Grammaticalized number , implicated presuppositions , and the plural

Plural morphology exhibits differing interpretations across languages. For example, in downward entailing contexts in English, the plural receives a one or more (or inclusive) interpretation, whereas in Korean-like languages the plural always receives a more than one (or exclusive) interpretation, regardless of context. Previous experimental work using an artificial language suggests that such differences may follow from structural properties of these languages (Liter, Heffner & Schmitt 2017), namely lack of grammaticalization of the plural/singular distinction. In this paper we adopt Sauerland, Anderssen & Yatsushiro’s (2005) implicated presupposition analysis of the plural (the English plural is semantically unmarked, whereas the Korean plural is semantically marked, carrying a presupposition that the cardinality of its referent is greater than one) in order to test two hypotheses about the interpretation of the plural. Using an artificial language learning paradigm identical to that in Liter, Heffner & Schmitt (2017) with non-grammaticalized number but with a much greater frequency of singular/plural NPs in the input, we test (i) whether semantic markedness of the plural should be linked to the non-grammaticalization of the number paradigm; or (ii) whether semantic markedness follows from insufficient statistical evidence for simplifying the lexical entry for the plural. Our results show that participants continue to assign an exclusive interpretation to plural morphology under the scope of negation, which is compatible with the hypothesis that non-grammaticalized number entails semantic markedness.


Introduction
If we were to ask a speaker of English what the plural means, we would presumably hear that the plural means more than one.This intuition is perhaps correct at a surface level of description, but the plural morpheme in English does not always receive such an interpretation.The interpretation actually depends on the environment.For example, in downward entailing contexts such as under the scope of negation, the plural actually receives an interpretation of one or more (henceforth inclusive interpretation) and not the intuitive more than one interpretation (henceforth exclusive interpretation) that most speakers might attribute to the plural (see, e.g., Sauerland, Anderssen & Yatsushiro 2005). 1 On the other hand, the pluralizer morpheme in a language like Korean always receives an exclusive interpretation, regardless of context (see, e.g., Kang 1994;Kwon & Zribi-Hertz 2004;Nomoto 2013).2This is illustrated in (1).
(1) a. John didn't see friends last night.
b. Con-un eceyspam chinkwu-tul-ul manna-ci anha-ss-ta.John-top last.nightfriend-pl-acc meet-nmlz neg-pst-decl 'John didn't see friends last night.'(1a) cannot truthfully be used to describe a scenario in which John saw one friend last night, whereas (1b) can truthfully describe such a scenario.This shows that, under the scope of negation, the plural morpheme in English can receive an inclusive interpretation.This contrasts with the interpretation that is assigned to the plural morphology in Korean under the scope of negation, since it can truly describe a scenario in which John saw one friend last night.That is, even in the scope of negation, the Korean plural receives an exclusive interpretation.An interesting question is whether the inclusive/exclusive interpretation of plural morphologyindifferentlanguagescanbeinferredfromparticularpropertiesofthedifferentlanguages.BecauseKoreanandEnglishhavemanydifferentproperties,tryingto answer this question by inspecting the natural languages themselves is quite complicated, astherearemanyconfoundingfactorssuchastheexistenceofclassifiers,case,lackof definiteandindefinitedeterminers,andsoon,whichmakethecomparisonmoredifficult.
If we concentrate our attention on how Korean differs from English with respect to number, we find two important differences.First, Korean is a language without grammaticalized number; that is to say, number morphology is not obligatorily expressed on most noun phrases, and noun phrases do not trigger obligatory verbal agreement.English, on the other hand, has grammaticalized number; number morphology is necessarily expressed on the count nominals and triggers verbal agreement.
TheseconddifferenceisthatKoreannounphrasesarenumber-neutralbydefaultand can refer to either a singleton or a plurality.Singular and plural morphemes can be added to disambiguate whether the referent is to be interpreted as a singleton or a plurality (Kang 1994;Kwon & Zribi-Hertz 2004), whereas, in English, bare count nominals with number-neutral interpretations are generally disallowed.Excluding mass nouns, all English nominals appear with number morphology, and number morphology is not linked toadefiniteorindefiniteinterpretation. 3 Given that there is no numberless alternative, number morphology is obviously much more frequent in English than in Korean, where the bare nominal is quite free and takes on a multiplicity of interpretations. 4hesebasicfactsbecomesomewhatconfoundedwhenweconsiderissuesof(in)defi-nitenessinKorean:first,becausethelanguagedoesnothaveovertdefiniteandindefinite determiners, bare noun phrases without any number information can be interpreted not onlyassingularorpluralbutalsoasdefiniteorindefinite,dependingonthecontext.The plural and singular morphemes, on the other hand, are quite restricted.The pluralizer seemstorequireD-linkedcontextsandthesingularizerisobligatorilyindefinite.These restrictions on overt singular and plural marking in Korean, together with the high use of the bare nominal, make number marking much less frequent than in English.
Because of these and other divergent properties, it is not easy to readily determine which of these properties might cause Korean speakers to always interpret the plural as exclusive, but English speakers to interpret the plural as inclusive in certain contexts.One waytotestwhichpropertiescontributetotherelevantinterpretationsistouseartificial languagelearningparadigms.Artificiallanguagelearningparadigmsallowforcomplete control of the properties of the input that learners are exposed to, in ways that are impossible in experiments using natural language acquisition settings.
In Liter, Heffner & Schmitt (2017), we used an artificial language learning experiment to examine to what extent the interpretation of a pluralizer morpheme could be inferred from properties of a linguistic system designed to mimic some properties of a Korean-like system.Despite being native speakers of English, a language where the plural receives an inclusive interpretation in certain environments, participants (without overt training) adopted an exclusive interpretation of plural morphology even under the scope of negation.We argued that our results suggested an entailment relation between having a Korean-like number system and having an exclusive interpretation of plural morphology in all contexts.Since this indeed seems to be the case cross-linguistically, as Mandarin and Japanese also only allow exclusive interpretations of their pluralizers, ourstudyaddedtotheartificiallanguagestudiesthatconvergeontypologicaltendencies and language universals.It was also rather striking that participants in our previous study did not transfer the interpretation of plural morphology from their native language tothe plural morphologyintheartificiallanguage,giventhattransfereffectsinsecond language learning are quite prevalent (see, e.g., Odlin 2003;Schwartz & Sprouse 1996;Jiang2004)andhavealsobeenclaimedtoaccountforsomeartificiallanguagelearning results (e.g., Goldberg 2013).
In our previous work, we sketched a rough account of the entailment relation between having a Korean-like number system and having an exclusive interpretation of plural morphology in all contexts on the basis of Sauerland, Anderssen & Yatsushiro's (2005) account of the plural (explained in more detail below, in §2.1).
In the present paper, we report a new study aimed at examining to what extent the exclusive interpretation of the plural is a natural consequence of the non-grammaticalization of number marking in a language or whether the exclusive interpretation results from the lower frequency distributions of plural and singular morphology in comparison to number-neutral bare nouns.In other words, we ask whether the architecture of the system (with bare nouns and optional plural and singular morphemes) is responsible for the exclusive interpretation independent of issues of frequency distributions, namely the overwhelminguseofbarenominalsintheartificiallanguage. 5hepaperproceedsasfollows.§2fleshesoutthetwoaccountsoftheproposed language universal in terms of semantic unmarkedness and implicated presuppositions.§3 presents thepresentexperimentincomparisontotheexperimentreportedinLiter,Heffner&Schmitt (2017)inordertodiscriminatebetweenthetwohypothesesfrom §2,and §4concludes.

The plural and implicated presuppositions
For concreteness we assume Sauerland, Anderssen & Yatsushiro's (2005) theory of the plural.Their theory relies on the notion of implicated presuppositions (see also Sauerland 2008).Implicatedpresuppositionsareanalogoustoscalarimplicatures(cf.Horn1972;1989) except that they are calculated in the domain of presupposition rather than in the domain of assertion; they are calculated in accordance with the pragmatic maxim, Maximize Presupposition, proposed by Heim (1991). (2) Maximize Presupposition Make your contribution presuppose as much as possible.
According to Sauerland, Anderssen & Yatsushiro, the English plural is semantically unmarked, and its usual meaning of more than one is derived via an implicated presupposition that is calculated against the singular, which presupposes that the cardinality of the referent is one (2005: 411-412).On the other hand, in contexts such as under the scope of negation, the implicated presupposition is not calculated because the environment is downward entailing andwouldthusactuallymaketheassertionweakerwereit calculated (2005:417-420).Asa consequence, the plural in English is interpreted inclusively under the scope of negation.
Although there is some controversy about what the exact triggers for inclusive and exclusive interpretations are and about what the correct formal analysis of these two interpretations is, it is worth noting that there is some experimental evidence which supports Sauerland, Anderssen & Yatsushiro's (2005) view of the plural.Pearson, Khan & Snedeker(2011)reportanexperimentwheretheyfindthatparticipantsacceptasingular referent for a plural noun phrase in a context which facilitates the cancellation of an implicaturesignificantlymorethantheyacceptitincontextsthatdofavorthecalculation of the implicature. 6Adjudicating between the many different analyses of the plural is, however, beyond the scope of this paper.Again, in this paper, we are assuming Sauerland, Anderssen & Yatsushiro's (2005) analysis.Now, while Sauerland, Anderssen & Yatsushiro do not explicitly address plural morphology in Korean, we can infer what their analysis of this pluralizer would probably be.Recall that (1b), repeated here as (3), can truthfully describe a situation in which John saw one friend last night; that is, the plural morphology in Korean receives an exclusive interpretation.Tobefair,thisstudyalsosupportstheanalysesofthepluraladvancedinSpector(2007)andZweig(2009), which,althoughimplementeddifferently,assumethattheexclusiveinterpretationofthepluralisderived by some inferencing process. (3) Con-un eceyspam chinkwu-tul-ul manna-ci anha-ss-ta.John-top last.nightfriend-pl-acc meet-nmlz neg-pst-decl 'John didn't see friends last night.'Since implicated presuppositions are not calculated in downward entailing environments, the more than one interpretation cannot be the output of an implicated presupposition.Therefore,therelevantdifferencebetweenthepluralinEnglishandthepluralinKorean must be that the English plural is semantically unmarked whereas in Korean it is not.In Korean, the plural is semantically marked, being associated to a cardinality greater than one; in other words, its meaning is not derived by calculating an implicated presupposition against the meaning of the singular, like in English.ThisisthecategoricaldifferencebetweenthesemanticsofEnglishpluralmorphology and the semantics of Korean-like plural morphology that we will assume going forward. 7heissueiswhetherthisdifferenceisanaturalconsequenceofthearchitectureofthe number system of Korean-like languages or whether this difference is to be linked to the frequency distribution of the various forms, which could lead learners to reinforce particular hypotheses.
In the next two subsections, we consider these two hypotheses about Korean-like number systemsthatwouldaccountforthedifferencesinthesemanticsoftheirpluralmorphology that we are assuming.In §2.1, we consider the hypothesis that non-grammaticalization of the number paradigm is the relevant factor.In other words, we ask whether exclusive interpretations are a natural consequence of the architecture of the system.In §2.2, we consider the hypothesis that the relative frequencies of the different types of noun phrases drives the learner to an exclusive interpretation of the plural, independently of the architecture of the system.Both of these hypotheses would account for the results reported in our previous study.In §3, we report a new experiment aimed at teasing apart these two hypotheses.

Non-grammaticalized number and semantic markedness
One possible explanation for why Korean-like languages have an exclusive interpretation of plural morphology in all contexts has to do with the non-grammaticalization of number.Kwon&Zribi-Hertz(2004:151-154)arguethatthemorphosyntacticdifference between the French/English plural and the Korean plural is that the former is realized asaninflectionalfunctionalhead(e.g.,NumP)withbothpositiveandnegativefeatural values (e.g., +PL and -PL),whereasthelatterisnottherealizationofaninflectionalhead but is instead a lexical plural marker with no corresponding negative value.We adopt this accountofthemorphosyntacticdifferencesbetweenthenumbermorphologyacrossthese languages, and we use the term grammaticalized to refer to languages like English where thenumbermorphologyistherealizationofaninflectionalheadinthesyntax.Korean, then, is a language where number is non-grammaticalized, as the number morphology is nottherealizationofaninflectionalheadintheextendedprojectionofthenounphrase.
Assumingthismorphosyntacticdifference,wehypothesizethatsemanticmarkednessof the plural is required outside of a grammaticalized paradigm.In other words, in virtue of being a lexical plural marker, not an obligatory head in the extended functional projection of the noun phrase, the Korean plural morphology cannot be semantically unmarked like the plural in English is.This would explain why Korean does not have the same interpretation of the plural under the scope of negation that English does.
Likewise, it would also explain why participants in our previous study adopted an exclusive interpretation of the plural under the scope of negation in contradistinction to their nativelanguage.IntheartificiallanguagethatwetaughtparticipantsinLiter,Heffner& Schmitt(2017),numbermarkingonthenominalswasliterallyoptional.Inthetraining input, participants heard nominals with singular or plural morphology 50% of the time, and the other 50% of the time there was no number morphology on the noun, for noun phrases in the same contexts.Moreover, there was no morphosyntactic number agreement on the verb.Both of these facts could be cues to the learner that the number morphology inthelanguagetheywerelearningisnottherealizationofaninflectionalhead,butrather an adjunct-like morpheme.Reaching this conclusion, the learner should hypothesize that the number morphemes in this language are independent lexical heads perhaps adjoined tothenounphrase,butcruciallynotdifferentvaluesofafunctionalheadandthusnot part of a morphological paradigm.
In sum, the hypothesis that non-grammaticalization of a number paradigm requires semantic marking of the number morphology would account for both the natural language facts of Korean (and other languages) as well as the results from our previous study.We next consider an alternative hypothesis that would also account for these facts.

Economy and semantic markedness
Another plausible hypothesis as to why participants in our study learned the plural as havinganexclusiveinterpretationcouldinsteadbeduetothewayfrequencyaffectshow participants learn the plural and singular morphemes.In a language like English, the singular and the plural are in complementary distribution, share the same semantic and syntactic space, and occur in pretty much every count noun phrase in an argument position.8Therefore, a learner might have good reason to treat them as in a binary opposition, which may then lead the learner to reduce the properties of one of the members of the opposition pair and infer its interpretation from the other member of the pair.Since the range of interpretations for the plural can be derived by positing that it is semantically unmarked and calculating an implicated presupposition against the singular, the learner does not store a meaning for the plural.In other words, if forms are frequent enough and belongtothesamesemanticspace(number),alearnermighttrytofindwaystominimize what they have to store in the lexicon for reasons of economy.Under this hypothesis, it is the sheer frequency of the singular and plural that creates the conditions for treating them as a pair.In other words, if a language does not frequently mark noun phrases as plural orsingular,thenthelearnermightnothavesufficientinformationtocompresswhatis stored in the lexicon.On the other hand, if the language marks noun phrases as plural or singular most of the time, then the existence of number-neutral bare nominals might not interfere with compressing the semantic information stored in the lexicon.
This hypothesis could possibly explain the Korean facts.As we have mentioned before, Koreanbarenominalscanbeinterpretedassingular,plural,definite,orindefinite,since there are no definite or indefinite determiners.Determinerless number-marked noun phrasesareeitherobligatorilyindefinite(singular)orobligatorilyD-linked(plural).Bare nominals therefore have a much wider range of uses and are used more frequently.Pluralmarked and singular-marked NPs, on the other hand, are rather infrequent in comparison.Given the infrequent use of number morphology in Korean, a learner might not have sufficientevidencefordecidingthatthemeaningofthepluralcanbeleftunderspecifiedand instead derived from the competition with the singular.As a result, the Korean learner stores the meanings of both the singular and plural morphemes independently.9 This hypothesis could also explain the results from our previous study where pluralmarked NPs and singular-marked NPs were rather infrequent and only constituted 25% of the training input each. 10Specifically,thelearnersofourartificiallanguagewouldnot havehadsufficientevidencetodeterminewhetherthemeaningofthepluralmorpheme can be derived by some means other than simply storing its meaning in the lexicon.

Teasing apart the hypotheses
Given that both the optionality and the lower frequency would explain the lack of inclusive readings for the plural morphology in natural languages, as well as the results from the artificial language learning paradigm from our previous study, it would be nice if wecouldteasethesetwohypothesesapartbyfindinglanguagesthatwouldsupportone hypothesis or the other.Unfortunately, we are not aware of a natural language useful for distinguishing between these two hypotheses.In Korean, number is not grammaticalized, and it is also not frequent.So we cannot decide on the basis of Korean which of the two hypotheses best explains the data.
Brazilian Portuguese would seem to be a good testing case as it has grammaticalized number but also has bare count noun phrases.In other words, every noun phrase (except for bare singulars) is marked as singular or plural; there is subject-verb agreement, and adjectives agree with the noun phrases they modify.However, number-neutral bare nominals-which can be interpreted as singular or plural depending on the context, as illustrated in (4)-are much less frequent than singular-and plural-marked noun phrases (Schmitt & Galves 2014).In other words, grammaticalization correlates with frequency of plural/singular marking.
(4) O João não encontrou amigo ontem de noite.the John neg meet friend yesterday at night 'John didn't see friends last night.'Again for Brazilian Portuguese both hypotheses make the same prediction, namely that Brazilian Portuguese would have an inclusive interpretation of the plural morphology underthescopeofnegation,justlikeEnglish.Andthatisinfactwhatwefind:(5)isa false description of John having seen one friend last night.
(5) O João não encontrou amigos ontem de noite.the John neg meet friend.plyesterday at night 'John didn't see friends last night.'This shows that the plural in Brazilian Portuguese is semantically unmarked like in English.Because the use of plural-marked and singular-marked NPs is much more frequent in Brazilian Portuguese than in Korean (Schmitt & Galves 2014) and because Brazilian Portuguese has grammaticalized number, we cannot use Brazilian Portuguese to distinguish between the two hypotheses discussed above. 11should not be taken to mean that learning is primarily/exclusively frequency driven.It is uncontroversial that learners use statistical properties to test particular hypotheses, but they do so in a linguistically informedmanneranddonottracksuperfluouspatterns(e.g.,Yang2002). 10We are aware that 25% is large when we consider that the plural in English likely appears between 10% and 15% of the time in child-directed speech (we are not aware of a study that counts the token frequency of plural forms in child-directed speech for English, but see Ravid et al. 2008: 41, for frequency counts in otherGermaniclanguagesthatrangebetween10%and15%).However,thelearnersofthisartificiallanguage receive a very small amount of input overall when compared to what a child immersed in a linguistic community receives as they acquire an adult grammar.
11 Areadermayaskwhatisthedifferencebetween(4)and( 5).Wearguethatwhile(4)completelyexcludes any cardinality comparison and information about number, (5) includes a one or more than one interpretation.The interpretations overlap extensionally, but when a bare singular is used all reference is to the kind.
Because we are unaware of a natural language that would allow us to distinguish between these two hypotheses, we conducted a follow-up artificial language learning experiment, where we change the proportion of bare number-neutral noun phrases in relationtosingular-andplural-markednounphrases.Specifically,wesignificantlydecreased the frequency of number-neutral nominals and increased the frequency of singular-and plural-markedNPsinordertodeterminehowthisaffectsthelearningoutcomes.

The experiment
In order to determine whether frequency plays a part in the interpretation assigned to the plural,weconductedafollow-upstudytothestudyreportedinLiter,Heffner&Schmitt (2017).Withtheexceptionoftwodifferences,thestudieswerethesame,inordertomake the comparisons easier.The two differences are that, in the present study, we greatly increased the frequency of plural/singular-marked NPs (cf.§3.1.2),and we also introduced anewtest(cf.§3.1.3).Importantly,otherthanthedifferentrelative frequenciesofnoun types,allotheraspectsoftheartificiallanguagethatparticipantsweretaughtremained the same, including the non-grammaticalization of number.That is to say, there were no cuesintheinputlanguagethatnumbermorphologywastherealizationofaninflectional head.There was no agreement between the verb and nominals, and number marking was still optional, although bare nominals did occur much less frequently.Importantly, bare nominals occurred in exactly the same contexts as the singular-and plural-marked NPs, suggesting to the learner that number marking really is optional and not that there is a specialized meaning of the bare form.
Giventhesignificantlyincreasedfrequencyofnumber-markednominalsinthe present study, we can use this follow-up study to distinguish between the two hypotheses discussed abovein §2.Specifically,ifsemanticmarkednessisnecessitatedbynon-grammaticalization (cf.§2.1), then we expect participants in the present study to interpret the plural exclusively under the scope of negation, just like they did in our previous study.On the other hand, if semantic markedness of plural morphology in Korean-like languages is the result of insufficient evidence for compressing the lexicon by treating the singular and plural morphemes as a pair at some level (cf.§2.2), then, unlike in our previous study, we expect participants to interpret the plural inclusively under the scope of negation in the present study because number-marked NPs are much more frequent and so learners would have more evidence that would warrant compressing the lexicon.
Throughout this section, we present the results from our previous study alongside the results of the current study in order to facilitate comparison of the two studies.More detailed informationaboutthepreviousstudycanbefoundinLiter,Heffner&Schmitt(2017).

The language
We taught participants in the present study the same 23-word artificial language from our previous study.The language had 16 nouns, 2 transitive verbs, 2 intransitive verbs, 2 number morphemes (a singular and a plural), and 1 negation particle. 12The word order oftheartificiallanguagewas(neg)-VSO; that is, when negation occurred, it occurred presententially.Additionally, number morphology, when present, occurred postnominally.

Training
The experiment was administered using E-Prime 2.0 Professional Edition software (Psychology Software Tools, Inc., Sharpsburg, PA).Participants were trained on the language over the course of ten sessions with testing occurring throughout.All training was passive; there was no explicit instruction.Participants saw animated events on the screen that were paired with sentences and had to learn the meanings of all of the words in the sentence by making inferences based on the event that it described.

Basic training
In the training that occurred in sessions 1-6, participants were introduced to the basic vocabulary of the language, the grammar, and the number morphology.In each session, participants heard 128 sentences (half intransitive, half transitive) paired with an animated event on the computer screen and had to infer the meaning of the morphemes in the sentence that they heard.
In the sentences that a participant heard, nouns marked with the singular morpheme, paya, always corresponded to singleton referents, and nouns marked with the plural morpheme, koho, always corresponded to multiple-item referents with between two and four entities.A noun without number morphology was number-neutral and occurred with singleton referents half of the time and multiple-item referents half of the time.
The breakdown of the frequencies between the previous study and the present study is giveninTable1.Themaindifferenceinthetraininginputinthecurrentstudy compared to the previous study is that, out of the entire input, singular-and plural-marked NPs were much more frequent.Specifically, in the previous study, 25% of the NPs in the input consisted of paya-marked nominals paired with singleton referents, 25% consisted of koho-marked nominals paired with multiple-item referents, 25% consisted of bare nominals paired with singleton referents, and 25% consisted of bare nominals paired withmultiple-itemreferents.Inthepresentstudy,ontheotherhand,43.75%oftheNPs in the input consisted of paya-markednominalspairedwithsingletonreferents,43.75% consisted of koho-marked nominals paired with multiple-item referents, 6.25% consisted of bare nominals paired with singleton referents, and 6.25% consisted of bare nominals paired with multiple-item referents.
Moreover, everything was counterbalanced so that each noun occurred equally with all three types of number (paya, koho, and bare) in all three grammatical positions (intransitive subject, transitive subject, and transitive object).

Negation training
In both studies, it was not until sessions 8 and 9 that participants were introduced to the negative particle, again without explicit instruction.In order to facilitate the learning of negation, the 128 training sentences were grouped into blocks of 4 sentence-event pairings.For example, in order to train participants on negation involving a negated transitive verb,participantswouldfirsthear'asnakeiscoveringamouse'andwouldseeasnake covering a mouse.On the next slide, they would then hear 'a snake is circling a mouse', and they would see a snake circling a mouse.On the third slide, they would hear 'a snake is not covering a mouse', and they would see a snake circling a mouse again.Finally, on the fourth and last slide in the block, participants would hear 'a snake is circling a mouse' and see a snake circling a mouse (cf. Figure 1, row 2).Participants received evidence in their input that the negative particle could negate the verb of an intransitive sentence (Figure 1, row 1), the verb of a transitive sentence (Figure 1, row 2), and the head of the object nominal of transitive sentences (Figure 1, row 3).Crucially, however, participants never received any training trials where the thing being negated by the negative particle was the number marker on the object nominal.This way, there was nothing in the training input that would bias participants toward assigning a particular reading to plural morphology in a downward entailing environment (i.e., under the scope of negation).

Testing
Sessions 7 and 10 were exclusively testing sessions.In sessions 2-6, 8, and 9, testing occurred prior to training so that the testing was indicative of the participants' knowledge at the end of the previous session.When multiple tests occurred in the same session, the tests occurred in the order that they are discussed below.See Table 2 for a complete training and testing schedule.
We included a variety of tests in our previous study and in the present study in order to be able to ascertain whether participants learned the language that they were being taught.If participants, for example, did not learn the basic vocabulary or grammar of the language, we cannot meaningfully interpret their performance on the plural morphology under the scope of negation.Most importantly, through pilot testing, we learned that negationwasquitedifficulttoteachwithoutovertinstruction.Thus,itisveryimportant to include basic negation tasks to ensure that we only include participants who successfullylearnednegationinthefinalanalysis.Thequestionofinterestishowparticipants interpret the plural morpheme in a downward entailing environment.If participants did not learn negation, then the environment would not be downward entailing in the task of main interest, so it would not be possible to meaningfully interpret their answers with respect to our question of interest.
Having all of these different tasks therefore allows us to screen out participants who did not learn basic aspects of the language, which ensures that, when interpreting the results of interest, our interpretation meaningfully bears on the two hypotheses we are evaluatinginthispaper.Below,wedescribeallofthesedifferenttests.

Vocabulary and number morphology
In this task, participants heard a noun phrase that was either marked with paya (the singular morpheme), koho (the plural morpheme), or bare.On the screen, they saw a singleton referent and a multiple-item referent.They had to choose which referent the noun phrase they heard referred to, and there were also options for saying that the noun phrase could refer to both the singleton referent and the multiple-item referent or that it referred to neither.Insessions7and10,therewere64trialseach;inallothersessionsthatthistest occurred in, there were 32 trials each.

General grammar
The general grammar task tested participants' knowledge of the argument structure of theartificiallanguage.Ineachtrial,participantssawaneventonthescreenandheard two sentences.They had to choose the sentence that sounded most like a sentence in the language that they were learning and that described the event on the screen.The ungrammatical sentences were ungrammatical because they either (i) had one too many arguments, (ii) had one fewer argument than required, or (iii) were missing a verb.There were 22 trials in every session that this test occurred in.

Bare nouns in sentence verification
InadditiontomanipulatingthefrequenciesofthedifferentNPtypesintheinput,theadditionofthissentenceverificationtestistheonlyotherdifferencebetweenthedesignofthe previous study and the design of the present study.In the present study, we added this task onlyinthetestingsessions(7and10).Ineachsession,therewere32trials.Alltrialsconsisted of a bouncing event on the screen paired with a sentence that used the intransitive verb nugipi 'bounce' and a bare nominal as the subject.Participants had to say whether the sentence they heard described the event that they saw on the screen.16 of the trials involved a mismatch between the identity of the referent and the subject noun, 8 trials involved a match between the identity of the referent and the subject noun and the referent was a singleton referent, and the remaining 8 trials also involved a match between the identity of the referent and the subject noun but the referent was a multiple-item referent.

Number negation 
Free response  

Free response
Thistaskalsoonlyoccurredinsessions7and10;therewere32freeresponsetrialsin each session (half intransitive, half transitive).Participants saw an event play on the screenandweregiventhefirstwordinthesentencethatdescribedthatevent.Theyhad tothencompletethesentence.Recallthatthewordorderforthisartificiallanguagewas VSO,sothistaskparticularlytestedhowparticipantswouldproduceNPsintheartificial language.Participants were also instructed to use the non-word "X" in case they could not recall a particular lexical item (as was done in Hudson Kam & Newport 2005;2009).This allowed them to complete the sentence even if they did not happen to remember one of the particular words.

Verb and object negation
The verb and object negation tasks occurred in sessions 9 and 10.Participants were asked whether the sentence that they heard matched the event that they saw on the screen.There were 24 verb negation trials, and there were 24 object negation trials.Half of the trials were true, and half of them were false.
The verb negation trials involved the negative particle, te, negating the verb, and the object negation trials involved the negative particle negating the object.For example, a true verb negation trial would have involved a participant hearing the sentence te disi hatepi paya yipi koho 'negcover cow sg cat pl' and seeing an event where a cow was circling multiple cats.That is to say, this trial would have been true because the cow was circling (not covering) the cats.On the other hand, object negation trials manipulated the identity of the object.For example, if participants heard the same sentence in a true object negation trial, it would have been paired with an event of a cow covering ladybugs.That is to say, it would have been a true trial because the cow was covering ladybugs (not cats).This is summarized in Figure 2.

Number negation
The number negation task occurred only in session 10.In this task, participants were asked whether the sentence they heard matched the event that they saw on the screen.Recall that participants never received training sentences in their input where the negative particle negated the number morpheme on the object of a transitive verb.Because of this,thenumbernegationtaskconsistedoffourdifferenttrialtypes.Thecrucialtrialtype involved a plural-marked NP, but we also had three other trial types in order to establish whether participants would allow the negative particle to negate the number morpheme at all.If not, it's not clear that we can meaningfully interpret their results on the crucial trial type of interest.
The four different trial types involved all possible combinations of number-marked object NPs crossed with the (non-)plurality of the referent object.We refer to these trials with shorthands of the form '¬number-morpheme X plurality-of-referent'. '¬' is a reminder that the sentence is negated, the number morpheme indicates which number morpheme occurs on the object nominal, and sg and pl indicate the cardinality of the referent (either a singleton referent or a multiple-item referent, respectively).
The crucial trials were thus the ¬kohoXsg trials, which were trials where the object was marked with the plural morpheme, koho, and the corresponding referent in the event on the screen was a singleton referent.Recall that these sorts of trials are where languages likeEnglishandKoreandiffer.AnEnglishspeakerwouldsaythatthisisafalsedescription of the event on the screen whereas a Korean speaker would say that it is a true description of the event on the screen (cf.( 1)).
However, to reiterate, in order to meaningfully interpret the results from the ¬kohoXsg trials,wemustfirstestablishthatparticipantsdidinfactlearnthatthenegativeparticle can negate the number morpheme on the object of a transitive verb since this is something for which there was no evidence in their input.To this end, there were three other trial typeswherethejudgmentswerenotexpectedtodifferbasedontheinterpretationthat participants assigned to the number morphology (¬kohoXpl, ¬payaXsg, and ¬payaXpl trials).This allowed us to determine whether participants did indeed generalize that the negative particle could negate the number morpheme on the object of a transitive verb.Specifically,ifaparticipantcorrectlyinferredthatthenegativeparticlecouldnegatethe number morphology on an object in a transitive sentence, they should judge ¬payaXpl trials to be true and payaXsg and ¬kohoXpl trials to be false.
Therewere7¬payaXpl trials, 5 ¬kohoXpl trials, and 6 trials of ¬kohoXsg and ¬payaXsg each, for a total of 24 trials in the number negation task. 13Examples of each trial type and the expected judgments are given in Figure 3.

Participants
In the previous study, 20 adult native English speakers were recruited to participate in thestudy.However,only17completedtheexperimentandsoonlythedataofthose17 participants is considered.In the present study, 16 adult native English speakers were recruited to participate in the study.All 16 participants completed the present study.
In both studies, participants generally did one session per day, occasionally two.Each session lasted approximately thirty minutes, and all 10 sessions were generally completed 13 There should have been 12 trials of each type.However, due to a small coding error in the design of the experiment, a ¬payaXpl trial was incorrectly coded as a ¬kohoXpl trial.Furthermore, there was another coding error in the design of the experiment that required half of the trials to be thrown out.(They could not be recovered after the fact because the coding error was in the experimental design and how the stimuli were presented, not in how the data was coded).

Results
The main results of interest are the ¬kohoXsg trials from the number negation task.However,inordertoensurethattheresultsaremeaningful,wefirstwanttoestablishthat participantssuccessfullylearnedtheartificiallanguage.Therefore,wefirstanalyzethe results from the other tasks, and we exclude participants who were not above chance on the tasks that tested the basic properties of the language from subsequent analyses.This ensures that the interpretation of the results is meaningful and that the results are not simply the result of chance, for example.Throughout, we also compare the results from the present study to the results from our previous study.

Grammar task
The grammar task establishes whether participants learned basic properties of the grammaroftheartificiallanguage.Recallthatthistasktestedbasicargumentstructureofthe artificiallanguage.
Two-sidedsigntestsoneachindividual'sresponsesinthefinalsessionwereperformed for this and subsequent analyses in order to determine if participants were above chance performance on a facet of the language (in this case, whether the participants had successfully learned the basic argument structure of the language by the end of the experiment).All of the participants in both the previous study and the present study were significantlyabovechanceintheirresponsestothegrammartask.Itthereforeseemsthat all participants learned the basic argument structure of the language, so no participants are excluded from future analyses on the basis of not knowing the argument structure of the language.
To compare the participants from the previous study to the participants from the presentstudy,weperformedmodelcomparisonusinggeneralizedlinearmixed-effectsmodels (cf.Baayen, Davidson & Bates 2008;Quené & van den Bergh 2008).We compared two models that explained trial-by-trial variation in accuracy on the grammatical responses.Both hadidenticalrandomeffectsstructures,withrandominterceptsforsessionandstudyand randomslopesforsessionbyparticipant.Thiswasthemaximallycomplexrandomeffects structure possible given the data, as items were not consistently repeated across sessions or studies, and nobody participated in both experiments.Session was coded continuously.

Judgments
False in English and Korean False in English and Korean T rue in English and Korean

False in English
True in Korean theparticipantsinthepreviousstudydifferedfromtheparticipantsinthepresentstudy), andfortheinteractionbetweenthesetwofixedeffects,andtheotherhadonlyafixed effectofsession.Asignificantdifferenceinmodelfitsbetweenthesetwomodelswould showthatincludingthestudyfactorsignificantlyimprovedmodelfit,andthusthataccuracydifferedbetweeneachstudy.However,nosignificantdifferencewasfoundinmodel fit between the two models (χ 2 (2) = 0.318, p = .85),indicating that the study factor did not influence participant accuracy in the grammatical task.This indicates that the best-fittingmodelonlyincludedasignificanteffectofsession(b = 0.424, p <.001); participants improved in their grammaticality judgments over the course of the experiment.

Vocabulary and number morphology task
The vocabulary and number morphology task allows us to determine whether participants learned the meanings of the basic nouns in the language.Recall from above that participants heard an NP and were asked to choose whether that NP referred to a singleton referent, a multiple-item referent, both, or neither.Regardless of their interpretation of the number morphology, we can use these results to determine whether they knew the base meaning of the noun.If the NP they heard did match either the singleton or multiple-item referent on the screen, choosing one of those referents (or both) would indicate that the participant at least knew the base meaning of the noun, even if they incorrectly interpreted the number morphology.The trials where participants chose the neither option were only informative if the base noun they heard actually did match the referents on the screen, as this suggests that the meaning participants had assigned to the nominal was incorrect.However, when the correct option was not displayed on the screen and participants rightly chose the neither option, it is not possibletoknowwhatoffscreenreferenttheyhadinmind.Thesetrialsarethereforenot informative and were discarded for the purposes of ascertaining whether participants knew the basic nominal vocabulary of the language.14of16participantsweresignificantlyabovechancebytheendoftheexperimentin the present study, suggesting that the vast majority of participants successfully learned thebasicvocabularyofthelanguage(chancewassetat75%sincethreeoutofthefour onscreen options were correct for the purposes of ascertaining whether participants knew the meaning of the base noun).The two participants that were at chance on this measure are not considered for further analyses.This compares to a 100% success rate in the previous experiment.
Unlikewithgrammaticality,theANOVAcomparingthemodelfitofthesetwomodels showedasignificantdecreaseinmodelfitwhenremovingthefixedeffectofstudy(χ 2 (2) = 22.0, p <.001), indicating that study did play an explanatory role for some of the variation present in the dataset.This indicates that the acquisition of vocabulary did depend on the study.Inspection of the parameter estimates within the full model indicates that this significantdifferencewasprimarilydrivenbytheinteractionbetweensessionandstudy (b = -0.323,p<.001),astherewasnosignificanteffectofstudy(b = 0.424, p = .34).Thenegativecoefficientontheinteractiontermindicatesthatparticipantsinthepresent experiment tended to learn slower than participants in the previous experiment.Session wasalsoasignificantpredictorofaccuracyonbasicvocabularytrials,withaccuracygenerally increasing across sessions (b = 0.513, p <.001).
In addition to allowing us to determine whether participants knew the base meaning of the noun, the vocabulary and number morphology task also provides information as to how participants interpret the three different types of NPs with respect to number.Regardless of whether the participant got the base meaning of the noun correct, we can infer that participants have assigned a singular meaning to an NP if they choose the singleton referent upon hearing that NP; such a response was coded as a singular response.Likewise, we can infer that participants have assigned a plural meaning to an NP if they choose the multiple-item referent upon hearing that NP; such a response was coded as a plural response.Similarly, we can infer that participants have assigned a number-neutral interpretation to an NP if they choose the option that indicates the NP they heard can refer to both the singleton and the multiple-item referent; such a response was coded as a both plural & singular response.Again, when the neither option was chosen, the trial wasuninformativebecauseitisnotpossibletodeterminethecardinalityoftheoffscreen referent that the participant had in mind; such responses were therefore discarded in this analysis.
Figure 4 plots the various types of responses across sessions that participants gave for thethreedifferenttypesofNPs.Thegraphedresultssuggestthatparticipantsdidlearn theintendedinterpretationsofthethreedifferentNPtypesinthelanguage.Tosubstantiate this inference based on inspection of the graphs, we compare individuals' performance in session 10 to chance using two-sided sign tests.In our previous study, one participant wasnotsignificantlyabovechance(33%)insession10withrespecttointerpretingthe number of the three different NP types in the intended manner.This suggests that the participant did not learn the three-way nominal system of the language and is thus not considered in subsequent analyses.In the present study, none of the 14 participants who had successfully mastered the grammar and basic vocabulary properties of the language used here were at or below chance chance in session 10 with respect to interpreting the number of the NP types in the intended manner.We only consider the 16 participants from the previous study and the 14 participants from the present study who were above chance in further analyses.Threegeneralizedlinearmixed-effectsmodelsforthecorrectnumberinterpretationof the three NP types were run.All three models included random intercepts by participant andbysession,andrandomslopesbyparticipantforsession.Thethreemodelsdifferedin thefixedfactorsincludedineachmodel.Thefullestmodelincludedfixedeffectsforsession (coded continuously), NP type (with the bare form of the noun used as a baseline and paya and koho treatment-coded), and study, as well as their interactions.Two other models dispensedwiththefixedeffectsofsessionandNPtypeaswellastheirinteractioncomponentstodeterminethesignificanceofeachfactor.ANOVAsshowedsignificantdecreases inmodelfitbetweenboththefullmodelandthemodelwithoutstudy(χ 2 (6)=72.8,p<.001)aswellasthefullmodelandthemodelwithoutNPtype(χ 2 (8) = 303, p <.001).
Thebestfittingmodel,therefore,wasthefullone.Thismodelhadsignificantsimple effectsforsession(b = 1.15, p <0.001), NP-koho (b = 2.81, p <0.001), and NP-paya (b=0.762,p=.02).Respectively,theseeffectsindicatethatparticipantsimprovedin their performance over time and that performance on bare NP trials was worse (but not wrong) than that on NP-paya and NP-kohotrials.Therewasalsoasignificantinteraction between session and NP status for NP-koho trials (b = 0.318, p <.001), which was related totherelativelyflatlearningcurvespresentforNP-koho trials, relative to the other trial types.And, finally, there was a significant three-way interaction between session, NP type for NP-paya trials, and study (b = 0.335, p = .003).This interaction is probably due to the relatively high performance on NP-paya trials during early sessions in the present experiment when compared to the previous experiment; participants learned the meaning of paya more quickly in the present study than in the previous one.

Bare nouns sentence verification task
Thistask,whichonlyoccurredinthepresentstudy,offersfurtherinsightintohowparticipantsinterpretedthebarenominal.Recallthattherewereeffectivelythreedifferenttrial types: trials where the event was not accurately described by the sentence because the noun did not match the referent on the screen (ReferentMismatch), trials where the noun did match the referent on the screen and it was a singleton referent (MatchingSingleston), and trials where the noun matched the referent on the screen and it was a multiple-item referent (MatchingPlural).
Figure 5 shows quite clearly that participants in the present study interpret the bare nominal as number neutral since they say that sentences with the bare nominal can accurately describe both a singleton and a multiple-item referent.In addition to the results from the vocabulary and number morphology task, this is further evidence that the participants in the present study learned the three-way nominal system.

Verb and object negation
Of crucial interest are the negation results involving number morphology.However, as noted above, pilot testing showed that negation was hard to teach without overt instruction.The verb and object negation tasks thus allow us to test whether participants learned that the negative particle could negate the verb and whether they learned that the negative particle could target the head of the object noun phrase.Participants received evidence in their input that both of these things were possible, so these tasks test whether participants acquired the basics of negation.
We performed two-sided sign tests on individuals' responses to the verb and object negationtasksinordertodeterminewhetherparticipantsweresignificantlyabovechanceon these trials.
Of the remaining 16 participants from the previous study,14 13participantsweresignificantlyabovechanceonverbnegationtrials.12ofthese13participantswerealsosignificantlyabove chance in their performance on object negation.As for the present study, 8 of14participantsperformedsignificantlyabovechanceonverbnegation,and,ofthese8 participants,7alsoperformedsignificantlyabovechanceonobjectnegationtrials.
Generalizedlinearmixed-effectsmodelsforboththeverbnegationtaskandobjectnegation task were run with random intercepts by participant and by item and with random slopesforsessionbyparticipant.Thefullestmodelrunforbothanalysesincludedfixed effectsforsession,study,andtheinteractionofthesetwofixedeffects.Whencompared toamodelwithouteffectsofstudy,therewasnosignificantdifferenceinmodelfit(χ 2 (2) = 2.02, p = .36),indicating that, although participants did improve in their performance from block 9 to block 10 (b = 2.94, p<0.001)therewasnosupportforasignificanteffect of study.The participants who were not above chance on verb negation were excluded from the models for object negation.

Number negation
Finally, the results of main interest are the results from the number negation task.Recall that the trial type of crucial interest is ¬kohoXsg.These trials are the main trial type of interest because these involved a negated sentence where the object is marked with the plural morpheme and the corresponding onscreen referent is a singleton referent.In other words, responses to trials of this type tell us whether participants have assigned an inclusive or exclusive interpretation to the plural under the scope of negation.If participants say that the sentence truly describes the scenario depicted onscreen, this is evidence for participants having an exclusive interpretation, whereas if participants say the sentence does not describe the scenario depicted onscreen, this is evidence for participants having an inclusive interpretation.
Remember that, crucially, participants were not trained on the fact that the negative particle could negate the number morphology on the object of a transitive sentence lest we bias the results by introducing evidence into the input as to how the plural is interpreted under the scope of negation.Therefore, in order to ensure that the results we interpret are meaningful, three other trial types were included where the judgments are not expected to differ,regardlessofinterpretationofthenumbermorphology(cf.Figure3).By lookingat these three trial types (¬payaXpl, ¬payaXsg, and ¬kohoXpl), we can determine whether participants generalized that the negative particle could negate the number morphology on the object of a transitive sentence.
We thus inspected the performance of those participants who were above chance on verb and object negation for these three trial types using sign tests.In our previous study, all participants who successfully learned both verb and object negation performed above chance on these three trial types indicating that they generalized that the negative particle couldnegatethenumbermorphologyontheobject.Inthepresentstudy,5ofthe7participants who successfully learned both verb and object negation performed above chance on these trial types indicating that they generalized that the negative particle could negate the number morphology on the object.
The responses of these 12 participants from the previous study and the 5 participants fromthepresentstudyareshowninFigure7forallfourtrialtypes.Inourpreviousstudy, 8 of the 12 participants who learned that the negative particle could negate the number morphology on the object of a transitive sentence were significantly more likely than chance to give a true response to the ¬kohoXsg trials.Likewise, in the present study, 4 of the 5 participants who learned that the negative particle could negate the number morphologyontheobjectofatransitivesentenceweresignificantlymorelikelythanchance to give a true response to the ¬kohoXsg trials.

Discussion
With respect to the interpretation of the plural in the ¬kohoXsg trials, it is clear that the participants from both our previous study and the present study interpret koho exclusively under the scope of negation, like in Korean (cf. Figure 7).Recall from above that this is predicted by the hypothesis that semantic markedness is necessitated when number is not grammaticalized.On the other hand, the hypothesis that semantic markedness is theresultofinsufficientevidenceforcompressingthelexiconpredictedtheopposite.It predicted that participants in the present study should have diverged from participants in the previous study on the ¬kohoXsg trials-namely, they should have assigned an inclusive interpretation to the plural under the scope of negation and said that these trials were false. 15 In addition to the main results of interest, a few comments about the differences we saw across the results from the previous study and the present study are in order and may provideuswithsomeinsightaboutthelearningmechanisms.Theonlytaskswithsignificantmaineffectsforstudywerethefreeresponsetaskandtheobjectnegationtask.The resultsfromthevocabularyandnumbermorphologytaskalsoexhibitedmaineffectsfor the interaction between study and session and the interaction between study, session, and the singular marked NP (NP-paya)thatapproachedsignificance.
Thefactthatthereweresignificantdifferencesinthefreeresponsetaskisnotsurprising. Participants in the present study clearly used the number morphemes much more frequently than in the previous study's production task.This is unsurprising, given that adult learnersinartificiallanguagelearningtasksareknowntomimicfrequenciesintheinput 15 A reviewer asked about English speakers' judgments of the ¬kohoXsg trials with the same materials.We did conduct a short control experiment with 20 English-speaking participants using the same materials but with English recordings.There were 4 items per participant of the ¬kohoXsg trials.The 20 participants gave judgments consistent with an inclusive interpretation of the plural 25.32% of the time, and they gave judg-mentsconsistentwithanexclusiveinterpretation74.68%ofthetime(SE=4.89%).Thismightinitially seem unexpected; however, it would not be surprising if these results are due to something of a metalinguistic nature.The task that we asked native English speakers to do was both short and very simplistic and thus very transparent in terms of what was being tested.Moreover, a t-test comparing the 20 participants in the control experiment to the participants of both our previous and present studies shows that the participants inthecontrolexperimentweresignificantlymorelikelytogiveaninclusiveinterpretation(t(122.38)= -2.18,p < 0.05).Lastly, it is already known from the experiments reported in Pearson, Khan & Snedeker (2011) that there are certain contextual environments where the implicated presupposition that gives rise to the exclusive interpretation is hard to cancel.So given that the control task was so simplistic and transparent in virtue of using the same materials and given that the implicature is known to be hard to cancel in certain environments, these results are not entirely surprising.This makes it all the more noteworthy that participantsinthecontrolexperimentweresignificantlymorelikelytointerpretthepluralinclusivelythan theparticipantswholearnedtheartificiallanguage,suggestingthatthebehavioroftheparticipantswho learnedtheartificiallanguageisnotsimplyaresultoftheirnativelanguage.(cf.Hudson Kam & Newport 2005;2009) and the frequency of the number morphemes in the input was much greater in the present study than in the previous study.It is interesting though that in the present study, by session 10 participants were basically not using the bare nominal any longer, suggesting that frequency did play a role and that, in the task, participants did prefer to be as explicit as possible in their production.However, the results from comprehension tasks show that this does not mean that they did not learn the interpretation of bare nominals.
For the vocabulary and number morphology task, there were interesting effects that approachedsignificancebetweenthetwostudies.Writlarge,participantsexhibitedthe samelearningtrajectorywithregardtotheinterpretationofthethreedifferentNPtypes from the previous study to the present study (cf. Figure 4).In both studies participants initially treated payaaspluralinthefirsttestingsessions,despitetherebeingnoevidencein the input for payaeverbeingplural.InLiter,Heffner&Schmitt(2017),weattributethis toaninitialtransfereffectfromparticipants'nativelanguageofEnglishthatiswashed out over time.Since the singular has no overt morphology marking in English but the plural does, we suspect that participants might have initially treated the bare nominal as singular and both koho and paya as plural.Over time, this behavior disappears, and participants come to learn the three-way nominal system. 16These same trends are exhibited in the present study, but they are weaker and disappear much more quickly.This is again unsurprising given that there was much more quantitative evidence in the input for the present study that paya really did mean singular.
As for the significant main effect of study in the object negation task, it is not clear why there would have been a difference from the previous study to the present study in this task.Perhaps this is related to the fact that participants took longer to learn the vocabulary of the language, and so negation of the object referent was harder for the participants in this study; however, this is just speculative.
Insum,wefindthatthelearningtrajectoriesarethesameindependentofthedifferences in frequencies between the two studies.What changes seems to be the speed in which certain interpretations are learned and the frequency with which the forms are used.Furthermore, the frequency of use of plural and singular forms in relation to bare nominals was not enough to change the interpretation assigned to the plural.

Conclusion
Torecapitulate,thepresentworkfleshesouttwopossibleaccountsofwhylanguageslike Koreanappeartoalwayshavesemanticallymarkedpluralmorphology.Thefirsthypothesis is that non-grammaticalization of number entails semantic markedness (cf.§2.1), and thesecondhypothesisisthatsemanticmarkednessistheresultofinsufficientevidence for compressing the lexicon (cf.§2.2).Both hypotheses would account for the natural languagefactsandourpreviousartificiallanguagelearningresults,since,inthesecases, lack of grammaticalization correlates with a lower frequency of the forms.In the study we presented in this paper, we increased the frequency of singular-and plural-marked noun phrases, but we maintained the non-grammaticalization of number marking. 17 We found that native English speakers assumed the plural was semantically marked when learning both artificial languages, independent of the frequency with which the 16 A reviewer asks why some studies show transfer effects and others do not.Although a full analysis of differentresultsisbeyondthescopeofthispaper,wesuspectthatoureffectwashedoutastheparticipants learned that paya was singular.Treating the bare nominal as singular would amount to violating the principleagainstsamemeaningfortwodifferentforms. 17It is important to reiterate that, in this case, it was a case of true optionality given that both the bare nominal and the number-marked noun phrases occurred in exactly the same contexts and had no (in)definitenessconfounds.
forms appeared and despite the fact that the plural is semantically unmarked in their native language.The results are consistent with the idea that what matters is the nongrammaticalization of number.In other words, the results did not support the hypothesis that semantic markedness is the result of infrequent number-marked NPs constituting insufficientevidenceforcompressionofthelexicon.
Nonetheless, there are two issues that can be raised when we examine our results in light ofthehypothesestested.Thefirstissuehastodowiththeunderlyingassumptionthatwe have made about the analysis of the interpretation of the plural, and the second issue has to do with the underlying representations that participants may have had of the plural.
Remember that both hypotheses assumed an implicated presupposition account of the number interpretation facts in English (Sauerland, Anderssen & Yatsushiro 2005).Morespecificallyweassumedthat(i)thepluralissemanticallyunmarkedinEnglishand receives an inclusive interpretation in downward entailing contexts in which the implicated presupposition gives rise to a stronger statement; and (ii) if the plural allowed an exclusive interpretation in downward entailing contexts, that would mean that the plural was semantically marked.However, as mentioned before, Grimm (2013) and Mathieu (2014) have recently argued that an implicature-based (or implicated-presuppositionbased)18 analysis of the plural is wrong and that the correct analysis is in terms of weakly and strongly referential NPs, with plural instances of the former having an inclusive interpretation and plural instances of the latter having an exclusive interpretation.
As noted above, it is beyond the scope of this paper to adjudicate between this analysis, on the one hand, and the implicature-based analyses on the other hand (Sauerland, Anderssen&Yatsushiro2005;Spector2007;Zweig2009).Nonetheless,itisworthnoting that the papers of Grimm (2013) and Mathieu (2014) are concerned about the correct analysis of English.In this paper, we are ultimately concerned about ascertaining why languages like Korean always seem to have an exclusive interpretation of their plural morphology.If Grimm (2013) and Mathieu (2014) are ultimately correct about English and if the weakly/strongly referential distinction is also relevant to explaining the Korean facts(ratherthansemanticmarkedness),thenthissuggeststhatourfirsthypothesismight needtobereframedintermsofweaklyandstronglyreferentialNPs.Specifically,itwould suggest that non-grammaticalization of number may entail that plural-marked NPs are always strongly referential and therefore disfavored in downward entailing contexts, among other contexts.Alternatively, if we take Mathieu's (2014) analysis it would suggest that Korean-like languages only have one type of plural (the referential one) and that learners would need some type of evidence to postulate a second type of plural (the non-referential one).
Thus, we think that the import of our results does not rest entirely upon Sauerland, Anderssen & Yatsushiro's (2005) analysis of the plural being correct.And we leave deciding whether the Grimm (2013) and Mathieu (2014)-style analyses are correct and, if so, whether they are relevant to the Korean facts, to other work.
The second issue has to do with the actual representation of the plural in the study presented.Based on our assumptions, we argued that the learner did not infer that plural and singular were grammaticalized based on the fact that participants did not treat the plural as unmarked and the fact that they did learn a three-way distinction, even though they basically did not produce bare nominals by session 10. 19 The small amount of bare nominals in the production component of the study presented here is not however unexpected and should not be used as evidence for grammaticalization.As the studies by Hudson Kam & Newport (2005;2009) pointed out, adult participants tend to match input frequencies, and they are also known to try to be as informative as possible(cf.Fedzechkina,Jaeger&Newport2012;Kurumada&Grimm2017);bothof these facts would lead to the bare nominal being dispreferred.That is, the smaller frequency of bare nominals in the present study combined with its less informative nature may have led participants to use it less often.Nonetheless, the results from the comprehension task suggest that they did learn that bare nominals could be used for singletons and pluralities, after they overcame the bias towards treating them as singular.The only differencebetweenthetwostudiesisthatthisbiaswentawayfasterwhenthefrequencies of marking singular and plural were higher.Thus, an interesting question for future work(alsoaskedbyarevieweranddiscussedbrieflyinnote16)wouldbetoinvestigate how much input is necessary to undo the initial biases a learner might have from their native language and whether all of the L1 biases have the same signature.What our study tentatively suggests with regard to these questions is that implicature-dependent interpretations are calculated on the options available and do not transfer, but more studies need to be done in order to replicate these results with both plurals and other types of linguistic features.
With regard to our main question (namely, whether the non-grammaticalization of number drives the semantic markedness of plural morphology or whether infrequent use of singular and plural morphology does), we have shown that our results are consistent with the hypothesis that non-grammaticalization entails semantic markedness, and we have given an account of why there is such an entailment relation in terms of Sauerland, Anderssen & Yatsushiro's (2005) analysis of the plural.

Figure 1 :
Figure 1: Examples of negation training in sessions 8 and 9.

Figure 2 :
Figure 2: Examples of verb and object negation trials.

Figure 3 :
Figure 3: Number negation trial types and expected judgments.

Figure 4 :
Figure 4: Responses for the three NP types in the vocabulary and number morphology task by session.

Figure 6 :
Figure 6: Usage of three NP forms in the free response task.

Figure 5 :
Figure 5: Responses to sentence verification task involving bare nominals by trial type collapsed across participant and session; a doesn't describe response means the participant said the sentence does not describe the event, whereas a describes response means the participant said the sentence does describe the event.

Figure 7 :
Figure 7: Responses to the number negation trials by trial type.

Table 1 :
Frequency of the different nominals in the training input.

Table 2 :
Schedule of testing and training.