For Dependencies, let us first specify the term since our view about them is explicated by appeal to formal logic. Frege (1879) invented the notion of a bound variable that represents one way to understand dependencies, though alternatives exist (e.g., combinatorial logic of Schönfinkel, 1924). In English, there are primarily two ways a bound element may be articulated: as a gap/trace (i.e., not pronounced at all) or as a pronoun. The presence of a dependent element in (4a) is indicated by the stilted English paraphrase (4b) involving the dog in both the trace and the pronoun position and by the representation in (4c) in the style of Kratzer and Heim (1998) that invokes actual Fregean variables.

It has been argued that both traces and pronouns must be complex concepts and share some lexical material with the binder [i.e., the representation in (4c) is inaccurate]. For traces, this is known as the copy theory of traces (Chomsky, 1995; Sauerland, 1998, 2004; Fox, 2000). For bound variable pronouns, Sauerland (2000a,2008) argues in favor of the same point. Also relevant is the work on so-called donkey pronouns that cannot be directly captured as bound by an overt phrase in the logical sense but have been analyzed via a similar indirect relationship by Evans (1980), Heim (1990), Elbourne (2001), and Sauerland (2007). We take the evidence on traces and pronouns to indicate that overall bound variables must share some primitive concepts with their binder. By this we mean that the concepts lexicalized in the binder and the bindee must totally or partially overlap. As a result, for example, if the binder lexicalizes the concepts “animate” and “dog,” the same may be lexicalized in the bindee. Furthermore, the discussion of traces has led theoreticians to distinguish between so-called A and A’ traces, and Takahashi and Hulsey (2009) have argued that A’ traces have to share more material with their binder than A traces need to, but propose that A-traces also at least share the conceptual information related to nominal category. The A/A’ distinction correlates with the structural distance between a trace and its binder. Thus, the number of primitive concepts shared between the binder and bound element correlates with the structural proximity of the two: the greater the structural distance, the more concepts must be shared. As a result, the binder can identify the relevant bindee, thus incorporating for free some form of locality between dependencies (see Sauerland et al., submitted). Therefore, we arrive at the following generalization as the basis for our investigation of acquisition. In (5), we leave the full domain of application of the generalization open since not all relevant cases have been scrutinized.

Within a class of cases that includes at least A’ traces, any concept that can be bound in the sense of variable binding must share one or more primitive concepts with the concept binding it.

For the meaning of verbs (and possibly of other categories), it has been argued that it can be decomposed into a number of more primitive units, which are hierarchically organized. Specifically, it has been argued that multi-argument verbs include unpronounced light verbs and verbal stem (cf. Rappaport-Hovav and Levin, 1998, 2010; Borer, 2005; Levin and Rappaport-Hovav, 2005; Alexiadou et al., 2015; Ramchand, 2018; among others; see Senghas et al., 1997 for a type of decomposition in the genesis of Nicaraguan Sign Language). Thus, in the case of (6), we have a core dynamic event, CAUSE, that combines with a result component, BROKEN, and a layer above the dynamic event associated with the external argument. By contrast, the internal argument is associated with the result component. In this example, the concept CAUSE is compressed or not pronounced, while the result is exponed by the verb stem. Verbs associated with only one argument do not show such complexity, and (7) simply involves a dynamic event and a layer above the dynamic event associated with the external argument.

Rappaport-Hovav and Levin (2001) put forward the one argument per subevent principle, according to which there must be one argument in the syntax to identify each sub-event in the event structure template. We can reformulate this principle in the following generalization:

Within a class of cases that includes at least causative verbs, any concept that takes more than one argument of the type of individuals must be complex and include light verbs along with a root stem.

Antonymic expressions are found in several different grammatical categories, for example, quantificational determiners a-none, verbs continue-stop, adjectives tall-short, prepositions inside-outside, adverbs sometimes-never, and nouns child-adult (Déprez and Espinal, 2020). For all antonym pairs, there is an intuition that the negation of one member is logically equivalent to the other, e.g., not continue is equivalent to stop, and also, not stop is equivalent to continue. But antonym pairs in many cases display also subtle asymmetries. For negative quantificational determiners, Bech (1955) showed that German allows interpretations where a negative part and a positive existential seem to contribute to sentence meaning in different positions (see Penka, 2011). Sauerland (2000b) argued that across languages, the negative existential seems never to be a primitive concept but would need to be composed of negation and an existential. For adjectives, Bierwisch (1967) has have pointed out that there frequently are subtle markedness asymmetries between the two members of an antonym pair. For example, the question How tall are they? is more neutral than the question How short are they? indicating that short is the marked member of the pair. Another way to look at this asymmetry with dimensional adjectives is by noting that while tall has no upper bound in principle, short must have a minimum size. So, the marked member must have a minimal lower bound, while the unmarked has no upper bound. Looking cross-linguistically, there are cases where the marked member can only be expressed by means of negation of the unmarked member, e.g., the pair kawo–kawo-hra (“long”—“short,” lit. “long-NEG”) in Hixkaryana (Derbyshire, 1985). These data and other pieces of evidence have led several theoreticians to conclude that one member of antonymic adjective pairs has to be decomposed across all languages into a negation marker and a positive adjective (Heim, 2006; Büring, 2007; Bobaljik, 2012; Rett, 2014; Moracchini, 2019). For prepositions, the English pair with—without is similar to Hixkaryana if we assume that out is a morphological exponent of negation in this domain. Thus, we assume that antonymic pairs of concepts fall under the following generalization:

Within a class of cases that includes at least negative quantifiers, dimensional adjectives and without, the marked member of an antonym pair is never a primitive concept, but is composed of negation and the unmarked member of an antonym pair.

The generalization concerning dependency in (5) holds that the binder and the bindee must share one or more primitive concepts. In the light of this, the CLUH predicts that children may sometimes expone not only the binder, but also the bindee or some concepts forming it. Underlying this prediction is the assumption that relative clauses results from the assembly of several complex concepts. Let’s illustrate this assumption in an informal way by considering (10). One piece is the CR underlying “the uncle” and another piece is the CR underlying “the boy hugged the uncle.” When these two pieces are put together, as in a relative clause, a dependency is created with the binder and the bindee being identical, as in the CR in (10), which contains two heads sharing concepts. We further assume that the relative head, N-root, as all nouns, is accompanied by a classifier (CL), which contain functional concepts characterizing the category noun; concepts relevant for agreement may occur as CLs without articulation, while adjective modifiers would be articulated (see below for evidence supporting this assumption). Similarly, the bindee includes the N-root and a classifier. Kayne (2007) and Cinque (2020) develop similar conceptions, though they generally seem to adopt only a single classifier. At this point, we leave underspecified whether (10) corresponds to a raising or matching structure in the sense of Sauerland (1998, 2000c) and Hulsey and Sauerland (2006) since both are predicted to have a double-headed structure. Thus, in this representation the binder, the relative head, and the bindee, the double in the internal position, share concepts, in agreement with our generalization in (5). When this representation is articulated into language, typically only one head is articulated (the internal or external). In some cases, both heads are articulated (double headed RCs), and in this case, one can be the noun and the other a pronoun or again a noun, that is, the double head can be identical to the first or can articulate less concepts.

The above CR is supported by comparative research on adult languages. Cinque’s 2013; 2015; 2020 typological overview describes head-external relative clauses, head-internal ones, and actual double-headed relatives (see also Dryer, 2005). Double-headed relative clauses, in turn, display variation in line with our assumptions discussed earlier. In some examples, the relative head in both positions features the same noun (though the relative head contains a demonstrative and a classifier, while the double includes just a bare noun), as in (11) from Ronghong Qian (Tibeto Burman family) (cited in Cinque, 2020 from Huang, 2008) and (12), from Wenzhounese, a language spoken in South-East China (Hu et al., 2018):

“The place where rockslides often occur.”

“the child that the grandma draws.”

In yet other languages, however, the external head is a general term, while the internal head is a more specific expression. In the example below from Kumbai (Trans-New Guinea; Papua, Indonesia, cited in Cinque, 2020), the external head is ro “thing” and the internal one is gana “bush.knife.”

“The bush.knife that you took away, is my bush knife.”

The reverse is found in the Japanese example in (14) (cited in Cinque, 2020, from Kuno, 1973), where the internal head is the more general term and the external one the more specific one.

“A guest whose name I have forgotten.”

The presence of general and more specific terms in RCs is an indication that nouns are always accompanied by classifying material, CL, and what happens in the last two types of languages is that either the classifying material or the noun is articulated in head or gap positions. Indeed, Kayne (2007) and Cinque (2020) argue that nouns are always associated with functional nouns (N) that classify them, e.g., [_FP [_DP guest] person], [_FP [_DP chair] furniture]. Typically, these functional nouns are not articulated or are dropped. However, Cinque notices that there are cases in which they are retained as in New York city, which alternates with New York.

Relevant to the prediction emanating from the CLUH are primarily languages in which relative clauses feature the presence of a gap and an external head in the adult language. And this prediction is that children may produce lexical material in the gap position that shares feature with the relative clause head. In other words, given the CR in (10), they may produce relative clauses in which the head and the double can be identical or either one be a general or a more specific term. This prediction is borne out by several elicited production studies conducted in a variety of early languages with children from age 3;0 up to age 10;0. First, children produce relative clauses featuring the presence of a resumptive pronoun in the gap position (or close to it in languages with clitic pronouns). Second, children produce relative clauses, where the gap is filled with the same material as the relative head, i.e., with resumptive DPs. Third, children may use a more specific term in the external position than in the gap position or the reverse. These productions have been found in Catalan (Gavarró et al., 2012) European Portuguese (Costa et al., 2014), English (Pérez-Leroux, 1995 citing Finer, 1992), French (Ferreiro et al., 1976; Labelle, 1990; Guasti et al., 1996), German (Yatsushiro and Sauerland, 2018), Hebrew (Armon-Lotem et al., 2005), Jakarta Indonesian (Tjung, 2006), Italian (Guasti and Cardinaletti, 2003), Mandarin (Hsu et al., 2009; Hu et al., 2016), Palestinian Arabic (Armon-Lotem et al., 2005), Serbo-Croatian (Goodluck and Stojanovic, 1996), Spanish (Ferreiro et al., 1976; Pérez-Leroux, 1995), Turkish (Özge et al., 2010). Relevant examples are below:

Relative clauses with resumptive pronouns.

Relative clauses with resumptive-DPs with (almost) the same DP, general and specific terms.

Although both resumptive pronouns and resumptive DPs are present in several early languages, resumptive pronouns seem to be more frequent in early languages like French. Labelle (1990) reports that French-speaking children produce 33% resumptive pronouns and 16% resumptive DPs. However, the resumptive pronouns advantage holds for the direct object, locative and genitive RCs; a resumptive DPs advantage is observed for indirect object RCs. Resumptive DPs are more frequent than resumptive pronouns in early Mandarin, but only subject and object RCs were elicited in this case (Hu et al., 2016). Thus, a systematic investigation of these resumptive elements is certainly more than needed (see Guasti and Shlonsky, 1995 for a discussion of the two types of resumption in children’s RCs). We can notice that resumptive relatives with pronouns are common in a variety of languages (Hebrew, Palestinian Arabic, Welsh) and in many colloquial varieties of Romance (French, Italian, Spanish). Thus, in several languages, children hear resumptive relative clauses, along with relative clauses with gaps (Guasti and Cardinaletti, 2003 and reference cited there).

Although the presence of relatives with resumptive DPs has been noticed in several studies, they have been the focus of interest in three studies by Hu et al. (2018) on Wenzhounese, Hu et al. (2016) on Mandarin and Yatsushiro and Sauerland (2018) on German. As noted above, Wenzhounese allows resumptive DPs (along with gaps) also in the adult language, while German and Mandarin do not. Thus, we will report on the last two languages, both using the same elicitation method (Novogrodsky and Friedmann, 2006). Resumptive DPs are massively used in object RCs and sometimes also in subject RCs (50% of the non-target responses) by 6 groups of Mandarin speaking children ranging in age from 3;0 to 8;0 (Hu et al., 2016) (along with some resumptive pronouns, 21% of the non-target responses). Interestingly, monolingual Mandarin-speaking adults also employ resumptive DPs, but only in their object RCs (56%) during the experiment (Hu et al., 2016), although Mandarin does not feature any kind of doubling RCs. In addition, Mandarin-speaking adults accept subject and object RCs with resumptive DPs, although to a lesser extent than RCs with a gap (Hu et al., 2016). Similarly, Yatsushiro and Sauerland’s (2018) found that German-speaking children (age range 4;6–8;7; mean age 6;6) have no trouble in producing target subject RCs, but produce few target object RCs (18%) and most of the time (41%) produce resumptive DPs along with resumptive determiners/pronouns in this case, as in (17).

“I want to be among the children that Oma malt the children.”

German and Mandarin feature two different types of RCs: head initial and head final. Yet, children in both languages use DP-resumption, indicating that this is clearly an option for them, although at this point we cannot tell whether it is more frequent in one or the other language and we do not have adult data from German.

In sum, child language provides evidence that in uttering relative clauses children may sometimes realize more of the CR than in their target model. In fact, not only children but also adults can realize it on occasions (e.g., when relative clauses are more complex, as object relative clauses are). Although at this point we lack evidence, we may conjecture that input may modulate the amount and type of possible realizations; nouns or pronouns may be more or less used by children depending on the language.

Another structure involving a dependency and for which we predict that children may undercompress are wh-questions. Recall that according to our generalization, the binder and the bindee in a dependency must share some concepts. For a monoclausal matrix question this is illustrated by (18).

We therefore might expect that children should articulate “which cookie” in the position following “eat” at some stage of development. But it is also possible that children may have sufficient cognitive resources to avoid this type of undercompression error from the start of their use of questions. And in fact, to our knowledge undercompression errors with monoclausal matrix questions haven’t been reported. But, for more complex questions involving extraction from an embedded clause, undercompression errors have been reported. Three-to-six-year-old children speaking Dutch (van Kampen, 1997; Jakubowicz and Strik, 2008), English (Thornton, 1990), French (Oiry and Dermidache, 2006), Spanish and Basque (Mangado, 2006) have been found to produce non-target structures in their language of exposure like in (19), featuring wh-copying of the wh-word (McDaniel, 1986; examples from Thornton, 1990).

In (19), the wh-phrase content isn’t articulated in the argument position of the verb, but in an intermediate position. As far as we know, articulation in the argument position has not been found in child language for languages that are not adult wh-in situ languages in neither monoclausal nor long-distance questions. Our proposal for the analysis of (19) as undercompression errors adopts the assumption that cognitive representations minimize the length of dependencies in a non-additive fashion (Fox, 2000; Sauerland, 2018). This implies that a CR with two short dependencies is preferred over a CR with one dependency that has double the length of the short dependencies. This assumption leads us to postulate the following preliminary CR if an intermediate position for a wh-phrase is available [QUESTION would mark the clause as a question, while we understand who (analyzed as WH PERSON) here as an indefinite element]. So (20) could be paraphrased as “Some person’s identity is relevant and you think that Grover wants to hug that person”:

Adult languages differ in what of this CR is articulated and how. In several languages only one set of concepts is articulated. Thus, a question extracting from an embedded clause looks like in (21), where the wh-word/phrase fronted in sentence-initial position conflates the concepts WH-N and QUESTION and the intermediate WH-N concept is not articulated.

But children may sometimes pronounce the medial wh-position, resulting in productions like those in (19) above, where they spell out the two short dependencies.

There are also adult languages, where two sets of concepts can be articulated. In fact, there are two varieties of such strategies: Wh-copying, such as in Afrikans, dialects of German, Dutch, Frisian, and Romani (McDaniel, 1986; Felser, 2004) and scope marking (or partial movement strategy), such as in dialects of German, Malay (Cole and Hermon, 2000), and Hindi (Dayal, 1996). So, even adults in some languages may undercompress. But the fact that the undercompression is spontaneously produced by children acquiring an adult language that doesn’t have the structure supports our proposal.

We also predict that children may produce some material in the place of the gap. This type of production has not been reported so far in the literature, but preliminary evidence from Italian seems to suggest that children can sometimes express an indefinite (someone) in the gap position (Dal Farra et al., 2022a).

Another prediction is that not only children will attempt to produce in a more transparent way the CR, but they will interpret sentences through the 1-to-1 mapping principle and, in this respect, they may assign to a sentence a different interpretation than an adult would. de Villiers et al. (2008) found that children may interpret questions like (22) as scope marking questions and answer the medial indirect question (“how she ripped her dress”), rather than the matrix question. Hence, they may answer with “with the wire on the fence.”

These types of errors of interpretation indicate that children take the embedded wh-word as the element introducing the real question and the fronted one to be a scope marker. In our framework, these answers are the mirror image of what children do in production and their source is the attempt to transparently map the CR. From 4 to 5 years, we observe a decline of these “medial” answers, which disappear by age 7 (see Guasti, 2017 for review). Interestingly, these ages match the age in which wh-copying and medial wh-questions are produced, suggesting that their source is the same, the use of the transparency principle.

By “cum sine” from Latin, we intend to refer to antonymic concepts that refer to the presence of something “cum” (positive member), expressed in English by “with” and the absence of something “sine” (negative member) expressed in English by “out.” We assume that while the positive member is a primitive, the negative one is complex and must be decomposed into “cum” plus a negative expression. Thus, the CR of “sine” is (27).

In languages like English, this CR is overtly realized into language with the morphemes “with-out.” In other languages, it is expressed as “CUM” plus sentential negation or a negative element; in yet other languages, it is a monomorphemic word that overtly and univocally expresses the absence, while the concept of presence is not articulated into language. This is the case in Italian or German, where the words, senza, ohne, are used respectively. Children, who may prefer to overtly realize all pieces of the CR are expected to produce “con senza,” “mit ohne,” thus making the mapping between the CR and language more transparent. And this is indeed the case as children have been found to produce sentences like (28) (see Sauerland et al., submitted).

A survey we have done indicates that similar productions are found in child Dutch (met-zonder), Greek (me-ohi), Portuguese (com-sem), Shugnan (gati na), Basaa (ngi ni), Tagalog (may walang), Chabacano (tiene nuay), Indonesian (nggak pake). Although at this point, this evidence in only anecdotal and more investigation is needed (see Sauerland et al., submitted), we think that these data are highly suggestive and supportive of the idea of a CR as in (27).

Antonymic adjectives are pairs like big/small, long/short, tall/little. Like for the prepositional antonym “cum sine,” one member of the pair is positive (e.g., big) and the other is negative (e.g., small). While the positive member of the pair is a primitive concept, i.e., it is not further decomposable, the negative member does not and is decomposed into two concepts comprising a negative concept and the corresponding positive one. Thus, the CR of “small” is.

As before, since children are biased to a 1-to-1 correspondence we predict that children may sometimes say “not big” rather than “small”; we also predict that acquisition of the positive member is easier than acquisition of the negative one. As for the first prediction, we do not know of any relevant evidence, while for the second, various investigations have been conducted which have led to different results. Some studies found that positive antonyms are mastered earlier than negative ones (Clark, 1972; Ehri, 1976; Barner and Snedeker, 2008) and others that they were mastered at the same time (Carey, 1978; Phillips and Pexman, 2015). No study has found that negative adjectives are mastered earlier than positive ones. In a recent study on Italian, Pagliarini et al. (2022) have probed the comprehension of antonymic adjectives, grande/piccolo (big/small), lungo/corto (long/short), alto/basso (tall/little) in three groups of Italian-speaking children aged 3, 4, 5-year-olds and one adult group. They used a card selection task with novel nouns. Children were asked to categorize into two sets 9 objects named after the novel noun according to whether they were considered big or small. The results showed that from age 4, but not 3, children and adults behaved the same with positive adjectives. However, for negative adjectives all children’s groups differed from adults, that is, even the 5-year-old’s comprehension of the negative antonym was not adult-like. This fact is compatible with the idea that the negative member of the antonymic pair is more complex than the positive one and in our framework that its underlying CR is as in (29).

Negative quantifiers, like none, stand in the antonym relation with existentials like someone. The antonym generalization, therefore, predicts that none and its counterparts across languages should be composed out of negation and an existential. Cross-linguistically the situation is more complicated because of the difference between double negation and negative concord structures. In Standard English, sentences like (30) featuring the presence of two negative elements yield a double negation reading, whereby the two negative elements cancel each other and the meaning of the sentence is equivalent to John bought something.

By contrast, in languages like Italian, the two negative elements in the same structure, as in (31), give rise to a negative concord interpretation, whereby the two negative elements count as a single negation.

Along with Bech (1955), Sauerland (2000b), Penka (2011), and Zeijlstra (2011) we assume that negative words, like nobody, kein, nessuno are decomposed into an Existential quantifier (positive quantifier) and negation, thus the CR containing a negative word is as in (32):

A transparent expression of this CR is one in which NEG is expressed as sentential negation and EXIST is articulated as a quantifier, which in the context of negation would turn out to be a negative word, like nessuno (nobody) as in negative concord structures. In English, NEG is compressed (or not pronounced) and EXIST, being in the context of (covert) negation, is articulated with the negative word nobody. When EXIST is not in the context of the negation, it is articulated as someone (in both languages) [see Temmerman, 2012 for an alternative view, which builds on Bech, 1955 and which is likely incompatible with our proposal, as in our framework, this alternative would involve fusion of NEG and EXIST into a negative word plus addition of negation to obtain (31)].

Given the CR in (32), we expect children speaking languages in which two negative elements in the same structure lead to a double negation reading to be biased to produce negative concord sentences. Interestingly, English-speaking children produce negative concord sentences. Below are some examples from Adam and Sarah (Childes, MacWhinney, 2000) reported in Thornton et al. (2016):

In these examples, children map NEG to the negative morpheme (n’t) and express EXIST as a negative word (nothing, nobody) because it is in the context of negation, as we said earlier, i.e., they express (32) transparently. Furthermore, the negative concord interpretation seems to be the default for English-speaking children. Thornton et al. (2016) designed a Truth-Judgment value experiment in which they presented to 4;7-year-old children and adults sentences like (34), which could be amenable to a double negation or a negative concord interpretation.

While adults generally attributed a double negation reading, children attributed a negative concord reading. Thus, unlike adults, English-speaking children seem to allow negative concord structures. In the same experiment, Thornton et al. (2016) established that children interpret as adults do sentences like (35), which are grammatical in the adult language.

Furthermore, Nicolae and Yatsushiro (2020) investigated 4;2–6;5 (M = 5;2) year old Northern German–speaking children’s comprehension of negative concord sentences like (36):

Standard German, and possibly the variety to which the children were exposed, is not a negative concord language, while dialects spoken in Southern Germany are, as is Austrian German. As in Thornton et al. (2016) German-speaking children assigned a negative concord reading to sentences such as (36), while adults a double negation reading. In addition, Nicolae and Yatsushiro (2020) report that German-speaking children from the age of 2 years produce negative concord sentences both in spontaneous speech (Childes, MacWhinney, 2000) and in experimental settings:

Thus, children speaking languages where two negative elements in the same sentence lead to a double negation reading, English and German, produce negative concord sentences and assign a negative concord reading to sentences (34) and (36), as do children speaking a language where two elements in the same structure lead to a negative concord interpretation. In this respect, English and German-speaking children are unlike adults, and they behave in line with our hypothesis that they attempt to transparently produce and interpret sentences. One may object that English- and German-speaking children do not accept the double negation reading because it is difficult. First, this criticism can be leveled at the comprehension’s study, but not at the production of children’s negative concord sentences. Second, children, in Thornton et al. (2016) study, did not have any trouble in interpreting correctly sentences with two negative elements, as in (38), in which a negative concord reading is not possible because negation does not c-command the negative quantifier (see Zhou et al., 2014 for additional evidence from Mandarin):

The fact that children can process two negative items in the same sentence weakens the criticism that children cannot process two negations, but this point is certainly one to keep in mind in future research.

So far, we have seen that English- and German-speaking children produce non-target negative concord sentences, interpret sentences with two negative elements as cases of negative concord. The third prediction of our approach is that when the CR is transparently expressed into language, abiding by the 1-to-1 mapping between the CR and the linguistic expressions, the acquisition of negative quantifiers should be easier. This prediction boils down to the fact that negative quantifiers should be easier to acquire in Italian than in English or German, as in the two last languages NEG is compressed. Katsos et al. (2016) examined the comprehension of negative quantifiers in 31 early languages and found earlier acquisition of negative quantifiers in negative concord languages than in non-negative concord ones, as our approach predicts.