Additive particles with a built-in Gricean pragmatics : The semantics of German noch , Chinese hái and Hungarian még

NOCH-type additive particles (e.g., German noch, Chinese hái, Hungarian még) have a widespread distribution that roughly covers the uses of English still, also, and even. We propose that with a built-in Gricean Maxim of Quantity Be Informative in its lexical semantics, a NOCH-type particle explicitly requires that the discourse be incremental, and the NOCH-marked sentence add new information and further narrow down the context set, making the whole discourse even more informative. We also show that the cross-linguistic widespread distribution of NOCH-type particles is not arbitrary: there are three ways to build an incremental discourse structure, and these three implementations give rise to the three major uses of NOCH-type particles.

Our goal is threefold.First, we show that these NOCH-type particles form a cross-linguistic natural class that is distinct from the group of AUCH-type particles.Second, since it is highly improbable that the widespread, yet similar, distribution of NOCH-type particles in different languages is due to some coincidental polysemy, we propose that there is a fundamental semantic contribution underlying their various uses.Third, we argue that their widespread distribution is not arbitrary, and provide a principled account for this distribution.
We start in Section 2 with a presentation of three major uses and an extended interpretation shared by NOCH-type particles cross-linguistically. Then we show in Section 3 the essential semantic contribution of NOCH-and AUCH-type particles respectively (see the summary in (2)).
(2) a. NOCH-type particles: they require a discourse be incremental.b.AUCH-type particles: they indicate parallelism in a discourse.
As shown in (2), in a nutshell, the use of NOCH-type particles explicitly requires that a discourse be incremental, i.e., become more and more informative from one (potentially silent) proposition to the next, while the use of AUCH-type particles indicates that there is some kind of similarity (i.e., parallelism) among distinct events in a discourse.Given that NOCH brings the incremental discourse requirement, in Section 4, we propose a principled account for the generation of the three major uses of NOCH-type particles introduced in Sections 2.1-2.3.We argue that there are two parameters modulating discourse structure: (i) entailment relation among propositions, and (ii) order among propositions.When working together, these two parameters give rise to three distinct types of incremental discourses.
In Section 5, we further discuss the extended interpretation introduced in Section 2.4: sometimes, NOCH suggests interlocutors' expectation.We show how a mechanism similar to scalar implicature computation gives rise to expectation-related readings of NOCH-marked sentences.
We briefly discuss two other approaches to the semantics of NOCH-type particles in Section 6. Section 7 concludes the whole paper and suggests avenues for future research.
Here we merge the comparative use and the marginality use, and present data showing three major uses of German noch, Chinese hái, and Hungarian még: the temporal use, the additive use, and the scalar use.In addition, we discuss an extended interpretation of temporal or scalar uses, and show how these uses of NOCH-type particles can reflect the expectation of interlocutors.With the temporal use of these NOCH-type particles, (3) -( 5) not only assert that it is raining at the moment that serves as the reference time (say t 0 ), but also convey the meaning that it has been raining for a while, i.e., raining, a stative event, began at a certain (contextually relevant) moment previous to t 0 (for example, t such that t is earlier than t 0 , or t ≺ t 0 ), and this raining state has been constant from the moment t to the reference time t 0 (see (6)).
( The temporal use of NOCH-type particles in NOCH q (at t 0 ) : Assertion: q is true at t 0 .
Inferred meaning: ∀t [t t ≺ t 0 → q is true at t ].

ADDITIVE USE.
The examples shown in ( 7) -( 9) illustrate the additive use of NOCH-type particles.As shown in (10), with the additive use of NOCH-type particles, the latter sentence in ( 7) -( 9), i.e., 'NOCH q', asserts that q is true while presupposing some contextually relevant proposition p is also true.p can be uttered prior to the utterance of 'NOCH q', but it can also be silently accommodated when the content of p is evident in a context.The additive use of German noch, Chinese hái and Hungarian még is very similar to the use of AUCH-type particles, and we will compare and contrast NOCH-and AUCH-type particles in greater detail in Section 3.
( The additive use of NOCH-type particles in (p) NOCH q : Assertion: q is true.Presupposition: p is true.(p can be either (i) uttered prior to q or (ii) accommodated.)2.3.SCALAR USE.1 Both the marginality use and the so-called comparative use of German noch, as discussed in Umbach (2009aUmbach ( ,b, 2012)), involve a set of alternatives that form a scale.Therefore, here we merge these two uses and present the third major use of NOCH-type particles: the scalar use.To a certain extent, this use is reminiscent of the semantics of English even.Sentences ( 11) -( 13) convey this idea: in the geographic configuration under discussion, Osnabrück is inside Lower Saxony area -this is the assertion part, not to mention those other cities in the contextually relevant set of alternatives (i.e., Alt(Osnabrück)) -this is the inferred part.
Our intuition is that, when compared with Osnabrück, it is just too evidently true that those other cities are inside Lower Saxony area, and claims that are too evidently true seem to have little worth of mention: we feel that they are already entailed by the asserted part.
Thus, we can consider that items in Alt(Osnabrück) form a scale of informativeness in which Osnabrück (the focused part) is ranked at such a position that the asserted proposition 'Osnabrück is inside Lower Saxony area' is more informative than (i.e., entails) alternative propositions '[λ x.x  Similarly, in ( 14) -( 16), the scalar use of NOCH suggests that the asserted part 'Berta is taller than Adam' is more worthy of mention than 'Berta is taller than X (X ∈ Alt(Adam) ∧ X = Adam)'.Or we can consider that items in Alt(Adam) form a scale such that the property 'λ x.height(x) > height(Adam)' entails alternative properties '[λ y.λ x.height(x) > height(y)](y) (y ∈ Alt(Adam) ∧ y = Adam)'.Thus ( 14 19), when Berta, instead of Adam, is used to construct the alternative set -Alt(Berta), these sentences suggest that the asserted part 'Berta is taller than Adam' is more worthy of mention than 'X is taller than Adam (X ∈ Alt(Berta) ∧ X = Berta)'.Or in other words, items in Alt(Berta) form a scale such that the property 'λ x.height(Berta) > height(x)' entails alternative properties '[λ y.λ x.height(y) > height(x)](y) (y ∈ Alt(Berta) ∧ y = Berta)'.Thus ( 17 In sum, (20) characterizes the interpretation of the scalar use: here x ≺ Q x means that x ranks lower than x in making the proposition Q(x) (x ∈ Alt(x)) informative or worthy of mention. (20) The scalar use of NOCH-type particles in NOCH Q(x) :

EXTENSION: THE EXPECTATION OF INTERLOCUTORS.
Temporal or scalar uses of NOCHtype particles often reflect the expectation of interlocutors.For example, ( 21) -( 23) assert that he hasn't come.However, the temporal use of NOCH-type particles here cannot be felicitous unless interlocutors have the expectation for his coming: they either expect for him to come at a later time, or just suggest that it is not the case that his coming is totally out of consideration.24) -( 26), the inferred meaning brought by the temporal use of NOCH-type particles can be totally trivial: if he is young at the reference time, how can he not be young before the reference time?Thus the point of uttering this kind of NOCH-marked sentences is almost entirely about expressing the expectation of interlocutors: they either expect for him to grow up, or express a kind of wish 'How I wish he can be older!But after all, he is just too young'.( 24 (27) The expectation brought by the use of NOCH-type particles: a. Expectation in the temporal use NOCH q (at t 0 ) : In the scalar-flavored use NOCH q : ¬q is not totally out of consideration.
3. Auch-vs.noch-type particles.In Section 2.2, we have mentioned that the additive use of NOCH-type particles is very similar to the use of AUCH-type particles.Actually, if the NOCH-type particles used in examples ( 7) -( 9) are replaced by AUCH-type particles, both the assertion and the presupposition of the sentences still remain untouched, as shown in ( 28) -( 30).( 28 However, beyond these cases, AUCH-type particles and other uses of NOCH-type particles have their own particularities.Section 3.1 shows that the scalar use of NOCH is sensitive to the order among sentences in a discourse, while AUCH-type particles (and the additive use of NOCHtype particles) are not.Section 3.2 shows that the use of AUCH-type particles requires the existence of distinct events, which is not always required by NOCH.

ORDER-SENSITIVITY IN THE SCALAR USE OF NOCH-TYPE PARTICLES.
We focus on Chinese data to demonstrate the order-sensitivity in the scalar use of NOCH-type particles.In Chinese comparative sentences, the comparative standard has to be stressed and focused when it precedes hái (see ( 32)).Thus only the scalar reading of hái is available here, and the comparative standard is used in building an alternative set for interpreting the non-asserted meaning brought by hái scalar . (31) Context for (32) -( 33): the height of Adam < the height of Berta.
(32) Mandarin Chinese: scalar use of q hái additive /yě p Given the context (31), the property of being taller than Berta asymmetrically entails the property of being taller than Adam.Therefore, 'Edda's being taller than Berta' (shorthanded as q) entails (or is a stronger claim than) 'Edda's being taller than Adam' (shorthanded as p).
(33) shows that both 'p, hái additive /yě q' and 'q, hái additive /yě p' are acceptable under the context (31), indicating that with the use of hái additive or yě, the order between p and q does not make a difference.In contrast, (32) shows that 'p, hái scalar q' is acceptable, but 'q, hái scalar p' is not, indicating that with the use of hái scalar , the order between p and q matters: crucially, the latter utterance in a discourse, i.e., the NOCH-marked one, needs to be the semantically stronger one.
3.2.IDENTICAL EVENT SCENARIO. 4Under the context (34), 'John ate apples' and 'John ate two apples' describe the same event, but 'John ate two apples' is more informative and more worthy of mention.5 ( 35) and (36) show that German noch and Chinese hái can be felicitously used to connect these two propositions that describe the same event (as far as the weaker claim 'John ate apples' precedes the stronger claim 'John ate two apples'), but AUCH-type particles are infelicitous here.Thus, the upshot is that the use of AUCH-type particles requires the existence of distinct events. (34) Context for ( 35) and ( 36): John was forbidden to eat anything sweet, apples surely included, but he violated the ban by eating two apples.
( As shown in (37), NOCH requires that a discourse be incremental: as the discourse progresses, each sentence has to guarantee the increase of information and the decrease of the context set (i.e., the set of possible worlds that make true each relevant proposition in a discourse).In contrast, as shown in (38), AUCH requires the existence of distinct (but somewhat similar) events.6 (37) p, NOCH q (i) asserts p ∧ q, and (ii) requires that p ∧ q asymmetrically entail p (i.e., q is required to add new information).
p, NOCH q def = p ∧ q (p∧q)⊂p being incremental from p to p ∧ q (38) p, AUCH q (i) asserts p ∧ q, and (ii) indicates that p and q describe distinct events e p and e q (that share some kind of similarity).
p, AUCH q def = p ∧ q e p =e q ∧e p is not part of e q ∧e q is not part of e p parallelism between p and q 4. Two parameters modulating discourse structure and three types of incremental discourses.Now we aim to answer this question: what is the relation between the incremental discourse requirement of NOCH-type particles and the three major uses of NOCH?We propose that there are two relevant parameters that modulate discourse structure here, and when working together, they generate three distinct types of incremental discourse structures.
Our proposal is influenced by Schlenker (2008Schlenker ( , 2009Schlenker ( , 2010))'s pragmatic view of presupposition phenomena.According to Schlenker's work, presupposition projection can be explained by the interaction between two pragmatic principles of manner: (i) Be Articulate, and (ii) Be Brief.Essentially, we should express a meaning complex with a series of conjunctions (Be Articulate), and presupposition arises when some conjuncts go silent (Be Brief!) with no meaning loss -it is the presupposition triggers that save meaning loss.Based on their specific lexical semantics, presupposition triggers supply or provide clues to the meaning of those silent conjuncts.
(39) -( 41) illustrate the pattern in interpreting NOCH.The interpretation of each NOCHmarked sentence can be considered as a series of conjunctions: the NOCH-marked conjunct is explicitly asserted (and bolded here), while other conjuncts can be explicit (e.g., in additive uses) or silent (e.g., accommodated in additive uses, or inferred in temporal or scalar uses). (39) The temporal use of The use of too conveys (probably with a coercion) the meaning that Sue's being abroad is a waste of time.
Cross-linguistically, some AUCH-type particles have both (i) a single use (e.g., 'p, AUCH q') and (ii) a double use (e.g., 'AUCH p, AUCH q'), and these two uses have the same semantics: they assert 'p ∧ q', and, in addition, convey the idea that there is some similarity between the events described by p and q (see Brasoveanu & Szabolcsi 2013 for a discussion on this double use of AUCH).Here is a Sherpa example for the double use of AUCH: (ii) nam sky

Numbu blue
NaN also nok.

SENTENCE-FINAL-PARTICLE tsa grass dZungiu green
NaN also nok.

SENTENCE-FINAL-PARTICLE
'The sky is blue and the grass is green.'Similarity: the environment is good.
Therefore, we actually need to explain how NOCH recruits the meaning of (potentially silent) non-NOCH-marked conjuncts by providing the information that the discourse is incremental.
In the following, Section 4.1 discusses the parameter of entailment relation among conjuncts, which determines how to make a discourse incremental; Section 4.2 discusses the parameter of order among conjuncts, which determines whether the meaning of some conjuncts of a discourse can be inferred so that these conjuncts can go silent.Finally, Section 4.3 shows that these two parameters generate three types of incremental discourse structures.
4.1.PARAMETER 1: ENTAILMENT RELATION AMONG CONJUNCTS.Suppose in a discourse composed of p and q, p precedes q (actually p can be considered as the conjunction of all previous conjuncts).As shown in ( 43), among all the possible entailment relations between p and q, there are only two ways for the latter conjunct q to add new information to the previous discourse p and narrow down the context set: (i) p and q do not entail each other (see (43b)), or (ii) q asymmetrically entails p (see (43c)).( 43) The possible entailment relations between two propositions p and q: 2. PARAMETER 2: ORDER AMONG CONJUNCTS.Whether there exists a contextually salient order (which should be, of course, independent of the order of utterance) among the conjuncts in a discourse can determine whether it is practically necessary to spell out (i.e., utter) every conjunct.
For a discourse D, if there does exist a contextually salient order among conjuncts, then based on (i) the information of this order and (ii) the meaning of some conjuncts, a pattern can be inferred, and the meaning of other relevant conjuncts can be inferred.As a consequence, these conjuncts don't need to be uttered and can be silent.
As shown in (44), this parameter can have two possible values: for a certain discourse, a contextually salient order among the conjuncts of the discourse either exists or does not exist. (44) For a discourse D composed of p 1 , p 2 , ..., p n , ..., a.There exists a contextually salient scale K independent of the order of utterance such that ∀p i , No such a scale K exists for the discourse D.
(45) illustrates how the existence of a contextually salient order saves the effort of uttering each conjunct.The interpretation of faster in (45) makes use of the existence of a temporal order among years, and the relevant conjuncts here need to be arranged in the temporal order of years.The temporal use and the additive use of NOCH-type particles are similar in that there is no entailment relation among conjuncts.For example, in the additive use of NOCH shown in (40), John's drinking beer and John's drinking wine do not entail each other.Similarly, in the temporal use shown in (39), raining at t i and raining at t j (i = j) do not entail each other.
On the other hand, the temporal use and the scalar use of NOCH-type particles are similar in that there is a contextually salient order among conjuncts.For example, in the temporal use, it is the temporal order among events.In the scalar use, based on and due to the entailment relation among conjuncts, it is the informativeness order among conjuncts.As a consequence, given the information of order and the meaning of the NOCH-marked conjunct, the meaning of previous conjuncts in the discourse can be inferred.Therefore, those conjuncts can go silent, and the NOCHmarked conjunct can usually be uttered out of blue.In contrast, since the additive use usually does not involve a contextually salient order among conjuncts, non-NOCH-marked conjuncts in the discourse need to be either uttered or accommodated.
5. The rise of expectation.As we have shown in Section 2.4, temporal or scalar uses of NOCH often suggest the expectation of interlocutors.Here we argue that expectation-related readings of these uses can be accounted for with a mechanism similar to scalar implicature computation.
As shown in (47), uttering the sentence (47a) in most cases communicates the assumption in (47b).According to Gricean pragmatic principles, speakers should try to be as informative as possible, so that if they were in a position to make a stronger statement, they would have; then since the speaker did not, s/he must believe that the stronger statement is not true.In the case of (47), since some and all form a scale, and 'Bill has got all of Chomsky's papers' is stronger than (47a), the fact that this stronger statement is not uttered suggests the speaker's belief of (47b). (47) Example of scalar implicature: a. Bill has got some of Chomsky's papers.b. Bill has not got all of Chomsky's papers.
We propose that a similar mechanism works in interpreting temporal or scalar uses of NOCH and gives rise to expectation-readings. Notice that the hallmark of temporal or scalar uses is the existence of an order among conjuncts, a necessary ingredient in scalar implicature computation.or knowledge.In other words, due to the use of NOCH that invokes this scale of knowledge in interpreting the utterance 'NOCH q', '¬q' is certainly within consideration, but beyond the limit of the things believed by or known to interlocutors.
Given the discussion in Section 4 and in this section, it is obvious that when uttered out of blue, a NOCH-marked sentence might be ambiguous among several readings, and the interpretation might involve several layers of meaning.However, in the real life, prosody and contextual information help to disambiguate and facilitate the multi-dimensional interpretation.Specific issues on the processing of NOCH-marked sentences are left for future work.
6. Comparison to related work.In the following, we briefly discuss two other approaches to the meaning of NOCH-type particles in the formal semantics literature: (i) the speech-act-based approach (e.g., Umbach 2009a,b, 2012, Beck 2016), and (ii) the focus-based approach (e.g., Liu 2000).Of course, NOCH-type particles have been a hot topic for decades, so a more comprehensive comparison of theories is beyond what we can do here.
6.1.SPEECH-ACT-BASED ANALYSES.Previous work on again (Klein 2001, Sauerland & Yatsushiro 2015) has analyzed again as a speech-act-based particle, as illustrated in ( 51) and ( 52 Following this line, Umbach (2009aUmbach ( ,b, 2012) ) and Beck (2016) propose that German noch is a speech act operator and accounts for the use of German noch in (53) with a speech-act-based proposal: the use of noch reflects the order of mention.
( Our proposed theory is similar to Umbach (2009aUmbach ( ,b, 2012) ) and Beck (2016)'s theory in that in both theories, NOCH is analyzed as a discourse-level operator.However, in Beck (2016)'s theory, at least in some uses, NOCH operates on the act of speech utterance, while in our current theory, the use of NOCH always operates on the information content of speech utterance.
Anna Szabolcsi (p.c.) points out that these two kinds of accounts make different predictions for accommodation.
In information-content-based accounts, operators work as normal presupposition triggers, and accommodation of silent content is not only possible, but independent of any acts.For example, when a kid asks for a doll and says 'I also want to have a doll', she does not need to make any additional speech acts or use any silent acts to point out that other kids have their dolls.
Thus, the use of also is purely about information itself, and independent of any acts.In terms of accommodation, what needs to be accommodated is just information, and certainly not acts.
However, in speech-act-based accounts, since a speech-act-based operator needs to operate on speech acts themselves, when there is silence (i.e., absence of speech acts), accommodation of speech acts is simply impossible.Even if we consider acts in a broader sense, when there is silence and accommodation is needed, what needs to be accommodated is acts.
This prediction is borne out in Klein (2001) and Sauerland & Yatsushiro (2015)'s analysis of again: in both ( 51) and ( 52), to use again felicitously in these cases, some previous speech acts or silent pointing acts are necessary.
However, in the use of Thus, it seems that after all, NOCH-type discourse particles only operate on information content in a discourse, but not on speech acts.Fillmore et al. (1988) and Kay (1990)'s work on the semantics of even, Liu (2000) claims that Chinese hái indicates discourse persistence and evokes a relation between the text proposition (TP, i.e., the conjunction of all sentences in a discourse) and the context proposition (CP, i.e., the conjunction of non-hái-marked sentences): hái is analyzed as a focus particle associated with the TP, which should be stronger than the CP.The spirit of Liu (2000)'s and our analyses is the same, but in our account, NOCH is not associated with the whole TP, but the difference between the TP and the CP, i.e., the part that makes the discourse stronger.

FOCUS-BASED ANALYSES. Based on
Our account has three advantages.First, there is no need for us to explain the source of focus in temporal or additive uses of NOCH (because there is no focus), but for Liu (2000), some ad hoc tweaks are needed in these cases.Second, our account can relate the distribution of NOCH with its fundamental meaning.Third, in our account, since NOCH is associated with the difference between the CP and the TP, the use of NOCH has to presuppose the existence of CP; while in Liu (2000)'s account, it remains unclear why, for example in the German example (55), NOCH can only be used in the second conjunct of the discourse, but not in the first conjunct or in both conjuncts.In fact, the use of NOCH in ( 55) is reminiscent of the use of another and moreover in (56).Thus, it seems that in natural language, there exists a group of morphemes that express the semantics of an increment by marking the difference / differential part (see also Zhang & Ling 2015 for an analysis of English comparative morphemes, i.e., more / -er, in this line of thought).A: Two parameters determine respectively (i) how to make a discourse incremental and (ii) whether some parts of a discourse can go silent.Together, they generate three ways of building incremental discourses, giving rise to the three uses of NOCH.
We have only discussed the triggering problem of NOCH.How is NOCH interpreted when scoping under various kinds of operators?What is the interplay between NOCH and other discourse particles or presupposition triggers?These projection-related issues are left for future research.
More particularly, as pointed out in Umbach (2012), AUCH-and NOCH-type particles seem to have complementary distribution when used in questions, as generalized in ( 58): (58) The distribution of AUCH-and NOCH-type particles in questions: wh-questions yes/no-questions AUCH-type particles incompatible compatible NOCH-type particles compatible incompatible We hope that our current pragmatics-based proposal can be extended to not only account for this pattern, but further shed light on the pragmatics of questions as well as the relation among sentences with different illocutionary force in a discourse.Finally, we would like to point out that the Gricean Maxim of Quantity Be Informative, as used in the current paper, is defined on the base of informativeness, or logical entailment, and throughout our discussion, we assume that worth of mention depends on informativeness and we use these two terms interchangeably.However, as already suggested in Footnote 5, there seems to be a difference between informativeness and worth of mention.Informativeness certainly contributes to worth of mention, but worth of mention might include something beyond.Eventually, we need to rethink what worth of mention is and perhaps recast our current proposal in terms of worth of mention.We also leave this issue for future research.
2.1.TEMPORAL USE.The examples shown in (3) -(5) illustrate the temporal use of NOCH-type particles.Here the semantic contribution of German noch, Chinese hái and Hungarian még is similar to that of English still.

7.
Concluding remarks.In this paper, we focus on cross-linguistic NOCH-type particles, and analyze them as discourse-level pragmatics-based presupposition triggers.More specifically, we provide an answer to the following three questions: (57) Three questions on NOCH-type particles: a. Q: What do NOCH-type particles do?A: They have three uses: the temporal use, the additive use, and the scalar use.b.Q: Why do they do what they do?A: With a built-in Gricean principle Be Informative in their lexical semantics, NOCHtype particles bring the incremental discourse requirement.c.Q: How do they do what they do?

) -(19) suggest that Berta is probably not very tall, perhaps just taller than Adam.
Osnabr ück is in Lower Saxony (Here A ≺ in LS B ≺ in LS ... ≺ in LS Osnabrück: this is the order of informativeness (or worth of mention) on the issue of their being inside Lower Saxony.) NOCH: NOCH raining at t 0 = raining at t 1 ∧ raining at t 2 ∧ raining at t 3 ∧ ... ∧ raining at t 0 (Here t 1 ≺ t 2 ≺ t 3 ≺ ... ≺ t 0 : this is the temporal order.)(40)Theadditiveuse of NOCH:(John drank beer,) NOCH John drank wine = John drank beer ∧ John drank wine(41)The scalar use of NOCH: NOCH Osnabr ück is in Lower Saxony = A is in Lower Saxony∧ B is in Lower Saxony∧...∧ Klein (2001)'s analysis: the use of again is justified not by a sequence of eventualities (i.e., n was a prime number at an earlier time), but by what has been said before.Interpretation: you must make it once more known what your name is.
NOCH, previous speech acts or silent pointing acts are not necessary.As shown in (54) (to facilitate information accommodation, here the context is slightly different from the context shown in (53)), the interpretation of the additive use of German NOCH is totally independent of any speech acts or silent pointing acts.
John is counting how many beers Mary has had today.a.Like everyone else, she had a beer during dinner.Oh, she had another beer before.b.Like everyone else, she is now having a beer.Moreover, she had a beer during lunch.