It is well-known that lexical frequency is positively correlated with word learning and processing speed. The more frequently children hear certain words, the faster they learn to use those words correctly. Higher frequency words (common words) are recognized and processed faster than lower frequency (or rare) words (see the discussion in Harley 2014: 143, 171–172). Furthermore, higher frequency words tend to be shorter than words with lower frequency, cf. ‘Zipf’s Law’ (Zipf 1935). In spite of this negative correlation between word frequency and word length, and though function words tend to be shorter than content words, the correlation between processing speed and frequency only applies to lexical content words, not to grammatical function words, e.g. auxiliary verbs, determiners, and complementizers (Harley 2014: 315; see also Bell et al. 2009; Piantadosi et al. 2011). Likewise, children’s acquisition of function words depends less on frequency of exposure than on the level of complexity (see section 1.5 below).

The question then is how this affects parsing, i.e. whether lexical frequency guides the online formation of the syntactic representation. It has been debated whether or not lexical frequency of e.g. verb-bias (selectional properties) is part of the lexical information which is directly available to inform online parsing strategies to resolve structural ambiguity (see e.g. Trueswell 1996; Bever et al. 1998; Pickering et al. 2000). However, the picture that emerges is that lexical frequency does not seem to have a clear, uniform (across the board) effect on processing, but instead seems to interact with other factors, including word class and word length. (For a brief discussion, see Newmeyer 2003: 695–698.)

Just like lexical frequency, the connection between acceptability and construction frequency (how often certain types of syntactic structures occur in corpora) seems to be less clear than one might expect. On the one hand, a close connection between construction frequency and acceptability rating has been reported by e.g. Bybee & Eddington (2006), Featherston (2008), and Kempen & Harbusch (2008). However, the study by Kempen & Harbusch (2008) on scrambling in German also shows that structures that received high acceptability ratings showed considerable variation in frequency of occurrence. Both Featherston (2008) and Kempen & Harbusch (2008) also found that structures with the highest acceptability ratings were also the most frequent ones, whereas differences in lower acceptability ratings were not reflected in the frequencies. Similar results were found by Bader & Häussler (2010), who also found that acceptability cannot be predicted from low construction frequency: Sentences with high acceptability ratings span a frequency range from high to very low (close to zero). Furthermore, very low frequency was associated with a wide range of acceptability ratings, from low to high.1 In a study on different types of wh-questions in French, Adli (2015) found that acceptability ratings and frequency of occurrence in spontaneous speech did not correlate. Though all types of wh-questions (nine in total, incl. wh in-situ and wh-fronting with and without subject-auxiliary inversion) were found to be fully acceptable, some of them were very common, others very rare. In addition, those with the highest acceptability scores were those which were considered more formal (or not colloquial), even though they had lower frequencies.

Overall, the empirical evidence shows that there seems to be a relationship between how acceptable people find a given sentence, and how frequent the individual lexical words (but not the function words) are (section 1.1), and how frequent the given construction is (at least if the construction is not very rare, and if the acceptability rating is not at ceiling, Bader & Häussler 2010).2 This relationship, it seems, is more complicated than a simple positive correlation between frequency and acceptability.

In order to argue that different levels of structural complexity itself might be a determining factor on acceptability independently of frequency of construction, lexical frequency, or indeed meaning, the first step is to determine whether it is possible to disentangle the semantics (the meaning, the individual lexical item) from syntactic structure (the construction). Indeed, evidence from neurolinguistic and psycholinguistic research suggests that this is actually possible.

Brain imaging studies have shown repeatedly that syntactic processing, as well as (some) semantic processing, engages the left inferior frontal gyrus, LIFG (also called Broca’s area) (e.g. Stromswold et al. 1996; Grodzinsky & Friederici 2006; Christensen & Wallentin 2011; Pallier et al. 2011; Grodzinsky et al. 2021). Furthermore, it has also been argued that the posterior superior part (pars opercularis, BA 44) is involved in syntactic processing, whereas the frontal superior part (pars triangularis, BA 45) is involved in thematic integration (e.g. Dapretto & Bookheimer 1999; Newman et al. 2003; Clos et al. 2013; Zaccarella et al. 2015; Schell et al. 2017). From a neurolinguistic point of view, there is ample evidence to support the hypothesis that semantic and syntactic information are processed differently and can be disentangled (see also Friederici 2002). In other words, in language comprehension, the structure itself also matters, not just the meanings of the words, and the associated brain activation is a function of complexity: The localization depends on the nature of the complexity, and the amount of activation is determined by the level of complexity.

Psycholinguistic studies also suggest that semantic information and syntactic information are processed differently. According to Bever et al. (1998) semantic information is processed before syntactic information. In addition, probabilistic information (i.e. frequency) is used to propose an initial semantic representation which forms the basis for the syntactic analysis. In particular, the frequency of the construction (the frequency with which the syntactic representation or construction occurs) constrains the parser such that at all times, it chooses the most likely interpretation. However, other studies have shown that syntactic information has priority over semantics, and that temporary (intermediate), implausible (semantically incongruous) interpretations are made during parsing, but only if such analyses are compatible with syntactic selectional properties of the verb (Kizach et al. 2013; Nyvad et al. 2014; cf. also Clifton et al. 2003; but see Trueswell 1996).3 Furthermore, studies have also shown that (at least some kinds of) grammatical illusions, such as More people have been to Paris than I have, are parsed via direct syntactic analysis in accordance with syntactic properties, not via semantic coercion (Christensen 2016; but see also Wellwood et al. 2018). Similarly, “nonliteral interpretation” of implausible, anomalous sentences, such as The mother gave the candle the daughter, have been shown to reduce structural priming compared to well-formed double object constructions, e.g. The mother gave the daughter the candle (Cai et al. 2022). Interestingly, the reduction in priming was larger for the corresponding anomalous DP-PP versions, such as The mother gave the daughter to the candle. The authors argue that their results (showing significant interaction between structure and plausibility) support the hypothesis that language comprehension involves constructing a syntactic representation which forms the basis for semantic decoding, and that their results are incompatible with a semantic approach, according to which meaning can be inferred from semantic relations among the words.

In sum, the studies discussed in this section suggest that meaning and structure (construction) can be teased apart, and that parsing is primarily, though not necessarily exclusively, guided or informed by syntactic properties, rather than by semantic ones. These findings favor a structure-based account and strongly suggest that if we want to understand what determines how and why speakers find some sentences more acceptable than others, and why some sentences are more difficult than others, we need to take into account their structural properties.

According to usage-based approaches, linguistic rules (i.e. the grammar of the ambient language) are structural regularities emerging from learners’ lifetime analysis of the distributional characteristics of the language input. Moreover, it is assumed that acceptability judgements reflect the particular frequencies of the speaker’s “accidental experience” (Ellis 2002; see also Reali & Christiansen 2007). “When people repeatedly use the same particular and concrete linguistic symbols to make utterances to one another in “similar” situations, what may emerge over time is a pattern of language use, schematized in the minds of users as one or another kind of linguistic category or construction” (Tomasello 2003: 99). In other words, the idea is that the sentence types that people find most acceptable are the ones that they frequently hear or have frequently heard. From this, it seems to follow that acceptability patterns are expected to show a high degree of inter-individual variation, since a lifetime of “accidental experience” plays out at the level of the individual speaker. Ellis (2002: 161–162) also argues that a speaker’s grammar is “a statistical ensemble of language experiences that changes slightly every time a new utterance is processed” and that intuitions about grammaticality are “unstable” and “fluid”. However, there is ample evidence that intuitions are stable across as well as within speakers, and that while intuitions do change slightly with exposure, such repetition (priming, satiation, or trial) effects are constrained by the grammar. Not all constructions are affected to the same degree, quantitatively as well as qualitatively, if at all (Snyder 2000; Sprouse & Almeida 2017; Snyder 2022). Furthermore, as we saw in section 1.2, while high frequency is generally correlated with high acceptability, low frequency does not entail low acceptability. A construction or sentence type may be rare or indeed nonexistent for a number of reasons, including high complexity, formality, or ungrammaticality, or indeed there might be an accessible simpler alternative (e.g. I expect it to rain instead of I expect that it will rain).

Contra the usage-based accounts in section 1.4, others have argued that grammatical principles interact with and often override frequency effects, e.g. in ambiguity resolution (Pickering et al. 2000; Bornkessel et al. 2002) and acceptability of subcategorization (White & Rawlins 2020). It has also been shown that sentences with derived (non-canonical) word order are difficult to comprehend and produce for people with agrammatism, independently of construction frequency and information structure (Bastiaanse et al. 2009). For example, in Dutch, sentences with the finite verb in the second position (main clauses with V2) are more frequent than sentences with the verb in final position, and scrambled order is as frequent as base order. However, sentences with V2 and scrambling (all highly frequent) are more impaired than sentences with base (canonical) orders (which have lower frequency). Indeed, agrammatism is also characterized by impaired or non-use of function words, such as determiners, pronouns, prepositions, complementizers – the most frequent types of words (Damasio 1992).

In language acquisition, children show production patterns that deviate robustly from the input they receive from their surroundings. Children tend to ignore the speech errors they hear from others (positive evidence), and they also ignore when the errors they make themselves are corrected (negative evidence). Furthermore, they produce overgeneralizations and syntactic structures that are neither in the target grammar nor in the actual input they get (Thornton & Crain 1994; Pinker 2004; Yang 2004). In their earliest productions, children also show a preference for structurally simpler, less frequent forms over more frequent, but more complex forms. For example, in Norwegian, the phrase corresponding to my car can be constructed either as min bil (‘my car’), the simplex version, which has low frequency, or as bil-en min (‘car-the my’), highly frequent, but complex, and derived by fronting bil (bil₁-en min t₁). Norwegian children show a production preference for the former (simplex structure, low frequency) over the latter (complex structure, high frequency) (Anderssen & Westergaard 2010).

The frequency of the input not only underdetermines what aphasics and children actually produce, but also what language users do not produce. As Yang (2015: 290) puts it: “To account for the things speakers cannot say, the role of input frequency seems either minimal or insufficient: ungrammatical forms would rarely if ever appear in the input, and crucial disconfirming data may not be robustly represented to be useful to the learner”.

Based on the discussion above, we take the acceptability rating given by a participant to be a function of the total amount of difficulty experienced by the comprehender due to various types of complexity. We thus take acceptability judgments to reflect processing difficulties (Fanselow & Frisch 2006; Hofmeister & Sag 2010; Christensen et al. 2013a), and therefore, we predict that acceptability ratings depend less on construction and/or word frequencies than on complexity factors (grammar-based processing factors), which we now turn to.

We take it to be fairly uncontroversial that the list of factors that increase the ‘complexity’ of a sentence is long, but also that it includes morpho-syntactic structure and clause type, constituency, noncanonical word order (derived word-orders), number, type, and length of dependencies (e.g. extraction or movement, and coreference), argument structure, number of propositions, pragmatics, finiteness, etc. Here, we will focus on the following five factors which we will employ as our complexity metric: clausal embedding, adjunction, move-out (crossing a clause boundary), number of fillers (moved elements), and path (structural distance between filler and gap in movement).

Clausal embedding increases structural complexity by increasing the number of constituents, and it is well-known that structural expansion increases working-memory (WM) load and, hence, the processing load (Hawkins 1994; Pallier et al. 2011), in particular finite clauses, which are full propositions with full syntactic representations, and which arguably constitute derivational phases, cf. the Phase-Impenetrability Condition (PIC) (Chomsky 2001: 13). (Compare e.g., Someone [wearing a tinfoil hat] was arrested and Someone [who was wearing a tinfoil hat] was arrested.) People with agrammatism also have production problems with finiteness and with embedded clauses (Friedmann & Grodzinsky 1997; Friedmann 2001; 2003). In this paper, by embedding, we refer to the presence of two propositions, one embedded in the other, not simple clefting (e.g. It was someone who was wearing a tinfoil hat).

Adjunction, the process of modifying one phrase with another (e.g. the [_NP [_AdjP completely untuned] [_NP electric guitars]]), always increases the number of XPs (i.e. phrasal constituents). In addition to the combined structure of the two clauses involved, adjunction creates another instantiation of the modified constituent (unlike complementation), cf. the trees in (7)–(10) below. As such, it also increases the syntactic WM load. Extraction, e.g. by wh-movement, from an adjoined position (typically adverbials such as where, when, or why) is more difficult to process than extraction from a position selected, e.g. by a lexical verb such as see or read or by a preposition such as (talk) to or (point) at (typically what, which, or who) (Nyvad et al. 2014). A gap (or trace of movement) in an adjoined position is more difficult to reconstruct than a gap in a selected position, cf. the Empty Category Principle (ECP) (Haegeman 1994: 442). Furthermore, adjunct clauses are often assumed to be islands, that is, structural configurations that (to varying degrees) block extraction, cf. the Condition on Extraction Domain (CED) (Huang 1982: 505; but see Müller 2019; Bondevik et al. 2020; Nyvad et al. 2022). In agrammatism, patients seem to have an adjunction deficit which means that they tend to avoid modifiers and prefer to produce predicative adjectives over attributive ones (Lee & Thompson 2011; Meltzer-Asscher & Thompson 2014). In an EEG study on healthy speakers of Hebrew, Prior & Bentin (2006) investigated the electrophysiological effects of anomalous or incongruent nouns (arguments), verbs (predicates), and adjectives (adjuncts modifying a noun phrase). The results showed that incongruent adjectival adjuncts (inside NPs) induced much smaller (or nonsignificant) N400s than incongruent verbs and nouns. This, again, suggests that complements and adjuncts are processed differently, even when they are not clauses. All in all, adjunction (modification) increases complexity, and adjuncts have different structural and semantic properties than complements.

Extractions are in themselves costly, as they create long-distance dependencies and fillers that have to be kept in working memory until they can be integrated at the gap site. As mentioned above, sentences with derived word order also cause processing problems for people with agrammatism (Bastiaanse et al. 2009). Derived word orders tend to have lower acceptability, and the longer the path of movement (the structural distance between filler and gap), the lower the acceptability (Clifton & Frazier 1989). Here we follow Hawkins (1999: 248–249) and measure length of path or distance in terms of the number of overt XPs (“those that are actually perceived and processed”) between the filler and the gap in the base-position (the ‘Filler-Gap Domain’) (see also Collins 1994: 56; O’Grady et al. 2003: 435; Christensen et al. 2013a). In short, only overt XPs count for length of path, while non-overt ones (gaps/traces, non-overt subjects, and non-overt operators) do not. In addition to path, the relative ease or difficulty of extraction also depends on the number of fillers (i.e. extracted elements), compare They did the job (no filler), What did they do? (1 filler: what), and Why did they ask which job to finish? (2 fillers: why and which job).

Extraction from an embedded clause, which we here refer to as ‘Move-Out’, following Christensen et al. (2013b), is particularly costly in terms of processing, because it creates a long-distance dependency spanning two clauses (i.e., two propositions). As mentioned, extraction from an adjunct clause is often difficult or perhaps even impossible, resulting in (various degrees of) reduced acceptability (Nyvad et al. 2022). However, extraction from complement clauses is also costly. In theoretical syntax, it is standardly assumed that extraction proceeds via a position at the left periphery in the embedded clause, CP-spec, cf. the PIC (Chomsky 2001: 13). When this position is occupied, e.g. by a wh-element, extraction is impeded, leading to reduced acceptability or ungrammaticality (Christensen et al. 2013a; Christensen & Nyvad 2019). In a brain imaging study with fMRI, Christensen et al. (2013b) found that the effect of increased syntactic processing typically found in and around Broca’s area only reached significance when the extraction crossed a clause boundary. In other words, moving out of the embedded clauses induced a massive increase in activation in Broca’s area and other frontal regions, compared to movement targeting a position within the embedded clause.

As the discussion of these five factors show, there is a close connection between structural complexity on the one hand, and processing load and acceptability on the other, and that the former causes the latter seems to be the standard assumption in psycho- and neurolinguistics, at least since Miller and Chomsky (1963) showed that unacceptability of a structure that does not violate any syntactic constraints may be the result of processing complexity. In theoretical syntax, the preference for structural simplicity is linked to computational economy and it is captured in the principle of Economy of Derivation: “make derivations as short as possible, with links as short as possible” (Chomsky 1995: 91; cf. also the processing accounts of Hawkins 1994; 2004; Gibson 1998). In turn, this seems to be the central tenet of the Derivational Theory of Complexity (Fodor & Garrett 1967). As noted by Christensen (2005: 308): “In fact, this unification of WM and theoretical syntax also seems to call for a revival of the much vilified Derivational Theory of Complexity (DTC) in some form, as also suggested by Marantz [(2005)]” (see also Hornstein 2014).

One of the non-structural factors that has been argued to interact with morpho-syntax and, hence, to affect constraints on word order and the level of acceptability, is animacy, i.e., whether an NP denotes a living being or not. Furthermore, there seems to be a preference to maximally differentiate subject and object, especially if both are animate, and even more so if the object is a topic. According to Aissen (2003), many languages have differential object marking, which means that the case marking of the object of a transitive verb depends on the animacy or definiteness of that object. The prototypical subject is Agent (hence, also animate) and Topical, and to maximally differentiate subject and object, the higher on the animacy scale (Human > Animate > Inanimate) and/or the definiteness scale (personal pronoun > proper name > definite NP > indefinite specific NP > non-specific NP) the object is, the more likely it is to be case-marked. The point here is that animacy, which is a semantic property, influences or interacts with the grammatical constraints on word order and case marking.

Animacy has also been shown to be relevant for superiority effects in wh-movement. In a multiple question, that is, a clause with two wh-elements, it is more acceptable to front the highest wh-element and leave the second, lower one in situ than vice versa, where extraction of the lower wh-element crosses the position of the higher one, compare Who will buy what? and *What will who buy (Clifton et al. 2006). This superiority effect is stronger in English (where it leads to ungrammaticality) than in German (where it only lowers the acceptability) (Fanselow et al. 2011; Häussler et al. 2015). In German, however, there is a significant interaction between word order and animacy. Fronting a wh-object across a wh-subject is significantly less acceptable when both are animate (hence, not maximally distinct) than when they differ in animacy. In short, fronting a wh-object across a wh-subject is significantly less acceptable when the two are both animate (They knew who₁ who critized t₁) than when the subject is animate and the object inanimate (They knew what₁ who critized t₁) (Fanselow et al. 2011; Häussler et al. 2015).4

Animacy has also been shown to interact with relativization (Gennari & MacDonald 2009). Relative clauses with an inanimate antecedent and an animate subject (The movie that the director watched received a prize) are easier to process than ones with an animate antecedent and an inanimate subject (The director that the movie pleased received a prize).

In an fMRI study on German simplex transitive clauses with scrambling, Grewe et al. (2006) found that sentences where an inanimate subject preceded an animate object or where an inanimate object preceded an animate subject (both inanimate > animate) increased activation in Broca’s area in the brain (compared to their animate > inanimate counterparts), presumably reflecting an increase in processing load. However, though this fixed/main effect was significant, they did not find any significant interaction between extraction (or word order) and animacy, neither in the acceptability ratings, nor in the brain signal. The animacy effect in Broca’s area was also only detectable using a so-called region-of-interest analysis. Furthermore, in the behavioral data, there were no fixed/main effects of order or animacy on acceptability either. At the very least, these complications suggest that the overall effect of animacy might be subtle.

In short, it is possible that animacy is relevant to the acceptability of extraction, such that at least part of a potential reduction in acceptability stems from having an inanimate argument before an animate one, as in Grewe et al. (2006). Alternatively, it could be that having both an animate subject and an extracted animate object leads to reduced acceptability, as in Fanselow et al. (2011). In either case, we would expect to see a significant (main or interaction) effect of animacy.

Based on the review of frequency effects and complexity factors, we made a number of experimental predictions, all of which are based on processing factors:

To test prediction I and prediction II (acceptability is a function of complexity rather than construction frequency), we included sentences with different structural complexities, each with and without extraction/fronting of an object: simplex (mono-clausal) sentences, sentences with an embedded complement clause, sentences with a clausal adjunct, sentences with an embedded relative clause, and a set of ungrammatical sentences (see the Materials section below). Relative clauses were included because they are grammatical and highly complex, and because extraction from relative clauses significantly lowers acceptability (but to varying degrees). We also included so-called parasitic gaps (Engdahl 1983), sentences with a clausal adjunct and one extracted filler but two gaps (i.e. they are also highly complex), because they are notorious for being acceptable in spite of apparently being very rare (Mayo 1997; Newmeyer 2003; Phillips 2013; Boxell & Felser 2017; Momma & Yoshida 2023).5 In this way, we had fully grammatical sentences with high, intermediate, and low frequency, plus ungrammatical ones with low (zero) frequency, which enabled us to test for the effects of complexity and construction frequency. Relative clauses are interesting because it has been shown that in Danish, the acceptability rating is affected by extraction as well as by lexical frequency of the matrix verb (Christensen & Nyvad 2014).

To test prediction III (lexical frequency can affect the average acceptability of grammatical structures), we constructed the sentences from a set of lexical items controlled for low, middle, and high frequency of occurrence in a Danish text corpus (KorpusDK).6 This procedure ensures that we had examples with continuous frequency across the full frequency span from very low to very high.

To test prediction IV (animacy interacts with extraction), we constructed our stimuli such that while all the sentences had an animate subject, half of them had an animate object [+Anim], the other half an inanimate one [–Anim].

The stimulus consisted of 24 sets of four conditions with increasing complexity plus one filler condition (A–E), each with and without object extraction, corresponding to (2)–(6) below, resulting in 240 items in total. The sentences were each preceded by a context to make them as natural as possible and to maximally facilitate acceptability (following the approach in Nyvad et al. 2022). The context as well as the target sentences were carefully constructed to be as coherent as possible.7 Each set shared the same unique context, as in (1). Half of the sentences had an animate object [+Anim], the other half an inanimate one [–Anim], all with an animate, pronominal subject (jeg ‘I’ / han ‘he’ / hun ‘she’). The main verb in condition A (simplex, cf. (2)) was used as either a matrix or an embedded main verb in conditions B-D (complex, (3)–(5)). All object nouns were definite and non-compound. High-frequency discourse particles (PRT) were inserted to make the sentences more natural and colloquial (e.g. jo, da, and bare, which can be translated roughly as ‘after all / you know’, ‘at least’, and ‘just / simply’, respectively). (The entire stimulus set, including frequencies, is available on the OSF repository, see the ‘Data availablity’ section below.)

The ungrammatical controls/fillers (E2), as in (6)b, had scrambled, impossible word order and were ungrammatical for three reasons: (i) There is extraction from the second conjunct of a coordinated DP (cf. *What did they like cookies and?), (ii) The order violates the verb-second constraint on Danish main clauses, and (iii) the (remnant of) the object and the particle da and the adverb allerede are in the wrong order.

The syntactic structures of conditions A-D are given in (7)–(10). The XPs that count in the sum measurement of distance/path between filler and gap in extraction are marked with red. Recall that only overt XPs count (Hawkins 1999: 248–249).

The complexity of each of the four target conditions [±Ex] is summarized in Table 1. In order to avoid additional trivial movement steps in the derivation to skew the length of path, and hence, the sum complexity, the number of XPs in the path (the red ones in (2)–(6)) was normalized with z-score transformation (path.z). Otherwise, A2 would be six times as complex as A1, A2 would be 11 times more complex than A1, etc. The z-transformed Path also has the positive effect of (almost) neutralizing the complexity of fronting the subject (i.e. the filler effect), which results in canonical word order. In Table 1, the numbers of XPs used in the calculation are provided in parentheses.

Based on Table 1, the conditions can be arranged in a complexity hierarchy from least to most complex:

Note that in this paper, extraction is used as a short hand for object extraction unless explicitly specified otherwise. Note also that the difference between subject extraction and object extraction can be reduced to a difference in length of movement path (compare, for example, the two trees in (7)).

To investigate the effect of lexical frequency, the stimuli was balanced over three (relative) frequency zones within each condition, based on the frequency of occurrence of each lemma form of the main verb, medial adverbial, and object noun in a Danish corpus (KorpusDK). We used corpus frequency as a proxy for individual exposure (which is inaccessible to us in the absence of comprehensive longitudinal data). The same set of main verb, medial adverb, and object noun was used to construct a set in one of the frequency zones. For example, in (2)–(6) above, we used kender ‘know’ (freq. = 25,215), barnet ‘the child’ (freq. = 62,538), and allerede ‘already’ (freq. = 28,232) to construct a set in the high frequency zone. In the analysis, we used the mean of the log₁₀ transformed frequencies of verbs, nouns, and adverbs to get a single, composite measure of lexical frequency.

To investigate the relationship between the acceptability of a construction type and how common it is, we looked up the frequency of the construction in each of the eight target conditions (A1–D2) in KorpusDK.10 The search frame for each condition is given in Table 3. In A1–A2, the search frame begins with a coordinating conjunction (og/men ‘and/but’) in order to avoid error examples where the fronted object is the object of a fronted embedded clause, which would lead to an overrepresentation of OSV orders. The pronouns den ‘it (common gender)’, det ‘it (neuter gender)’, and de ‘they’ are avoided because of syncretism between nominative and accusative case and because they can be used as determiners, which would lead to an overrepresentation of SVO orders. The search frames only provide a subset of possible examples as the number of auxiliary verbs are fixed and adverbials are excluded, so the search results are very conservative (for a different approach, see Gries & Ellis 2015). However, the relevant feature is the relative (log₁₀ transformed) frequencies, not the actual number of hits.

The search results show that, all things being equal, simple SVO sentences are by far the most frequent type. Furthermore, there are 9.7 times as many simple SVO sentences as corresponding OVS sentences. They also show that there are 49 times as many complement clauses with an in-situ object (and with a simple matrix clause) as corresponding ones with object extraction. Again, these are conservative estimates as they only include sentences with transitive verbs, pronominal subjects and objects, and no adverbials, and where the matrix clause is headed by a complementizer.

The entire set of stimulus sentences was distributed over 10 lists using a Latin-square design, such that each list contained 24 tokens.

The experiment was set up as a survey using Google Forms. Participants were recruited through social media platforms and pseudo-randomly assigned to 1 of 10 lists based on their birth month. Each stimulus sentence was preceded by a context, such as (1) above. Participants were instructed to rate the acceptability of each sentence on a 7-point scale ranging from 1 (‘completely unacceptable’) to 7 (‘completely acceptable’), and they were instructed to base their rating solely on the target sentence following the context.

The survey was posted on Facebook and Instagram. A total of 211 people (196 female, 14 male, 1 other) participated in the survey. The mean age was 28.8 years (range = 18–63, std. dev. = 8.8). The number of participants per list ranged from 9 to 33 (32, 30, 33, 11, 9, 13, 18, 27, 22, and 16).12

We treat the acceptability rating scale, for which we only provided the endpoints (1 = ‘completely unacceptable’, 7 = ‘completely acceptable’), as an ordinal approximation of a continuous variable, and analyzed the data using parametric models (Carifio & Perla 2008; Norman 2010; Sullivan & Artino 2013). This makes it easier to interpret the effect sizes directly in terms of differences in acceptability ratings. The data was analyzed using R version 4.1.2 (R Core Team 2021) with the lmerTest Package (Kuznetsova et al. 2017) for mixed effects models and the MASS Package (Venables & Ripley 2002) for sliding, pair-wise contrasts. The models in the analysis are the largest models that converged without any errors. All plots were made using the ggplot2 package (Wickham 2016).

Following Taylor et al. (2022), we also analyzed the data as ordinal with cumulative mixed effects models (clmm), using the ordinal package for R (Christensen 2015) and got the same results as we got with parametric models (linear mixed effects), i.e. the same significant contrasts. We also applied z-transformation to the ratings, which corrects for potential individual participant scale-bias (Sprouse et al. 2012; Nyvad et al. 2022), before analyzing the data with a parametric lmer test (Kuznetsova et al. 2017). Again, we got the same overall result. These models are summarized in the supplementary material. In short, the results we present below are highly robust across different types of analysis. Indeed, we had no a priori reason to assume that the results would not be robust, given the number of participants, the number of tokens per type, and the effect sizes. As we have sound reasons for treating the Likert scale as continuous (or as a continuous approximation of an ordinal variable), i.e. that effect sizes are easier to interpret, we have used parametric linear regression in the analysis. Furthermore, as Norman (2010: 631) points out, “parametric statistics can be used with Likert data, with small sample sizes, with unequal variances, and with non-normal distributions, with no fear of “coming to the wrong conclusion””.

Prediction I was borne out. Overall, the levels of acceptability match the levels of complexity, such that the more complex a grammatical structure is, the less acceptable it is. Note that the order of conditions sorted by decreasing acceptability in Figure 1 (B) corresponds to the order of increasing complexity (see Table 1 and (11)) (except the order of C1 and D1, which do not differ significantly in acceptability). First of all, this negative correlation between acceptability and complexity is clear for short versus long movement (types A and B). We predicted that the acceptability would decrease as a function of increased complexity, as measured in terms of embedding (complementation) and length of path (number of overt XPs between filler and gap). The overall effect of embedding a complement clause was significant (p = 0.019, see Table 6), though the difference in acceptability between A2 and B1 was non-significant (p = 0.099, see Table 4). (Recall that by embedding, we refer to the presence of two propositions, one embedded in the other, not simple clefting.) For simple, mono-clausal sentences, the effect of extraction was non-significant (compare A1 and A2), whereas the effect was significant for bi-clausal sentences where the embedded clause is the complement of the matrix verb (B1 vs. B2, p= 0.003), similar to the results by Christensen et al. (2013a; 2013b). The major difference between extraction in A2 and B2 is that in B2, the filler is extracted across a clause boundary. That is, there is an effect of Move-Out. Interestingly, the effects of lexical frequency also only become significant when the extraction crosses a clause boundary.

All things being equal, compared to an embedded complement clause, an adjunct clause is structurally more complex and costly in parsing, and hence less acceptable, cf. (8)a and (9)a, and the acceptability levels for B1 and C1 in Figure 1. The parasitic-gap version in C2 (see the structure in (9)b) is even more complex, because it involves two fillers instead of one, and longer movement paths. Consequently, the acceptability drops significantly, cf. C1 vs. C2 in Figure 1.

Admittedly, C2 and B2 cannot be compared directly, as B2 does not involve extraction from an embedded (adjunct) clause to the front of the matrix clause. For recent data and discussion on extraction from adjunct clauses in English, see Nyvad et al. (2022). Extraction from relative clauses, on the other hand, does involve Move-Out, (10)b, as well as two fillers. This long extraction also has a long movement path (it crosses many XP nodes in the structure). The result is, as predicted, a severe reduction in acceptability. Importantly, however, it is significantly higher in acceptability than ungrammatical fillers (1.3 points on the 7-point scale), compare D2 and E2 in Figure 1. Though the ungrammatical filler type E2 has a much simpler structure on all parameters, it is much less acceptable (p < 0.001).

This prediction does not seem to be borne out. As shown in Figure 4, there is indeed a positive linear correlation between (log₁₀) frequency of construction and acceptability which describes 69% of the variation in the data (R² = 0.69). However, the acceptability of a construction could also, and to a higher degree, be predicted from its level of complexity (prediction I), both from the predicted level of complexity (Figure 4, R² = 0.83) and from the fitted level (Figure 5, R² = 0.86).

According to the processing account presented in Culicover et al. (2022), probabilistic expectations concerning which structures we are likely to be exposed to next emerge on the basis of prior experience. They posit that higher complexity (defined as the result of many different factors, including memory constraints, parsing difficulty and dependency length) naturally leads to lower frequency, which in turn results in lower acceptability due to “surprisal” (i.e. degree of surprise triggered by a given structure). Frequency and surprisal should hence be inversely related, and we would predict that the more frequent a construction is, the more acceptable it is, and the more complex it is, the less frequent and the less acceptable it is. These predictions appear to be borne out in Figure 4 and Figure 5 (see also Featherston 2008, who found the same pattern; Kempen & Harbusch 2008).

However, it is important to note that zero-occurrence is associated with huge variation in acceptability, which is surprising from the perspective of a usage-based account. In other words, frequency does not appear to drive the level of acceptability. This is evident from, in particular, C2 (parasitic gaps), D2 (extraction from relative clauses), and E2 (ungrammatical fillers), all of which have (close to) zero occurrence, but significantly different acceptability ratings, 3.35, 2.61, and 1.31, respectively (p < 0.001). In fact, it seems that the (very) low frequency of C2, D2, and E2, follows naturally from the relatively high complexity of C2 and D2, and from the ungrammaticality of E2. Not the other way around. This is also evident in Figure 4 (B) and Figure 5 (B), which show that there is a significant linear negative correlation between complexity and acceptability which describes 83–86% of the variation (predicted complexity: R² = 0.83, fitted complexity: R² = 0.86; p < 0.002), i.e., 14–17% more than the effect size for construction frequency.

In short, even though the level of acceptability can to some extent be predicted by construction frequency, the level of complexity has more predictive power and is hence able to explain more of the variation – as well as the relative levels of construction frequency. The question is whether what we are observing is merely a negative correlation between two factors (complexity and construction frequency) – indeed, as shown in Figure 4 (C) and Figure 5 (C), that negative correlation is significant and strong, R² = 0.92 and R² = 0.77, respectively) – or whether there is actually a causal link between the two, and if so, what the direction of causality is. It seems to us that it is more likely that increased complexity causes speakers to disprefer certain constructions over others, which leads to decreased frequency of occurrence, rather than rarity causing certain constructions to be more complex (Hawkins 1994; 2004). As Newmeyer (2005: 125) puts it: “The more processing involved, the rarer the structure”.

Overall, lexical frequency has a significant but very small effect: An increase of 1 on the 7-point acceptability scale requires an increase of more than 12 million in raw lexical frequency (ie. tokens in the corpus). This variation also shows that it is very important to have a sufficiently large number of tokens per type in order to avoid accidental effects of selection bias. However, as shown in Figure 6, the effect size, polarity, and significance of frequency effects are highly dependent on the complexity of the syntactic construction. Crucially, there are no effects of lexical frequency on ungrammatical sentences. This is consistent with the hypothesis that in parsing, syntactic information takes priority over semantic and pragmatic information, i.e. ‘structure before meaning’ (Kizach et al. 2013). Lexical frequency effects seem to only apply to sentences with acceptability ratings in the intermediate zone; this is parallel to what has been found for satiation (repetition / trial) effects, namely, that it also applies to the intermediate zone (Sprouse 2008; Christensen et al. 2013a; but see also Brown et al. 2021). Ungrammatical sentences do not get better with more frequent words (a floor effect), and sentences with very high acceptability, do not get better either (a ceiling effect). To a large extent, the relative rating within the intermediate zone depends on the syntactic complexity, cf. the factors in Table 1 and the plots in Figure 1 and Figure 4 (B). The relative ranking can then be affected by the lexical frequencies of the words in the sentences, as shown in Figure 6. With complement clauses, the effect seems to depend on Move-Out. Comparing conditions A1 through B2 in Figure 6, top row, shows the general trend that as complexity increases, so does the effect of lexical frequency.

As also shown in Figure 6, there is a negative correlation between acceptability and lexical frequency in the adjunct clause condition C1 (i.e. an inverse or negative frequency effect). The effect is considerable, accounting for 27% of the variance (R² = 0.27, p < 0.01). In the parasitic gap condition (C2), which involves extraction, the effect is not significant (p > 0.2). The question is what drives this negative effect. A possible answer might be that the negative effect of adjunction on acceptability (as complexity increases, acceptability decreases) has more ‘weight’ when the effect of lexical frequency has less ‘weight’ (i.e. with higher lexical frequency, adjunction is easier to process and therefore more acceptable). However, then we would expect relative clause extraction (D2) to show the same pattern, which is not the case.15 Furthermore, it is also unclear why the negative effect of adjunction in C1 should be ameliorated by extraction in C2.

Another possibility could be that with high-frequency lexical material, the ‘unnaturalness’ of the syntactic structure itself becomes more apparent. In a sense, low frequency words might mask the ‘strangeness’ of the construction. Indeed, Christensen and Nyvad (2019) also found a negative correlation between the frequency of the matrix verb and long adjunct-extractions from wh-questions in English, which are argued to be ungrammatical. However, then we would also expect to see a negative effect especially with ungrammatical fillers (E2), but also with extraction from relative clauses (D2), which we do not (cf. Figure 6). Yet another possibility might be linked to finiteness: In C1 and C2, the embedded clauses is nonfinite, whereas in B1, B2, D1, and D2, it is finite, and the negative effect of lexical frequency is only found in C1 and (to a smaller degree) in C2. For speakers with Broca’s aphasia, finite verbs are more difficult to produce than infinitive verbs (Friedmann 2001; Bastiaanse & Edwards 2004)). Finite adjunct clauses have also been argued to be more resilient to extraction than nonfinite ones (e.g. Ross 1967; Truswell 2011; Michel & Goodall 2013; but see Müller 2019; Nyvad et al. 2022). In our study, the nonfinite clauses also do not have any auxiliary verbs, so the structure is simpler. However, there is no negative frequency effects for the much simpler conditions A1 and A2. (It is also not clear how this could be explained with factivity, coherence, relevance, etc.; for a recent discussion, see Christensen & Nyvad 2022.) At present, we have no clear answer to why the acceptability of clausal adjunction, which is fairly common, is negatively correlated with lexical frequency in our data, or why the effect is small and non-significant for parasitic gaps, which are very rare.

In a previous study on extraction from relative clauses in Danish, the frequency of the matrix verb was positively correlated with acceptability (Christensen & Nyvad 2014), and this was particularly the case for sentences with extraction, where it described 78% of the variation (R² = 0.78, p < 0.001), see Figure 8. In the present study, there was no significant correlation between lexical frequency of the matrix verb and acceptability, neither with nor without extraction (R² < 0.04, p > 0.5). Though we emphasize that the two studies used different sets of verbs and that a direct comparison between the two is not possible, the difference in the size and significance of the frequency effects is striking. It seems plausible that the difference is due to the presence or absence of context. Without a facilitating context, the acceptability is more sensitive to lexical frequency. A facilitating context, on the other hand, helps to parse the complex structure, which involves a long-distance dependency into a relative clause. Easier and faster lexical access in turn reduces working memory load, which increases acceptability.

Interestingly, in a study on extraction from relative clauses in English, Christensen & Nyvad (2022) found no effect of matrix verb frequency and acceptability of extraction. In this study, the sentences were also presented without a facilitating context, and it was argued that the absence of a frequency effect supports the assumption that English relative clauses are indeed strong syntactic islands. Like ungrammatical fillers, they are immune to any positive effect of high lexical frequency. The results from the present study together with the results from Christensen & Nyvad (2014), as shown in Figure 8, are compatible with the assumption that, unlike English, extraction from relative clauses is grammatical in Danish: Though the average rating for extraction is around 2.5 with context and 3 without context, cf. Figure 8 (right panels), the range in acceptable ranges from very low to 4–5 depending on frequency; furthermore, they are easy to find in spoken as well as written language (Müller & Eggers 2022).

The prediction that acceptability of extraction interacts with the animacy of the object was not borne out. Neither the interaction between animacy and extraction nor the fixed effect of animacy were significant (cf. Table 7). The effect of extraction, on the other hand, was highly significant (p < 0.001). As shown in Figure 7, the effects of animacy were also extremely small, while the effects of extraction were large, in particular when the syntactic complexity is already high (types C and D).