On the emergence of an aspectual NPI : comparative polysemy & the case of Diyari marla *

Cross-linguistically, morphological material that expresses comparison (e.g. more ) appears to be colexiﬁed with aspectual (“phasal”) adverbs that, under negation, encode the termination of some eventuality ( CESSATIVE s, e.g. *(not)... anymore ). Using data drawn from the Diyari language of central Australia, we propose a diachronic trajectory for the lexical item marla ‘very, truly’. This word ﬁrst developed a comparative semantics and, subsequently, a cessative reading restricted to negative polar contexts. This proposal moves us towards a lexical entry that permits for the uniﬁcation of comparative and aspectual readings for items which exhibit this polysemy and—on the basis of robust pragmatic principles— predicts their polarity-sensitive distribution cross-linguistically.


Introduction
The notion of "phase quantification" has attracted considerable attention within semantics/pragmatics and linguistic typology, particularly regarding the meaning contribution of those expressions which realise temporal phase operations (i.e.phasal adverbs) and how these semantic domains are lexicalised differently across languages.Operators that perform "phase quantification" are generally modelled as predicates that encode transitions between possible temporal/sequential transitions between the truth and falsity of a predicate along a given scale (i.e. at a given time; 1 Löbner 2019: 229, also Horn 1970; Doherty 1973; Muller 1975; van Baar  1997 a.o.).In this paper, we provide a case study of the Diyari (Pama-Nyungan) comparative-cessative marla in order to explore the paths by which this polysemy arises and to interrogate why these items appear to exhibit robust polarity sensitivity.
1.1 Background: the meaning of phasal adverbs Horn (1970) models pairs of phasal adverbs as encoding a presupposition (projecting through negation) that some property respectively holds in the future or the past of reference time, 2 and asserts that it holds at reference time.Lexical entries capturing these intuitions are given in (1) and examples (including one demonstrating interaction with negation) provided as (2), and the general principles are schematized in Figure 1.
already/yet = λ Pλt : ∃t ′ [t ′ ≻ t ∧ P(t .¬ she swims (t) An important (if controversial) observation due to Löbner (1986;1989 et seq), is that, as with other quantificational elements in natural language (construed as second-order predicates in the sense of Barwise & Cooper 1981), lexicalisation patterns of phasal adverbs give rise to a (version of a) "square of opposition" with (possible) elements related by internal and external negation (fig.2).A consequence of this view is a conception of ALREADY-and STILL-type operators as logical DU-ALS of one another; this follows from the relationship between the sentences in (3).In order to better distinguish metalinguistic labels for these operators from the English lexical items that they correspond to, we adopt the terms IAMATIVE (IAM) and CONTINUATIVE (CNTV).
As we suggest above, this treatment of the semantics & pragmatics of phasal adverbs-viz.that the meanings of these four items relate to each other in terms of an Aristotlean square of opposition-has run up against significant problems (e.g., Klein 2018;Mittwoch 1993 a.o.).Significantly, van der Auwera (1993) claims that it is unclear that the entailment relation between, for example (3a) and (d), is symmetric: a crucial prediction of the duality hypothesis.In effect, van der Auwera's claim relies on the observation that, within the A corner (see Fig. 2), already competes with adverbs like finally (3e (3) e. the light's finally on For van der Auwera, then, while (a) and (e) both entail (3d), the reverse entailment doesn't hold, evincing an asymmetry in their meanings-namely an additional meaning component in already/finally that is absent in still.
In response to these data, van der Auwera's formulation of a "double alternative" hypothesis (1993) 5 locates the additional meaning component in an appeal to some salient "counterexpectational" situation: the distinction between already and finally is basically that the predicate is understood to obtain earlier than expected in the former case, as opposed to later in the latter case.A similar distinction in the continuitive domain exists in a number of languages of Europe (e.g.(pas) ncore vs. toujours (pas) in French, not yet vs still not in English).
Van der Auwera goes on to suggest that the considerable amount of crosslinguistic variation in terms of lexicalisation strategies can be predicted on the basis 5 Van der Auwera adduces other data in his dismantlement of the duality-square view of phasal adverbials, including a claim that ALREADY-type items additionally encode inchoativity -that is, contiguity between a negative and positive phase -and thus contrast with the continuitive semantics of STILL/YET/ANYMORE-type items.This is challenged in van Baar (1997: 36ff ).Additionally, it is pointed out that, cross-linguistically, the derivation of CUNCTATIVE (not yet-type) marking from CONTINUITIVES (as in the Nahuatl situation, fig 2) is reported to be extremely rare (see also van Baar 1997), a fact not apparently predicted by the Duality Hypothesis (van der Auwera 2021).

The scalar model of polarity
Of especial relevance for the current analysis, the 'Scalar model of polarity'-as formulated by Israel (2011, in addition to his and others' earlier work)-provides crucial additional insights.This treatment focuses on nature of the lexical domain occupied by phasal adverbs (his "aspectual operators") as an "inherently scalar domain [in that it] depends on the way an eventuality is construed with respect to time, [...] itself a scalar phenomenon," (Israel 2011: 151).
On this style of analysis, then, sentences involving phasal operators 'involve the evaluation of an overtly expressed text proposition [in the sense of Kay 1990] with respect to a presupposed scalar norm or background expectation' (Israel 1998: 125, italics added).These propositions are related with respect to an INCEPTIVE scaleordering them in terms of relative earliness of the start time of the eventuality being described-or a DURATIVE scale-which orders them in terms or the lateness of their endtimes (compare Fig. 1).
Israel's scalar model account hinges on conceptualising propositions with respect to (a) their position along a given scale-their Q-values; in addition to (b) their notional INFORMATIVITY: construed as proportional to the number of propositions within the model that they entail-their -values (Israel 2011: 81).Particular expressions, then, can be understood as conventionally encoding a high I-value (emphatics, marking a proposition that entails the scalar norm) or a low one (attenuators, marking a proposition entailed by the scalar norm), effectively situating their prejacent within a scalar model.
On an Israel-style analysis, then, still and anymore both situate their prejacent high on a durativity scale-i.e. the eventuality described is marked as "lasting later" than some scalar norm.The difference between these items is located in a difference in their informativity-emphatic still is licensed when the prejacent entails some contextual norm, whereas attenuating anymore is licensed when it is entailed by the norm.For Israel, these features of the items' lexical semantics predict their polarity sensitivity behaviour: ...in order for its [prejacent] to count as emphatic, still requires a context allowing inferences from high to low Q -values; anymore, in order for its [prejacent] to count as [attenuating], requires a context in which inferences run from low to high Q-values.(Israel 1997: 223) This contrast-and how it relates to the polarity sensitivity of these expressions-is shown in (4-5) below.In (6), the felicity of both adverbs is expected, given the non-monotonic entailing behaviour of questions.
PREJACENT.Sam was cooking as late as midnight ⇓ NORM.Sam was cooking as late as 9 [sc.some more reasonable endtime] b. *Sam wasn't still cooking at midnight.
PREJACENT.Sam wasn't cooking as late as midnight ̸ ⇓ NORM.Sam wasn't cooking as late as 9 (5) Attenuating anymore requires that some contextually-retrieved "lateness" norm entails its prejacent a. * Will was asleep anymore.
PREJACENT.Will was asleep as late as noon ̸ ⇑ NORM.Will was asleep as late as 9 b.Will wasn't asleep anymore.
PREJACENT.Will wasn't asleep as late as noon ⇑ NORM.Will wasn't asleep as late as 9 Importantly, the contrast that obtains between the sentences in (6)-namely that (a) is reported as encoding a degree of mirativity (or judgmentalism) that is absent in (b)-can be understood as a function of still's emphatic character: the lateness of Gladys's pot-smoking is taken to outstrip some contextual norm.6 (6) Felicity of still and anymore in questions (Israel 1997: 224) a.Does Gladys smoke pot still?
b. Does Gladys smoke pot anymore?
2 Data: comparative/cessative colexicalisation According to the considerable amount of typological work on phasal polarity, expressions that encode comparison represent perhaps the most productive source of cessatives cross-linguistically (see van Baar 1997;van der Auwera 1998;Vandeweghe 1986).The colexicalisation of COMP and CESS expressions is exhibited in languages from many different families, including Albanian, Dutch, French, Georgian, Irish, Lingala, and Vietnamese (some examples are given in figure 2).In many (most?) of these languages-including English and French-a CNTV reading of this morphology is unavailable.That is, the aspectual reading of comparative morphology is restricted to negative polar contexts.This is illustrated for French in (7-8) below (see also van  In other languages, comparative morphology is "liberated" from these licensing conditions.For example, Romanian comparative mai (from Latin magis 'more, greater') has a cessative function (e.g. when co-occurring with nu 'NEG') but can also occur in positive contexts as a continuitive.Durative (as opposed to additive/iterative) uses seem to emerge when the interpretation is stative (Donazzan & Mardale 2010: 257 van Baar 1997 (190-1).Additional examples come from van der Auwera (1998: 51, 100), who cites cross-linguistic evidence to argue for a cycle where comparative morphology is recruited to encode cessative meanings before apparently developing an IAMATIVE (already-type) function in positive contexts (e.g. for numerous Balkan languages, see also van Baar 1997: 184-7). 8 final example come from English "positive anymore"9 for relevant dialects of US English (as investigated by e.g.Horn (1970); Hindle & Sag (1973) a.o, see also van der Auwera 1998: 32).In these varieties, anymore P appears to assert that P holds at reference time t, while giving rise to a presupposition that ¬P at a time prior to t (a schema that resembles our IAMATIVE semantics).

Understanding Diyari marla
The Karnic subgroup of Pama-Nyungan comprises approximately 10 languages spoken in the Lake Eyre Basin region of Central Australia (Bowern 2023: lxxxviii, see also Breen 2007).In the 19th Century, German Lutheran missionaries "[chose] Diyari as their language of evangelisation" (Hoffman 2008: 44).Diyari's adoption as a "mission language" by missionaries in Bethesda and Hermannsburg had as consequences both the development of vernacular literacy among the indigenous population in addition to a significant amount of structural standardisation and concomitant grammatical and lexical change, relative to pre-contact varieties.Further, given its extended contact history, Diyari is unusual in the Australian context for being the subject of descriptive and sociolinguistic attention dating back to the middle of the nineteenth century; see Kneebone 2005; Stockigt 2016; Moore 2019 for recent historiographical work.
Language data is drawn from several sources.Austin (1981) is a reference grammar-a publication of his 1978 dissertation and substantially updated in 2011 on the basis of new material.It draws on a combination of work with older sources and fieldwork with Diyari speakers, particularly Ben Murray.In the 19th Century, descriptive materials, including a dictionary and comparative grammar, were com-piled and distributed as Reuther & Strehlow (1897). 10e identify three major functions for marla; labelled here as the INTENSIFIER (shown in 10), the COMPARATIVE (11) and the CESSATIVE (12) uses.Explicit comparative morphology is all but absent in other Australian languages.Comparative strategies across the continent commonly involve conjoined/juxtaposed clauses (this fact is further discussed below, see also Schweiger 1984Schweiger /2005)).Additionally, a striking result of recent and in-progress work is the near absence of polarity sensitivity in the lexicons of Australian languages.When phasal adverbs are introduced in translation, they tend to correspond with morphology that performs an apparently information-structural function (e.g.focus-marking).

.1 Intensification
As shown in (10) and below in ( 14), Austin (2011: 40)  In light of the observations mentioned above regarding the apparent absence of degree expressions (including explicit comparative morphology) in most Australian languages (see Schweiger 1984;Bowler 2016), we propose a semantics for marla on its intensifier reading that is compatible with a negative setting of the degree semantics parameter (DSP)-that is, a "degreeless" semantics (see Beck et al. 2009, Bochnak 2013 a.o.)In order to implement this proposal, we assume Klein's (1980) "vague predicate" style of analysis, where the extension of a gradable adjective is analysed as a partial function which is evaluated relative to a discourse context, as in (15) below: (15) pirna c = λ x.big c (x) In a given discourse context c, pirna refers to the set of things that count as big at c (i.e. the positive extension of big, given c) In ( 15), the discourse context provides a comparison class (which we notate ≁ c ) -the set of entities being compared.A given vague predicate P, then, establishes 11 Arabana arla also appears multiple times in Hercus 1994 as a stative predicate with an apparent meaning of 'true, visible, manifest'.Arabana has initial nasal deletion as a regular sound change, though the regularity is sometimes obscured by subsequent loanwords.Note that none of the other Karnic languages, to our knowledge, have a cognate of *marla, but that is not particularly surprising given the high turnover of these adverbs across Pama-Nyungan languages.12 Austin additionally identifies a similar intensifying function for pirna 'big' when this item co-occurs with nouns and other predicates.
a partition over ≁ c : a positive and negative extension (both of which must be nonempty) and an "extension gap"-those items in ≁ c for which it's unclear whether they count as P or not-P.
Intensifier morphemes then are taken to invoke an accessibility relation R which makes available a set of alternative discourse contexts R(c). 13Again following Klein (1980: 25), this can be understood as the set of contexts which make available the positive extension of the predicate at the matrix context as the comparison class-that is R c = {c ′ |≁ ′ c = pos good (c)} .
Crucially, this "iterative" semantics for intensification captures the intuition that for any arbitrary c, P c ⊃ marla P c .We can now provide truth conditions for (10), on the basis of the "degreeless intensification" semantics for marla outlined above.( 17)

Comparison
The semantics for marla can be straighforwardly extended to give a degreeless semantics for comparative constructions like shown given in (11), simplified as ( 18) below (where the possessive NPs nga-/ying-karni kinthala 'my/your dog' are replaced with the "names" a and b respectively.) According to the survey of 24 Australian languages in Schweiger 1984, there are several languages for which INTS morphology is co-opted to perform a comparative function.In these languages, as in Diyari, the LOCative case is made available to mark an explicit standard of comparison.
Extending the intensifier analysis to account for the comparative function, we take the locative-marked standard phrase to realise a contextual modifier (in the sense of Francez's 2009 analysis of existential predication).That is, the function of LOC is to restrict the accessibility relation introduced by marla (R above) to a doubleton consisting only of the comparandum (α) and the individual denoted by the standard phrase.Truth conditions for (18) are derived in ( 19) below, where the underlined locative phrase restricts R c to the set {c ′ |≁ c ′ = {α, b}}.
In effect, the truth conditions in ( 19) guarantee that any context in which b counts as big will also be a context in which a does-λ c.big c (a) ⊋ λ c.big c (b)effecting a comparison of the two dogs' sizes.
However, in addition to translating comparisons of vague, adjectival predicates, marla also occurs in comparisons of verbal and nominal predicates, examples given in ( 20). ( 20 'He eats more meat than I.' (Austin 1978: 294) We take this to be a subsequent development in the distribution of marla as a comparative morpheme (vis-à-vis its intensifier use and its usage in comparing gradable predicates), as well as generating a need to appeal to a domain of degrees in order to properly model its semantic contribution (that is the DSP is "switched on", see Hohaus 2018 for a similar trajectory in Samoan).
That is, we model gradable predicates as functions from degrees to individuals (21a) 14 and we model marla-comparatives as directly comparing the degree to which the objects being compared realise a particular predicate; this is derived in (21b-e).
14 That is, we follow Cresswell's (1976) analysis of English comparative constructions.On this re-analysis, then, ( 18) is true iff those size-degrees realised by a are a proper superset of those realised by b: Crucially, the degreeless ( 19) and degreeful (21e) analyses for ( 18) are understood to be truth-conditionally equivalent.The semantics for marla can then be restated as (22) below:

Phasal polarity
A property of many dynamic, durative predicates is a direct relation between the temporal stage of a given eventuality and the degree to which it has been effected.For the predicate 'gather more eggs' in (23) for example, the gathering of more eggs entails a greater duration for the event.We formalise this property-conceptualised as a correspondence between degree (effected) and runtime-as (24) below.
( (24) A property of dynamic predicates: degree-time (dt) monotonicity A predicate P is dt-monotonic iff, for any two times in the runtime τ(e) of some eventuality P(e), max(λ We take sentences like the scopally ambiguous (25) to represent a plausible "bridging context" (in the sense of Eckardt 2006).Where wata marla is interpreted as a modifier of the subordinate clause, (25) permits of an additive/comparative reading, similar to those described in the previous section: namely that the speaker desires that there be no increase to the degree of eating/amount eaten.A dt-monotonic predicate, this implies that the speaker desires that there be no time later than reference time at which the eating obtains.
Conversely, if wata marla is interpreted as a modifier of the matrix attitude predicate-as in the logical representation in (25b)-a temporal reading is more plausible.That is, the speaker asserts there is no time subsequent to the reference time at which the predicate ('I want to eat') holds.
We suggest, then, that predicates which exhibit dt-monotonicity provide a possible context for the reanalysis of marla in its comparative function to an aspectual operator.A lexical entry is given as ( 26).
Given a reference time t and predicate P, the times at which P is instantiated are a proper superset of instantiation times that are prior to reference time.
In ( 27), we derive truth conditions for the example sentence in (12) above, given this lexical entry for the phasal-marla.

Polarity sensitivity and "pragmatic pressures"
The lexical entry in (26)-marla asserts that the instantiation time of P is a superinterval of the intersection of its instantation time prior to t-implies that the P is not a subinterval of (∞,t]; i.e. it is not restricted to the past of t).This can be rephrased equivalently-as in (28b)-as imposing a requirement that the latest point of P's instantiation time is at or after t.
The negation of marla P, then, imposes a converse requirement: namely that P be instantiated prior to reference time (equivalently, that the latest time at which P is instantiated precedes t r ).
The core meaning contribution of aspectual adverbs, as described in §1, is the encoding of information about shifts in "phasal polarity" relative to a reference time.Figure 3 shows that, given its compatibility with inceptive, prospective and continuitive configurations, the lexical entry that we have proposed for marla is aspectually underinformative in positive polar environments.
As shown in figure 4 on the other hand, under negation, marla appears to effect a stronger requirement, requiring the endpoint of its prejacent's instantiation time to be located (at or) prior to reference time.Figures 4(a-b) both capture temporal configurations that involve switching from a prior positive state for P to a subsequent negative one (at or before t r ).
Conversely, the schema in 4(c)-where P is instantiated at the empty intervalis also predicted to vacuously verify (wata) marla's truth conditions: ∅ ⊆ [∞,t r ).We take this configuration, then, to be pragmatically blocked.This can be understood as arising due an economy constraint (e.g.Horn's (1984) formulation of the "R-principle": say no more than you must) -in these cases, the contribution of wata marla would be equivalent to that of wata 'NEG' simpliciter.We take this blocking effect to be conventionalised as a presupposition that P is (non-trivially) instantiated; this is represented in (29).
According to (29a), (wata) marla (P)(t) presupposes that P is nontrivially instantiated at some time prior to t.In effect, the "classical" semantics proposed by Horn (1970) are implied by these conditions, viz. a presupposition of anterior instantiation and an assertion that the prejacent (doesn't) hold at reference time.
In this section, we have seen how the availability of an 'intensifier' particle in composing implicit comparative constructions appears to have permitted for the reanalysis of marla as a comparative morpheme.We take its broad distribution (cooccurrence with a wide range of predicates) as evidence of this reanalysis and the availability of a degree semantics.In Diyari-as in an array of other languages ( §2)-comparative morphology appears to have been recruited to fulfil the function of a phasal adverb.We showed how ambiguity between an comparative/additive reading and an aspectual one (arising when modifying dt-monotonic predicates) furnished a possible bridging context from which a comparative morpheme can be associated with an aspectual reading.
Further, we showed that the presuppositionalisation of a felicity condition of marla-namely that the set of times (interval) at which the prejacent obtains is non-empty.In concert with the instantiation time being restricted to times anterior to reference time, the comparative semantics for wata marla, extended into the temporal domain, end up converging with the meaning contribution of phasal adverbs like anymore as proposed in, e.g., Horn 1970.Drawing on data from Diyari and comparative and typological evidence, we have advanced a hypothesis about a trajectory of meaning change and emergent polysemy for the Diyari lexical item marla.In the main part of this paper, we proposed a diachronic semantics for marla, seeking to understand (and semantically motivate) the colexification of its three apparent primary functions: as an intensifier, a comparative and a marker of cessative aspect (when occurring under negation).Three observations emerge from this analysis: i Comparative semantics are naturally extensible to the aspectual domain: a fact perhaps predicted by previous work which has treated phasal adverbs as scalar operators (e.g., Israel 2011: §6.4 cited above, see also Michaelis 1993).
Here, a standard comparative semantics-which involves relating entities relative to a scale-is extended to the temporal domain: relating propositions in terms of how late the state they describe obtains.
ii Related to this conception of phasal adverbs (where they are taken to encode scalar operators) is the prediction that they are prone to polarity sensitivity.For Israel (2011), polarity sensitivity is broadly understood as a lexically encoded feature (his Q-/I-values).
Here, we have suggested that the fact that an aspectual reading of marla is only available in negative polar contexts is a consequence of its emergence out of comparative morphology.Specifically, the "ex-comparative" semantics was shown to be compatible with numerous temporal configurations in positive polar contexts.As a consequence it fails to effectively lexicalise an aspectual operator except under negation, where it is only compatible with configurations where the endpoint of a temporal property precedes reference time-the defining property of cessative semantics.
This gives rise to the (strong) hypothesis formulated in (30): (30) comparative cessative hypothesis.Aspectual operators/phasal adverbs that arise from comparative morphology will (initially) be negative polarity items.
Languages where aspectual readings of an erstwhile comparative have been "liberated" from negative polar contexts (such that CONTINUITIVE, IAMATIVE or nowadays-type readings are available, see §2) are taken to be the result of subsequent semantic change.By hypothesis, this may engender functional pressure to recruit novel comparative morphology, instantiating a cycle.
iii Additionally, in (29), we make a related claim that an utterance of (wata) marla P presupposes that {t | P(t)} ̸ = ∅, a claim that amounts to existential quantification over D t (thence dovetailing with the phasal semantics of Horn 1970 a.o.).This strengthening can be understood as involving the conventionalisation of an Rimplicature (in the sense of Horn 1984).
Further, this observation-and those in (26)-can potentially be taken to be revelatory of the organisation of the temporal domain.That durative adverbs like anymore are compatible only with stative predicates (which we assume to refer to sets of times) is a likely prediction of the current proposal.
We leave it to further (and forthcoming) work to provide a more complete, integrated treatment of these observations.

Figure 4
Figure4Three temporal configurations predicted to be compatible with wata marla Pi.e. those where the latest time that P is instantiated is located in the past relative to a reference time t r .
Figure3Three temporal configurations predicted to be compatible with marla P i.e. those where the latest time that P is instantiated is non-past relative to a reference time t r .Red lines represent the instantiation time