1 Introduction

The acquisition of prepositional relative clauses (RCs) in European Portuguese (EP) has been investigated both in first (L1) and second language (L2) acquisition research. Studies on EP L1 acquisition of RCs indicate that prepositional RCs are acquired later and develop with schooling. This is applicable to EP, as demonstrated by Vasconcelos (1991; 1996), Valente (2008) and Fontes (2009) as well as other languages such as Italian (Guasti & Cardinaletti 2003), French (Labelle 1990), English (McDaniel et al. 1998), and Spanish (Pérez-Leroux 1995). To the best of our knowledge, there are limited studies that look at the L2 acquisition of prepositional RCs in EP (Espírito Santo 2020; Espírito Santo et. al. 2024). The L2 research on the acquisition of prepositional RCs in other languages focuses mostly on the differences in markedness between Pied Piping (PiP) and Preposition Stranding (PS) strategies, predominantly in L2 English acquisition. Instead, the present study investigates the phenomenon of deleting the mandatory preposition in prepositional RCs, by native and non-native speakers of EP. The study of this systematic phenomenon raises interesting questions about the nature of interlanguage grammar (ILG) or the limits of recoverability of deletion.

In standard EP, prepositional RCs are produced using PiP, which involves fronting the mandatory preposition (1). Resumption (2), where the preposition remains in situ and is followed by a resumptive element, it is also attested, but it is not sanctioned by prescriptive grammars and it is considered non-standard (e.g., Alexandre 2000). The strategy that is the focus of the present paper is also non-standard1 and consists of deleting the mandatory preposition (3).

    1. (1)
    1. Foi
    2. be-pst.3sg
    1. um
    2. det.indf.m.sg
    1. debatei
    2. debate
    1. [[obl
    2.  
    1. a
    2. to
    1. que]
    2. rel
    1. valeu a pena
    2. be.worth-pst.3sg
    1. assistir ti]].
    2. watch
    1. (2)
    1. Foi
    2. be-pst.3sg
    1. um
    2. det.indf.m.sg
    1. debatei
    2. debate
    1. [[obl
    2.  
    1. que]
    2. rel
    1. valeu a pena
    2. be.worth-pst.3sg
    1. assistir
    2. watch
    1. a
    2. to
    1. ele]].
    2. 3sg
    1. (3)
    1. Foi
    2. be-pst.3sg
    1. um
    2. det.indf.m.sg
    1. debatei
    2. debate
    1. [[obl Ø
    2.  
    1. que]
    2. rel
    1. valeu a pena
    2. be.worth-pst.3sg
    1. assistir ti]].
    2. watch
    1. All: ‘It was a debate that was worth watching.’

The strategy described in (3) is known as P-Chopping (P-Chop) or PP-deletion in the literature on Portuguese (Tarallo 1985; Alexandre 2000; Arim et al. 2004; Alexandre 2012; Duarte 2013; among others). The literature that primarily focuses on L2 acquisition uses the Null-Preposition (Null-Prep) designation to refer to the same phenomenon (Klein 1993; Perpiñán 2010; 2020; among others). This non-standard strategy is documented not only in the grammar of native EP speakers (Brito 1995; Alexandre 2000; Brito & Duarte 2003; Arim et al. 2004; Antunes & Brito 2008; Alexandre 2012; Duarte 2013; Espírito Santo 2020; Amorim 2021), but also in the ILG of non-native EP speakers (Espírito Santo 2022).

The main research question (RQ) of this paper is whether the omission of the preposition in the ILG has the same nature as the omission of the preposition in an adult L1 grammar, specifically in the grammar of EP.

This paper is structured as follows: Section 2 describes the P-Chop phenomenon in EP. To enable a comparison with the participants’ native language and to speculate about potential transfer effects, section 3 briefly presents the main properties of prepositional relative clauses in Chinese. Section 4 discusses some of the explanations for the omission of the preposition in natural languages (i.e., not in L2 acquisition contexts) presented in the literature. Section 5 covers the omission of the preposition in L2 acquisition (Null-Prep). The experimental design adopted in the present study is detailed in section 6, followed by the results, in section 7. Section 8 presents the discussion and section 9 shows the conclusions.

2 P-Chopping in European Portuguese

P-Chop RCs in EP are preferentially introduced by que, which works as a neutral element, irrespective of the syntactic function of the relativized element (e.g., Peres & Móia 1995; Espírito Santo 2020). The same was noted for Brazilian Portuguese (BP) (see Kato 2010). This strategy has both diachronic and synchronic attestations. Sentence (4) illustrates an example of the omission of the preposition in the diachrony (example from the 13th century):

    1. (4)
    1. o
    2. det.m.sg
    1. dia Ø
    2. day
    1. que
    2. rel
    1. eu
    2. 1sg
    1. tal
    2. such
    1. pesar
    2. grief
    1. vi
    2. see-pst.1sg
    1. ‘the day (in) which I saw such grief’
    2.                                                                                                                    (Cancioneiro da Ajuda 10224; Huber 1933, from Duarte 2013: 8)

Synchronically, this strategy is present in other varieties of Portuguese, such as Santomean Portuguese (5), Cape Verdean Portuguese (6) and BP (7) (Tarallo 1985; Kato & Nunes 2009; Gonçalves 2010; Alexandre et al. 2011; Alexandre & Hagemeijer 2013; among others).

    1. (5)
    1. Tenho
    2. Have-prs.1sg
    1. uma
    2. one
    1. moça lá
    2. lady there
    1. em casa Ø
    2. in home
    1. que
    2. rel
    1. não
    2. not
    1. chamo
    2. call-prs.1sg
    1. empregada
    2. cleaner
    1. [a uma moça].
    2. (to one lady)
    1. ‘I have a girl there at my place that I do not call a waitress.’
    1. (6)
    1. Faz
    2. Do-prs.3sg
    1. umas
    2. some
    1. coisas Ø
    2. things
    1. que
    2. rel
    1. eu
    2. 1sg
    1. não gosto [de umas coisas].
    2. not like (of some things)
    1. ‘He does some things that I don’t like.’
    2. (both from Alexandre et al. 2011: 22)
    1. (7)
    1. Nova Iorque
    2. New York
    1. é
    2. be-prs.3sg
    1. uma
    2. one
    1. cidade
    2. city
    1. Ø
    2.  
    1. que
    2. rel
    1. você
    2. 2sg
    1. respira
    2. breathe
    1. Gershwin [em Nova Iorque].
    2. Gershwin (in New York)
    1. ‘New York is a city where you breathe Gershwin.’
    2. (Tarallo 1985: 358)

There is increasing evidence of the use of this strategy in EP, showing that P-Chop incorporates speakers’ oral discourse, regardless of their level of instruction (Brito & Duarte 2003: 6672; Santos 2014; Aßmann & Rinke 2017; among others).

Researchers do not always take the same approach when describing the preferred contexts for P-Chop. Some focus on the syntactic function of the relativized object, like Veloso (2013) and Aßmann & Rinke (2017), while others adopt a lexical approach, underscoring the verbs and prepositions with which P-Chop RCs are more frequent. For example, Arim et al. (2004) highlight the use of certain prepositional combinations such as gostar de ‘like of’, falar de ‘talk about’, precisar de ‘need of’, necessitar de ‘need of’ and chamar a ‘call to’, as well as the prepositions em ‘in’ and a ‘to’.

The authors who follow the syntactic approach do not agree on the preferred contexts for P-Chop. Veloso (2013: 2128–2129) claims that P-Chop is more frequent in the relativization of temporal or locative PPs, followed by the cases where the preposition has a purely grammatical function, required by verbs such as gostar ‘like’, falar ‘talk’ and precisar ‘need’. The prepositions introducing indirect objects and oblique semantic objects are less likely to be dropped, as schematized in (8) (from Aßmann & Rinke 2017: 34).

    1. (8)
    1. temporal/local > grammatical oblique > indirect > semantic oblique

Santos (2014: 38) emphasizes that complements are more frequently the subject of P-Chop than adjuncts, based on a corpus-based approach. These assumptions contradict those made by Veloso (2013) and require further attention. Additionally, Santos (2014: 37–38) notes that nominal complements and adjuncts have a higher percentage of P-Chop than verbal complements and adjuncts, and that de is the preposition most frequently chopped among the ones analyzed in her study (em, “in,” de, “of,” a, “to,” and com, “with”).

Aßmann & Rinke (2017: 31) also conduct a corpus-based analysis that confirms P-Chop is more commonly used to relativize arguments than adjuncts. The researchers found that P-Chop occurs most frequently in the relativization of indirect objects (97.4% of the analyzed sentences), followed by verbal complements (93.1%), temporal PPs (76.8%), locative PPs (58.6%), and oblique PPs (51.5%).3 Considering the prepositions selected by the verb, according to the analysis of corpora by Aßmann & Rinke (2017), de and a are the most frequently omitted prepositions.4

Espírito Santo (2020) follows a lexical approach, in an experimental study run with native EP speakers. The study tests the omission of the preposition in simple declarative sentences and RCs with the verbs more commonly associated with P-Chop, as well as with other verbs that select the same prepositions.5 One of the objectives is to determine if P-Chop in RCs results from a change in the theta-grid of certain verbs, which might be selecting a DP instead of a PP. The findings of this study suggest that some verbs have alternative theta-grids (V + Prep + DP and V + DP).6 However, native speakers do not accept the deletion of the preposition in declarative clauses with the same verbs that occur in P-Chop RCs, indicating that these verbs are selecting a PP and not a DP, not evidencing changes in their theta-grid. For example, gostar de is one of the verbs with which P-Chop RCs are more frequent, but the participants rejected the omission of the preposition with gostar in declarative sentences. This finding aligns with Brito’s (1995) claim that the presence of P-Chop RCs with certain verbs does not necessarily correlate with a modification in the theta-grid of those verbs.

Other V + Prep pairings that allow P-Chop in RCs are noted in Espírito Santo’s (2020) study, including assistir a ‘watch (to),’ lembrar-se de ‘remember (of),’ recordar-se de ‘remember (of),’ esquecer-se de ‘forget (of)’. Nonetheless, this study does not provide conclusive findings on the conditions that favour P-Chop. Neither the absolute frequency of the sequence V + Prep nor the preposition’s poor auditory salience can reliably predict the use of P-Chop in relativization (Espírito Santo 2020: 168). P-Chop seems to be the result of combining an [-animate] head with a less phonetically prominent preposition. Interestingly, the data suggest that native speakers’ preference for P-Chop may also be related to specific thematic roles associated with the PP, with native speakers being less likely to accept P-Chop when the relativized element is a locative (Espírito Santo 2020: 169–171).

3 Prepositional relative clauses in Mandarin Chinese

Mandarin Chinese (MC) RCs are head-final, meaning that the RC comes before the head in linear order. This is in contrast to Portuguese RCs, which are head-initial (9):

    1. (9)
    1. [Xiaoming
    2. Xiaoming
    1. xihuan
    2. like
    1. de ]
    2. rel
    1. [dem-cl
    2.  dem-cl
    1. na-ge ren ]
    2. person
    1. jiao Zhenni.
    2. named Zhenni
    1. ‘The person that Xiaoming likes is named Jenny.’
    2. (Xu 2009: 26)

Contrary to Portuguese, MC does not use relative pronouns. Instead, an invariable relativizer (DE) introduces the RC domain. Resumptive elements are mandatory when the object of an overt preposition is relativized. MC behaves exactly like Welsh (Rouveret 1994) or Hausa (Tuller 1986) in this respect. Neither of these languages permits PiP or PS and, as a result, oblique relativization is always done through resumption (10).

    1. (10)
    1. [Wo
    2. 1sg
    1. dui
    2. to
    1. taj
    2. 3sg
    1. hen
    2. very
    1. bucuo
    2. not.bad
    1. de]
    2. de
    1. na-weipéngyouj
    2. that-cl-friend
    1. ‘The friend to whom I am very kind’
    2. (Pan 2016: 287)

In MC, the omission of the preposition in in-situ relativization generates an ungrammatical structure:

    1. (11)
    1. Zhe
    2. this
    1. jiu
    2. exactly
    1. shi [NP
    2. be
    1. [CPta
    2. 3sg
    1. *(cong nar)
    2. from there
    1. lai
    2. come
    1. de]
    2. de
    1. na-ge xiaozhen]
    2. dem-cl town
    1. ‘This is the town where he came from’
    2. (Ning 1993:96, 134, apud Wen 2020: 96)

Due to the properties of prepositional RCs in MC, eventual cases of omission of the preposition in prepositional RCs in the L2 acquisition of EP by MC native speakers cannot be transferred from the L1, where resumption is the only available strategy.7

If cases of omission of the preposition are found, they can be explained in one of two ways: learners are using/accepting the non-standard strategy of EP (P-Chop), provided by the input, or learners are on a developmental path towards the acquisition of lexical properties. These two possibilities are addressed further, in the discussion.

4 Possible explanations for the omission of the preposition in natural languages

Various explanations have been proposed for the absence of prepositions in RCs in natural languages, including Baker (1988) and Kato (2010). In this paper, we adopt Kato’s proposal, which is further developed in the following paragraphs. Kato & Nunes (2009) explain the omission of the preposition in BP by native adult speakers as a lexical idiosyncratic matter, associated with particular theta-roles. Following Kato (2010), a preposition may be optional in the numeration when the displaced element is discourse-linked and the preposition is licensed by the verb (in line with Bouchard 1981, for French). Kato (2010) notes that the absence of the preposition involves only A’-movement positions, where the DP can have a default Case. If the preposition is absent in the numeration, the relevant DP remains with its Case unvalued and the derivation crashes (Chomsky 2001), unless the DP is moved to a ‘default’ Case position (nominative, in BP):

    1. (12)
    1. a.
    1. *A
    2.   det.f.sg
    1. Maria
    2. Maria
    1. precisa
    2. need-prs.3sg
    1. Ø
    2.  
    1. esse
    2. det.3sf
    1. dinheiro
    2. money
    1. amanhã.
    2. tomorrow
    1.  
    1. b.
    1.   Esse dinheiro
    2.   det.3sf money
    1. a
    2. det.f.sg
    1. Maria
    2. Maria
    1. precisa
    2. need-prs.3sg
    1. para
    2. for
    1. amanhã.
    2. tomorrow
    1. (Kato 2010: 178)

Additionally, Kato proposes that prepositions selected by the verb assigning inherent Case, with verbs like precisar ’need,’ gostar ‘like,’ etc., may be Inherent Case Marking Prepositions (ICP). ICP do not occur with adjuncts (i.e., when the PPs are not selected by the verb), but they appear with arguments. Nevertheless, ICP do not occur with all argument PPs, but relate to specific theta-roles (Kato 2010: 176). According to the hierarchy of theta roles proposed by the author (13), the prediction is that PPs playing the role of theme are more likely to have prepositions absent in the numeration than benefactives:

    1. (13)
    1. Theme> Goal> Locative> Instrumental> Benefactive

Additionally, the author admits that “inherent case splits the hierarchy according to speaker or dialect” (Kato 2010, footnote 6: 177).

Following Kato, in BP, verbs selecting ICP can display three types of RCs: PiP, resumption, and P-Chop. PiP and resumption emerge when the preposition is selected in the Numeration. The preposition is merged inside IP, and it is dragged along with the extracted wh-element (14a). Resumption presupposes a resumptive pronoun in the Numeration. The preposition merges with it and a co-referent DP is merged at Left Dislocation (LD), from where extraction occurs (14b). When the verb does not select the preposition, the DP complement moves to TopP and receives the default nominative Case. Extraction occurs from this position (14c).

    1. (14)
    1. a.
    1. [DP o
    2. det.m.sg
    1. autor]
    2. author
    1. [CP
    2.  
    1. com
    2. with
    1. quemi
    2. rel
    1. [IPeu
    2. 1sg
    1. falei
    2. talk-pst.3sg
    1. ti]]
    2.  
    1.  
    1. b.
    1. [DP o
    2. det.m.sg
    1. autor]
    2. author
    1. [CP
    2.  
    1. quei [LD ti.default nom]
    2. rel
    1. [eu
    2. 1sg
    1. falei
    2. talk-pst.3sg
    1. com
    2. with
    1. ele i]]
    2. 3sg
    1.  
    1. c.
    1. [DP o
    2. det.m.sg
    1. autor]
    2. author
    1. [CP
    2.  
    1. quei [TopP ti.default nom]
    2. rel
    1. [eu
    2. 1sg
    1. falei [dpt i]]]
    2. talk-pst.3sg
    1. (adapted from Kato 2010: 181)

5 The omission of the preposition in second language acquisition (Null-Preposition)

In the context of L2 acquisition, Mazurkewich (1985) and Bardovi-Harlig (1987) conducted the first studies indicating that L2 learners omit the preposition from wh-questions and RCs that select PPs. However, the authors did not provide a detailed analysis of this aspect. For instance, Bardovi-Harlig did not explore the possible reasons behind the “no-prep” findings and instead interpreted them as a grammatical developmental stage.

The deletability of the preposition in RCs and wh-questions by L2 learners who were aware of the subcategorization properties of the verbs was first addressed by Klein (1993). Klein analysed the acquisition of prepositional RCs in English by speakers of different L1s. She found that participants who do not accept the omission of the preposition in declarative sentences (15a) often admit its deletion in interrogatives (15b) or RCs (15c):

    1. (15)
    1. a.
    1.   The children are waiting for the bus.
    1.  
    1. b.
    1. *Which bus are the children waiting?
    1.  
    1. c.
    1. *This is the bus that the children are waiting.
    2. (Klein 2001: 37)

While some of Klein’s participants’ L1s allowed for the omission of the preposition in RCs, this was not the case for all of them. Therefore, it was concluded that Null-Prep in RCs and wh-questions is not dependent on the L1, but specific to the acquisition of L2 English.

Furthermore, Klein (1995) conducted a cross-linguistic study and concluded that in some languages (such as Haitian Creole, Northern Greece dialects, colloquial Brazilian Portuguese, colloquial Puerto Rican, Venezuelan Spanish, colloquial Italian, Catalan, Montreal French and Québecois) the subcategorized verb can omit its preposition in RCs, but not in questions. The examples from Haitian Creole, in (16), illustrate this asymmetry. The declarative sentence requires the preposition ‘de’ (16a), while the RC does not (16b). However, the corresponding interrogative is not allowed without the preposition (16c). Thus, the author assumed that the permissibility of Null-Prep in questions was unattested in natural languages.

    1. (16)
    1. a.
    1. Twa
    2. Three
    1. zanmi-yo
    2. friends-(pl)
    1. ap pale
    2. are talking
    1. de sinema
    2. about movie
    1. sa
    2. this
    1. a
    2. (top)
    1. ‘The three friends are talking about this movie.’
    1.  
    1. b.
    1. Men
    2. Here-is
    1. sinema
    2. movie
    1. (que)
    2. (that)
    1. twa
    2. three
    1. zanmi-yo
    2. friend-(pl)
    1. ap pale
    2. are talking (top)
    1.  
    1. c.
    1. De/*Ø
    2. About
    1. ki
    2. what
    1. sinema
    2. movie
    1. twa
    2. three
    1. zanmi-yo
    2. friends-(pl)
    1. ap pale?
    2. are talking
    1. ‘What movie are the three friends talking about?’
    2. (adapted from Klein 2001: 39)

Faced with the evidence that L2 learners (L2ers) of English accept and omit the preposition in questions (15b), the author concludes that the use of null prepositions could potentially violate Universal Grammar’s (UG) rules related to identification, licensing, and recoverability, particularly the Empty Category Principle. The proposal is that Null-Prep in ILG is evidence of a wild grammar, which does not conform with UG.

To determine if the absence of the preposition is unique to English, as claimed by Klein (1993), Jourdain (1996) analysed the omission of the preposition in French L2ers. She found that the deletion of the preposition may be constrained by the thematic role associated with the PP. Prepositions such as à ‘to’ and de ‘from,’ in argument positions, are more easily omitted than pour ‘to, for’ and avec ‘with,’ which introduce adjuncts. The omission of the preposition occurs in both RCs and questions (Jourdain 1996: 179). However, the asymmetry between PP arguments introduced by à and de and PP adjuncts introduced by avec is only statistically significant in questions. Jourdain speculates that the omission of the preposition results from a misconfiguration of parameters. Nevertheless, she disagrees with Klein and argues that some parts of UG are available when the preposition is omitted (Jourdain 1996: 240–244). The participants in her study showed sensitivity to the nature of the prepositions involved, revealing an asymmetry between weak and strong prepositions. This suggests that the faculty of language plays a role in the deletion of the preposition as well.

Dekydtspotter et al. (1998) propose that Null-Prep results from two related phenomena: interpretation of movement constructions as construals, not involving movement, and incorporation of the preposition within the verb. In particular, it is argued that L2 learners interpret interrogative and cleft sentences, such as those shown in (17) and (18), respectively, as construals where the null element is an A-bar bound pro (19a), rather than the trace of a moved element (19b).

    1. (17)
    1. De quel homme
    2. of which man
    1. es-ce
    2. be-prs.3sg-it
    1. que
    2. that
    1. tu
    2. 2sg
    1. as vu
    2. voir-pst.2sg
    1. une
    2. det.indf.f.sg
    1. peinture
    2. painting
    1. par/?de
    2. by/of
    1. ce
    2. DEM
    1. peintre?
    2. painter?
    1. ‘Of which man is it that you have seen a painting by/of this painter?’
    1. (18)
    1. C’est
    2. It-be-prs.3sg
    1. d’Aristotle
    2. of Aristotle
    1. que
    2. that
    1. tu
    2. 2sg
    1. as vu
    2. voir-pst.2sg
    1. une
    2. det.indf.f.sg
    1. peinture
    2. painting
    1. par/?de Rembrandt.
    2. by/of Rembrandt.
    1. ‘It is of Aristotle that you have seen a painting by/of Rembrandt.’
    2. (adapted from Dekydtspotter et al. 1998: 343)
    1. (19)
    1. a.
    1. [CP Opi [IP……… [PP proi ] …..]]
    1.  
    1. b.
    1. [CP Opi [IP……… [PP ti ] …..]]
    2. (adapted from Dekydtspotter et al. 1998: 348)

Since categorical uniformity is a UG requirement on chain formation, the authors resort to Baker’s (1988) concept of Preposition Incorporation (PI) to explain the categorical mismatch between the moved wh-word (DP) and the PP gap. Dekydtspotter et al. note that an empty category like pro must be governed by a lexical category. However, a preposition cannot license a pro complement because it interferes with and blocks the government from the lexical V head. The authors adopt Baker’s proposal that the preposition moves out of the PP and incorporates into V’, enabling the head-licensing condition on object pro to be satisfied. The reason for this is that the VP complex resulting from the inclusion of the preposition takes a DP as its complement, not a PP. This proposal bans Null-Prep from sentence adjunct constructions since incorporating a preposition into a verb should not be possible across a CP, as required in sentence adjuncts.

Klein & Casco (1999) contrasted prepositional arguments and adjuncts in the L2 acquisition of wh-questions in English L2. The participants in their study completed a grammaticality judgment task (GJT) including questions with PiP, PS and Null-Prep. They found that, contrary to Dekydspotter et al. (1998), L2ers accepted the omission of the preposition with adjuncts.

Their analysis is as follows: a wh-element is base-generated in top, being “an in situ element that learners misanalyse from wh-constructions in the input which they are not secure enough to generate in a lower position and consistently move overtly” (Klein & Casco 1999: 357). Furthermore, the authors claim that in Null-Prep the object of the preposition is a null resumptive pronoun which takes the form of an operator, a big PRO. The preposition before the big PRO is also null:

    1. (20)
    1. [top wh] [CP . . . . . [PP PØ OP]]
    2. (adapted from Klein & Casco 1999: 357)

The wh-features of the operator need to be checked and trigger covert movement, pied-piping the empty PP into Spec/CP, as proposed in Den Dikken’s (1995) analysis of dative prepositions in English:

    1. (21)
    1. [top
    2.  
    1. wh] [CP [PP PØ OP]i [IP
    2. Who
    1. VP [PPt]
    2. did she listen?
    1. (adapted from Klein & Casco 1999: 357)

This explanation accounts for the existence of Null-Prep with both adjuncts and arguments (Klein & Casco 1999).

Klein later argues that L2ers exhibit incomplete acquisition of wh-movement due to a bias against PS in English, “particularly because prepositions are generally very weak and clitic-like in most languages and are prohibited from separating from their objects” (Klein 2001: 59).

Perpiñán (2010) examined the acquisition of prepositional RCs in L2 Spanish by Arabic and English native speakers. The study employed an experimental design with various tasks. In the oral production task (which inspired the one presented in this paper, see section 6), PiP was the strategy most produced by all groups (including a control group of Spanish native speakers). However, instances of Null-Prep were also recorded. Although the omission of the preposition was residual among native speakers (4.2%), it reached 19.8% among English learners and 16.7% among Arabic L2ers. Since Arabic does not display PS, Arabic participants’ results are not compatible with Klein’s hypothesis (2001), according to which the omission of the preposition is a consequence of the incomplete acquisition of wh-movement combined with a bias of the English speakers against PS. The results of Perpinán’s online GJT indicated that PiP was appropriately processed by all groups, against the idea that the deletion of the preposition resulted from economy principles in the derivation, as suggested by Dekydtspotter et al. (1998). Finally, a self-paced reading comprehension task was conducted to test whether L2ers violated the universal principle of recoverability of deletion with Null-Prep RCs. The overall results indicate that L2ers have comprehension accuracy results quite close to those of native speakers, suggesting that “convergence at the comprehension level is possible” between native and non-native speakers (Perpiñán 2010: 196). Furthermore, L2ers did not present problems in interpreting RCs with the omission of the preposition. However, in sentences with PiP, native speakers had better scores, indicating that the preposition contributes to the overall meaning of the sentence among them, but makes no semantic contribution for L2ers. In other words, L2ers’ interpretation of RCs is not affected by the strategy used. To sum up, Perpiñán (2010) argues that the omission of the preposition does not indicate a “wild grammar” but is a “systematical developmental stage” of the ILG that L2ers (and L1 learners) go through during the acquisition of oblique RCs (Perpiñán 2010: 183). The omission of the preposition results from the optionality of the preposition, which happens when the DP is in an A-bar position and the preposition is not necessary to the overall meaning of the sentence (as proposed by Kato 2010 for natural languages). Therefore, the preposition does not assign the Case of the DP, which is instead assigned by default. As a result, the P-Chop structure is found in the ILG and conforms to UG constraints.

More recently, Perpiñán & Cardinaletti (2024) analysed the omission of the preposition in wh-questions, prepositional RCs and sluicing constructions in L1 and L2 Spanish speakers (native English and Arabic speakers). They conclude that the omission of the preposition is a scalar phenomenon, occurring more frequently in RCs, followed by wh-questions and finally by sluicing constructions. The authors claim that this phenomenon applies to both native speakers and L2ers, but acknowledge that it is more prevalent in ILG. They attribute this to various factors: “The complexity of pied-piping, together with the weak L2 knowledge of functional prepositions and their relatively easy semantic recoverability makes perfect ground for missing the obligatory preposition along the way in the (complex) movement derivation” (Perpiñán & Cardinaletti 2024: 165).

To summarize, scholars have suggested that the omission of the preposition in L2 may be a result of impaired access to UG (Klein 1993; Jourdain 1996), a strategy to avoid movement constructions (Dekydspotter et al. 1998; Klein 2001), or a developmental stage (Perpiñán 2010; Perpiñán & Cardinaletti 2024). The omission of the preposition in the ILG of L2ers has been explained as a phenomenon of PI (Dekydspotter et al. 1998), building on Baker, or as an instance of inherent case marking (Perpiñán 2010), in line with Kato’s (2010) analysis of the same phenomenon in BP.

The authors agree that L2ers omit and accept the omission of the preposition in questions and RCs (Klein 1993; Jourdain 1996; Dekydtspotter et al. 1998; Klein & Casco 1999; Perpiñán & Cardinaletti 2024). Empirically, these proposals differ in the predicted contexts for the omission of the preposition: while some scholars expect it to occur with arguments and adjuncts (Klein & Casco 1999), others predict that the preposition is omitted more often with arguments than adjuncts (Jourdain 1996; Dekydtspotter et al. 1998).

6 The study

6.1 Research questions and hypotheses

We are examining a situation where the L2 (the target grammar) allows for the omission of the preposition (P-Chop) as a non-standard strategy to relativize prepositional PPs. In the learners’ native language, when the preposition is overt, prepositional RCs are produced with one single strategy, i.e., with resumptive elements. Although L2ers are exposed to P-Chop in the naturalistic input, it is not explicitly taught in the classroom.

The researchers noted that, in natural languages, the preposition is often omitted when the PP selects for an argument (contrasting with adjuncts), due to A-bar movement of the object of the preposition (Baker 1988; Kato 2010). Jourdain (1996) found similar results for the acquisition of wh-questions in the L2, but not for RCs; however, there is no general agreement on these findings. Klein & Casco (1999), for instance, provide evidence of Null-Prep in the L2 acquisition of wh-questions with both adjuncts and arguments. Given the differences between the omission of the preposition in natural languages and L2 acquisition, and the fact that non-native speakers are exposed to P-Chop in the naturalistic input, the aim of this study is to investigate whether L2ers are acquiring this property from the native EP input or if they are exhibiting instances of Null-Prep, found in L2 acquisition. In other words, we aim at understanding if the grammatical knowledge of second language learners differs from that of native speakers. Differences in P-Chop productions and acceptability rates between L2ers and native speakers may provide clues regarding L2ers’ access to UG, feeding the debate on whether adult L2ers have full access (Flynn & Martohardjono 1994; Schwartz & Sprouse 1994; 1996; Lardiere 2000), partial access (Eubank 1994; 1996; Hawkins & Chan 1997), or no access (Clahsen & Muysken 1986; Bley-Vroman 1990; Meisel 1997; Bley-Vroman 2009) to UG. Considering this, we formulate our first research question and related hypothesis below:

RQ1: Does native P-Chop have the same nature as the Null-Prep structure found in L2 acquisition?

Hypothesis 1: Native speakers show regularities in the omission of the preposition that are not necessarily reflected in the ILG of non-native speakers. More specifically, native speakers omit the preposition preferentially when it is selected by the verb (specifically with the combinations gostar de ‘like (of)’, precisar de ‘need (of)’, pensar em ‘think (about)’ and participar em ‘participate (in)’). Non-native speakers omit the preposition in all contexts (including when it introduces an adjunct). The omission of the preposition has a different nature in native production (P-Chop) and L2 acquisition (Null-Prep).

Several studies have suggested that the omission of the preposition in the context of L2 acquisition is a developmental phenomenon (Bardovi-Harlig 1987; Perpiñán 2010; Perpiñán & Cardinaletti 2024). Therefore, our second RQ and related hypothesis address the potential effect of proficiency on the manifestation of this phenomenon:

RQ2: Do advanced and intermediate speakers show differences in the production and acceptance of prepositional RCs omitting the preposition?

Hypothesis 2: A proficiency effect is expected, with intermediate speakers showing more evidence of Null-Prep (developmental). Advanced speakers are closer to the target grammar and show more instances of P-Chop.

6.2 Participants

A total of 102 participants (N = 102) successfully completed the experiment, including a control group of 30 native EP speakers and 72 MC learners of EP. All non-native participants were exposed to MC through school at a very young age, regardless of their native dialect.8 In addition, non-native participants (61 female, 11 male; mean age = 19.32 years, SD = 3.79) were attending or had attended a course in Portuguese as a Foreign Language (PFL), and they were divided into two groups based on the level of the language course they were taking or that they had completed: 36 intermediate learners (B1–B2 levels of the Common European Framework of Reference for Languages; CEFR) and 36 advanced learners (C1–C2 levels; CEFR). Most participants had also been exposed to or instructed in English. However, EP is here considered an L2 since the L2 concept is understood broadly, as one of the main non-native languages acquired by the speakers outside the family context.

The native control group of EP speakers (28 females and 2 males) attended Lisbon University’s School of Arts and Humanities (mean age = 24.71, SD = 18.15), except for one participant (already graduated).

To ensure that participants were familiar with the argument grid of the verbs tested, they took a pre-test consisting of a cloze test with the 8 experimental verbs and 14 fillers (Learnclick platform), where they had to select one of four options, including an option without a preposition. Failure to recognize that the experimental items required a preposition resulted in exclusion from the study. Out of the initial group of 118 non-native speakers who took the pre-test, only 74 (63%) met the inclusion criteria for the study. However, two of these were later excluded as they did not complete all of the experimental tasks. All participants answered a linguistic questionnaire based on Carrol & Conklin (2017) and Slabakova (2015), including questions on how frequently they spoke, wrote, listened to, and read in Portuguese.

6.3 Experimental Items

Only verb + preposition (V + Prep) pairings compatible with the prepositions em and de were selected. These were chosen based on their frequency in EP (see Santos 2014: 35) and in the manuals and syllabus of PFL. The experimental combinations of V + Prep were also controlled for the type of PP: prepositional arguments of the verb and adjuncts introduced by a preposition were tested.

The prepositions introducing a PP argument do not assign the same theta roles to the 4 arguments analysed. The PPs selected by gostar ‘like,’ precisar ‘need,’ and pensar ‘think’ bear the theta role of theme, while the PP selected by participar ‘participate’ may be interpreted as a theme or an abstract locative. With adjunct PPs, the preposition expresses a locative origin meaning (gritar de ‘scream from’ and telefonar de ‘call from’) or a locative stative value (trabalhar em ‘work in’ and estudar em ‘study in’).

Pied-Piping (standard) with the invariable relativizer que ‘that’ or with the variable relativizer o (a) qual (literally: ‘the which’), also available in EP, is expected in the 8 scenarios considered. In the cases where the PP has a locative value, a subtype of PiP with the relativizer onde ‘where’ (instead of the standard combination Prep + relativizer) is also possible, in particular with the combinations participar em (este é o concerto onde a cantora participou ‘this is the show where the singer participated’), estudar em (esta é a biblioteca onde a Tatiana estuda ‘this is the library where Tatiana studies’), trabalhar em (este é o aeroporto onde o piloto trabalha ‘this is the airport where the pilot works’), telefonar de (este é o escritório onde a Joana telefona todos os dias ‘this is the office where Joana calls every day’), gritar de (este é o jardim onde a Nádia gritou ‘this is the garden where Nadia screamed’). Table 1 provides a schematic representation of the possible combinations of relativizer and preposition.

Table 1

Experimental verbs and possible combinations of relativizer and preposition.

Relativizer(s) Que ‘that’ o (a) qual (‘the which’) onde ‘where’
Prepositions de (from) em (in) de Ø
Verb selecting an argument PP gostar ‘like’ yes
precisar ‘need’ yes
pensar ‘think’ yes
participar ‘participate’ yes yes
Verb preceding an adjunct PP gritar ‘scream’ yes yes yes
telefonar ‘call’ yes yes yes
trabalhar ‘work’ yes yes
estudar ‘study’ yes yes

6.4 Tasks

6.4.1 Oral Production Task

The goal of this task was to identify the preferred strategy for producing RCs: the standard PiP or non-standard P-Chop or Resumption. On a computer screen, participants saw a scenario (two sets of pictures) together with information about each image. The researcher read aloud the information that was written on the screen using the procedure adopted in Perpiñán’s (2010) study. Participants had to reply to a question on the following slide, which featured a portion of the preceding image. To make sure that the extracted component for each sentence was the intended one, the initial words of each response were given. The material was presented both verbally and in writing to guarantee that the non-native participants had no trouble remembering the details they needed to build the RC. The participants were instructed to say the sentence as quickly as they could, using the information given, to elicit a more implicit response. Eight target items for prepositional RCs (four arguments and four adjuncts) were included in the experimental items. As control items, eight target items elicited direct object RCs, to confirm that participants could produce RCs. Additionally, 18 pure fillers with unrelated structures were added to the task. There were 34 items in total (16 RCs items, 18 non-RCs items), in 68 slides (see Supplementary Files Instrumentation, A2).

Scenarios were randomly divided into two lists, each with identical items but in a different sequence. To prevent skewed results, half of the participants performed the task in order A and the other half in order B. Figure 1 illustrates an example of an experimental item from the oral production task.

Figure 1: Example of an experimental item of the oral production task.

6.4.2 Self-Paced Reading Acceptability Judgment Task

The purpose of the Self-Paced Reading Acceptability Judgment Task (SPR-AJT) was to tap into the implicit ILG, assessing if participants accepted prepositional RCs with the standard and non-standard relativization strategies. It contained 100 sentences pseudorandomized into 10 blocks, ensuring that two items from the same condition or containing the same verb would not follow one another (see Supplementary Files, Instrumentation, A1). If necessary, breaks could be taken in between each block. On a computer screen, participants read each sentence in a non-cumulative, word-by-word format. The participants were asked to rate the sentence as soon as the final word disappeared and a sliding bar appeared on the screen. The sliding bar’s left edge had a 0 with the words “very bad” beneath it, while the extreme right had a number 1 with the words “very good.” Participants were informed that this line went on continuously and that they could rate the sentence using the computer’s trackpad at any point along the scale. The utilisation of a sliding bar instead of a Likert scale was intended to facilitate a more intuitive response and circumvent the issue of uneven gaps. The SPR-AJT included a time constraint; participants had to press the space bar on their keyboard to reveal the next word in each segment, which showed as a row of dashes. The word would, however, automatically disappear after 300 milliseconds and be replaced with the following section if the participants had not moved on to the subsequent word. Time pressure, which is thought to be important to tap into the implicit knowledge of these structures, is present in this method while still permitting the participants to choose their own reading path (allowing for varying reading speeds for native and non-native speakers). Before the experiment began, participants read the instructions and completed four practice trials. Non-native participants received instructions in Portuguese and Mandarin Chinese. The experiment was programmed using PsychoPy 3.2.3.9

6.4.3 Selection of Items for the SPR- Acceptability Judgment Task

The experimental items included only prepositional RCs; as in the oral production task, direct object RCs were included as baseline/control items, making sure that the participants had no problem with RCs. Prepositional RCs were tested for the three relativization strategies (PiP, P-Chop, and resumption) and the same V + Prep combinations were included as in the oral production task. As a result, there were a total of 24 experimental prepositional RCs: 12 with arguments (4 verbs × 3 strategies) and 12 with adjuncts (4 verbs × 3 strategies). The task also included 60 fillers, 20 of which were grammatical and 40 of which were not (in sum, 16 direct object RCs, 24 prepositional RCs, and 60 filler sentences, 100 sentences in total, see Supplementary Files, Instrumentation, A1).

Argument (22) and adjunct (23) RCs are illustrated below. The standard strategy presents the preposition; in the non-standard P-Chop the preposition is not pronounced.

    1. (22)
    1. O
    2. det.m.sg
    1. filme
    2. movie
    1. (em)
    2. in
    1. que
    2. rel
    1. a
    2. det.f.sg
    1. aluna
    2. student
    1. pensou
    2. think-pst.3.sg
    1. é
    2. be-prs.3.sg
    1. interessante
    2. interesting.
    1. ‘The movie about which the student thought is interesting.’
    1. (23)
    1. O
    2. det.m.sg
    1. café
    2. coffee-shop
    1. (em)
    2. in
    1. que/onde
    2. rel/rel-where
    1. a
    2. det.f.sg
    1. rapariga
    2. girl
    1. trabalha
    2. work-prs.3.sg
    1. tem
    2. has-prs.3.sg
    1. muitos clientes.
    2. many customers
    1. ‘The coffee-shop that the girl works in it has a lot of costumers.’

6.5 Procedure

The tasks involved in this study were performed in a single session of around 45–60 minutes. First, the participants completed the oral production task and then the SPR-AJT.

Before the Covid-19 epidemic, the tasks were administered to 47 participants in person. Every face-to-face meeting took place in a quiet setting. However, during the pandemic, the experiment had to be modified to accommodate the lockdown restrictions. The process remained the same, but Zoom sessions took the place of face-to-face meetings; the self-paced reading task was conducted on PsychoPy, but it was accessed remotely. 54 Chinese-speaking participants and one Portuguese-speaking participant had remote access to the author’s computer. The reaction times were not taken into consideration since it was not possible to ensure that the remote access had not materially affected the results.

7 Results

7.1 Oral Production Task

Table 2 presents the global results of the oral production task.

Table 2: Strategies produced by the three groups in the relativization of arguments and adjuncts.

Arguments Adjuncts
PiP Loc. P-Chop Others Total PiP Loc. P-Chop Others Total
Native EP n 54 2 53 11 120 42 58 7 13 120
(n = 30) % 45% 2% 44% 9% 100% 35% 48% 6% 11% 100%
Adv. L2ers n 103 2 33 6 144 81 34 21 8 144
(n = 36) % 72% 1% 23% 4% 100% 56% 24% 15% 6% 100%
Int. L2ers n 75 2 46 21 144 63 29 44 8 144
(n = 36) % 52% 1% 32% 15% 100% 44% 20% 31% 6% 100%

The sentences (24)–(27) illustrate each one of the strategies with arguments (a.) and adjuncts (b.):

[Pied-Piping]

    1. (24)
    1. a.
    1. Este
    2. dem.m.sg
    1. é
    2. be-prs.3sg
    1. o
    2. det.m.sg
    1. espetáculo
    2. show
    1. em que
    2. in rel
    1. a
    2. det.f.sg
    1. cantora
    2. Singer
    1. participou.
    2. participate-pst.3sg
    1.  
    1. b.
    1. Este
    2. dem.m.sg
    1. é
    2. be-prs.3sg
    1. o
    2. det.m.sg
    1. aeroporto
    2. airport
    1. em que
    2. in rel
    1. o
    2. det.m.sg
    1. piloto
    2. pilot
    1. trabalha
    2. work-prs.3sg

[Locative]10

    1. (25)
    1. a.
    1. Este
    2. dem.m.sg.
    1. é
    2. be-prs.3sg
    1. o
    2. det.m.sg
    1. espetáculo
    2. show
    1. onde
    2. where
    1. a
    2. det.f.sg
    1. cantora
    2. singer
    1. participou.
    2. participate-pst.3sg
    1.  
    1. b.
    1. Este
    2. dem.m.sg.
    1. é
    2. be-prs.3sg.
    1. o
    2. det.m.sg
    1. aeroporto
    2. airport
    1. onde
    2. where
    1. o
    2. det.m.sg
    1. piloto
    2. pilot
    1. trabalha.
    2. work-prs.3sg

[P-Chopping]

    1. (26)
    1. a.
    1. Este
    2. dem.msg
    1. é
    2. be-prs.3sg
    1. o
    2. det.m.sg
    1. espetáculo ∅
    2. show
    1. que
    2. rel
    1. a
    2. det.f.sg
    1. cantora
    2. singer
    1. participou.
    2. participate-pst.3sg
    1.  
    1. b.
    1. Este
    2. dem.f.sg
    1. é
    2. be-prs.3sg
    1. o
    2. det.m.sg
    1. aeroporto
    2. airport
    1. que
    2. rel
    1. o
    2. det.m.sg
    1. piloto
    2. pilot
    1. trabalha.
    2. work-prs.3sg

[Resumption]

    1. (27)
    1. a.
    1. Este
    2. dem.msg
    1. é
    2. be-prs.3sg
    1. o
    2. det.m.sg
    1. espetáculo
    2. show
    1. que
    2. rel
    1. a
    2. det.f.sg
    1. cantora
    2. singer
    1. participou
    2. participate-pst.3sg
    1. nele.
    2. in-it
    1.  
    1. b.
    1. Este
    2. dem.f.sg
    1. é
    2. be-prs.3sg
    1. o
    2. det.m.sg
    1. aeroporto
    2. airport
    1. que
    2. rel
    1. o
    2. det.m.sg
    1. piloto
    2. pilot
    1. trabalha
    2. work-prs.3sg
    1. nele.
    2. at-it

Both in relativizing arguments and adjuncts, L2ers deviated from native EP by producing a wider variety of sentences, including grammatical and non-grammatical ones.11 Notably, resumption was not produced by any participant, native or non-native.

PS, which has been identified as the most productive strategy in English (see, for example, Klein 1993 and Salles 1997), was produced residually with the two types of PPs (arguments or adjuncts). As stated in section 6.2., the non-native participants had prior exposure to or instruction in English. Although English may have facilitated the acquisition of wh-movement, it is not possible to draw any conclusions regarding the role of English in this process, given that the knowledge of English RCs was not controlled. Evidence of the influence of English would be the use of PS in the oral production task. Nevertheless, the study identified only a small number of sentences with PS, predominantly from the same participant and categorised as “others.” This indicates that the influence of English on non-native production was relatively limited.

7.1.1 Arguments

Looking at the general data (Table 2), the first noteworthy aspect is that advanced L2 speakers, as opposed to native speakers, were more likely to use PiP (72% vs. 45%) showing lower rates of P-Chop (23%). A chi-square test of independence was performed using Jamovi (version 2.3) to evaluate the relationship between the strategies and the groups. The relationship between these variables was significant (χ2 (6), N = 408, 26.6, p = <0.001, Cramer’s V = 0.180). Native speakers used P-Chop (44%) and PiP (45%) as their preferred strategies to relativize arguments.12 The three groups diverge significantly in their use of PiP to relativize arguments (χ2 (2) = 8.858, p = <0.012, Cramer’s V = 0.2), and also in the production of P-Chop (χ2 (2) = 9.299, p = <0.010, Cramer’s V = 0.27). The locative strategy was not manipulated as a dominant variable in an identical χ2 test with arguments, because there was only one verb subcategorizing an argument admitting the locative strategy (participar, ‘participate’).

Table 3 shows the results of the oral production task considering the relativization of arguments by verb.

Table 3: Strategies produced by the three groups in the relativization of arguments (by verb).

Verb + Prep Group Strategy Total
PiP Loc. P-Chop Others
n % n % n % n % n %
gostar de ‘like (of)’ Native EP 10 33% N/A 17 57% 3 10% 30 100%
Adv.L2ers 30 83% 4 11% 2 6% 36 100%
Int. L2ers 23 64% 7 19% 6 17% 36 100%
precisar de ‘need (of)’ Natives 8 27% N/A 19 63% 3 10% 30 100%
Adv.L2ers 25 69% 9 25% 2 6% 36 100%
Int. L2ers 23 64% 8 22% 5 14% 36 100%
pensar em ‘think (about)’ Native EP 17 57% N/A 12 40% 1 3% 30 100%
Adv.L2ers 21 58% 13 36% 2 6% 36 100%
Int. L2ers 13 36% 20 56% 3 8% 36 100%
participar em ‘participate (in)’ Native EP 19 63% 2 7% 5 17% 4 13% 30 100%
Adv.L2ers 27 75% 2 6% 7 19% 0 0% 36 100%
Int. L2ers 16 44% 2 6% 11 31% 7 19% 36 100%

The analysis by verb (Table 3) indicates that native speakers show a preference for P-Chop with the verbs selecting de (gostar de ‘like’ (of) and precisar de ‘need’ (of)), using more PiP with the verbs selecting em (pensar em ‘think’ (about)), especially with participar em ‘participate’ (in)). On the contrary, the learners have higher rates of P-Chop with pensar em ‘think’ than with the other verbs, showing that learners and the control group do not necessarily converge in the relativization strategies chosen for each combination of V + Prep.

7.1.2 Adjuncts

With adjuncts, a chi-square test of independence was conducted using Jamovi (version 2.3) to evaluate the relationship between the strategies and the groups. The relationship between these variables was significant (χ2 (6), N = 408, 54.1, p = <0.001, Cramer’s V = 0.258). The locative strategy was preferred by native speakers – a χ2 test shows that the difference between groups in the production of locative with adjuncts is statistically relevant (χ2 (2) = 20.287, p = <0.001, Cramer’s V = 0.41). The differences in the production of P-Chop are also significant: intermediate speakers have higher rates of P-Chop, followed by advanced speakers and native speakers. A χ2 test taking the P-Chop strategy as the dominant variable, and comparing its production in the three groups, indicates a significant difference (χ2 (2) = 23.853, p = <0.001, Cramer’s V = 0.58).

Advanced Chinese learners prefer PiP (56%), followed by the locative strategy (24%) and then P-Chop (15%). A χ2 test shows that these differences are significant for advanced learners (χ2 (3) = 84.389, p = <0.001). Native speakers alternate between PiP (35%) and the locative strategy (48%), and these differences are statistically relevant (χ2 (3) = 58.200, p = <0.001). Intermediate Chinese participants are divided between PiP (44%), locative (20%), and P-Chop (31%), showing relevant differences (χ2 (3) = 45.167, p = <0.001).

The results obtained in the relativization of adjuncts by verb are presented in Table 4.

Table 4: Strategies produced by the three groups in the relativization of adjuncts (by verb).

Verb + Prep Group Strategy Total
PiP Loc. P-Chop Others
n % n % n % n % n %
gritar de ‘scream (of)’ Native EP 10 33% 16 53% 2 7% 2 7% 30 100%
Adv. L2ers 28 78% 1 3% 5 14% 2 6% 36 100%
Int. L2ers 20 56% 6 17% 7 19% 3 8% 36 100%
telefonar de ‘call (from)’ Natives 9 30% 12 40% 1 3% 8 27% 30 100%
Adv. L2ers 18 50% 7 19% 7 19% 4 11% 36 100%
Int. L2ers 17 47% 2 6% 15 42% 2 6% 36 100%
trabalhar em ‘work (at)’ Native EP 13 43% 13 43% 2 7% 2 7% 30 100%
Adv. L2ers 15 42% 15 42% 5 14% 1 3% 36 100%
Int. L2ers 12 33% 7 19% 15 42% 2 6% 36 100%
estudar em ‘study (in)’ Native EP 10 33% 17 57% 2 7% 1 3% 30 100%
Adv. L2ers 20 56% 11 31% 4 11% 1 3% 36 100%
Int. L2ers 14 39% 14 39% 7 19% 1 3% 36 100%

In the analysis of adjuncts, the first aspect to highlight is that, for native speakers, the use of the locative strategy does not depend on the preposition since they produce it with em and de. The two groups of learners show more expressive rates of the locative strategy with the verbs that precede the preposition em, perhaps indicating that they associate this preposition with a semantic locative feature. Finally, intermediate speakers stand out by showing higher percentages of P-Chop with all verbs. The preposition does not seem to be the factor motivating this choice, since they have equal rates of P-Chop with telefonar de ‘call (from)’ and trabalhar em ‘work (at)’ (42% in each case), and with gritar de ‘scream (of)’ and estudar em ‘study (in)’ (19% in each case).

7.1.3 Production of P-Chop in the relativization of arguments and adjuncts

The data described above seem to indicate that native and non-native speakers omit the preposition in different contexts. Our first hypothesis (see 6.1.) is that the omission of the preposition has a different nature for native and non-native speakers. To verify this conjecture, a logistic mixed-effects regression model13 was fit, predicting the oral production of P-Chop against any other strategy, by group. A model with random intercepts for participant and item, as well as group and type, with the interaction, was included. Then, a model without that interaction was also fit. The model with the interaction had a significantly improved model fit as evidenced by the likelihood ratio test.14 The results are shown in Figure 2.

Figure 2: Predicted probability of P-Chop, by group.

The model confirms that, on the one hand, native speakers tend not to omit the preposition when an adjunct is relativized, diverging significantly from Intermediate L2ers in this respect (p = 0.0004). On the other hand, native EP speakers use P-Chop and PiP in the relativization of arguments, diverging significantly from Advanced L2ers (p = 0.0181), who choose mainly PiP in this context. The results from the native speakers’ group confirm that P-Chop is significantly more productive with arguments (p = 0.0001) than with adjuncts. However, the difference between these types of sentences was not significant for advanced (p = 0.1066) nor for intermediate learners (p = 0.8425) (see Supplementary Files, Results, A3, Table 3).

7.2 Self-paced reading acceptability judgment task

In the SPR-AJT, the data were analyzed using a mixed-effect logistic regression fit using the lme4 package in R (Bates et al. 2015; R Core Team 2021).15 As the nature of the percentage rating data could not be analyzed as continuous data,16 it was binarized to be either 0 or 1, with the cutoff being based on the distribution of the data. The models included random intercepts for participant and item, as well as random slopes for both Argument/Adjunct contrast and Strategy (PiP or Resumption), by participant.17 A model containing these two predictors and language background was fit. As it was pertinent to our research questions whether or not the effects of each predictor would vary, based on the levels of other predictors, all potential interactions were tested. The contribution of these interactions was tested by comparing nested models with the likelihood ratio test. The final models reported here all provided significantly improved fits over reduced models. In keeping with recommended statistical practices, all experimental conditions were kept in all models regardless of their contribution to model fit.

Figures 3, 4, 5 display the mean acceptability rates (before binarization) given to RCs formed with PiP (Figure 3) and P-Chop (Figure 4) by the three groups of speakers, where 0 meant “very bad” and 1 meant “very good”; recall that participants could choose any intermediate point in the scale (see Supplementary Files, Results, A4). All participants gave higher ratings to RCs formed by PiP. In the overall results (that include arguments and adjuncts), P-Chop was rated at chance level by the three groups.

Figure 3: Mean SPR-AJT ratings for oblique RCs formed with PiP (0.4–1.0).

Figure 4: Mean SPR-AJT ratings for oblique RCs formed with P-Chop (0.0–1.0).

Figure 5: Predicted rates of acceptance of each strategy with arguments and adjuncts by group.

The full statistical model was the one adopted in this task. The reported model had an improved fit over the reduced model as evidenced by the likelihood ratio test χ2 (4) = 27.193, p = 1.817e-05.18 Following the application of the statistical model, Figure 5 shows the projected likelihood of acceptance of each strategy by group while examining the distinctions between arguments and adjuncts.

This plot already gives us an idea that the status of the relativized PP is more relevant with P-Chop, especially for native speakers. Whether the relativized element is an adjunct or an argument does not seem relevant with PiP. Resumption is rejected more strongly by native speakers and advanced learners than by intermediate learners, regardless of the status of the relativized PP.

7.2.1 Between Groups differences19

After running the statistical model, the interaction between groups and relativization strategies reveals that the differences between native speakers and advanced learners are not relevant in the acceptance of PiP in the relativization of adjuncts (p = 0.0697) or arguments (p = 0.9998). Similarly, the two groups of learners do not diverge significantly in the acceptance of PiP with adjuncts (p = 0.3776) and arguments (p = 0.5274). Native speakers differ from intermediate learners in the acceptance of PiP with adjuncts (p = 0.023), but not with arguments (p = 0.5518) (see Figure 5 in section 7.2., and Tables 4 and 5 Supplementary Files, A3). The difference between intermediate learners and native EP in the acceptance of PiP with adjuncts indicates that intermediate learners’ intuitions of the standard PiP strategy are not as robust as those of native speakers’ and advanced learners’.

The interaction between groups and relativization strategies also indicates that native speakers diverge significantly from advanced L2ers (p = 0.0304) and intermediate L2ers (p = 0.0005) in the rating of P-Chop with adjuncts (see Supplementary Files, A3, Table 8). Native speakers and the two groups of L2ers do not diverge significantly in the acceptance rates of P-Chop with arguments (advanced, p = 0.1363; intermediate, (p = 0.0676) (see Supplementary Files, A3, Table 9). Intermediate and advanced learners do not differ significantly in the acceptance of P-Chop with adjuncts (p = 0.3915) (see Supplementary Files, A3, Table 8).

7.2.2 Within Groups Differences

The comparison of the 3 options in the context of the interactions predicts that, for native speakers, the difference between strategies (P-Chop vs. PiP; P-Chop vs. Resumption and PiP vs. Resumption) is statistically relevant within arguments and within adjuncts (all with p = <0.001) (see Supplementary Files, A3, Tables 10 and 11). Furthermore, the model shows that the differences in the acceptance of P-Chop with arguments vs. adjuncts for native speakers is statistically significant (p = <0.001), but this does not occur with the other strategies (see Supplementary Files, A3, Table 12).

Advanced learners also distinguish the three relativization strategies. The difference of the predicted ratings assigned to PiP and P-Chop, and PiP and Resumption are statistically significant (p < 0.0001) with arguments and adjuncts. These results show that advanced learners recognize PiP as the standard strategy with confidence. The expected ratings given by advanced learners to P-Chop and Resumption are also statistically significant with arguments (p = 0.0008) and adjuncts (p = 0.0247) (see Supplementary Files, A3, Tables 13 and 14). Advanced learners do not differ significantly in the acceptance of P-Chop with arguments vs. adjuncts (p = 0.5026), nor in the acceptance of resumption with arguments vs. adjuncts (p = 0.6828), but the difference in the acceptance of PiP with arguments vs. adjuncts is significant (p = 0.0262) (see Supplementary Files, A3, Table 15).

Finally, intermediate speakers show a less stabilized grammar. The only relevant differences are between P-Chop and PiP with arguments (p = <0.0001), and PiP and Resumption with arguments (p = <0.0001) and adjuncts (p = 0.0001). The other contrasts are not statistically significant, showing that intermediate learners do not distinguish P-Chop from Resumption with arguments (p = 0.3446) nor with adjuncts (p = 0.1010). The differences between the standard strategy (PiP) and the non-standard P-Chop are also not relevant when adjuncts are relativized (p = 0.0624) (see Supplementary Files, A3, Tables 16 and 17). When the rates attributed to each strategy with arguments and adjuncts are compared, the data show that the acceptance of P-Chop with arguments vs. adjuncts is not statistically significant for intermediate learners (p = 0.3031). Intermediate learners do not rate resumption as significantly different with arguments and adjuncts either (p = 0.7139). Like advanced learners, the ratings attributed by intermediate learners to PiP with arguments and adjuncts differ statistically (p = 0.0141) (see Supplementary Files, A3, Tables 18).

8 Discussion

Although the outcome of P-Chop and Null-Prep is superficially the same – the absence of the preposition –, these two mechanisms seem to have a different nature: P-Chop is part of the grammar of native speakers, while Null-Prep is developmental for L2ers. The claim that P-Chop is grammatical seems radical since it is not described in prescriptive Portuguese grammars. However, different experimental studies (Antunes & Brito 2007; Espírito Santo 2020; Amorim 2022) and corpus-based research (Alexandre 2000; Santos 2014; Aßmann & Rinke 2017; a.o.), as well as the present work, have shown evidence that the P-Chop strategy exists in complementary distribution with the PiP strategy in the grammar of native speakers. Therefore, even though it is not sanctioned by prescriptive grammars or manuals, it can be said to be grammatical.

The regularities demonstrated by native speakers, who preferentially produce and accept P-Chop with arguments, confirm the findings of studies on EP (e.g. Santos 2014; Aßmann & Rinke 2017; Espírito Santo 2020). This calls into question the claims made by Veloso (2013), who suggests that P-Chop is more commonly used with adjuncts (e.g. the relativization of temporal or locative PPs). However, native speakers do not accept the omission of the preposition with the same verbs if the sentence is declarative (i.e., not involving wh-movement) (Brito 1995; Espírito Santo 2020). So, there is no evidence of changes in the argument grid that would explain the omission of the preposition in relative clauses. The question is, if there are regularities, what is the reason underlying native P-Chop and in what contexts may it occur?

Following Kato (2010), we assume that the omission of the preposition in EP is determined by a set of formal and semantic features, occurring preferentially when the Prep is selected by the verb and assigns inherent Case (with arguments). According to Kato (2010) and Espírito Santo (2020), we believe that the theta roles connected to the relativized elements might also be playing an important part in determining the absence of the Prep. Indeed, native EP speakers seem to consistently accept the omission of the preposition with other verbs not tested in the present study that also select an object playing the theta role of theme, such as lembrar-se de, recordar-se de ‘remember of’, esquecer-se de ‘forget about’, assistir a ‘watch to’, chamar a ‘call to’, falar de ‘talk about’ (Espírito Santo 2020: 169–170).

However, native speakers judge as ungrammatical P-Chop RCs with verbs that combine with a locative or goal, such as viver em ‘live in’ or chegar a ‘arrive to’ (Espírito Santo 2020: 170). Possibly it is not a coincidence that native speakers did not produce P-Chop as frequently with participar em ‘participate in’ (see Table 3) as with the other 3 verbs that select for an argument, given that the complement of participar ‘participate’ may be interpreted as a locative (the word espetáculo ‘show’ may refer to the physical surroundings at the moment of the show, see earlier Figure 1 and Supplementary Files, Instrumentation, A2). In addition, unlike the verb participar ‘participate’, the verbs gostar ‘like’, precisar ‘need’, and pensar ‘think’ can take a complement clause without a preposition (e.g. gosto que…’I like that…’, preciso que ‘I need that…’, ‘I think that…’), which may lead to the omission of the preposition.20

In the relativization of adjuncts, native speakers alternated between the locative and PiP strategies. In other words, given that the adjuncts tested hold a [+] locative semantic feature, the locative strategy replaced P-Chop and is in complementary distribution with PiP. This strategy may explain the absence of P-Chop when the object of the relativization has a [+] locative semantic feature.

The present paper adopts Kato’s proposal that an argument P-Chop RC involves an ICP that is not present in the Numeration. ICPs can only be absent when the argument is in an A’ position. If an ICP occurs in an A position, the resulting sentence will not be acceptable, as shown previously, in sentence (12a). This explains why P-Chop occurs in RCs involving movement, and not in declarative clauses (Brito 1995; Espírito Santo 2020). However, we propose a different derivation. While Kato assumes that the DP complement moves to TopP inside CP, adopting a raising analysis (Bianchi 1999; 2000; de Vries 2002; Kayne 1994; Kenedy 2007; Kato & Nunes 2009), we follow Rinke & Aβmann’s head external analysis for RCs in EP (Rinke & Aβmann 2017: 19 and following). Their proposal accounts for all RCs in EP and avoids some of the theoretical and empirical issues that the raising analysis poses in EP (see Rinke & Aβmann 2017, who provide a deeper discussion of this issue, which is out of the scope of the present paper). Since, according to Kato 2010, the preposition is not selected in the Numeration, I assume that the element introducing P-Chop RCs is the same as in subject/direct object relative clauses (a transitive determiner, following Rinke & Aβmann 2017) and that the derivation is equivalent. Accordingly, que is generated in the argument base position, holding an empty NP as its complement. The empty NP relates with the external head NP through coindexation. Cº holds an unvalued uWh feature and probes for an iWh value feature, targeting the DPREL, which moves to Spec, CP. Figure 6 illustrates the derivation starting from Stage 2, as Stage 1 consists of the Numeration, where the preposition is not selected.

Figure 6: Proposed structure for P-Chop RCs.

The L2 data collected in our study do not point towards the same regularity. Intermediate learners omit/accept the omission of the preposition regardless of the status of the relativized PP (arguments/adjuncts) and regardless of the theta role at stake (theme or locative). Advanced learners produce and choose PiP in contexts where native speakers are divided between PiP and the omission of the preposition (with arguments playing the theta role of theme).

It seems that L2ers are not necessarily acquiring the Null-Prep mechanism from the native input, given that they produce it in different contexts (also in adjunct relativization). Indeed, the L2ers’ results do not reflect the regularities of native P-Chop, which confirms our first hypothesis: native speakers show regularities that are not visible in L2 production, corroborating previous findings, namely, that the omission of the preposition is more likely to happen when an argument of the verb is relativized than when the preposition precedes an adjunct.

Our findings reveal a proficiency/formal learning effect: advanced learners prefer the standard PiP, differing from the behavior of native speakers, who alternate PiP and P-Chop with arguments/themes. Intermediate learners show instances of Null-Prep with arguments and adjuncts. A similar proficiency effect was found in Klein & Casco’s (1999) data. Thus, our second hypothesis is partially confirmed: intermediate speakers exhibit a less stable grammar, with more evidence of developmental Null-Prep. However, advanced speakers are not closer to the target grammar, given that they do not exhibit the same regularities that native speakers do. This outcome is possibly an effect of explicit classroom learning, since advanced L2ers prefer the standard language target strategy.

So, why do Chinese L2ers of EP omit the prepositions with adjuncts? It is true that the lack of knowledge of the verb’s selectional properties may provide an explanation for the omission of the preposition in the relativization of arguments (Perpiñán 2010; Perpiñán & Cardinaletti 2024), even more so under time-pressure. Nevertheless, as adjuncts are not selected by the verb, the lack of knowledge of the selectional characteristics of the verb does not explain the entire phenomenon.21

The lack of an asymmetry between arguments and adjuncts has been found in other studies on the L2 acquisition of RCs (Klein 1993; Jourdain 1996) and wh-questions (Klein & Casco 1999). In particular, Klein & Casco (1999) argue that L2ers are pied-piping a null resumptive which takes the form of a big PRO (Klein & Casco 1999: 357). Following the PRO theorem, PRO must be ungoverned (Chomsky 1981; Kayne 1991), and this rules out an overt preposition: “PRO may function as an empty operator, requiring null case which can be assigned by the null preposition”. The null preposition is pied-piped with the null operator, in null operator movement. This analysis accounts for the occurrence of Null-Prep instances with adjuncts and explains the contrast with the data from native speakers. It also fits within the limits of UG, since L2ers drop the preposition when they are doing covert movement, as predicted by the PRO theorem. Nevertheless, contrary to what Klein & Casco (1999) and Klein (2001) claim for L2 English, this cannot be due to a bias against PS, given that PS practically does not exist in EP. We believe that this incomplete acquisition of wh-movement is a developmental stage that may be overcome with exposure to the language, as proficiency advances, as our results also indicate.

Finally, this study demonstrates that native and non-native representations of P-Chop structures are not entirely equivalent. The data indicate that while native grammars may exclude the preposition in the numeration for certain types of arguments, non-native speakers consistently include a null preposition in all P-Chop cases. This explains why non-native speakers overextend P-Chop to the relativization of adjuncts. As proposed by Klein and Casco (1999), this does not imply that L2 learners are not accessing Universal Grammar (UG). Instead, it appears to indicate that L2 learners are accessing UG to restructure their ILGs in a developmental path towards the acquisition of this structure.

9 Conclusion

To conclude, we have argued that the omission of the preposition in prepositional RCs is a grammatical phenomenon in EP that does not relate to changes in the argument grid of the verb. It depends on the type of PP that is being relativized (argument or adjunct) and on the thematic role of the relativized element (the preposition seems to be more easily omitted with themes than with locatives). These findings are in line with the studies of Baker (1988) and Kato (2010), according to which the omission of the preposition is less likely to occur with adjuncts. To draw a hierarchy of thematic roles for EP, more experimental data need to be collected, controlling the thematic roles of the relativized PPs.

In L2 acquisition, the omission of the preposition seems to occur more randomly, and it is not determined by the same factors as in native grammars. Possibly the L2ers pied-pipe a covert operator and, following UG constraints, move a null preposition along with it. This explanation is supported by the high rates of overt PiP that L2ers produce, in comparison to native speakers. This explanation also accounts for the lack of contrast between arguments and adjuncts, showing, at the same time, that the L2 grammar is constrained by UG, even at developmental stages.

Abbreviations

1 First person
2 Second person
3 Third person
BP Brazilian Portuguese
CEFR Common European framework of reference for languages
cl Classifier
dem Demonstrative
det Determiner
EP European Portuguese
f Feminine
GJT Grammaticality judgment task
ICP Inherent case marking prepositions
ILG Interlanguage grammar
indf Indefinite
L1 First language
L2 Second language
LD Left dislocation
m Masculine
MC Mandarin chinese
Null-Prep Null-preposition
P-Chop Preposition-Chopping
PFL Portuguese as a foreign language
PI Preposition incorporation
PiP Pied-piping
pl Plural
Prep Preposition
ps Preposition stranding
prs Present
pst Past
RCs Relative clauses
rel Relativizer
RQ Research question
sg Singular
SPR-AJT Self-paced reading acceptability judgment task
UG Universal grammar
V + Prep Verb + preposition

Data availability

https://osf.io/v3ng4/?view_only=45458ba612f84509a4847faf5e8afc95.

Ethics and consent

The study was approved by the Ethics Committee of the School of Arts and Humanities of Lisbon University.

Funding information

The author acknowledges the financial support from the Portuguese National Science Foundation (FCT) to the Centre of Linguistics of the University of Lisbon (reference UIDB/00214/2020) and with the Ph.D. Scholarship (SFRH/BD/146971/2019).

The author acknowledges the financial support from the Rectorate of the University of Lisbon, with the Ph.D. Scholarship (BD2015#53558).

Acknowledgements

I would like to extend my gratitude to Nélia Alexandre, Sílvia Perpiñán and Ana Madeira for their invaluable contributions and comments on an earlier version of the manuscript. Furthermore, I would like to express my gratitude to Paula Luegi for her assistance with Psychopy and to Chao Zhou for his contributions to the Mandarin Chinese translations.

My gratitude extends to the three anonymous reviewers who offered constructive criticism on various aspects of the manuscript, as well as to the editor. I am most grateful to them for their time and insights.

My gratitude extends to all those who participated in the study.

Competing interests

The author has no competing interests to declare.

Notes

  1. Although non-standard strategies are attested in the oral and written speech of European Portuguese native speakers, they are considered non-standard because they are not sanctioned by prescriptive grammars of Portuguese and they are not taught to native-EP acquiring children’ nor in L2 language lessons. [^]
  2. “Embora numa perspetiva purista ambas as estratégias [cortadora e resumptiva] sejam consideradas marginais, o que é certo é que a primeira (estratégia cortadora) faz actualmente parte do registo oral de falantes altamente escolarizados, o que permite supor que estamos perante uma tendência de mudança, mesmo no português europeu.” [Although, from a purist perspective, both strategies [P-Chop and resumption] are considered as non-standard, the fact is that the first (P-Chop strategy) integrates the oral speech of highly instructed speakers, which allows us to suppose that we are facing a trend of change, even in European Portuguese.”] (Brito & Duarte 2003: 667, the translation is mine). [^]
  3. The authors treat oblique and verbal PPs separately without clarifying what criteria they take into consideration, which may have influenced their overall results. Duarte (2003), for instance, includes all syntactic functions that are not central under the designation ‘oblique’: “Chamam-se oblíquas (abreviadamente OBL) às relações gramaticais que não são centrais. Têm relações gramaticais oblíquas tanto argumentos obrigatórios e opcionais do predicador verbal (i.e., complementos do verbo) como adjuntos (…) os constituintes com relações gramaticais oblíquas são tipicamente de natureza preposicional, adverbial ou frásica. [We call oblique (abbreviated OBL) the grammatical relations that are not central. Mandatory and optional arguments of the verbal predicator (that is, complements of the verb) and adjuncts may have oblique grammatical relations (…) the constituents that have oblique grammatical relations are typically prepositions, adverbs or sentences.] (Duarte 2003: 294) (the translation is mine). [^]
  4. The authors consider verbal chopping cases that are usually classified as complement adjectival clauses, such as ser/estar habituado ‘be used to,’ estar ligado a ‘be connected to,’ ser curioso por ‘be curious by’. [^]
  5. The verbs tested were: agradar a ‘please (to),’ assistir a ‘assist to,’ esquecer-se de ‘forget (of),’ falar de ‘talk about,’ gostar de ‘like (of),’ lembrar-se de ‘remember (of),’ necessitar (de) ‘need of,’ precisar de ‘need (of),’ recordar-se de ‘remember (of)’. [^]
  6. This seems to be the case with the verbs agradar ‘please,’ precisar ‘need,’ necessitar ‘need’ and falar ‘speak’ (Espírito Santo 2020). [^]
  7. Ning (1993) identified gapped adjunct RCs in Mandarin Chinese, but, contrary to what is observed in EP, these are not a consequence of the relativization process. They occur with verbs that show the same behavior in matrix clauses. For this reason, we consider that non-native P-Chop cannot be explained as L1 transfer from these structures. [^]
  8. Thirty-nine of the participants were native speakers of Mandarin Chinese, 18 could speak Cantonese as their first language, 11 could speak both Mandarin and Cantonese, and 4 could speak other Chinese dialects as their first language. Cantonese native speakers were included in the study due to the structural similarities between prepositional RCs in Mandarin Chinese and Cantonese. [^]
  9. The participants in this study completed two SPR-AJTs, one designed to assess the participants’ ratings of each relativization strategy, which is described in this section, and a second one, which was focused on the ratings given to RCs formed with constituents extracted from syntactic islands. The second SPR-AJT focused on the acceptability of movement constraints that are beyond the present paper. [^]
  10. The relativizer ‘onde’, which has a [+locative] feature, cannot be combined with different prepositions in a linear way. The combination ‘*em onde’ (‘in where’) is ungrammatical because the preposition and the relativizer incorporate the same locative value. Additionally, native speakers exhibit inconsistency when combining ‘onde’ with other prepositions. For instance, they may omit the prepositions a ‘to’ and de ‘from’ when they are mandatory due to the lack of social prestige of the conflated forms aonde and donde (see Veloso 2013). Therefore, I argue that the omission of the preposition in relativization with ‘onde’ is not equivalent to other cases of P-Chop, as it seems to be motivated by social and historical factors. Instances of relativization with ‘onde’ have been classified as ‘locative’, regardless of the presence of the preposition. [^]
  11. These include the use of possessive structures, adjectives, descriptive expressions in place of the RC, the deletion of the relativizer, and cleft constructions. All these sentences were grouped under “others”. [^]
  12. Another unexpected result was the absence of resumption in oral production data. However, this result is not discussed in this article. See Espírito Santo et al. (2024) for a detailed analysis of resumption. [^]
  13. See Supplementary Files Analysis, Oral_production_analysis.R and A6_GLMM_OPT. [^]
  14. The random slope for Type by participant was abandoned because of a singular fit, but the results did not change significantly when the random slope was included. [^]
  15. See Supplementary Files, A5_GLMM_AJT1. [^]
  16. The data collected for this task could not be modelled as continuous nor as proportion data, as fitting a linear model leads to heteroskedastic patterns in the model residuals due to the bounded nature of the data. It also does not meet the requirement to be analysed as proportion data, as the ratings from participants are not a proportion of a binary outcome in a series of trials. [^]
  17. The distribution of the data showed a minimum in the density distribution at 0.61. Anything equal to or below 0.61 was treated as 0, and anything above it was treated as 1. [^]
  18. See Supplementary Files (Analysis, AJT_analysis.R and Generalized Linear Mixed Models, A5). [^]
  19. All results provided are given on the log odds ratio (not the response) scale; P value adjustment: Tukey method for comparing a family of 3 estimates. [^]
  20. I thank to one of the reviewers for pointing this out. [^]
  21. I am grateful to Ana Lúcia Santos for bringing this to my attention during the oral presentation of an earlier version of this paper. [^]

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