discuss which use counterfactual marking, this morphology always co-occurs with the necessity modal. Other languages may well use alternative morphosyntactic strategies that do not involve the necessity modal since not all languages have lexicalized necessity modals in the first place (see, e.g., Narrog 2012: pp. 251-252), or because counterfactual marking to derive weak necessity is ruled out for independent reasons (see, e.g., Rubinstein 2014 on Modern Hebrew). We also would expect there to be languages that do not opt for using counterfactual marking or lexicalisation since there does not seem to be a reason why only these two strategies could derive weak necessity modality. We report such a strategy in Section 4 for Javanese. The language uses dedicated functional morphology to weaken the strength of a necessity modal and in this way transparently derives weak necessity from strong necessity. This morphology does not, however, mark counterfactuality. Before we turn to these data, we provide a brief background on the language and our fieldwork methodology, and introduce the modal system of Paciran Javanese.

12:18
Weak necessity without weak possibility 3 Background on Javanese

The Javanese language
Javanese is an Austronesian language from the Malayo-Polynesian branch and primarily spoken in Central and East Java, Indonesia. With close to 70 million speakers, it is the largest language worldwide with no official status (Indonesian being the official national language). 10 Dialects of Javanese are highly divergent, with three main dialectal groupings of West, Central and East Javanese (Nothofer 1981, Hatley 1984). In addition, Javanese has three speech levels, krama 'high', madya 'mid' and ngoko 'low', which are most prominent in the courtly cities of Yogyakarta and Surakarta/ Solo (see, e.g., Poedjosoedarmo 1968, Smith-Hefner 1989, Errington 1998. Our data are from an East Javanese dialect spoken in Paciran village, Lamongan Regency, East Java. Paciran village is located on the North shore of East Java, near the town Tuban as shown on the map in Figure 3. 11 The data in this paper are in ngoko 'low', which is the speech level most widely used in Paciran given its geographical distance from the Javanese courtly centers. The other speech levels are used to a lesser extent in Paciran but remain ideologically important (see also Vander Klok 2019).
The basic word order of modern Javanese is SVO, and verbal morphology marks a reduced symmetrical voice system, which indicates which thematic argument is the subject (see, e.g., Conners 2008, Robson 2014. All examples in this paper are in Actor Voice (AV), which is indicated by nasal substitution with a homorganic nasal prefix, as in (34)  Javanese is relatively understudied, and there is no previous formal research on the topic of this paper, the semantics of -NE and the modal strength distinction. This aspect of -NE has not received attention in the descriptive literature either, although Robson & Wibisono (2002) do note a translationbased strength distinction between necessity modals with and without -NE in their dictionary. Other descriptive resources discuss only the morphosyntactic properties of -NE, and again, hint at strength distinctions in translations to Indonesian (Ekowardono et al. 1999, Wedhawati et al. 2006).

Methodology
All data presented in this paper are from original fieldwork conducted in Paciran, Java, Indonesia, by the first author from periods throughout 2011 to 2019. A variety of methods were used including recorded natural conversations as well as the semantic elicitation techniques described in Matthewson 2004, 2011, translation tasks, and storyboards (Burton & Matthewson 2015). The elicitation judgments typically represent judgments from two to four language consultants. In some cases, individual speakers were asked to give acceptability judgments of sentences in an elicitation set, and then the same elicitation set was discussed individually with other speakers, who also gave acceptability judgments. In other cases, group elicitation sessions with two to four speakers were held. In asking for semantic judgments, a discourse context was constructed by the first author or offered by the lan-12:20 guage consultants. Elicitation was almost exclusively conducted in the target language, and specifically, in the variety of Javanese spoken in Paciran. We follow Matthewson (2004) in that translation can only provide clues, not results, as to the contribution of meaning of a given morpheme. Where appropriate, translation tasks were either from Indonesian or English to Javanese; the contact language used for storyboards was English. Data also come from a questionnaire study on modality which was implemented as an acceptability judgment task using a likert scale (with ten participants) and a semiforced choice task (with 15 participants); see also Vander Klok 2012 The modal questionnaire was presented using only Paciran Javanese (for the instructions, contexts, and items). Unless stated otherwise, the examples in this paper are based on elicitation.

The modal system of Paciran Javanese
In order to understand the composition of weak necessity, we first give an overview of the modal system of Paciran Javanese focusing on the dimensions of force and flavour. 13 With respect to these two dimensions of description, the Javanese modal system instantiates a mixed system, as illustrated in Table 1  In terms of their syntax, these modals do not form a uniform class. The epistemic modals mesthi and paleng are adverbs, while the root modals are auxiliaries, with one exception: The modal kudu 2 is a main verb (Vander Klok 2012 Table 1 Modal force and flavour in the modal system of Paciran Javanese With respect to modal force, mesthi is compatible with necessity, but not possibility contexts, as shown in (35) and (36). In the latter, the epistemic possibility modal paleng is used instead. Concerning the modal flavour of mesthi, it is only acceptable in epistemic contexts such as (37). Infelicity results when mesthi is tested in any other modal flavour context, be it deontic or circumstantial, as shown in (38) and (39). Instead, the root necessity modal kudu 1 is most appropriate in both of these cases. sation and occurs below negation. Due to its differential syntactic properties, we set kudu 2 aside here (see also Section 4.1).

12:22
Weak necessity without weak possibility (37) a. Context: -epistemic -"They can't be hiding in the box", says the policeman. "It's too small. And they can't be hiding under the bed. It's too low …" 15 b. Thus, the modal auxiliary mesthi lexically specifies both its modal force (as necessity), and its modal flavour (as epistemic). Similar tests were used for all the other modals in Table 1 to determine their force and flavour (see Vander Klok 2013 for details).

12:23
Jozina Vander Klok, Vera Hohaus that -NE-marked modals meet the definition for weak necessity (Section 4.2), but that -NE is not counterfactual morphology (Section 4.3). We also discuss other properties of -NE that will be relevant for our analysis: Unlike counterfactual morphology in other languages, the suffix is restricted to those modals that encode necessity (Section 4.4), and its addition does not change the modal flavour of its root (Section 4.5).

A note on the morphosyntax and phonological form of -NE
Our focus in this paper is on suffixation with -NE 1 (elsewhere just referenced as -NE), whose distribution is restricted to modal adverbs and auxiliaries.
-NE-suffixed modals are always adverbial (Wedhawati et al. 2006: pp. 331, 336). The form of this suffix is phonologically predictable: When the stem ends in a vowel, -ne appears, and elsewhere -e. We set aside here a homonym with a distinct morphosyntax and semantics: -NE 1 is homophonous with the clitic -NE 2 in the nominal domain that marks definiteness, as in (40). (See also Section 7.1, where we discuss directions for future research.)

(40)
Kucing-e 2 cat-def nyolong av.steal iwak. fish 'The cat stole some fish.' (Davies & Dresser 2005: p. 61) Assuming that Javanese has zero derivation, a nominal syntactic analysis for the weak necessity modals mesthi-ne and kudu-ne is ruled out for distributional reasons: While nouns can occur with pronominal possessive marking (like -ku 'my'), the weak necessity modals cannot. Thus, *mesti-ku is ungrammatical and does not translate to 'my certainty', nor does *kudu-ku translate to 'my obligation'. The morphosyntactic restrictions on the distribution of -NE 1 will be relevant for Section 4.3, where we will use it as an argument against an analysis of -NE 1 as counterfactual morphology.

Meeting the definition of weak necessity
In this section, we show that -NE-marked modals behave like weak necessity modals under the definition proposed by Rubinstein (2020), repeated here:

12:24
Weak necessity without weak possibility (10) A modal word is a weak necessity modal if (i) to (iii) hold, for any proposition .
(i) The conjunction of ( ) and (¬ ) is a contradiction.
(ii) There is a necessity modal such that ( ) entails ( ).
(iii) There is a possibility modal such that ( ) entails ( ).
Like a necessity statement (but unlike the possibility counterpart), a -NE-marked modal cannot be true of both the prejacent and its negation, as required by the first condition of the definition in (10). We show this for epistemic modality in (41). We find the same pattern of acceptability judgments for deontic necessity, in (42) We next present data that allow us to locate the meaning of a -NE-marked necessity modal with respect to both mere possibility and necessity, in accord with the conditions in (ii) (44), where speakers were asked to judge the acceptability of the sentences following the discourse contexts, while keeping in mind the two discourse contexts were connected. In this case, the follow-up (= the additional facts that the speaker remembers about the sandals) results in the speaker weakening her epistemic commitment to the proposition that Dur be at home. Speakers accepted the order where the first modal claim is with the strong necessity modal mesthi and the second is with the same modal plus -NE, suggesting again that the -NE weakens the strength of the necessity. Crucially, in (44d) epis.nec 'Dur should be at home, but it's not a must/ not certain.' 18 Unlike its English counterpart must, mesthi can scope under negation, as shown in (44d); see also Ekowardono et al. 1999 for Standard Javanese. This point of variation between English and Javanese is also reflected in the translation of the example.

12:27 Jozina Vander Klok, Vera Hohaus
We suggest that the negated necessity claim is in fact an implicature that the -NE-marked necessity modal gives rise to. We show in (45)  Importantly, too, when the modal statements are in the opposite sequence than in (44) and (45), the respective follow-up is infelicitous: First, in the discourse context in (46a), the weak epistemic necessity modal mesthine is felicitous. However, it is not felicitous to then follow up with mesthi after weakening the speaker's epistemic commitments. In other words, the necessity modal mesthi cannot have a weaker modal claim than its -NE-marked counterpart. Second, in the context set up in (47a), the epistemic necessity modal mesthi is felicitous. However, in the context of (47c) that is set up to require further strengthening, the follow-up with mesthine is judged to be unacceptable. Additional examples that show that -NE-marked necessity modals like kudune and mesthine give rise to the implicature that the stronger necessity statement is false (and that this implicature can be cancelled) are in (48) to (51). Crucially, unlike in (45), the cancellation here does not rely on a follow-up context, but a correction with sa'benere 'in fact, actually' or sa'tenane 'actually, truly'. Examples (50) and (51) involve question-answer pairs, which block self-repair strategies on the part of the speaker (see also Mayol & Castroviejo 2013 We conclude from the discussion of the data in this section that -NE indeed has a precise role in the weakening of the strength of a necessity modal expression. In how far is it functional morphology dedicated to that purpose, though? That is, is -NE also used for counterfactual marking, as in the languages discussed in von Fintel & Iatridou 2008? We resolve these questions in the next section.

Not counterfactual marking
While -NE allows us to build a weak out of a strong necessity modal, this suffix is not counterfactual (CF) marking, for distributional and morphosyntactic reasons.
Across languages, counterfactual marking occurs in two environments (see, e.g., Iatridou 2000, von Fintel & Iatridou 2008, Romero 2017: Present and past counterfactual conditionals like (52), and present and past counterfactual wishes like (53). In both English and Spanish, counterfactuality is marked by a past tense that is not interpreted as such (and hence has also been called a fake), obligatorily in combination with subjunctive mood in Spanish. In Javanese, -NE is not obligatory in either of these environments.  (25)) An example of a past CF conditional from Javanese is in (54), and examples of present CF conditionals are in (55) and (56). While we have to leave a more in-depth description of counterfactuality in Javanese for another time, the examples show that -NE is not required in this type of conditional, even though it can optionally occur on a necessity modal in the consequent, as in the first example. What appears to be necessary to form a CF conditional in Javanese is the overt presence of the prospective aspect marker ape or of some modal expression in the consequent: In (56c), the absence of mesthi renders the example infelicitous in this context; it can not receive a CF interpretation. 19 19 Once we know more about counterfactuality in Javanese, it will be worthwhile to investigate whether Javanese fits in with the languages discussed in von Fintel & Iatridou 2008, which use CF-marking in co-occurrence with the necessity modal verb to derive weak necessity.
If it turns out that Javanese does not mark CF overtly, then there is nothing more to say. If Javanese has morphosyntactic strategies to mark CF, but does not use CF-marking to derived weak modal strength, it will be important to understand why (see also Rubinstein 2014: p. 521. We thank a reviewer for discussion of this point. Attempts of forming CF conditionals by using -NE marking on the verb in either the antecedent or the consequent of the conditional are not successful for independent reasons: Recall from Section 4.1 that -NE 1 can only attach to auxiliaries and adverbs. In (57), the suffix is thus interpreted as -NE 2 attaching to a nominalised verb and is thus ungrammatical. Even just in terms of its morphosyntactic distribution, -NE is thus not a good candidate for CF marking. For this reason, we also do not expect -NE to occur in the expression of CF wishes such as (58) We conclude that -NE is not CF marking. The data from Javanese thus contribute a new crosslinguistic pattern in how weak necessity modality can be derived.

Restriction to necessity modality
Counterfactual morphology in languages like French can also combine with possibility modals, as in (59). In Javanese, the distribution of -NE differs in that it may not attach to possibility modals, even though they are of the right morphosyntactic category: Recall from Section 3.3 that the epistemic modals mesthi, paleng in Javanese are adverbs, while the root modals kudu 1 , iso, and oleh are auxiliaries. the.vacuum 'I could do the dishes, the cleaning, the ironing, and the vacuuming.' 20 As discussed in Section 2.2 above, weak possibility is also not ruled out on conceptual grounds, and it will be crucial that the semantics for -NE capture the incompatibility with possibility modals. Retracing our discussion from that section, a domain restriction approach does not predict such a distribution without further assumptions. In fact, it would predict that -NE suffixation results in strengthening with possibility modals. Degree-based approaches would not make this prediction, but also do not predict the distribution of -NE. (We will return to this discussion in Section 5.1.)

No change in the modal flavour
We explore in this section whether we can identify any other meaning components of -NE, apart from the weakening it induces. A morphologically induced change in modal flavour is attested in German, for instance (see Matthewson & Truckenbrodt 2018). The data in (63) to (65) however show that the broad overall modal flavour under -NE remains constant across epistemic, deontic, and teleological modality.
The epistemic necessity modal mesthi, when modified by -NE, still only expresses epistemic modality, as in (63). It can neither receive the deontic reading that is plausible for (64), nor the teleological reading that the context in (65) sets up, which are parallel to the examples with mesthi in (37) to (39) above. The root necessity modal kudu 1 when modified by -NE still cannot receive an epistemic reading, as illustrated in (63). Kudune may however receive a deontic reading as in (64) or a teleological reading as in (65) We conclude that the affixation of -NE to necessity modals mesthi and kudu does not result in a change of their modal flavour.

Interim summary
Javanese encodes the weakening of a modal necessity claim with a dedicated functional morpheme, -NE. Unlike in the languages discussed by von Fintel & Iatridou (2008) that derive weak modal strength in a morphologically transparent manner with counterfactual morphology, -NE does not mark counterfactuality. Within the modal paradigm of Javanese, its distribution is restricted to strong necessity modals. Our semantics for -NE will have to capture two empirical observations in particular: First, it will need to account for 21 It might be for that reason that the sentence only has a counterfactual interpretation. The intricacy of this example is beyond the scope of this paper. We thank one of the editors, Magdalena Kaufmann, for raising this issue.
12:35 the weakening of the necessity claim (as witnessed in the entailment patterns that arise, and the behaviour with respect to the conjunction of mutually exclusive propositions). Second, it will also have to account for its distribution in the modal system of Javanese, and explain why -NE cannot combine with possibility modals.

A semantics for Javanese -NE: Deriving weak necessity without weak possibility
In this section, we develop an analysis for Javanese -NE that is a new variant of a domain restriction approach: While we maintain with von Fintel & Iatridou (2008) that weak quantificational strength in Javanese is a result of quantifying over a subset of the original domain of quantification that is determined by the accessibility relation and the primary ordering source, we propose that this quantification is over a contextually provided, non-empty subset of a minimal witness set for the quantification. This analysis predicts weak necessity without weak possibility, unlike the existing analyses that we introduced in Section 2.3. We will first spell out the reasons for not adopting these approaches in Section 5.1 and then introduce our proposal in Section 5.2.

Against previous approaches
Problems for the standard domain restriction approach. Under domain restriction approaches to weak modal strength, weak necessity can be characterised as quantification over a subset of the domain of its strong counterpart. Under the analyses in von Fintel & Iatridou 2008and Rubinstein 2012, this smaller domain of quantification is a result of a secondary ordering source (see Section 2.3 for details). We could thus analyse -NE as marking the presence of a secondary ordering source, a prima facie plausible analysis. Why not, then? Such an analysis would make wrong predictions as to the distribution of -NE, at least without any further assumptions: If -NE were indeed to flag the presence of a secondary ordering source, this option should also be available for possibility modals in Javanese, contrary to fact. In addition, as we have discussed in Section 2.3 as a concern for the analysis of English weak modal strength, a smaller quantificational domain in the case of a possibility modal results in strengthening and would thus derive what one could call an extra strong possibility modality. To address this problem, one could stipulate 12:36 that -NE-suffixation must result in weakening, hence its unacceptability with possibility modals, as in (67). 22 It is unclear though what the status of (67) would be in the grammar of Javanese, and whether it could be derived from more general grammatical principles.

(67)
Weaken, don't strengthen! -NE is licensed only if the resulting proposition is weaker; that is, the unmodified proposition logically entails its -NE-marked counterpart.
Under such an analysis, -NE would be a close relative (or rather, the mirror image) of the English Negative Polarity Item any, for which Kadmon & Landman (1993) suggest the strengthening requirement in (68) The conceptual parallels between (67) and (68) should not, however, disguise that any and -NE would be very different creatures, the former an alternativesensitive operator that interacts with exhaustification, and the latter merely a placeholder for a secondary ordering source that brings about a restriction of the domain of quantification. Deriving a requirement like (67) from more general grammatical principles would require an alternative-based semantics for -NE that is sensitive to the entailments of different quantificational operators. We do not pursue such an analysis any further in this paper. We will however adopt an analysis under which -NE suffixation results in a smaller domain of quantification, albeit through different technical means. Before spelling out the details of this analysis, we discuss the arguments against a degree-based approach to the semantics of -NE.
Against a degree-based approach to the semantics of -NE. A degree-based approach to the semantics of -NE does not seem feasible for at least two reasons: First, such an approach does not lend itself to explaining the distribution of -NE, as it does not rule out weak possibility (an advantage it has 22 We would like to thank one of our reviewers for discussion on this point. 23 This idea has been spelled out in greater technical detail more recently by Chierchia (2013) and Fox & Spector (2018), who derive this restriction as an economy condition on the exhaustification of alternative propositions.
12:37 over the domain restriction approach for the analysis of English). Second, unlike their English counterparts, weak necessity modals in Javanese do not participate in any of the comparison constructions of the language.
In the typology of Stassen (1985), Javanese adopts a particle comparative, in which the gradable adjective or adverb is obligatorily marked by luweh 'more'. The standard of the comparison in Javanese is introduced by timbang 'than' or teko 'from', as is illustrated in (69) to (71). We follow Vander Klok (2011) in assuming that the semantics of comparison constructions in Javanese is degree-based (for crosslinguistic variation in the grammar of comparison, see also Beck et al. 2009, Bochnak 2015, Deal & Hohaus 2019, Hohaus & Bochnak 2020. Following von Stechow (1984), evidence for such an analysis comes from differential comparatives like (70) and from comparison with a degree as in (71) Weak necessity modal adverbs are however not gradable and are unacceptable when they occur in the comparative, as we show in (72) and (73). Consultants instead offer the borrowed mending 'better' from Indonesian in (74)  The ungrammaticality of weak necessity modal adverbials in the comparative suggests that they do not have an underlying degree-based semantics.

Our proposal
Javanese -NE is used to weaken modal strength, but is sensitive to the distinction between possibility and necessity, which translates to existential and universal quantification over the favoured worlds under the standard quantificational analysis of modality. How can we capture these properties of -NE? We suggest here a different type of domain restriction analysis: We propose that Javanese -NE weakens a necessity modal expression by requiring that the prejacent be true throughout a non-empty subset of those worlds that would have to make the prejacent true in order for the strong necessity modal statement to hold.
The proposal additionally exploits a distinction between existential and universal quantification when it comes to the sets that make the quantification true: For a strong necessity statement to be true, the prejacent has to be true in all of the favoured worlds. We can characterise those worlds, the worlds minimally required to vouchsafe for the truth of the overall modal 12:39 claim as the truthmakers or witnesses. We suggest that -NE relies on this notion of witnesses, or more specifically of minimal witness sets (see also Barwise & Cooper 1981, Szabolcsi 1997, Endriss & Hinterwimmer 2009), as defined in (75).

(75)
A set is a minimal witness set WIT for a generalised quantifier if and only if ∈ , and there is no set ′ ⊂ such that ′ ∈ .
Applied to an example from nominal quantification, the minimal witness set for every lawyer (assuming no further contextual domain restriction) is ⟦ lawyer ⟧, the set of all lawyers. For three lawyers, any set with cardinality three where each of the members is a lawyer qualifies as a minimal witness set. For some lawyer, any singleton set that contains an individual that is a lawyer qualifies as such a witness set. Minimal witness sets for existential quantification under this definition are thus singleton sets, a feature which we will exploit (together with the subset requirement) to explain why -NE cannot combine with possibility modals: Their minimal witness sets are singleton sets which don't have any non-empty (proper) subsets. We implement this idea more formally in (76).
(76) For any ∈ ⟨ , ⟩ , any ∈ ⟨⟨ , ⟩, ⟩ , and any ∈ ⟨ , ⟩ ∶ ⟦ -NE ⟧( )( )( ) is defined iff Under this analysis, the sentence from (45), repeated below, is interpreted on the basis of the Logical Form sketched in (77a), where the first argument of -NE is a set of worlds that is contextually supplied but depends on the world of evaluation. 24 These are the worlds upon which -NE adds a definedness condition, but ultimately also the worlds which will have to make the prejacent true for the sentence to be true. The resulting interpretation of the example is in (77b). iff ∀ ∈ C @ ∶ Mrs. Deli be at home in For the sentence to be true, all of the worlds in some non-empty proper subset of the favoured worlds that is accessible from the actual world will have to be such that Mrs. Deli is at home in those worlds. These truth conditions do not prevent the stronger necessity claim from being true, namely that the prejacent is true in all of the favoured worlds. This is a welcome result, as it allows for a weak necessity to be strengthened to a strong necessity, in line with the data we presented in Section 4. Standardly, as we saw, there will be an implicature to the exclusion of the strong necessity case. If the prejacent had been true in all of the favoured worlds, the speaker would have used mesthi. Strengthening a weak to a strong necessity cancels this implicature. The analysis captures the two properties of -NE that have featured most prominently so far: It accounts for the weakening in modal strength but crucially also predicts the incompatibility of -NE with possibility modals. In the case of our example in (45), for there to be a possibility of the prejacent being true, we need at least one world that would make it so. Under the semantics for -NE in (76), the interpretation of the sentence will not be defined, and hence unacceptable: It is not possible to find a non-empty set of worlds 12:41 that is a proper subset of the minimal witness set for existential quantification. Possibility modals do not make available any subset alternatives to their minimal witness sets. Hence, -NE cannot be used to weaken the strength of a possibility claim. 25 As is, the semantics of -NE does not say anything about the nature of the subset that weak necessity modals in Javanese quantify over.
The nature of the domain restriction. How can we characterise the properties of beyond its relation to the original domain of quantification (and thus beyond being a subset of a witness set for the quantification)? Ultimately, we do not think that the data from Javanese offer new insight into this question, even though it will be important to identify the relevant constraints. 26 As discussed in Section 2.2, English weak necessity modals have been suggested to reflect an additional requirement on the favoured worlds that is sensitive to commitment (Jones & Pörn 1986, Rubinstein 2012, Portner & Rubinstein 2016, Silk 2019. Under this analysis, the smaller domain of quantification derives from taking into account propositions in the common ground that are considered to be negotiable. The question therefore arises whether commitment could also play a role in determining the smaller domain of quantification for -NE-marked modals in Javanese. While this is a very subtle question to investigate in the fieldwork setting, the very least we can say is that -NE is compatible with contexts where the weakening