Children interpret disjunction as conjunction:Consequences for theories of implicature and

child development∗

Raj Singh1, Ken Wexler2,3, Andrea Astle4, Deepthi Kamawar1,4,and Danny Fox2

1Carleton University, Institute of Cognitive Science2MIT, Department of Linguistics and Philosophy

3MIT, Department of Brain and Cognitive Sciences4Carleton University, Department of Psychology

January 14, 2015

1 Introduction

1.1 A summary of the empirical challenge: Children’s con-junctive interpretation of disjunctive sentences

It is commonly assumed that children pass through a stage of development atwhich they know the meanings of logical operators but do not strengthen the ba-sic meanings of sentences by computing scalar implicatures (e.g., Noveck, 2001and much work since). Consider the interpretation of sentences containing logi-cal operators like some and or. An adult who understands John ate some of thecookies based on its basic (i.e., unstrengthened) meaning will conclude that thesentence is true if John ate one or more of the cookies. In a context in which∗An earlier version of this manuscript was circulated on 7 Dec 2013. Acknowledgments to be

added.

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John ate all of the cookies, the sentence is true under its basic meaning, but ifthe adult computes the sentence’s scalar implicature, that John did not eat all ofthe cookies, the sentence will be judged false. Similarly, the sentence John atecake or ice-cream on its basic meaning is true as long as John ate at least one ofthe cake or ice-cream. In a context in which John ate both cake and ice-cream,the sentence is true on its basic meaning, but if the adult computes the sentence’sscalar implicature, that John did not eat both, the sentence is judged false.

Simplifying considerably for the moment, there are two steps in the computa-tion of implicature: (1) ALT (for ‘alternatives’): generate an alternative sentence,and (2) EXH (for ‘exhaustify’): negate the alternative generated in step (1). Forexample, suppose the uttered sentence is John ate some of the cookies, ∃. At step(1) ALT will return John ate all of the cookies, ∀, as an alternative. At step (2)EXH will negate this alternative, ¬∀, and this is the scalar implcature (SI) of thesentence: that John did not eat all of the cookies. The overall strengthened mean-ing of the sentence is the conjunction of its literal meaning and its SI: that Johnate some but not all of the cookies, ∃ ∧ ¬∀. Now suppose the uttered sentence isJohn ate cake or ice-cream. At step (1) ALT returns John ate cake and ice-creamas an alternative. At step (2) EXH negates this alternative, and the SI is that Johndid not eat cake and ice-cream. The strengthened meaning is thus that John atecake or ice-cream but not both, (A ∨ B) ∧ ¬(A ∧ B); this of course is equivalentto an exclusive-disjunction.

Evidence has been presented that preschool children do not compute thesescalar implicatures. For example, when presented with a picture or story in whichJohn ate all of the cookies, a child – unlike the adult – will judge the sentence Johnate some of the cookies to be true (e.g., Noveck, 2001), and when presented witha picture or story in which John ate cake and ice-cream, a child – unlike the adult– will judge the sentence John ate cake or ice-cream to be true (e.g., Chierchiaet al., 2001; Gualmini et al., 2001).

(1) Child-adult behavior:

State of affairs Sentence Adults Children∀ ∃ F T

A ∧B A ∨B F T

What (1) has been taken to show is that children pass through a stage of devel-opment at which they know the meanings of logical operators but do not computescalar implicatures (note that this leaves open whether the child’s difficulties are

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with ALT or EXH or both).We present evidence that challenges this characterization of the relevant devel-

opmental stage. Specifically, we present evidence that many preschool children –the majority in our sample – understand disjunctive sentences like the boy is hold-ing an apple or a banana as if they were conjunctions (that the boy is holding anapple and a banana). This finding is consistent with earlier studies showing that achild will accept A∨B when both A and B are true; our crucial finding, replicat-ing previous results (e.g., Paris, 1973; Braine and Rumain, 1981; Chierchia et al.,2004), is that a child will reject A∨B when only one of the disjuncts is true. Thisis consistent with neither logician nor adult behaviour, but is instead suggestive ofa conjunctive interpretation.

The apparent conjunctive interpretation of disjunctive sentences found in pre-vious studies has not received much attention. We wish to highlight these previ-ous results, and to add our findings to this set of studies. Ignoring for the momentthose children and adults who understand or as inclusive disjunction, in (2) belowwe provide a snapshot summary of the ways in which children and adults deviatefrom inclusive-disjunction readings of A ∨ B (in section 2 we give a full reportof our findings, as well as a more detailed description of Paris, 1973; Braine andRumain, 1981; Chierchia et al., 2004):

(2) Truth-value judgment for matrix disjunctions A ∨ B that deviate frominclusive-disjunction

State of affairs Child (conjunction) Adult (exclusive-disjunction)¬A,¬B F FA,¬B F T¬A,B F TA,B T F

In fact, the data we report show evidence for such conjunctive readings not onlyin matrix disjunctions but also when disjunctions are embedded under every. Forexample, we will see that many children understand every boy is holding an appleor a banana to be asserting that every boy is holding an apple and a banana.

It seems clear that the difference between the child and adult cannot be re-duced to a difficulty with computing scalar implicatures, for this difficulty shouldnot lead to ‘false’ judgments for A ∨ B when just one disjunct is true. Paris(1973) and Braine and Rumain (1981) suggested that children at this stage of de-velopment might interpret A ∨ B by applying an ad-hoc strategy that involves

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ignoring the operator and instead ‘matching’ disjuncts with parts of the picture.This assumption needs to be worked out, but we would like to argue that it is notnecessary to account for the data, and in fact is problematic given the observationthat the child’s deviant behaviour with or disappears in downward-entailing (DE)contexts; in such contexts, there is evidence suggesting that pre-school childrenunderstand or as inclusive disjunction, just like adults (e.g., Chierchia et al., 2001;Gualmini et al., 2001; Chierchia et al., 2004; Crain, 2008; Crain and Khlentzos,2010).

(3) DE contexts obliterate the difference between children and adults: In DEcontexts, children’s understanding of disjunction is inclusive disjunction,like adults.

We will suggest that recent developments in the theory of implicature, in par-ticular theories that aim to derive so-called ‘free-choice’ inferences as a specialcase of scalar implicature (Fox, 2007; Chemla, 2009b; Franke, 2011), might allowus to avoid a special stipulation and explain the child’s behaviour within a gen-eral theory of logical semantics, implicature computation, and the development ofthese capacities as a child transitions to the steady state.

1.2 A summary of our proposal: Relating conjunctive readingsin the child to free-choice inferences in the adult

We propose that the child’s understanding of or as conjunction in upward-entailingcontexts and as inclusive-disjunction in downward-entailing contexts is teachingus that the child’s conjunctive interpretation is the result of a scalar implicature.1

If we are right, it is incorrect to characterize the child’s developmental trajectoryas one in which they transition from a logician to the adult state, for here they arecomputing an implicature, A ∧ B, which moreover is the opposite of the adult’simplicature, ¬(A ∧B).

What, then, is the correct characterization of the difference between the child’sdevelopmental stage and the adult steady state? We will argue that the child at

1Implicatures are not computed for operators in downward-entailing contexts, at least notwithout marked accent (e.g., Geurts, 2009; Fox and Spector, 2008), because the logical strengthof alternatives is reversed. For example, the sentence If the boy is holding an apple or a banana,the girl is holding a pear is logically stronger than its alternative If John is holding an apple anda banana, the girl is holding a pear; thus, the sentence with a disjunctive antecedent can only beinterpreted with its literal meaning.

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the relevant stage of development possesses the adult capacity to compute scalarimplcatures,EXH , and that the only relevant difference is that the child’s alterna-tives are systematically a subset of the adult’s alternatives (building on Chierchiaet al., 2001; Gualmini et al., 2001; Papafragou and Musolino, 2003; Reinhart,2006; Crain, 2008; Barner and Bachrach, 2010; Barner et al., 2011). Specifically,we will argue that the child does not access the lexicon in generating the alterna-tives of a sentence. For example, in the adult, a sentence ∃ has as alternative asentence in which some is replaced with all, ∀. Thus, ALTAdult(∃) = {∀}, andEXH ends up negating ∀, ¬∀, resulting in a strengthened meaning ∃∧¬∀. How-ever, the child does not access the lexicon in generating alternatives, which in thiscase means that they cannot replace some by all. Thus, there is no alternative,and EXH therefore has nothing to do. The only available meaning of ∃ is thusthe literal one. This explains the quantificational part of (1): children say ‘true’to ∃ when ∀ is true because there can be no implicature without an alternative tonegate.

With disjunctions A ∨ B, there are two mechansisms for generating alterna-tives in the steady state. In addition to lexical replacements, there is also thepossibility of deleting material to generate an alternative (Katzir, 2007; Chemla,2009b). These two steps, when applied to A ∨ B, operate as follows: (i) lexicalreplacements, in which or is replaced by and, yield the alternativeA∧B, (ii) dele-tion, which picks up subconstituents of the uttered sentence, yields the constituentdisjuncts A, B as alternatives. Thus, ALTAdult(A ∨ B) = {A,B,A ∧ B}. Forvarious reasons that we explain in more detail later, when given this set of alterna-tives EXH can only negate A ∧ B, resulting in the ¬(A ∧ B) implicature foundin the adult. Under our proposal, the child cannot perform lexical replacements,so their alternatives are: ALTChild(A ∨ B) = {A,B}. It turns out that under var-ious characterizations of EXH (Fox, 2007; Chemla, 2009b; Franke, 2011), theapplication of EXH to A ∨ B with these alternatives is predicted to result in aconjunctive strengthened meaning for the same reason that you’re allowed to eatcake or ice-cream is strengthened to a conjunction ‘you’re allowed to eat cake andyou’re allowed to eat ice-cream’ (see (9) for a connecting statement and section 4for discussion). If we could find or create a population with these alternatives wecould test this prediction; our claim is that the child at this stage of developmentprovides us with such a population. If this is correct, the child at this stage of de-velopment is merely one among several populations that display this behaviour; aswe discuss in section 5, adult interpretations of disjunctive sentences in Warlpiriand American Sign Language seem to be quite similar in crucial respects (Bowler,2014; Davidson, 2013).

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Let us briefly summarize how this proposal meets the challenge laid out in(1)-(3). The conjunctive strengthened meaning in the child explains why the childaccepts A ∨ B when both disjuncts are true (cf. (1)): here, unlike with some, thetruth-value judgment follows not because the child does not compute an implica-ture, but because they compute a conjunctive implicature, one that is different thanthe implicature computed by the adult. Evidence for this implicature comes fromthe observation that the child says ‘false’ when just one disjunct is true (cf. (2));the difference between the child and the adult in (2) is explained by this differencein implicatures, which under our proposal follows from their difference in alter-natives. The behavioural difference between the child and adult vanishes in DEcontexts because implicatures are not computed in such environments (cf. (3));thus, in such environments the lexicalized meaning of or is all that is available,and the child and the adult are both seen to possess an inclusive-disjunction entryfor or.

A further challenge we take up is that children ‘cluster’ into sub-populations.Building on Noveck and Posada (2003), we propose a set of interpretive strate-gies that naturally follow from the assumption that children and adults are bothcapable of strengthening. All of the theoretically-motivated strategies we identifyare attested in our sample, but the one that is dominant is the group of childrenwho understand disjunctions conjunctively, even when the disjunction is embed-ded under every. Here again we connect the child’s behaviour to adult free-choiceinferences. Adults have been found to prefer free-choice inferences (Chemla andBott, 2014), even when the relevant sentences are embedded under every (Chemla,2009c; e.g., adults prefer to understand every boy is allowed to eat cake or ice-cream as asserting that every boy has free-choice). Under our proposal, the child’spreference for conjunctive (free-choice) readings of disjunction is thus a specialcase of a general preference for free-choice. We tentatively follow Gualmini et al.(2008) and suggest (section 4.3) that this general preference might follow from apreference to provide a complete answer to the question under discussion (Groe-nendijk and Stokhof, 1984; Lewis, 1988; Roberts, 1996).

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2 Experimemt

2.1 Motivation: previous findings of conjunctive interpreta-tions of disjunction

There is a fair amount of evidence that children understand or as inclusive dis-junction in DE-contexts (e.g., Chierchia et al., 2001; Gualmini et al., 2001; Chier-chia et al., 2004; Crain, 2008; Crain and Khlentzos, 2010). There also seemsto be evidence that children understand or as conjunction in matrix disjunctions.Here we briefly summarize the experimental results that show this tendency. Ourown experiment, discussed in the next section, was designed to examine whetherthese results are replicable and whether they would be affected by embedding inupward-monotone environments.

The first report of a conjunctive interpretation that we know of is in Paris(1973). Second-graders were shown a slide presentation together with a verbaldescription (e.g., the bird is in the nest or the shoe is on the foot), and they wereasked to decide whether the verbal description was true or false. Paris (1973)found that when A and B were both true, participants responded ‘true’ to A ∨B almost 98 percent of the time, and when A, B were both false, participantsresponded ‘false’ to A∨B roughly 98 percent of the time. This is consistent withan inclusive disjunction. However, when only one of A, B was true, participantsresponded ‘true’ to A ∨ B roughly 30 percent of the time (see Table 3 in Paris,1973, p.285). These results are expected if roughly 70% of responses were basedon a conjunctive interpretation A ∨ B and the rest were based on an inclusivedisjunction interpretation.

Another study showing an apparent conjunctive interpretation is Braine andRumain (1981). Here the methodology was slightly different: children (5-6 year-olds) were shown boxes with toys in them, and a puppet made a statement aboutthe scene (e.g., ‘either there’s an X or a Y in the box’). The child was asked to saywhether the puppet was right. Again, as with the Paris (1973) study, participantsmostly responded ‘right’ to A ∨ B when both A, B were true, and ‘false’ toA∨B when both disjuncts were false: around 95 percent of participants displayedthis behaviour. However, when only one disjunct was true, only 18 percent ofparticipants responded ‘true’ (see Table 3 in Braine and Rumain, 1981, p.58).This result is expected if most of the participants interpret A ∨ B as somethingother than inclusive-disjunction. Of these, 32% clearly gave a pattern of responsesconsistent with conjunction, and the others – given the option to say the puppetwas ‘partly right’ – had a complex mix of ‘true, false, partly right’ responses

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to these so-called ‘mixed truth-forms.’ Although it is not clear how to interpretthe ‘partly right’ response, it is clear that more children understood A ∨ B asconjunction rather than inclusive disjunction.2

More recently, Chierchia et al. (2004) presented children with a story togetherwith a disjunctive statement A ∨ B describing the story. When A,B were bothtrue, children accepted A ∨ B 95 percent of the time, but when only one of A,Bwas true, they accepted A ∨ B only 78 percent of the time. This result would beexpected if roughly 17% of responses were based on a conjunctive understandingof A ∨B.

What we have, then, is three different studies using different methodologiesand different sets of children that found more rejections of a disjunction whenjust one disjunct is true than when both disjuncts are true. This makes sense if aconjunctive interpretation of disjunction is available to many of these children butis mysterious otherwise.3

Conjunctive interpretations have also been found in imperative contexts. Chil-dren have sometimes been found to understand sentences like Give me A or B! as‘give me A and B’ (Neimark and Slotnick, 1970; Suppes and Feldman, 1971), butthis result is not as robust as for matrix disjunctions (Johansson and Sjolin, 1975;Hatano and Suga, 1977).4 This is not very surprising if the strengthening is theresult of a scalar implicature, for note that in the adult state Give me some of thecookies is a demand to give the speaker some of the cookies, with a global impli-cature that the hearer is not required to give the speaker all of the cookies, but it

2We will propose that children derive a conjunctive reading with a scalar implicature that ‘notjust A’ and ‘not just B;’ the ‘partly-right’ response might thus be reporting the insight that thesentence is true on its basic meaning but false if its SI is taken into account.

3It is well-known that disjunctions A∨B typically lead to ignorance inferences that the speakeris ignorant about the truth-value of each disjunct (e.g., Gazdar, 1979; Sauerland, 2004; Fox, 2007;Chemla, 2009b). One might try to explain the child’s rejection of A ∨ B when just one disjunctis true as the result of an implausible ignorance inference, but this would not explain why thechild accepts the disjunction when both disjuncts are true. Furthermore, as we will see, this lineof explanation would not account for the conjunctive readings of disjunction our sample producedunder every; in such embeddings ignorance implicatures are not computed (e.g., Sauerland, 2004;Fox, 2007).

4Other studies from that period also identified particular problems with disjunction, but it ishard to discern whether the difficulty had to do with a conjunctive inference (e.g., Furth et al.,1970; Sternberg, 1979). As far as we know the conjunctive inference was not taken very seriouslyin the literature. For example, Sternberg (1979) cites and discusses the Paris (1973) study, butnevertheless assumes without comment that a child’s developmental trajectory takes them from astage at which they understand or as inclusive disjunction to one in which they understand it asexclusive disjunction.

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is not readily interpreted as a demand to give the speaker some but not all of thecookies. The conjunctive reading in imperatives would only follow from an em-bedded conjunctive implicature under the imperative, but embedded implicaturesseem to be generally dispreferred in such environments.

Taken together, the results suggest the following picture. Assuming that in-terpretations in DE contexts reveal literal meanings that are guarded from variousinterfering inferences, the child can be assumed to know that or denotes inclusivedisjunction. In matrix disjunctions many children seem to be strengthening themeaning to a conjunction. This strengthening might also be available, though notvery robust, in imperative contexts.

This background guided the design of our own study. We were specificallyinterested in children’s truth-value judgments for matrix disjunctions when atleast one of the disjuncts is true (this is precisely where children and adults seemto differ). Furthermore, given that imperatives do not readily permit embeddedstrengthenings, we embedded disjunctions under every to examine the robustnessof children’s apparent conjunctive interpretations.

2.2 Materials and MethodsParticipants for the present study were 63 preschool-aged children. Four childrenwere excluded from the sample: one child refused to finish the task and threedid not speak English at home. The remaining sample consisted of 59 English-speaking children (36 girls) ranging in age from 3 years 9 months to 6 years 4months (M = 4;10). Of these, another three failed to complete the task, leavinga sample of 56 children (M = 4;11, range = 3;9 to 6;4). All participants wererecruited by contacting child care centres in the Ottawa area and we obtainedinformed consent from the centre coordinator, the parents of the children whoparticipated, and the children themselves (verbal consent). The participants weretested either in a separate room or quiet area in the centre. Regardless of whetherthey completed the task, children were thanked and given stickers as a token ofappreciation.

Participants were tested individually in one session approximately 15 minutesin length. Prior to beginning the task, children talked briefly with an experimenterto allow them the opportunity to get acquainted. The session involved looking at apicture book together while the child interacted with the experimenter and a koalabear hand puppet.

The task used in the present study was created based on variations of the truth-value judgment task (Crain and McKee, 1985; Crain and Thornton, 1998) used

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in studies of children’s understanding of disjunction (e.g., Paris, 1973; Braineand Rumain, 1981) and implicature development (e.g., Chierchia et al., 2001,Gualmini et al., 2001, Noveck, 2001, Guasti et al., 2005, Barner et al., 2011).In our task, children were introduced to a puppet named Fuzzy and were told thattheir job was to help Fuzzy practice saying the right thing about pictures presentedin a book. We used pictures instead of stories to reduce the amount of time spenton each trial so that more data points could be collected. We also assumed that apicture would impose less demands on a child’s memory than a story.

Prior to beginning test trials, children were first asked to identify each of theitems used in the task to ensure they understood the labels being used. Further-more, children also completed straightforward practice trials where the questionswere similar to those in test trials but had obviously correct or incorrect responses.For example, the first practice trial depicted a picture of a boy holding a bananaand Fuzzy stated The boy is holding a banana. Children were asked if Fuzzywas right or wrong about that picture. In the second practice trial the pictureshowed a monkey holding a flower and Fuzzy said The monkey is holding an ap-ple. Again, children were asked if Fuzzy said the right thing or the wrong thing.They completed two more practice trials, one more correct and one more incor-rect statement, before proceeding to test trials. Children who made errors duringthe practice trials were provided with feedback by the experimenter, and thosequestions were repeated up to two more times before moving onto the test trials.All children, including those who did not ultimately finish the task, were able tocorrectly respond to the practice trials by the third attempt, with most (47 out of59) passing on their first attempt (11 passed on their second attempt, and 1 passedon his third attempt).

For each test trial, participants were shown a picture, heard a statement byFuzzy, and were asked if Fuzzy said the right thing or the wrong thing about thatpicture. The order in which the experimenter asked if Fuzzy was ‘right’ or ‘wrong’was counterbalanced between children. There were 40 test trials which consistedof eight conditions, with five trials per condition. In half of the conditions, Fuzzymade a disjunctive statement. In Condition 1 = ‘One,’ the character holds oneitem (e.g., there is a boy who is holding one item, such as a banana; see 1a inFigure 1), while in Condition 2 = ‘Both’ the character holds two items (e.g., theboy is holding two items, both an apple and a banana; see 1b in Figure 1). Inboth conditions Fuzzy asserts a disjunctive sentence stating that the character isholding one or the other item (e.g., the boy is holding an apple or a banana). InCondition 3 = ‘Every-one,’ three characters (e.g., three boys) each hold one item,though they do not all hold the same item (e.g., two of the boys hold an apple

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(a) One (b) Both (c) Every-one (d) Every-both

Figure 1: Sample of pictures for critical items

while one of the boys holds a banana; see 1c in Figure 1), while in Condition 4= ‘Every-both’ the three characters each hold two items (e.g., each of the threeboys holds both an apple and a banana; see 1d in Figure 1). In both conditions,Fuzzy asserts a disjunctive sentence embedded under a universal quantifier statingthat every character is holding one or the other item (e.g., every boy is holding anapple or a banana).

In the remaining conditions (Conditions 5-8), Fuzzy made an and statementinstead of an or statement using the same pictures from Conditions 1-4. In Condi-tion 5 subjects saw the picture from ‘One,’ in Condition 6 subjects saw the picturefrom ‘Both,’ in Condition 7 subjects saw the picture from ‘Every-one,’ and in Con-dition 8 subjects saw the picture from ‘Every-both.’ Conditions 5 through 8 wereintended to be used as controls to ensure children understood the task and werepaying attention to the questions being asked. After excluding participants whodid not perform significantly above chance on these conjunctive controls (this re-quired getting at least 16/20 correct responses on the items in Conditions 5 through8, p = .044), 31 of the 56 child participants remained (23 girls). However, our mainfindings do not change if we include the whole sample (see note 7 in section 2.4).5

5We noticed several patterns among the group of subjects who failed to pass the conjunctivescreener. Most prominent among them was a bias to say that Fuzzy was right. The conjunctivesentences are true in Conditions 6 and 8, and false in Conditions 5 and 7. Nevertheless, eight of thetwenty-five excluded subjects said ‘true’ to Conditions 5 and 7 at least eight times out of ten trials(the mean number of ‘true’ answers this sample gave out of 40 critical and control items was 37.4).Another group of six subjects displayed a slightly weaker bias pointing in the same direction,saying ‘true’ to Conditions 5 and 7 five times out of ten trials (the mean number of ‘true’ answersthis sample gave out of 40 critical and control items was 31.5). There was also a group of threesubjects who displayed the opposite bias, saying ‘false’ to most conditions, and in particular toConditions 6 and 8 at least nine times out of ten (the mean number of ‘true’ responses this samplegave out of 40 critical and control items was 4). Finally, there was a group of three subjects whoseemed to have particular difficulties with Condition 7 only, incorrectly responding ‘true’ on eachof the five trials. Condition 7 also gave particular trouble to two other subjects: one of themincorrectly responded ‘true’ four out of five times, and another one incorrectly responded ‘true’

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The children in the remaining sample ranged in age from 3 years 9 months to 6years 4 months, M = 4;11.

The task had five trials for each of the eight conditions. In addition to theboys with apples and/or bananas, we also showed children pictures of monkeyswith flowers and/or books, trucks with pigs and/or tigers, horses with birds and/orcrabs, and men with forks and/or spoons. There were three fixed orders of thetask, and each fixed-order was determined by randomizing the presentation of thetrials. In all versions, a response that Fuzzy was right was coded as ‘one’ whereasa response that Fuzzy was wrong was coded as ‘zero.’ Total scores per conditionwere calculated.

Finally, we also recruited 26 adults from the Ottawa area. All were nativeEnglish speakers, and all passed the conjunctive controls in Conditions 5-8 (25of the 26 adults performed perfectly, and one adult made a single error on theconjunctive control).

2.3 Basic predictions of commonly assumed developmental tra-jectory

Recall that the commonly assumed developmental trajectory for children at thisstage posits that: (i) children possess the meanings of logical operators in thesteady state, and (ii) unlike adults, they do not compute implicatures. Thus, chil-dren at the relevant stage of development are expected to only access reading (4-a)whereas anyone who has matured into the steady state might access either of (4-a)or (4-b).

(4) Readings of A or B:a. Logician Reading: A ∨B (inclusive disjunction)b. Strengthened Reading = Logician Reading + not (both A and B)

Now consider a disjunction embedded under every, as in (5). Under commonassumptions about development, children will be expected to access only the read-

three out of five times. Children have been shown to sometimes have difficulties with indefinitesembedded under universal quantifiers (e.g., Inhelder and Piaget, 1964; see e.g., Philip, 1995; Crainet al., 1996; Drozd and van Loosbroek, 1998; Geurts, 2003; Gualmini et al., 2003 for more recentdiscussion), but the problem there has been that they say ‘false’ even when the sentence is true.It is not clear to us whether these issues are related, and we hope that the biases reflected in thesamples discussed here do not affect our conclusions about the sample of 31 subjects who passedthe conjunctive filter.

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ing in (5-a), whereas an adult will be expected to access either (5-a) or (5-b), withthe choice between the two depending on whether they choose to compute an SI.6

(5) Readings of Every X is A or Ba. Logician Reading: [∀x : Xx][Ax ∨Bx]b. Strengthened Reading: Logician Reading + not every X is A + not

every X is B

Thus, children will be expected to accept the disjunctive sentences in all fourof our critical conditions, because the sentence on its logician reading is true inall of these conditions. The adult – because of the possibility for computing SIs –might sometimes reject ‘Both’ and ‘Every-both’ but will have no reason to reject‘One’ or ‘Every-one.’ Thus, the adult is expected to have at least as many trueresponses on ‘One’ as on ‘Both,’ and is expected to have at least as many trueresponses on ‘Every-one’ as on ‘Every-both.’

2.4 Results: SampleOur results showed that children do not behave like logicians. A logician wouldnot differentiate between any of the four conditions, because the sentence is trueon its literal reading on all conditions. However, the following table shows thatchildren rejected ‘One’ and ‘Every-one’ more than they rejected ‘Both’ and ‘Every-both.’7

Table 1: Children’s mean number of ‘Fuzzy was right’ responses (out of 5 items)for test conditions, with 95 percent confidence interval, n = 31

Condition M (SD) 95% CIOne 1.77(1.89) [1.08, 2.46]Both 3.81(1.92) [3.51, 4.51]

Every-one 2.32(1.80) [1.66, 2.98]Every-both 3.77(1.84) [3.10, 4.44]

6We ignore embedded implicatures for the moment; the reading ‘every X is an ((A or B)and not both)’ would give the same truth-values as (5)b in both the ‘Every-one’ and ‘Every-both’condition.

7 The results are similar when the whole sample of 56 children is included. The scores (re-ported as M(SD)) for the entire sample on each condition are: (i) One: 2.45(1.94), (ii) Both:3.80(1.91), (iii) Every-one: 2.93(1.82), (iv) Every-both: 3.91(1.67).

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Indeed, a repeated-measures ANOVA showed that the within-subjects factor Con-dition was significant, F (1.58, 47.39) = 10.92, p < .001 (we violated the assump-tion of sphericity (p < .001), but we corrected for it using the Huynh-Feldt cor-rection). Of particular note are the following significant pairwise differences (allps < .01, with Bonferroni corrections for multiple comparisons): (i) ‘One’ wasaccepted less than ‘Both’: M (One) - M (Both) = -2.032 (95% CI of difference =[-3.51, -.55]), (ii) ‘One’ was accepted less than ‘Every-both’: M (One)-M (Every-both) = -2 (95% CI of difference = [-3.5, -.5]), (iii) ‘Every-one’ was accepted lessthan ‘Every-both’: M (Every-one)-M (Every-both) = -1.45 (95% CI of difference= [-2.84, -.06]), (iv) ‘Every-one’ was accepted less than ‘Every-both’: M (Every-one)-M (Every-both) = -.148 (95% CI of difference = [-2.88, -.09]).

The participants who rejected ‘One’ and ‘Every-one’ did so systematically:children who said the puppet was wrong in ‘One’ also had the tendency to saythe puppet was wrong in ‘Every-one’ (r = .47, p< .01), and children who said thepuppet was right in ‘Both’ also had the tendency to say the puppet was right in‘Every-both’ (r = .96, p< .01).8 Furthermore, these rejections are not the resultof a handful of outliers. To give a sense of the spread of the data while helpingcontrol for outliers it is often useful to consider the interquartile range (IQR) ofresponses. To determine the IQR, for each condition we order participants’ scores(out of 5) from least to greatest and find the score ranked at the first quartile Q1,the median MED, and the third quartile Q3. The range Q1-MED-Q3 locates themiddle fifty-percent of responses. The boxplot in Figure 2 displays the IQRs oneach condition, and the median score on each condition is marked with boldface(only two values are visible on ‘Both’ and ‘Every-both’ because in these casesMED = Q3 = 5):9

There are a few things the boxplot reveals. First, the bulk of participants inCondition One had lower scores than those in Both. In particular, the medianscore for ‘One’ was 1 and the median score for ‘Both’ was 5. Similar contrastsare evident between ‘Every-one’ and ‘Every-both.’ Note also that there is morespread in the responses in One, Every-One than in Both, Every-Both: Q3 − Q1

= 3 on ‘One’ and ‘Every-one,’ but Q3 − Q1 = 1 on ‘Both’ and Q3 − Q1 = 2 on‘Every-both.’ We will return to individual response patterns in greater detail insection 3, where we suggest ways of making sense of this pattern. For now, theimportant point is that these results are totally unexpected if the child differs from

8We were somewhat surprised to find no correlations between age and behaviour in any of thefour main conditions.

9The min score on each condition was always 0, and the max on each score was always 5, sowe leave that information out of the plot, and show only Q1, MED, and Q3.

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One Both Every-one Every-both0

1

2

3

4

5

IQR

ofSc

ore

Figure 2: Boxplot of interquartile range of children’s scores on each condition (n= 31; the median score on each condition is marked with boldface)

the adult only by not computing the exclusive SI inference that adults do.Turning to our adults, their behaviour was consistent with expectations (recall

that adults are characterized as having either a ‘logician’ reading, or an SI reading;see (4) and (5)).

Table 2: Adults’ mean number of ‘Fuzzy was right’ responses (out of 5 items) fortest conditions, with 95 percent confidence interval, n = 26

Condition M (SD) 95 % CIOne 3.73(1.80) [3.00, 4.46]Both 3.35(2.04) [2.53, 4.17]

Every-one 4.23(1.42) [3.66, 4.80]Every-both 3.69(1.95) [2.90, 4.48]

The scores on ‘One’ were numerically greater than the scores on ‘Both,’ andthe scores on ‘Every-one’ were numerically greater than the scores on ‘Every-both,’ but these differences were not significant (note that there is overlap in theCIs). The most likely explanation is that the subjects in our sample largely resistedcomputing SIs: eight subjects always responded ‘true’ on each of the five items ofthe four conditions (20 out of 20 trials), two subjects responded true all but once(19 out of 20 trials), and three subjects responded true all but twice (18 out of 20trials). There were only five subjects who behaved as if they often computed SIs

15

(i.e., who mostly said ‘true’ to ‘One’ and ‘Every-one’ but ‘false’ to ‘Both’ and‘Every-both’).

When we compare the 31 children to the 26 adults in our sample, we find thattheir scores differ significantly on ‘One’ and on ‘Every-one’, but do not differ on‘Both’ and do not differ on ‘Every-both.’

One Both Every-one Every-both0

1

2

3

4

5

Mea

nsc

ore

Children Adults

Figure 3: Comparing children (n = 31) and adult (n = 26) mean scores on criticalconditions (error bars indicate 95% confidence intervals)

The lack of any significant difference between children and adults on ‘Both’and ‘Every-both’ can be explained if we assume that children generally do notcompute SIs and that the adults in our sample largely did not compute SIs. How-ever, the significant difference between ‘One’ and ‘Every-one’ cannot be ex-plained by these assumptions; under these assumptions there is no obvious ra-tionale for why children should respond ‘false’ as much as they do.

3 Interpretive strategies and individual behaviourIt is clear that the children in our study, presumably like the children in previousstudies (e.g., Paris, 1973; Braine and Rumain, 1981; Chierchia et al., 2004), areemploying some interpretative strategy to disjunctions in upward-entailing con-texts that deviates from the logicians’ strategy. Moreover, this strategy is not

16

the adult strategy of computing an exclusive-disjunction implicature. Assumingthat any given sample of children might include children at the relevant stage ofdevelopment as well as some individuals who may have matured into the adultstate, under the commonly assumed Logician-to-Adult developmental trajectorywe would expect all subjects to have at least as many acceptances on ‘One’ ason ‘Both,’ and we would expect all subjects to have at least as many acceptanceson ‘Every-one’ as on ‘Every-both.’ Call a subject that satisfies this prediction an‘Expected’ participant, and call a subject that does not satisfy this prediction an‘Unexpected’ participant. In our sample, only 10 of 31 subjects (roughly 32 per-cent) behave as ‘Expected.’ A 95 percent confidence interval extends this from 17percent to 51 percent (Clopper-Pearson Exact CI for binomial proportions). Un-der this model, then, in the best-case scenario only half of pre-schoolers would beaccounted for. Something is amiss.

We believe that an examination of individual behaviour reveals important in-formation about the way children deviate from both logicians and adults. In fact,we will see that the children who deviate from these commonly assumed strategiesdo so systematically enough to cluster into various groups.

3.1 Predicting clusters from commonly assumed strategiesParticipants had five chances to say ‘true’ or ‘false’ on each of four conditions:(One, Both, Every-one, Every-both). Supposing that subjects are consistent inwhether they strengthen or not (e.g., Noveck and Posada, 2003), a logician is ex-pected to always say ‘true’ on each condition, (5,5,5,5), and an adult strengtheneris expected to always say ‘true’ to ‘One’ and ‘Every-one’ and to always say ‘false’to ‘Both’ and ‘Every-both,’ (5,0,5,0). In our sample of 31 children, we found fourLogicians and four children who might be Adult Strengtheners. Their profiles aredisplayed in Tables 3 and 4 below.

Table 3: Logicians (Predicted: (5,5,5,5))

ID Number One Both Every-one Every-both18 5 4 5 427 5 5 5 456 5 5 5 558 5 4 4 4

Mean 5 4.5 4.75 4.25

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Table 4: Adult Strengtheners (Predicted: (5,0,5,0))

ID Number One Both Every-one Every-both7 4 0 2 0

15 3 2 3 257 3 0 3 060 5 0 5 0

Mean 3.75 0.5 3.25 0.5

Another conceivable strategy is to accept a sentence if it is both true and fe-licitous and reject it otherwise (e.g., Katsos and Bishop, 2011; Clark and Amaral,2010). Thus, taking adult judgments as representative, the boy is holding an appleor a banana is odd in both ‘One’ and ‘Both,’ and every boy is holding an appleor a banana is odd in ‘Every-both’ but not in ‘Every-one.’ Perhaps this patternof oddness is rooted in the fact that the disjunctive sentence leads to misleadinginferences in ‘One, Both, Every-both’ but not in ‘Every-one.’10 Under a strategythat penalizes oddness, call it ‘Oddness-based,’ the expected profile is (0,0,5,0).We found two participants that might to have approximated this strategy:11

Table 5: Oddness-based (Predicted: (0,0,5,0))

ID Number One Both Every-one Every-both12 0 0 1 051 0 0 3 0

Mean 0 0 2 0

Supposing the classification in Tables 3-5 to be reasonable for the moment,we are still left with 21 out of 31 subjects who resist classification under commonassumptions. However, suppose that we admit the possibility that some children

10In the atomic case the sentence suggests that the speaker does not know whether the boy isholding an apple and does not know whether the boy is holding a banana, while in the embeddedcase the sentence suggests that the speaker does not believe that every boy is holding an apple anddoes not believe that every boy is holding a banana.

11Participant 12’s score on ’Every-one’ seems far from the idealized score of 5, but note that theoverall profile is quite accurate, and in fact out of all theoretically motivated clusters Participant12 fits best into Table 5 (see note 12). Whether the classification is appropriate or not is notentirely germane to our main point. We could just as well posit another category, ‘unclassifiable,’into which Participant 12 would fall; this would merely increase the difficulty for the classicalanalysis, for it would add yet another unexplained participant.

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have a strategy at hand that allows them to interpret disjunctive sentences con-junctively. Indeed, participants’ justifications for their rejection of A ∨ B whenjust one disjunct was true (A, say) systematically indicated a conjunctive inter-pretation. We collected 45 such justifications from participants at the end of theexperiment, and after excluding uninformative responses (e.g., ‘because Fuzzy(the puppet) was wrong’), 23 responses were of the form ‘because only/just A,’10 were of the form ‘because not B’, 5 were of the form ‘because A’ (here Aseems to be covertly exhaustified). These justifications make sense if these chil-dren are interpreting the relevant sentences conjunctively.

For reasons that will become clear in the next section, call the group of partici-pants generating a conjunctive reading ‘Child-Free-Choice’ (CFC). The predictedprofile of CFC subjects is (0,5,0,5). Assuming the CFC strategy to be available, itturns out that 16 of the remaining 21 subjects can be classified as ‘signal’ ratherthan ‘noise’:

Table 6: Child Free-Choice (Predicted: (0,5,0,5))

ID Number One Both Every-one Every-both4 2 5 2 48 0 5 2 59 1 5 0 5

21 0 5 2 522 2 4 1 323 0 5 1 528 2 4 2 536 0 5 0 542 0 5 2 545 0 5 0 552 2 5 2 553 4 5 0 554 1 5 0 574 0 5 0 575 3 5 1 486 0 1 0 3

Mean 1.06 4.63 0.94 4.63

For the moment, ‘CFC’ is just a label for the group of participants in our study.We furthermore expect that an analysis of individual behavior would reveal CFC

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groups in Paris (1973), Braine and Rumain (1981), and Chierchia et al. (2004).What is needed is a way to make sense of the CFC strategy. Ideally, what weshould like is a general strategy which outputs conjunction when applied to dis-junctive sentences in upward monotone environments, and otherwise returns thebasic meaning when a disjunction is in the scope of a DE operator or when thestrategy applies to other logical operators like some.

We will argue in the following section that this pattern can be explained with-out positing ad-hoc strategies for the case at hand. Instead, we propose a conserva-tive explanation of the child’s behaviour that merely reuses existing assumptionsabout child development and assumptions about strengthening in the steady state.Specifically, if the child is able to compute free-choice inferences using a strength-ening mechanism such as that proposed in Fox (2007), Chemla (2009b), or Franke(2011), we will see that two profiles are predicted that are not available under theLogician-Adult-Oddness strategies: (i) CFC, which we saw to be the majority inour sample, and (ii) what we will here call Child-Free-Choice II (CFCII), whichresults in a (0,5,5,5) pattern. It turns out that the remaining five children in oursample followed the CFCII profile:12

Table 7: Child Free-Choice II (Predicted: (0,5,5,5))

ID Number One Both Every-one Every-both5 0 5 4 5

19 1 5 4 526 0 5 4 531 1 4 4 455 1 5 5 5

Mean 0.6 4.8 4.2 4.8

12We subjected our data, the individual child vectors, to the ‘k-means clustering’ algorithmto examine which clusters would be found. The algorithm optimizes an objective function: itclusters points so as to minimize distance within each cluster, with an initialization of k clusterstogether with their centroids. We initialized with the five theoretically motivated ideal clustershighlighted above (Oddness-based, Logician, CFC, CFC II, Adult-Strengthener). The algorithmproduced exactly our clusters identified above, with cluster centers corresponding to the means ofeach cluster.

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4 An explanation of CFC and CFCII: Ambiguityand free-choice

In this section we spell out assumptions about child development and about thesteady-state that account for the existence of groups like CFC and CFCII, as wellas their prevalence (21/31 participants in our sample). The assumptions we makeabout development are (i) that the child accesses a specific subset of the adultalternatives, and (ii) that the child possesses the adult strengthening mechanism,EXH . The assumption about the steady state is that EXH is responsible forfree-choice inferences, and in particular EXH derives conjunctive inferences fordisjunctive sentences whenever the alternatives of the sentence are not closed un-der conjunction (Fox, 2007; Chemla, 2009b; Franke, 2011).

4.1 AlternativesWe assume that alternatives in the steady state are generated by a sequence of thefollowing operations (simplified version of Katzir, 2007):

(6) Alternatives in the steady state: (i) Replace nodes withtheir sub-constituents or other salient constituents, (ii) Replace terminalswith other lexical items

Under this assumption, the alternatives forA∨B in the steady state are: ALTAdult(A∨B) = {A,B,A ∧B}.

It has been argued that children do not perform scalar replacements (e.g.,Chierchia et al., 2001; Gualmini et al., 2001; Reinhart, 2006; Barner and Bachrach,2010; Barner et al., 2011; Stiller et al., 2011). For example, with the focus-sensitive operator only, children will reject only some of the animals are sleepingas a description of a picture in which all of the animals are sleeping (Barner et al.,2011). This can be explained if the child is unable to perform lexical replace-ments; with this assumption, all of the animals are sleeping cannot be generated,and thus only is vacuous. However, Barner et al. (2011) provide evidence thatwhen the alternatives are explicitly provided, the child rejects only the dog andthe cat are sleeping when the dog, the cat, and the pig are all sleeping.

What this suggests is that the child cannot yet perform lexical replacementsbut can access explicitly mentioned material.

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(7) Alternatives in the child: (i) Replace nodes with their sub-constituents or other salient constituents, (ii) Replace terminals with otherlexical items

Under this assumption, the child’s alternatives for A∨B are: ALTChild(A∨B) ={A,B}. Note the following important difference between disjunctions and ∃.Assuming for the moment that the only alternative for ∃ in the adult is ∀, the childcould not produce this alternative because it can only be generated with lexicalreplacement. Thus, no strengthening is possible with ∃. However, because theset of alternatives for A ∨ B in the child is non-empty, there is in principle thepossibility of some kind of strengthening. Our claim is that the child exploits thispossibility – it uses the constituents A and B and concludes (by a method weintroduce below) that both must be true.

4.2 The connection to free-choiceConsider the sentence in (8), together with its standard LF in (8-a) and the free-choice inference it receives in (8-b).

(8) You’re allowed to eat the cake or ice-creama. LF: 3(A ∨B) (⇐⇒ 3A ∨3B)b. FC inference: You’re allowed to eat the cake and you’re allowed to

eat the ice-cream (3A ∧3B) .

The free-choice inference does not follow from the semantics of (8-a) under stan-dard assumptions about the meanings of allowed and or (though cf. Geurts,2000; Zimmerman, 2000). Furthermore, the free-choice inference is unavailablein downward-entailing contexts. For example, no one is allowed to eat the cake orice-cream does not mean that no one has free-choice. Thus, it has been argued thatfree-choice inferences are the result of SI computation (Kratzer and Shimoyama,2002; Schulz, 2005; Alanso-Ovalle, 2005).

Recent theories of strengthening with otherwise quite different architectureshave converged on the idea that free-choice inferences follow from applicationof the strengthening function EXH to (8-a) (Fox, 2007; Chemla, 2009b; Franke,2011). We refer readers to the original sources for details. What they share incommon in deriving this result is a connection between the alternatives of a dis-junctive sentence and the availability of a conjunctive SI for the sentence:

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(9) Closure and Free-choice: Suppose p is a sentence that entailsq ∨ r, and that p does not entail q ∧ r and q, r ∈ ALT (p). Then:a. If q ∧ r ∈ ALT (p), then p can never be strengthened to entail q ∧ r:

EXH(p) will never entail q ∧ r.b. If q ∧ r 6∈ ALT (p), then under certain circumstances p could be

strengthened to q ∧ r: EXH(p) could sometimes entail q ∧ r.13

In the appendix we illustrate with the special case of p = A ∨B and the iden-tification of EXH with Fox’s (2007) strengthening mechanism. Briefly, whenEXH is identified with the covert exhaustive operator exh defined in Fox (2007),the parse exh(exh(A ∨ B)) – given the child alternatives – is equivalent to aconjunction A ∧ B, much like exh(exh(3(A ∨ B)) with the adult alternatives isequivalent to the free-choice inference 3A ∧3B.

For our purposes, what (9) buys us is a simple way to check for a disjunctivesentence whether a conjunctive strengthening is possible: if the sentence has aconjunctive alternative, this suffices to ‘block’ a conjunctive SI, otherwise a con-junctive SI might be associated with the sentence. For example, ALTAdult(A∨B)is closed under conjunction: A and B are both in the set and their conjunctionA ∧B is as well; thus, no conjunctive SI is possible in the steady state. However,the alternatives for 3(A ∨ B) for the adult are not closed under conjunction: 3Aand 3B are in the set, but their conjunction 3A∧3B is not. The alternatives for3(A∨B) are: ALTAdult(3(A∨B)) = {3A,3B,3(A∧B)}. It follows from (9)that the conjunction of the two constituent alternatives is a possible strengthenedmeaning of the sentence, 3A ∧3B, which is precisely the free-choice inferencein (8-b).

Children are unable to perform lexical replacements, and hence their alterna-tives for A ∨ B are: ALTChild(A ∨ B) = {A,B}. Because the conjunction ofthese alternatives is not itself an alternative, (9) predicts that a conjunctive infer-ence should be available. In fact, the child’s alternatives for 3(A ∨ B) are suchthat they are not closed under conjunction: ALTChild(3(A ∨ B)) = {3A,3B};hence, a free-choice inference 3A ∧ 3B should be available to the child. Thisprediction has been confirmed (Zhou et al., 2013).

Thus, CFC children are explained by the assumption that they strengthen A ∨B to A ∧ B by (9). What about disjunctions that are embedded under every?

13In the general case the possibility of conjunctive strengthening will depend on the makeupof ALT (p) (see Fox, 2007). In the cases under consideration here, where ALT (p) is computedusing (6) in the adult and using (7) in the child, the absence of a conjunctive alternative ensuresthat application of EXH yields a conjunctive strengthening.

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Assuming Fox’s (2007) approach for present purposes, because exh is realized inthe grammar as an unpronounced operator, it should apply in embedded positionsas well. Recursive application of exh below every but above disjunction capturesthe embedded conjunctive strengthening: every boy x, exh(exh(x is holding anapple or a banana)) is equivalent to ‘every boy is holding an apple and a banana’when the alternatives for the embedded disjunction are the child’s alternatives.14

What about the CFCII group? This differs from CFC only in the ‘Every-one’condition: children in CFC reject ‘Every-one’ and children in CFCII accept it. Atthe same time, given CFCII’s rejection of ‘One,’ they must be strengtheners. InFox’s (2007) system, this follows from the possibility of parsing the sentence witha single embedded exh and a single exh at the root. The conceptual and empiricalconsequences of having such a parse available in the steady state are explored indetail in Crnic et al. (2013); here we examine the consequences for children at therelevant stage of development. The meaning of this sentence is the conjunction ofthe literal meaning + not every X is just an A + not every X is just a B.15,16 This

14For Chemla (2009b) and Franke (2011), EXH is not grammatical but is shorthand for asequence of inferences computed globally. The conjunctive reading can be explained, however,if children are assumed to prefer a ‘wide-scope’ construal of disjunction, such that every X is Aor B is parsed as every X is A or every X is B; under this construal (9) becomes relevant, andthe conjunctive inference every X is A and every X is B ( ⇐⇒ every X is A and B) is produced(thanks to Emmanuel Chemla and Jacopo Romoli for suggesting this possibility). Note that thisgoes against common assumption that children have a preference for surface scope. Wide-scopereadings for disjunction have been found in children of some languages (e.g., Japanese), but theseseem to be connected to the PPI status of disjunction in these languages (e.g., Goro and Akiba,2004).

15If the sentence is something like every boy is holding an apple or a banana, the requiredparse is: exh(C ′)(every boy x, exh(C)(x is holding an apple or a banana)). The alternatives Cfor the embedded occurence of exh are just the child alternatives for a disjunction x is holdingan apple or a banana: C = {x is holding an apple, x is holding a banana}. Thus, the embeddedoccurrence of exh is vacuous; as noted in the appendix, application of exh on a disjunction withthe child alternatives does not change the meaning of the disjunction. The embedded exh does,however, affect the alternatives C ′ of the higher exh: C ′ = {[every boy x, exh(C)(x is holdingan apple)], [every boy x, exh(C)(x is holding a banana)]} = {that every boy is holding an appleand not a banana, that every boy is holding a banana and not an apple}. We leave it to the readerto verify that exh(C ′)(every boy x, exh(C)(x is holding an apple or a banana)) with alternativesC ′ and C identified here gives rise to the meaning paraphrased in the main text. See Crnic et al.(2013) for parsing assumptions that make it natural to expect groups like CFC II (cf. Table 7), aswell as for experimental evidence that such groups are attested among adult populations.

16For the globalist systems of Chemla (2009b) and Franke (2011), the CFCII pattern followsfrom a narrow-scope construal of the sentence: every X is A or B does not entail every X is A orevery X is B, and thus (9) is not relevant and no strengthening can take place.

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interpretation is true in both ‘Every-one’ and ‘Every-both.’Thus, we see that prior theoretical proposals give rise to five natural interpre-

tation strategies, all of which were attested in our sample. When we examine theclusters, we see that the CFC cluster was dominant; 16/31 participants ended upin that cluster. Why?

4.3 A note on preferencesLanguage comprehension is a complex task, and a variety of different consider-ations might be at play when clear preferences among competing interpretationof a linguistic stimulus are attested. Such considerations might include linguis-tic complexity (e.g., Miller and Chomsky, 1963; Frazier and Fodor, 1978; Fordet al., 1982; Gibson, 1998, 2000, inter alia), plausibility judgments (e.g., Crainand Steedman, 1985; Trueswell et al., 1994; Stolcke, 1995; Jurafsky, 1996; Good-man and Stuhlmuller, 2013, inter alia), preferences for parses that best answer thequestion under discussion (e.g., Gualmini et al., 2008), preferences for strongermeanings (possibly related to other interpretive strategies, e.g., Dalrymple et al.,1998), computation-storage tradeoffs (e.g., Johnson et al., 2007; O’Donnell et al.,2011), and many other factors that have been proposed in the psycholinguistic lit-erature. Our present concern is that, of the five theoretically motivated strategiesdiscussed above, one – the CFC strategy – was dominant.

(10) Observed distribution of subjects classified into predicted profiles

(0,5,0,5)

(0,5,5,5)

(5,5,5,5)

(5,0,5,0)

(0,0,5,0)

Number of participants

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The plot in (10) shows that the (0,5,0,5) group (the CFC group) attracted thegreatest number of participants. This looks different from what would be expectedof a model in which subjects fall into one or another group by chance. Under sucha model, with 31 participants and 5 idealized profiles, we would expect some-thing around 6.2 participants in each profile. The difference between the observedfrequencies of profiles and that expected from chance is summarized in the tablebelow.

(11) Expected (under chance) and observed frequencies of profilesFrequencies (0,5,0,5) (0,5,5,5) (5,5,5,5) (5,0,5,0) (0,0,5,0)

Expected 6.2 6.2 6.2 6.2 6.2Observed 16 5 4 4 2

A chi square was computed comparing the frequencies of actual and expectedoccurrences of the different profiles, and an extremely significant difference wasfound between the observed and expected values (χ2(4, n = 31) = 20.13, p =.0005). Recall that the CFC group computes matrix and embedded free-choice. Itmight thus be unsurprising that a preference for matrix (Chemla and Bott, 2014)and embedded (Chemla, 2009c) free-choice has been found in adults as well. Wecan thus state a generalization both for children and adults: there is a preferencefor free-choice in matrix positions and in embedding under every.17 The questionwe would like to ask is why there should be this preference for free-choice, bothin matrix positions and in embedding under every, both for children and adults.

We would like to tentatively suggest, following Gualmini et al. (2008), that thereadings of an ambiguous sentence can be ordered by how well they answer the(often implicit) question under discussion (QUD; cf. Groenendijk and Stokhof,1984; Lewis, 1988; Roberts, 1996). Specifically, they suggested that under therelevant ordering a complete answer will be preferred, if available.18 It seemsreasonable in the context of the picture-matching task to construe a sentence like

17As pointed out by Chemla (2009c), this might seem odd since there is no general preferencefor embedded exhaustification (see Geurts and Pouscoulous, 2009; Chemla and Spector, 2011).One of the goals of this section is to provide a way of thinking about the relevant preference thatwould make sense of this otherwise puzzling state of affairs.

18Following Groenendijk and Stokhof (1984), Lewis (1988), Roberts (1996), and others, theQUD is taken to be a partition of logical space or of the common ground, where the cells are thecomplete answers to the question. A partial answer to the QUD is a union of cells in the partition,and answers can be ordered in terms of goodness: an answer p is ‘better’ than another answer q ifp ⊂ q. From this it follows that the speaker’s best move is to identify for the hearer which cell ofthe partition is the true one.

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the boy is holding an apple or a banana as an answer to the question, What is theboy holding? Similarly, in many contexts it is reasonable to construe a sentencelike the boy is allowed to eat an apple or a banana as an answer to the question,What is the boy allowed to eat? Finally, it is reasonable to construe a sentence likeevery boy {ate/is allowed to eat} an apple or a banana as an answer to the pair-listmeaning of the question, what did every boy eat/what is every boy allowed to eat?Focusing on children at the relevant developmental stage, these questions are bestanswered by the doubly-exhaustified parse selected by the CFC group, for thisparse provides the complete answer that the boy ate an apple and a banana in theatomic case, and that every boy ate an apple and a banana in the quantified case.19

In the atomic case a parse without exh would leave open whether the boy ate anapple and whether the boy ate a banana, and in the quantified case, a parse withoutexh would leave open what each boy ended up eating. Our tentative suggestion,then, is that parsing preferences might follow from the more general assumptionthat speakers provide the best answer to the QUD; this general preference leads, inthe cases under consideration here, to a preference for conjunctive interpretationsof disjunctive sentences when the alternatives are not closed under conjunction.This leads to conjunctive inferences in the child, and to free-choice inferences inthe adult.

5 Concluding RemarksWe replicated findings from Paris (1973), Braine and Rumain (1981), and Chier-chia et al. (2004) showing that children sometimes interpret disjunctions as con-junctions, and we extended this result to embedding under every. We used thisresult to advance the view that (i) children at the relevant stage of developmenthave acquired the inclusive disjunction semantics of or, as shown in previousstudies (e.g., Chierchia et al., 2001; Gualmini et al., 2001; Crain, 2008; Crain andKhlentzos, 2010) and (ii) children have acquired the basic mechanism for comput-ing implicatures, EXH . Under our proposal children differ from adults only inthe alternatives they generate (e.g., Chierchia et al., 2001; Gualmini et al., 2001;Reinhart, 2006; Barner and Bachrach, 2010; Barner et al., 2011), and hence alsoin the implicatures they compute. We localized the difference to lexical access inthe generation of alternatives, and showed that this difference allows the child togenerate a conjunctive scalar implicature using the same mechanism adults use to

19None of these points change if there are other answers in the Hamblin denotation (e.g., thatthe boy ate/is allowed to eat a strawberry). These other propositions will all get negated.

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derive free-choice inferences (Fox, 2007; Chemla, 2009b; Franke, 2011).20 Wecharacterized this parallel between the developmental and steady state with (9); itseems that whenever (9) becomes relevant, the child and the adult prefer to take theoption to strengthen the sentence to a conjunction, a preference that we tentativelysuggested might follow from a general preference to resolve the question-under-discussion. This is to be understood as a strictly conversational preference that isnot specific to exh.

An immediate consequence of this parallel is that we should expect children(and adults) to have the possibility of generating conjunctive inferences of dis-junctive sentences when the alternatives are not closed under conjunction. Onenotable prediction along these lines is that children should compute free-choiceSIs, since their set of alternatives for 3(A ∨ B) is not closed under conjunction:under (7), ALTChild(3(A ∨ B)) = {3(A ∨ B),3A,3B}. As we noted in sec-tion 4.2, this expectation has been confirmed (see Zhou et al., 2013). Negatedconjunctions ¬(A ∧ B) are another case of this kind. Note that ¬(A ∧ B) ⇐⇒(¬A ∨ ¬B), and that under our proposal the child’s alternatives for this sentenceare: ALTChild(¬(A ∧ B)) = {¬A,¬B}. Thus, because of (9), we again ex-pect this sentence to receive the conjunctive interpretation ¬A ∧ ¬B. Jacopo Ro-moli, who pointed out this prediction (personal communication), reports a studyby Anna Notley showing that children do indeed generate such ‘wide-scope con-junction’ interpretations. We would also expect children to assign free-choice in-terpretations under every in the same way that adults do (Chemla, 2009a); indeedour explanation for the child’s behavior on ‘Every-one’ and ‘Every-both’ relies onthis assumption.

The connection between the child and the adult through (9) seems to be trans-parently realized in other languages. Specifically, American Sign Language (David-son, 2013) and Warlpiri (Bowler, 2014) have been analyzed as encoding a singlebinary connective that is ambiguous between inclusive disjunction and conjunc-

20We will leave it to future work to dissociate these proposals, however our remarks in note14 suggest that what is needed are environments in which local strengthening effects cannot bemimicked through global reasoning. In particular, embeddings under which (9) does not applyglobally are crucial test cases; in such environments, an embedded disjunction could still getstrengthened to a conjunction under Fox (2007) but the sentence could not receive a conjunctivestrengthening under Chemla (2009b) or Franke (2011). Such environments can be created, forexample, by embedding a disjunction under most, or by fixing the scope of disjunction underevery with the judicious placement of either (e.g., Larson, 1985; Schwarzschild, 1999). When wedo this, embedded free-choice readings in the adult continue to be available: most of the boys areallowed to eat cake or ice-cream suggests that most of the boys have free-choice, and every boy isallowed to either eat cake or ice-cream suggests that every boy has free-choice.

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tion. Bowler (2014) moreover shows that under negation only the inclusive dis-junction meaning is available. This description sounds a lot like preschool chil-dren, and is exactly what is expected if the connective in these languages is indeedlexicalized as an inclusive disjunction which gets strengthened to a conjunction.21

The strengthening here is expected because without and in the language no con-junctive alternative can be formed, and from (9) it follows that in such languagesa single connective should do double-duty between inclusive-disjunction and con-junction, much like the way English or seems to do double-duty between inclusiveand exclusive disjunction in the steady state.22

If we are right that children’s purported difficulties with implicature computa-tion reduce to the single operation of lexical replacement, then children’s observedresistance to computing implicatures is a historical accident stemming from useof sentences whose implicatures require access to the lexicon (e.g., ∃; ¬∀). Byexploiting the current understanding of alternatives and implicatures in complexsentences, children are better described as being both willing and able to computeimplicatures, sometimes resulting in inferences that are unavailable in the steadystate.

A Appendix

A.1 Sample computationHere we highlight important steps in the computation of a conjunctive meaningfor A∨B with the child alternatives C = {A,B}. Formal definitions that support

21Bowler (2014) provides evidence of this interpretation of the Walpiri facts (following ouraccount of the child data). Davidson (2013) provides a different interpretation of the ASL facts.Whether our interpretation can be extended to ASL is something that we will have to leave to futureresearch. See also Meyer (2013) for an argument that conjunctive entailments in certain Englishor-else constructions also follow for similar reasons (the conjunctive alternative is missing).

22This line of reasoning is in the spirit of Horn (1972), who noted a tight connection betweenthe lexicalization of logical operators and strengthening. On the one hand, when apparent ambigu-ities in logical inventories are not lexicalized, one of the readings – the strengthened one – can bedescribed as the conjunction of the weak literal meaning and its SI, and the SIs that get computedare sensitive to what has been lexicalized in the language. At the same time, the possibility ofstrengthening is a factor in restricting the inventory of simplex operators in natural language (seealso Katzir and Singh, 2013); for example, if the strengthened meaning of p is q, there is no needto lexicalize q. For these and other reasons mentioned above (e.g., behaviour in DE contexts), anexplanation of conjunctive interpretations of disjunctive sentences in terms of strengthening seemsmore explanatory than one in terms of lexicalization ambiguities or difficulties.

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these computations are given in (13) and (14) below.The conjunctive reading is derived with two applications of exh:

(12) Parse of sentence: exh2(C2)(exh1(C1)(A ∨B)).

The set of alternativesC1 for exh1 is {A,B}. When exh is appended to a sentenceit tries to negate as many of the sentence’s alternatives as it can while maintainingconsistency with the sentence. In (12), it tries to negate as many elements of C1

as it can while maintaining consistency with A∨B. However, the elements of C1

can’t both be negated because the result would be inconsistent, and negation ofone would force you to accept the other. Hence, neither A nor B is ‘innocentlyexcludable’ (see (14) below), and hence nothing can be negated at this stage: themeaning of exh1(C1)(A ∨B) is just the inclusive disjunction.

At the second level of exhaustification, exh2, the alternatives are: C2 ={exh1(C1)A, exh1(C1)B}. This set is derived by replacingA∨B with its alterna-tivesA,B in the sentence exh(C1)(A∨B). Thus,C2 = {exh1(C1)A, exh1(C1)B} ={A∧¬B,B ∧¬A}. exh2 tries to negate as many alternative in C2 as it can whilemaintaining consistency with exh1(C1)(A ∨ B) ( ⇐⇒ A ∨ B), and it turns outit can negate both alternatives at once: (A ∨ B) ∧ ¬(A ∧ ¬B) ∧ ¬(B ∧ ¬A) isequivalent to A∧B. (What the sentence asserts, therefore, is: A∨B and ‘not justA’ and ‘not just B;’ recall that the most prominent justification children gave forrejection was ‘just A’).

When C = ALTAdult(A ∨ B) = {A,B,A ∧ B} the parse exh(C)(A ∨ B) isequivalent to (A ∨ B) ∧ ¬(A ∧ B). This is because exh(C)(S) always entails S,and in this case there are two ‘maximal consistent exclusions’ (see (14) below forformal definitions): (i) {A,A∧B}, (ii) {B,A∧B}. The intersection of these setsis {A ∧ B}; thus A ∧ B is the only ‘innocently excludable’ alternative (see (14)below), and this is the SI. Further exhaustification is vacuous (Fox, 2007).

A.2 Formal definitionsLet S be an arbitrary sentence uttered in an arbitrary context c, and let [[S]] be thesemantic interpretation of S.

(13) Alternatives in the adult grammar (Katzir, 2007, Fox and Katzir, 2011):a. Formal Alternatives: The formal alternatives of S are derived by

a function, ALT , such that ALT (S, c) is the set containing sen-tences derived from S by successive substitution of focus-marked

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constituents of S from the substition source of S in c, SS(S, c).b. Substitution Source: Y ∈ SS(X, c) iff (i) Y is a constituent of a

focus-marked constituent ofX , (ii) Y has been explicitly mentionedin c, (iii) Y is a lexical item.

c. Actual Alternatives: Where Rc is the set of relevant sentences in c,the actual alternatives of S in c, A(S, c) = Rc ∩ ALT (S, c)

(14) The semantics of exh (Fox, 2007): Where c is the context of assertion,A(S, c) is the set of actual alternatives of S in c, and exh(A(S, c))(S) isthe LF that is used in context c:a. [[exh(A(S, c))(S)]] = [[S ∧

∧{¬Si : Si ∈ IE(A(S, c))}]]

b. Innocent Exclusion: The set of innocently excludable alternativesof A(S, c), IE(A(S, c)), is the intersection of the set of MaximalConsistent Exclusions of A(S, c).

c. Maximal Consistent Exclusion: A Maximal Consistent Exclusion ofA(S, c) is a set B such that: (i) B ⊆ A(S, c), (ii) S ∧ (

∧{¬Si : Si ∈

B}) is consistent, (iii) S∧(∧{¬Si : Si ∈ B})∧¬Sj is inconsistent,

for any Sj ∈ A(S, c) \B.

A.3 A possible concern about pruningIn general it is known that context can sometimes restrict the set of formal alter-natives by eliminating all those formal alternatives that are irrelevant (Horn, 1972,Rooth (1992), Fox and Katzir (2011), cf. (13-c)). If context could arbitrarily prunealternatives, we might expect conjunctive SIs A ∧ B to arise in the adult state bypruning A ∧ B. We assume that this pruning is impossible. Specifically, we as-sume following Fox and Katzir (2011) that pruning involves the choice of a subsetof relevant alternatives (see (13)) and that relevance is closed under conjunction(if A is relevant and B is relevant then A ∧B is relevant). This assumption aboutrelevance follows from the idea that the set of relevant propositions is determinedby a ‘partition’ of logical space (or of the common ground), and more specificallyfrom the idea that a sentence is relevant if its denotation, a set of possible worlds,is a union of cells in the partition (Groenendijk and Stokhof, 1984; Lewis, 1988).The reader can verify that this closure condition prevents the adult from pruningA ∧ B from ALT (A ∨ B), but does not prevent them from pruning 3(A ∧ B)from the set ALT (3(A ∨ B)). The latter pruning does not prevent free-choice;the set of alternatives isn’t closed under conjunction either way.

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ReferencesLuis Alanso-Ovalle. Distributing the disjuncts over the modal space. In Leah

Bateman and Cherlon Ussery, editors, Proceedings of the North East LinguisticSociety (NELS) 35. GLSA, 2005.

David Barner and Asaf Bachrach. Inference and exact numerical representationin early language development. Cognitive Psychology, 60:40–62, 2010.

David Barner, Neon Brooks, and Alan Bale. Accessing the unsaid: The role ofscalar alternatives in children’s pragmatic inference. Cognition, 118:87–96,2011.

Margit Bowler. Conjunction and disjunction in a language without ‘and’. Pre-sented at SALT 24, NYU, 2014.

Martin D.S. Braine and Barbara Rumain. Development of comprehension of ‘or:’Evidence for a sequence of competencies. Journal of Experimental Child Psy-chology, 31:46–70, 1981.

Emmanuel Chemla. Presuppositions of quantified sentences: Experimental data.Natural Language Semantics, 17:299–340, 2009a.

Emmanuel Chemla. Similarity: Towards a unified account of scalar implicatures,free choice permission, and presupposition projection. Under Revision for Se-mantics and Pragmatics, 2009b.

Emmanuel Chemla. Universal implicatures and free choice effects: Experimentaldata. Semantics and Pragmatics, 2:1–33, 2009c.

Emmanuel Chemla and Lewis Bott. Processing inferences at the seman-tics/pragmatics frontier: Disjunctions and free choice. Cognition, 130:380–396,2014.

Emmanuel Chemla and Benjamin Spector. Experimental evidence for embeddedscalar implicatures. Journal of Semantics, 28:359–400, 2011.

Gennaro Chierchia, Stephen Crain, Maria Teresa Guasti, Andrea Gualmini, andLuisa Meroni. The acquisition of disjunction: Evidence for a grammatical viewof scalar implicatures. In Proceedings of BUCLD25, pages 157–168. 2001.

32

Gennaro Chierchia, Maria Teresa Guasti, Andrea Gualmini, Luisa Meroni,Stephen Crain, and Francesca Foppolo. Semantic and pragmatic competence inchildren’s and adults’ comprehension of Or. In Ira A. Noveck and Dan Sper-ber, editors, Experimental Pragmatics, pages 283–200. Palgrave, New York,NY, 2004.

Eve V. Clark and Patricia Matos Amaral. Children build on pragmatic informationin language acquisition. Language and Linguistics Compass, 4:445–457, 2010.

Stephen Crain. The interpretation of disjunction in Universal Grammar. Languageand Speech, 51:151–169, 2008.

Stephen Crain and Drew Khlentzos. The logic instinct. Mind & Language, 25(1):30–65, 2010.

Stephen Crain and Cecile McKee. The acquisition of structural restrictions onanaphora. In Proceedings of NELS 15, pages 94–110. GLSA, Amherst, MA,1985.

Stephen Crain and Mark Steedman. On not being led up the garden path: theuse of context by the psychological syntax processor. In David R. Dowty, LauriKarttunen, and Arnold Zwicky, editors, Natural Language Parsing: Psycholog-ical, Computational, and Theoretical Perspectives, pages 320–358. CambridgeUniversity Press, Cambridge, 1985.

Stephen Crain and Rosalind Thornton. Investigations in Universal Grammar: AGuide to Experiments in the Acquisition of Syntax and Semantics. MIT Press,Cambridge, MA, 1998.

Stephen Crain, Rosalind Thornton, Carole Boster, Laura Conway, Diane Lillo-Martin, and Elaine Woodams. Quantification without qualification. LanguageAcquisition, 5(2):83–153, 1996.

Luka Crnic, Emmanuel Chemla, and Danny Fox. Scalar implicatures of embeddeddisjunctions. Unpublished manuscript, HUJI and ENS and MIT, 2013.

M. Dalrymple, M. Kanazawa, Y. Kim, S. Mchombo, and S. Peters. Reciprocalexpressions and the concept of reciprocity. Linguistics and Philosophy, 21:159–210, 1998.

33

Kathryn Davidson. ‘and’ and ‘or’: General use coordination in ASL. Semanticsand Pragmatics, 6:1–44, 2013.

Kenneth Drozd and Erik van Loosbroek. Weak quantification, plausible dissent,and the development of children’s pragmatic competence. In Proceedings of theTwenty-Third Boston University Conferene on Language Development, pages184–195. Somerville, MA, 1998.

Marilyn Ford, Joan Bresnan, and Ronald M. Kaplan. A competence-based theoryof syntactic closure. In Joan Bresnan, editor, The Mental Representation ofGrammatical Relations, pages 727–796. MIT Press, Cambridge, MA, 1982.

Danny Fox. Free choice disjunction and the theory of scalar implicature. In UliSauerland and Penka Stateva, editors, Presufofopposition and Implicature inCompositional Semantics, pages 71–120. Palgrave Macmillan, New York, NY,2007.

Danny Fox and Roni Katzir. On the characterization of alternatives. NaturalLanguage Semantics, 19:87–107, 2011.

Danny Fox and Benjamin Spector. Economy and embedded exhaustification.Handout, MIT and Harvard University/ENS, 2008.

Michael Franke. Quantity implicatures, exhaustive interpretation, and rationalconversation. Semantics and Pragmatics, 4(1):1–82, June 2011.

Lyn Frazier and Janet D. Fodor. The Sausage Machine: A new two-stage parsingmodel. Cognition, 6:291–325, 1978.

Hans G. Furth, James Youniss, and Bruce M. Ross. Children’s utilization of log-ical symbols: An interpretation of conceptual behavior based on piagetian the-ory. Developmental Psychology, 3(1):36–57, 1970.

Gerald Gazdar. Pragmatics. Academic Press, New York, NY, 1979.

Bart Geurts. Buoyancy and strength. Journal of Semantics, 17:315–333, 2000.

Bart Geurts. Quantifying kids. Language Acquisition, 11:197–218, 2003.

Bart Geurts. Scalar implicature and local pragmatics. Mind and Language, 24:51–79, 2009.

34

Bart Geurts and Nausicaa Pouscoulous. Embedded implicatures?!? Semanticsand Pragmatics, 2:1–34, 2009.

Edward Gibson. Linguistic complexity: Locality of syntactic dependencies. Cog-nition, 68:1–76, 1998.

Edward Gibson. The dependency locality theory: A distance-based measure oflinguistic complexity. In Y. Miyashita, A. Marantz, and W. O’Neil, editors,Image, Language, Brain, pages 95–126. MIT Press, Cambridge, MA, 2000.

Noah D. Goodman and Andreas Stuhlmuller. Knowledge and implicature: Mod-eling language understanding as social cognition. Topics in Cognitive Science,5:173–184, 2013.

Takuya Goro and Sachie Akiba. The acquisition of disjunction and positive po-larity in japanese. In G. Garding and M. Tsujimura, editors, Proceedings ofWCCFL 23, pages 101–114. Cascadilla Press, Somerville, MA, 2004.

Jeroen Groenendijk and Martin Stokhof. Studies on the semantics of questions andthe pragmatics of answers. Doctoral Dissertation, University of Amsterdam,1984.

Andrea Gualmini, Stephen Crain, Luisa Meroni, Gennaro Chierchia, andMaria Teresa Guasti. At the semantics/pragmatics interface in child language.In Proceedings of SALT 11, pages 231–247. 2001.

Andrea Gualmini, Sarah Hulsey, Valentine Hacquard, and Danny Fox. Thequestion-answer requirement for scope assignment. Natural Language Seman-tics, 16:205–237, 2008.

Andrea Gualmini, Luisa Meroni, and Stephen Crain. An asymmetric universalin child language. In Matthias Weisgerber, editor, Proceedings of Sinn undBedeutung 7, pages 136–148. Konstanz, 2003.

Maria Teresa Guasti, Gennaro Chierchia, Stephen Crain, Francesca Foppolo, An-drea Gualmini, and Luisa Meroni. Why children and adults sometimes (butnot always) compute implicatures. Language and Cognitive Processes, 20(5):667–696, 2005.

Giyoo Hatano and Yasuko Suga. Understanding and use of disjunction in children.Journal of Experimental Child Psychology, 24:395–405, 1977.

35

Laurence R. Horn. On the semantic properties of logical operators in english.Doctoral Dissertation, UCLA, 1972.

Barbel Inhelder and Jean Piaget. The Early Growth of Logic in the Child. Rout-ledge, London, 1964.

Bo S. Johansson and Barbro Sjolin. Preschool children’s understanding of ‘and’and ‘or’. Journal of Experimental Child Psychology, 19:233–240, 1975.

Mark Johnson, Thomas L. Griffiths, and Sharon Goldwater. Adaptor grammars:a framework for specifying compositional nonparametric bayesian models. InB. Sch”olkopf, J. Platt, and T. Hoffman, editors, Advances in Neural Informa-tion Processing Systems 19, pages 641–648, Cambridge, MA, 2007. MIT Press.

Daniel Jurafsky. A probabilistic model of lexical access and disambiguation. Cog-nitive science, 20:137–194, 1996.

Napoleon Katsos and Dorothy V.M. Bishop. Pragmatic tolerance: Implicationsfor the acquisition of informativeness and implicature. Cognition, 120:67–81,2011.

Roni Katzir. Structurally defined alternatives. Linguistics and Philosophy, 30:669–690, 2007.

Roni Katzir and Raj Singh. Constraints on the lexicalization of logical operators.Linguistics and Philosophy, 36(1):1–29, 2013.

Angelika Kratzer and Junko Shimoyama. Indeterminate pronouns: The view fromjapanese. In Yukio Otsu, editor, Proceedings of the 3rd Tokyo Conference onPsycholinguistics, pages 1–25. 2002.

Richard K. Larson. On the syntax of disjunction scope. Natural Language andLinguistic Theory, 3:217–264, 1985.

David Lewis. Relevant implication. Theoria, 54:161–174, 1988.

Marie-Christine Meyer. Generalized free choice and missing alternatives.Manuscript, MIT, 2013.

George Miller and Noam Chomsky. Finitary models of language users. In R.D.Luce, R.R. Bush, and E. Galanter, editors, Handbook of Mathematical Psychol-ogy, volume 2, pages 419–491. Wiley, New York, NY, 1963.

36

Edith D. Neimark and Nan S. Slotnick. Development of the understanding oflogical connectives. Journal of Educational Psychology, 61(6):451–460, 1970.

Ira Noveck. When children are more logical than adults: Investigations of scalarimplicature. Cognition, 78:165–188, 2001.

Ira Noveck and Andres Posada. Characterizing the time course of an implicature:An evoked potentials study. Brain and Language, 85(2):203–210, 2003.

Timothy J. O’Donnell, Jesse Snedeker, Joshua B. Tenenbaum, and Noah D. Good-man. Productivity and reuse in language. In Niels Taatgen and Hedderikvan Rijn, editors, Proceedings of the Thirty-Third Annual Conference of theCognitive Science Society. The Cognitive Science Society, 2011.

Anna Papafragou and Julien Musolino. Scalar implicatures: Experiments at thesemantics-pragmatics interface. Cognition, 80:253–282, 2003.

Scott Paris. Comprehension of language connectives and propositional logicalrelationships. Journal of Experimental Child Psychology, 16:278–291, 1973.

William C.H. Philip. Event quantification in the acquisition of universal quantifi-cation. Doctoral Dissertation, UMass Amherst, 1995.

Tanya Reinhart. Interface Strategies. MIT Press, Cambridge, MA, 2006.

Craige Roberts. Information structure and discourse: Towards an integrated for-mal theory of pragmatics. In J.H. Yoon and Andreas Kathol, editors, OSUWorking Papers in Linguistics, pages 91–136. 1996.

Mats Rooth. A theory of focus interpretation. Natural Language Semantics, 1:75–116, 1992.

Uli Sauerland. Scalar implicatures in complex sentences. Linguistics and Philos-ophy, 27:367–391, 2004.

Katrin Schulz. A pragmatic solution for the paradox of free choice permission.Synthese, 147(2):343–377, 2005.

Roger Schwarzschild. Givenness, Avoid F, and other constraints on the placementof focus. Natural Language Semantics, 7(2):141–177, 1999.

37

Robert J. Sternberg. Developmental patterns in the encoding and combination oflogical connectives. Journal of Experimental Child Psychology, 28:469–498,1979.

Alex Stiller, Noah D. Goodman, and Michael C. Frank. Ad-hoc scalar implicaturein adults and children. In Proceedings of the Cognitive Science Society. 2011.

Andreas Stolcke. An efficient probabilistic context-free parsing algorithm thatcomputes prefix probabilities. Computational Linguistics, 21:165–201, 1995.

Patrick Suppes and Shirley Feldman. Young children’s comprehension of logicalconnectives. Journal of Experimental Child Psychology, 12:304–317, 1971.

John C. Trueswell, Michael K. Tanenhaus, and Susan M. Garnsey. Semantic in-fluences on parsing: Use of thematic role information in syntactic ambiguityresolution. Journal of Memory and Language, 33:285–318, 1994.

Peng Zhou, Jacopo Romoli, and Stephen Crain. Children’s knowledge of freechoice inferences. In Proceedings of SALT 23, pages 1–15. 2013.

Thomas Ede Zimmerman. Free choice disjunction and epistemic possibility. Nat-ural Language Semantics, 8:255–290, 2000.

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