3.1 QR in simple clauses and Ellipsis

Based on a series of experiments (offline questionnaires and online self-paced reading experiments), Anderson (2004) shows that to adequately model speaker’s behavior regarding scope it is necessary to consider both syntactic complexity and extra-grammatical processing factors. A common strategy used in Anderson’s experiments is to diagnose the interpretation of sentences like (10) via the choice of a paraphrase as in (10a) (participants are asked to choose the paraphrase corresponding to their initial interpretation of the sentence) or the answer to a comprehension question as in (10b). If (10a.ii) or (10b.ii) is chosen, one can conclude that the speaker has an inverse scope interpretation in mind, since only the inverse scope interpretation is compatible with multiple referents corresponding to the indefinite QP. For all experiments involving the strategies in (10), the counting of inverse scope was done conservatively in that only ‘several’ answers, which unambiguously indicate inverse scope, were counted as evidence for inverse scope. Since ‘one’ answers are, in principle, compatible with both surface and inverse scope, those answers are less informative and the rates for inverse scope may in fact be slightly higher than the results given. However, this does not affect the main conclusions reached in this work.

The first noteworthy observation from Anderson’s experiments is that inverse scope is not easily available, not even in simple sentences such as (10). In an initial offline questionnaire experiment employing the strategy in (10a), sentences such as (10) are predominantly interpreted as involving surface scope:

Anderson (2004: 53): “Perceivers chose the paraphrase corresponding to the surface-scope interpretation in 81% of cases, a value that is significantly different from the chance value of 50% (z-test, p < 0.001). Twelve participants chose the surface-scope paraphrase for all of the items, and one item (A student solved every puzzle.) earned a surface-scope response from all participants. No participant had a surface-scope response rate of less than 46%, and no item had a surface-scope response rate of less than 50%.”

The availability of inverse scope increases, if the same sentences are embedded in linguistic contexts favoring inverse scope interpretations. Using a 2 × 2 design, Anderson compared the distribution of scope in ambiguous and non-ambiguous sentences embedded in contexts biasing for surface or inverse scope. The full paradigm of one stimulus item illustrating the four conditions is given in (11), with the test sentences highlighted. The items in (11a,b) involve situations which favor a surface scope interpretation—the president of the gourmet club is looking for a (possibly single) volunteer among the club’s members to test the recipes. The context in (11c,d) is different in that multiple members are required to test the recipes, which favors an inverse scope interpretation of the test sentences.⁴ Furthermore, each of the two contexts is given with an ambiguous and unambiguous test sentence. In (11a), the test sentence includes a definite subject (rather than an indefinite QP) which does not scopally interact with the object QP, hence the highlighted sentence in (11a) only leads to a surface scope interpretation. In (11c), the indefinite QP in the test sentence is modified by different, which in relation to the object requires a low scope interpretation of that QP. In contrast, the test sentences in (11b,d) are ambiguous.

The results of three of the experiments in Anderson (2004), Experiments (Exp) 2, 7, 12, are given in Table 1. As shown, the two items with unambiguous test sentences were nearly always associated with the expected interpretations—surface scope in (11a) and inverse scope in (11c), showing that the participants responded correctly to the questionnaire.⁵ The results also show a significant effect of context: for the two ambiguous conditions, (11b,d), surface scope was significantly more frequent in contexts with a surface scope bias (81%) than in contexts with an inverse scope bias (47%). Thus, the context clearly plays a role in the choice between surface and inverse scope, however, at the same time, it is not the case that the interpretation is solely determined by the context. The rate of surface scope in the ambiguous surface scope biasing context (11b)—81%—is the same as in the questionnaire which presented the test sentences without any context (see above). It can therefore be concluded that ambiguous sentences retain ambiguity, even when the context favors a particular interpretation, and that speakers have access to both interpretations. Furthermore, although an inverse scope biasing context raises the accessibility of inverse scope in an ambiguous sentence, (11d), to 53% (compared to 19% in cases without a biasing context), the rate of inverse scope still remains clearly lower than the rate of surface scope in a surface biasing context (81%). Put differently, the strong default preference for surface scope remains visible in these cases, as the surface scope rate still reaches 47%, despite the inverse scope bias. Overall, these results show that context plays a role in the choice of scope but does not eliminate ambiguity, and that inverse scope is generally disfavored.

Since QR in simple predicates is always allowed by the notion of syntactic Scope Economy introduced in the previous section (e.g., to solve a type mismatch), syntactic Scope Economy would not be an issue in any of the conditions in (11). Thus, an additional factor must be at work to yield the different patterns in Table 1. Anderson (2004) suggests that this factor is based on extra-grammatical considerations, which, importantly, operate on syntactic structure involving QR to derive inverse scope. Employing a syntactic approach to scope in general (though without the notion of Scope Economy) allows the formulation of increased complexity in inverse scope contexts: to derive inverse scope, covert movement is necessary, which yields a more complex syntactic configuration than a surface scope structure without movement. Anderson indeed argues for such a notion of complexity which she proposes to combine with the Processing Economy condition in (12).

That such a syntactically based processing account is the most plausible way to derive the data is demonstrated by a range of further experiments. Note first that all conditions in (11) introduce a plural set of individuals (the members of the gourmet club) corresponding to the indefinite QP in the context already. Since multiple participants are already part of the context, retrieving those, as is necessary for the inverse scope interpretation, should not pose a significant problem. Thus, a semantic parsimony approach (Altmann & Steedman 1988; Crain & Steedman 2005) according to which inverse scope interpretations are disfavored since they require the referentially more complex retrieval of multiple individuals for a singular QP (whereas a surface scope interpretation is compatible with a single referent) does not seem to be applicable for these data.⁶ In particular, the fact that in the ambiguous surface scope bias condition, (11b), the proportions of surface and inverse scope are identical to the ones in the experiment where no context was given at all might prove problematic in such an account.

Another way to approach the difficulty of inverse scope would be, following parallel processing models (MacDonald 1994; Spivey & Tanenhaus 1998; Trueswell 1996, among others), to relate it to competing analyses for an ambiguous sentence which cause difficulty for the parser when settling for one interpretation. Several of the online self-paced reading experiments in Anderson (2004) cast doubt on such an approach. The main findings are that quantified sentences (sentences with two quantifiers) are read significantly slower i) when the participant has an inverse scope interpretation in mind as diagnosed by the answer to the comprehension question; and ii) when the sentences appear in contexts biasing for inverse scope. Figure 1 shows that ambiguous sentences for which participants choose the ‘several’ answer were read significantly more slowly than sentences that had received the ‘one’ answer. Figure 2 gives the mean residual reading times for one of the experiments (Experiment 7), which included ambiguous and unambiguous sentences (such as (11)). As shown, both ambiguous and unambiguous sentences involve higher reading times in contexts that bias for the inverse scope interpretation—reading times showed a significant main effect of context, but there was no effect of ambiguity. Since a similar slowdown is observable for ambiguous and unambiguous inverse scope biasing sentences, the slowdown cannot be attributed to competing analyses for those sentences. That participants used only one parse for the unambiguous inverse scope sentences in this experiment is supported by the answers to the comprehension question, which, as shown in Table 1, again yielded almost only inverse scope answers (92%—i.e., participants performed near ceiling). Rather, these results support the view that inverse scope always comes at a cost, even when it is the only interpretation available.

Figure 1

Mean residual reading times for quantified sentences; ambiguous, contingent on comprehension question response (Anderson 2004: 111, Figure 8).

Figure 2

Mean residual reading times for quantified sentences; ambiguous and unambiguous (Anderson 2004: 111, Figure 7).

Although syntactic Scope Economy is not involved in the phenomena discussed so far in this section, it may still be the case that it is in other constructions. There are two noteworthy configurations for which syntactic Scope Economy has been employed—clause-boundedness effects of QR and scope restrictions in Ellipsis. The first empirical domain is the main focus of this paper; the second area has also been covered in Anderson (2004), which is the last major contribution of this work I summarize here.

Ellipsis raises the interesting issue illustrated in (13): ambiguous sentences such as (13a), appear to become unambiguous when followed by an elliptical sentence with a subject that does not scopally interact with the object QP, such as the definite DP subject in (13b) (see (Sag 1976; Williams 1977; Hirschbühler 1982; Fox 1995; 2000). This phenomenon has been accounted for by employing syntactic Scope Economy (Fox 1995; 2000) which is schematized in (13c–e). A condition on Ellipsis is that the antecedent and elided structure must be parallel in some way. For our purpose, this parallelism could be defined via scope relations or the application of QR: if the object takes scope over the subject in the antecedent clause, it must also do so in the elliptical clause. A derivation such as (13c) violates parallelism since QP-∀ only takes scope over the subject in the antecedent clause, but not the elliptical clause. However, since the subject of the elliptical clause does not scopally interact with the object, QR as in (13d) is blocked by Scope Economy. The only successful derivation is (13e) which yields a surface scope interpretation in the antecedent clause.

Anderson (2004) reports the results of several experiments which were conducted to test scope in contexts where a sentence following the test sentence disambiguates or is predicted by syntactic Scope Economy to disambiguate the test sentence. One full sample item with the options tested in Experiments 7, 9, and 12 is given in (14). As shown, these experiments include Ellipsis sentences with non-quantificational subjects, either as different sentences (Experiments 7, 9) or as part of a conjunction with the test sentences (Experiment 12).

The test sentences were again embedded in surface or inverse biasing contexts as in (11) ((14) only gives the inverse scope context). Restricting our discussion to the ambiguous conditions (test sentences as in (11b,d)), Table 2 summarizes the response rates of the comprehension questions for these experiments. The rates from Experiment 2 are repeated in Table 2 as a baseline.

As shown in Table 2, the response rates are very similar, independently of whether Ellipsis is involved or not. In other words, an Ellipsis sentence did not seem to have any effect on the scope of the test sentences. In all experiments, the surface scope answer was chosen roughly two thirds of the time in cases with a surface scope bias and about half of the time in cases with an inverse scope bias. In contrast to truly unambiguous test sentences (which, as we have seen in Table 1, yielded near ceiling surface scope rates), quantificational test sentences followed by (non-parallel) Ellipsis retain their ambiguity and only show the by now familiar strong default preference for surface scope. As noted in Anderson (2004), this behavior is unexpected under a syntactic Scope Economy account in which inverse scope should be ungrammatical in Ellipsis cases such as (14) since either parallelism or syntactic Scope Economy would be violated. The distribution in Table 2 is predicted, on the other hand, under a processing approach in which inverse scope is costly but in principle still available for sentences followed by non-parallel Ellipsis. Finally, one question remaining for a processing approach is why speakers feel that there is a difference in the availability of inverse scope in cases such as (13a) vs. (13b). Anderson (2004) suggests that this is an issue of acceptability vs. grammaticality. Like center-embeddings or garden path effects, speakers may treat grammatical sentences as unacceptable when the processing burden is too high. In addition to the “regular” processing cost associated with an inverse scope interpretation (cf. (12)), an inverse scope interpretation in an Ellipsis sentence like (13b) could be seen to further complicate processing due to lack of syntax–semantics parallelism. More specifically, the two clauses are parallel in syntax (A boy admires every teacher. Mary admires every teacher) but, under an inverse scope interpretation, not parallel semantically—the antecedent clause involves multiple boys admiring teachers, whereas the elliptical clause only involves one individual admiring teachers. If the processor’s preferred interpretation of an Ellipsis sentence is a parallel interpretation, an inverse scope interpretation in the antecedent clause would create an additional processing burden, leading to the difference in judgment between (13a) and (13b).

3.2 QR from finite clauses and islands

The availability of inverse scope across certain clause boundaries is investigated in Tanaka (2015a; b). Tanaka examined overt wh-extraction and QR from different types of adjuncts via acceptability judgment tasks, as well as a follow-up experiment on QR from finite clauses and subjunctive complements. One of the main observations in this work is that overt extraction from different types of islands shows different degrees of acceptability. The islands tested were temporal during PPs (WD), (15a), bare participial gerunds (WP; omitted here—see fn. 9), non-finite after clause gerunds (WA), (15b), and absolute islands such as complex NPs (W-Control*), (15c).

As shown in Figure 3, extraction from after gerunds shows a significantly milder island effect than extraction from absolute islands; after gerunds are significantly stronger domains than during PPs;⁸ and both conditions (WA and WD) are significantly degraded compared to non-island (locality obeying) wh-extraction (W-Control: no violation). The distribution is summarized in the scale in (16).

Figure 3

Mean acceptability of wh-extraction (Tanaka 2015b: 120, Figure 4.6).⁷

The same syntactic contexts were then used to test covert movement, (17a,b), with the results in Figure 4 which follow the same hierarchy as overt wh-movement in (16): inverse scope, like overt wh-movement, is hardest/impossible with quantifiers originating in an absolute island (Q-Control*). QR from an after gerund (QA) is more acceptable than from an absolute island, but less acceptable than QR from a during PP (QD) (the differences were significant). Both islands are stronger boundaries for QR than configurations without any island.¹⁰

Figure 4

Mean acceptability of QR (Tanaka 2015b: 125, Figure 4.9).⁹

As shown in Figure 4, the experiment also included another condition, namely QR from non-island finite clauses (Q-Control: long QR), and the acceptability rate of such “long” QR was higher than the rate of QR from all of the islands, but still (significantly) lower than the rate of QR in simple clauses. To confirm the higher acceptability of QR across finite clause-boundaries, Tanaka conducted a follow-up study the results of which are summarized in Figure 5 and (18). QR from indicative and subjunctive clauses is more acceptable/easier than QR out of an island (the difference is significant), but it is also judged significantly worse compared to QR within a simple predicate (local QR). Within the group of QR from finite and subjunctive complements, the only significant result is between the SubjSb and IndSb conditions (p < 0.01), that is, extraction of a subject was significantly easier from a subjunctive than from an indicative clause.

Figure 5

Mean acceptability of QR (Tanaka 2015b: 159, Figure 5.6).¹¹

These results show that QR from finite complements needs to be distinguished from movement that violates a clear syntactic locality condition such as an island.¹²

That QR from finite complements is not straightforwardly ungrammatical has also been found in the experiments reported in Syrett & Lidz (2011) and Syrett (2015). Examples such as (3b) (repeated as (19)) are usually interpreted with an embedded Ellipsis resolution, (19a), but “a third of the adults accessed the supposedly ungrammatical matrix interpretation [(19b), SW] at least once, and 4 adults accessed this interpretation at least half of the time, providing explicit justifications for doing so that referenced the matrix interpretation” (Syrett & Lidz 2011: 326). Similarly, Syrett (2015) shows that examples such as (19c) allow inverse scope as follows: “Of the 40 participants, 16 (40%) appeared to never access the wide scope. However, 24 (60%) did so at least once, and 15 (37.5%) did so for three or four of the test items.” (Syrett 2015: 588).

Furthermore, relevant for the current paper, Syrett & Lidz (2011) show that ACD with Ellipsis resolution requiring QR across a finite clause-boundary also poses significant processing difficulties. The availability of embedded and matrix Ellipsis resolution was tested in the configurations in (20) via truth-value judgment tasks. Participants were asked to rate such (in principle ambiguous) statements in situations in which the matrix and embedded Ellipsis interpretations yield different truth values. The results are summarized in Table 3, showing the acceptance rates of statements that are true only under the embedded Ellipsis interpretation (second column) or the matrix Ellipsis interpretation (third column). The baseline results for VP Ellipsis (VPE, see the first row of the table below) show that adults accept both embedded and matrix antecedents for VPE at a high rate (in fact the matrix readings received a higher acceptance rate than the embedded readings). However, when ambiguous ACD is involved as in (20b–d), which could in principle be resolved in two ways (though the contexts given to participants disambiguate), the acceptance of matrix readings drops significantly. In case of infinitives, matrix readings are still accepted at a rate of 50%, but in finite contexts, these rates are below 20%.

The clear bias for embedded Ellipsis resolution in contexts that require QR shows that non-local QR also does not come “for free” in ACD contexts. The large differences between the VPE and ACD conditions in the rate of matrix Ellipsis resolution (94% vs. 50% or 19%) can be taken to be a direct reflection of the additional burden imposed by QR. Similar to the difference between indicatives and subjunctives noted in Tanaka (2015b), we see here again that the cost inflicted by QR is gradient with respect to clause type: QR from infinitives is less costly (hence more available) than QR from finite clauses. Lastly, although ACD with matrix Ellipsis resolution is difficult, it seems to nevertheless be easier than “plain” QR out of finite clauses. I will thus assume that ACD essentially acts as an inverse scope biasing context in that it makes strenuous long QR less bothersome, very similar to the QR enabling contexts we have seen in Anderson’s experiments.

3.3 QR from non-finite clauses

In the introduction, we saw that different types of infinitives impose (clause) boundaries of different strengths: in terms of permeability for QR, Restructuring infinitives are grouped with simple clauses, whereas Non-Restructuring infinitives are grouped with finite clauses. In the previous section, we have seen a first indication that a more nuanced distinction is needed for different types of finite clauses—indicatives vs. subjunctives. This difference in clause-boundedness effects is also noted in Farkas & Giannakidou (1996) who show that in Greek, QR is not possible across an indicative clause boundary, but is possible from certain subjunctive clauses.¹³ An interesting pilot experiment conducted by K. Moulton (consisting of two pen-and-paper questionnaires) shows further that QR out of different types of infinitives is not a binary option, and, most importantly, that the grouping of Restructuring and simple predicates is not sufficient (see Moulton 2007). The experiments confirm the claim in Kennedy (1997) that QR out of Non-Restructuring infinitives is possible but more difficult than QR out of Restructuring infinitives. Crucially, the latter is also significantly more difficult than QR within a simple predicate.¹⁴

The questionnaires followed the experimental design used in Anderson (2004), and a sample example is given in (21). Since inverse scope is highly restricted in out of the blue contexts, even in simple predicates (see section for 3.1), Moulton, following Anderson, used contexts biased towards inverse scope interpretations. As shown in (21), speakers were presented with a short story, followed by a comprehension question targeting surface or inverse scope. As before, a ‘several’ answer unambiguously indicates that the speaker had an inverse scope interpretation in mind, and only those answers were counted in the inverse scope rates.

The mean proportions of the different categories are given in (22), and the paired t-tests of both items analysis and subjects’ performance in (23).

As indicated in (23), there are two significant effects: inverse scope from Non-Restructuring infinitives and from Restructuring infinitives was significantly harder than inverse scope within a simple predicate. The former may not be surprising in light of the claims found in the literature, however, the second finding is not expected in any of the syntactic accounts. As for the relation between Restructuring and Non-Restructuring, the results are not entirely conclusive, but they are suggestive.¹⁵ Although further testing is clearly necessary, these initial results can nevertheless be seen as suggestive of the following difficulty scale: simple predicate » Restructuring complement > Non-Restructuring complement.

To illustrate the issues arising for syntactic Scope Economy accounts consider the derivations in (24). The structure in (24a) represents a simple predicate with two quantificational arguments. Assuming that the subject can be interpreted in situ, inverse scope requires nothing beyond the first step of QR, which is motivated by type reasons. If Restructuring infinitives, following Wurmbrand (2001), are bare VPs as in (24b), which is also what Cecchetto (2004) assumes, no difference arises between (24a) and (24b). In both derivations, one single step of QR takes place, and the two constructions can therefore not be distinguished in their QR potential.¹⁶

(24)

a.

b.

A similar issues arise for approachs in which Restructuring infinitives are vPs as in (25) (see Wurmbrand 2013; Wurmbrand & Shimamura 2017 for recent analyses motivating a type of vP in Restructuring infinitives). In this case, two steps of QR are necessary—the first step would be driven by the need for a semantic type mismatch resolution and the second step by the need for a different scope relation. Thus, both steps meet (syntactic) Scope Economy. Since there is also no locality violation (each step only crosses one phase head), QR in (25) could again not be distinguished from QR in (24a) and the difference observed in (22)/(23) would be left unexplained.

At this point, we do not have experimental evidence for Italian to determine whether Italian restructuring cases such as (4b) also show an increased difficulty of QR compared to inverse scope in simple predicates. The following data provided in Cecchetto (2004), however, lend at least initial plausibility to the hypothesis that this may also be the case in Italian, and that inverse scope is not equally available in configurations such as (25) as opposed to (24a). Cecchetto also discussed perception verb constructions, which involve ECM into a vP complement. As shown in (26), there is a difference in the availability of inverse scope depending on whether the lower QP originates as a subject or an object, which is reminiscent of the difference noted for QR from English subjunctives in Tanaka (2015b) (cf. (18)). Cecchetto (2004: 369, fn. 17) notes: “I believe that inverse scope is better in (i) [=(26a), SW] than in (ii) [=(26b), SW], as the theory I am arguing for predicts. […] However, I must say that inverse scope is harder in (i) [=(26a), SW] than in (38) [=(26c), SW], in which the QNP that takes wide scope is in the subject position of the ECM clause. Presently, I have no explanation for this contrast.”

There are two noteworthy points. First, according to Cecchetto’s judgment, inverse scope in (26c) is not easily available (cf. the ?), which supports the hypothesis that QR spanning two verbal predicates (the matrix and embedded vPs, like in Restructuring complements) is harder than QR in simple predicates (of course this should be seen as a hypothesis, which should be confirmed by further experimental studies). Second, (26a) corresponds essentially to the structure in (25), namely a configuration in which two steps of QR are necessary for the embedded object to achieve scope over the matrix subject. Since both steps are motivated (by type mismatch resolution and different scopal properties), the difference is again not derivable from syntactic Scope Economy.

The obvious difference between (24a) and (25) would be the number of steps involved for the lower QP to take scope over the higher QP. Syntactic Scope Economy accounts do not seem to offer a way to relate this difference to the graded acceptability we find regarding inverse scope. I nevertheless disagree with Moulton who states that neither syntactic nor processing accounts can account for the significant difference in the availability of inverse scope between simple predicates and Restructuring complements. In what follows, I will show that a processing account operating on syntactic structure has exactly the properties needed to put all the observations summarized in this section together in a uniform account.

3.4 Summary

The conclusions reached in the above studies on scope are summarized in (27). The approach to inverse scope I take in this paper, which the data presented in this section support, is that an inverse scope interpretation is derived by (successive cyclic) QR. Costs associated with inverse scope can then be formulated as costs arising for the operation QR. In the following sections, I will present an account that aims to implement these observations.

4.1 The domains of complement clauses

Before proposing a specific processing algorithm, I need to take a short detour laying out the structure of different types of complements. In previous works, I have shown that there is a cross-linguistically stable split of embedded clauses (both finite and non-finite) into three types of complements which consistently display different morphological, syntactic, and semantic properties (Wurmbrand 2001; 2014b; c; 2015a; b). Based on the temporal and aspectual composition of complementation structures, three semantic types of complements can be defined. The first type are complements of attitude (believe) or speech predicates (claim), which involve a short reference time interval, the now of the propositional attitude holder, and some form of context operator or binder. The short attitude holder reference time interval is responsible for triggering a simultaneous, present-like interpretation of the complement, which is observable, for instance, in the impossibility of perfective aspect forms (e.g., in Bosnian/Croatian/Serbian or Greek) or the non-progressive form in English: like simple present tense statements (They are sleeping/*sleep right now), claim-type complements require the use of progressive/imperfective to refer to a non-generic eventive situation (They claim to be sleeping/*sleep). The second type of embedded contexts are complements to verbs like decide or expect, which trigger a shift of the embedded time interval to the future with respect to the matrix time. Like simple future statements, these complements can occur with non-progressive/perfective forms (e.g, They decided to sleep). The third type of complementation involves complements to verbs like try, begin, or manage, which form a single temporal domain with the matrix clause and only allow a simultaneous interpretation of the matrix and embedded times.

Approaching complementation from a syntactic perspective, the same classes emerge when, for instance, the cross-linguistic distribution of traditional Restructuring properties such as Clitic Climbing are considered: some languages allow Clitic Climbing only out of tenseless (try-type) complements, whereas other languages allow it from tenseless (try) and future (decide) complements. Clitic Climbing out of attitude/speech complements is very rare and not attested robustly in any language. An important observation is that the distribution of Clitic Climbing and other properties follows a clear implicational dependency: whenever Clitic Climbing out of future complements is possible in a language, it is also possible out of tenseless complements in that language, or in other words, there is no language in which future complements are more transparent than tenseless complements. The conclusion is that there is an implicational transparency scale of the form: attitude/speech » future » tenseless (non-/semi-intensional).

Such (apparent) gradient behavior of transparency poses a challenge for most traditional analyses of Restructuring which are built on a binary distinction between Restructuring and Non-Restructuring. The view of variable clause size I have been following, on the other hand, paired with a semantically motivated determination of clause structure, provides the tools to predict the implicational Restructuring hierarchy. The key assumptions are that the semantic properties map directly to syntactic structure (meaning reflects a structural property) and that languages have the option of constructing complements smaller than full CP complement clauses. Specifically, the building of clauses can stop at the completion of the theta-level (e.g. vP) or the tense/modal/aspect level (e.g., TP), provided that these “bonsai” clauses lead to well-formed interpretations in that all properties required by the matrix verb are recoverable from the structure. In such a system, the minimal structures of the three types of complementation are as in (28). I use the labels given in Grohmann (2003) to refer to the three clausal domains: Ω for the CP/A’-domain; Φ for the tense/modal/aspect/agreement domain, and Θ for the theta domain. Attitude and speech verbs have to combine with CPs to host the attitude reference time interval and context operator or binders. Future selecting verbs, on the other hand, can omit the CP-domain but must minimally include a TP-domain to host the future element. Finally, tenseless, non-intensional verbs can combine with just a vP. This yields exactly the implicational hierarchy observed. Claim-type complements are full clauses and hence show the least transparency. Decide-type complements are minimally TPs that can lack the A’-domain and are hence transparent for any operation that is hindered by CPs but not for operations that are hindered by TPs. Lastly, try-type complements can lack both the A’- and tense-domains and are therefore the most transparent complements.

(28)	a.	believe, claim	b.	decide, expect	c.	try, manage

The important consequence of this approach is that the Restructuring scale reduces to a syntactic complexity scale which shows effects in all languages, even when a language does not show the standard (Italian based) Restructuring diagnostics such as Clitic Climbing. The current paper is not the place to motivate this approach—I can only give a schematic summary of the variation that has led, misleadingly, to the claim that there is a Restructuring parameter, or the like. For instance, to derive differences in the availability of cross-clausal Clitic Climbing and scrambling, I have proposed a freezing mechanism which traps these elements in the first target position they reach. If the target position is within the Θ domain, as for instance in French or Brazilian Portuguese, clitics are necessarily clause/predicate bound, even in Restructuring contexts such as (28c). Importantly, although these languages do not allow cross-clausal Clitic Climbing, they can nevertheless be shown to involve Restructuring in the sense that certain clausal domains are not projected as in (28b,c) (see Modesto 2013; Wurmbrand 2014b; 2015b for Brazilian Portuguese). Evidence for such reduced structures must then come from other properties, for instance, negative concord or NPI licensing, the distribution of subjects, finiteness, temporal elements, negation, and many others. If the target position is within the Φ domain, as in Italian or Spanish, Clitic Climbing is possible in tenseless contexts, (28c), but not in future contexts, (28b). Lastly, if the target position is within the Ω domain, as in Polish or German, Clitic Climbing and Scrambling are possible in tenseless contexts, (28c), as well as in future contexts, (28b). Finally, this approach correctly predicts that infinitives involving an Ω domain (e.g., an embedded complementizer or wh-phrase is present) never allow Restructuring (which has been shown in several works, e.g., Wurmbrand 2001; Bondaruk 2004; Dotlačil 2004; Marušič 2005).

This summary of complementation is obviously very sketchy, but for the current paper, the essential point is that different types of complements, in any language, can differ in size—i.e., show different structural complexity defined by the three clausal domains as in (28). This provides us with the necessary tools to tackle the question of why inverse scope shows the gradation and variability that is observed.

4.2 Counting steps—towards a processing account

In this section, I provide the basic account for the observation in (27f): QR across clause/predicate-boundaries increases the processing burden along the syntactic complexity scale; the more steps of QR inverse scope requires, the less acceptable it is (up to possible unacceptability of an inverse scope interpretation). As mentioned above, this paper follows approaches that derive inverse scope via QR. Specifically, I propose that QR is an A’-operation with the same domain and locality restrictions as overt A’-movement, In other words, there is no special clause-boundedness restriction and also no syntactic Scope Economy requirement for QR. Instead QR can apply in a step-by-step fashion from one cyclic domain to the next. For the moment, I leave open whether these domains are phases or domains as defined in the previous section based on Grohmann (2003). This system thus allows, in principle, an unbounded sequence of QR steps. Furthermore, following Anderson (2004), I assume that QR is always costly for the parser, and, following Tanaka (2015b), that each step of QR comes with a reduction that adds to the processing costs.¹⁷ In section 4.3.2, I provide further details and a possible motivation for these costs.

Building on the complementation approach described in the previous section, we arrive at the syntactic complexity scale in Table 4. Although QR has not been directly tested for all of the distinctions in the table via uniform experiments yet, the available evidence is nevertheless suggestive of at least the plausibility of the hypothesis that the difficulty of QR correlates with the syntactic complexity as indicated. As shown, one cut is made by syntactic locality—absolute islands (such as complex NP islands) block movement in syntax and hence both A’-movement and QR yield (true) ungrammaticality (leaving open whether strong islands incur processing penalties in addition to the syntactic locality violation). I propose that complement clauses allow successive cyclic movement in syntax—both overt and covert, but that covert movement accumulates higher processing costs (calculated based on syntactic complexity), which obscure the inverse scope interpretation and make it less accessible (I return to differences between overt and covert movement below).

Let us start with simple clauses and complement clauses, which is the main focus of this paper (I comment on adjuncts below). Within a simple predicate/clause, inverse scope requires only a single step (see (24a) and hence no domains are crossed. Assuming that each step of QR incurs a processing cost (see section 4.3.2), simple QR ends up with a penalty of 1 (Ө). The number of steps required for an embedded QP to take scope over the matrix subject differs depending on the type of complement. QR from a tenseless restructuring complement requires two steps of covert movement (see (25) and fn. 16), hence a cost of 2 Ө. Based on the structures in (28), the number of steps and penalties are then as specified in Table 4 (the numbers refer to QR of an embedded object QP).¹⁸

Variable clause-size together with a processing approach that is dependent on syntactic complexity predicts differences for inter-clausal QR from subjunctive vs. indicative complements, insofar as these distinctions correlate with structural differences in a language. Cross-linguistically, subjunctive tends to occur in future and tenseless complements (though there are language-specific idiosyncrasies), whereas attitude and speech predicates more commonly combine with indicative complements. The syntax and semantics of subjunctives is rather controversial, but one trend is to represent subjunctives as complements that lack a contentful or domain/phase inducing CP (see works arguing that subjunctive markers are IP elements rather than complementizers; e.g., Terzi 1992; 1997; Philippaki-Warburton 1994; Rivero 1994; Giannakidou 2009; or works suggesting deficient and/or non-phasal CPs; e.g., Alboiu 2007; Wurmbrand 2013). Either approach predicts, as specified in Table 4, that QR is easier (more acceptable) across subjunctive clauses than indicative clauses, which we have seen is exactly the outcome of Tanaka (2015b)’s experiment in (18), as well as the data presented in Farkas & Giannakidou (1996).¹⁹

The assumption that each step of QR incurs a cost is also reflected in differences between QR by an embedded object vs. an embedded subject (see for instance the higher acceptance rates of subject QR compared to object QR in both the subjunctive and the indicative conditions in (18), as well as the discussion of (26) for Italian perception verb contexts; Farkas & Giannakidou 1996 also provide similar observations from Greek). Since subjects already occur at the edge of the embedded vP, whereas objects first have to get to that position, QR by an object will always involve one more step than QR by a subject, and if subject and object extraction are equally available, QR by a subject is predicted to be less costly.

Returning to the general issue of the availability of inverse scope, a structure–processing mapping as in Table 4 allows us to define a threshold for acceptability or parseability of inverse scope (which may vary among individual speakers). For speakers who do not accept inverse scope out of finite clauses, a QR processing burden of 4 reductions appears to be too much. As pointed out by a reviewer, this effect could be seen as a kind of garden path effect where the inverse scope (the “right” path) is simply too hard to see for speakers due to the complexity of the structure. Thus, as in the case of non-parallel Ellipsis as in (13), inverse scope is not ungrammatical, but simply unacceptable when the threshold for tolerable processing costs is reached (in other words, it’s not a competence issue but a performance issue). Furthermore, like in the case of garden path sentences where certain handholding can help guide the speaker onto the correct parse, there are also factors that can help access the inverse scope interpretations—as we have seen in section 3, among those are inverse scope biasing contexts and ACD (I return to this point in the next subsection).

A final (somewhat open) question is whether overt and covert movement impose the same processing costs or whether covert movement yields higher costs. The fact that sentences such as (29a) with overt long wh-movement are considered grammatical, whereas inverse scope in the parallel (29b) is very difficult to access for speakers and in many cases not available at all, may suggest that covert movement imposes a higher processing burden. Processing effects such as acceptability decrease and slower reading times have also been observed for wh-movement across finite clause boundaries (see for instance Kluender & Kutas 1993; Gibson 1998; Fiebach et al. 2002; Frazier & Clifton Jr 2002; Sprouse et al. 2012), but with the exception of Tanaka (2015b)’s study of extraction from islands, no direct comparisons of the processing of overt and covert movement is available. Since the difference between (29a,b) is quite palpable, even if overt movement also shows certain processing effects, the extent of the burden seems to be different.

If further experimental studies confirm that there is indeed a quantitative difference, this difference could be related to the way parsing proceeds in overt vs. covert movement. Overt wh-movement involves a filler-gap dependency where upon encountering the filler (the overt wh-phrase), the parser is instructed to look for a gap (the originating position). In doubly quantified sentences, on the other hand, there is no overt cue within the sentence for a long-distance dependency until the second QP is reached. Thus, in contrast to overt wh-movement, QR involves a retrospective search in parsing, which could be seen to be responsible for the higher processing cost for covert movement. Possible support for this direction could come from sentences such as A different member tested every recipe, which received almost exclusively the ‘several’ answer to the comprehension question in Anderson (2004)’s experiments (see Table 1). Since in such cases there is an early clause-internal cue for the costly interpretation—the modifier different, the costs of QR, although still existent and observable as increased reading times (see section 3.1), become tolerable and do not affect the acceptability of inverse scope. The prediction would be that in such cases, the processing costs of wh-movement and QR are comparable.²⁰

Let us finally turn to QR from adjuncts. The focus of the current paper is QR in clausal complementation configurations, but for completeness, I provide a preliminary suggestion for how one may approach QR from adjuncts here. This should only be seen as a first approximation with many data points still in need to be determined. As shown in Table 5, I assume that not all adjuncts cause a syntactic locality violation for A’-dependencies spanning across them. Specifically, weak islands of the kind discussed in Tanaka (2015b) could be assumed to allow successive cyclic movement across them (cf. the acceptability rates of 3/5 or higher in Figure 3), and the decrease in acceptability could arise as a processing issue (see also Kluender & Kutas 1993 for a similar claim regarding wh-islands). Recall from Figure 4 that QR from during PPs is less acceptable than long QR (e.g. across finite clauses), however, the difference has not reached significance. Based on that, an option similar to Tanaka (2015b)’s cost calculation is to assume that crossing a non-island adjunct (i.e., an island that in contrast to absolute islands allows successive cyclic movement across it) imposes a stronger processing burden—a double penalty—compared to QR along the clausal spine. This cost applies to overt and covert movement alike, since, as Tanaka (2015b)’s experiments show, wh-movement and QR show similar effects of decreased acceptability in weak islands (compare the acceptability rates in Figure 3 and Figure 4). Furthermore, after gerunds and during PPs need to be assumed to differ in structure, with the former involving a full clausal structure (vP, TP, and CP/PP), whereas the latter are simple PPs or have a reduced clausal structure.²¹ Since it is not clear at this point whether during PPs are stronger boundaries for QR than finite clauses, I leave details of the structure of these PPs open until further experimental evidence is available which could then shed light on the syntactic composition of these PPs.

Before concluding this section, a final comment on the claim that QR obeys the same locality constraints as overt A’-movement is in order. A construction which potentially involves a difference in mobility between overt and covert contexts is Inverse Linking as in (30a,b). To derive wide scope of DP2 (every city), two movement derivations are conceivable: movement to the edge of DP1 as in (30c), or movement through the edge of DP1 to a higher position in the structure as in (30d).

(30)	a.	May (1977; 1985: (26))
		Someone from every city despises it.
	b.	Larson (1985: 5, (12); 2»∀»∃; ∀»∃»2; *∀»2»∃)
		Two politicians spy on someone from every city.
	c.		d.

Both derivations have been proposed and motivated. The derivation in (30c), or some variation thereof, goes back to May 1977; 1985) (see also May & Bale 2006), and is compatible with DP1 being an island since DP2 never (fully) leaves DP1 (thus, (30c) can be the structure for (30a), given that subjects are typically islands for extraction). This derivation can also account for the bound variable interpretation in (30a) if a DP specifier or adjunct is assumed to c-command out of the hosting DP (see Kayne 1994). Furthermore, the scope restriction noted in (30b) can be derived since DP2 and DP1 act as a “unit” (see May & Bale 2006 for details and a specific implementation). The derivation in (30d), on the other hand, derives bound variable interpretations under any definition of c-command and predicts that scope splitting should be possible. This has been argued to be the case in Sauerland (2005) when scope between quantifiers and intensional verbs is considered as in (31a), which, according to Sauerland, can have the interpretation in (31b). The impossibility of scope splitting in contexts such as (30b) then requires a different account (e.g., a superiority approach, following Bruening 2001, as in Sauerland 2005).

The approach to QR taken in the current paper is compatible with both derivations in (30c) and (30d), however, the latter should only be possible if DP1 is not an island—i.e., if it does not block overt movement in the same context. Cases such as (31a), which provide the strongest argument for a structure such as (30c), readily allow wh-extraction of the from complement, as shown in (32a). The same is the case for the ACD example in (32b), in which the ACD VP can take a narrow (embedded) or wide (matrix) antecedent. Crucially, under the wide antecedent interpretation, scope splitting is still possible: the example can be interpreted with the every DP2 taking scope over want and the someone DP1 taking scope under want (i.e., ‘For every city such that John has the desire to meet someone from it, Mary also has the desire to meet someone from it.’ Sauerland 2005: 307, (13b)). As shown by the grammatical paraphrase of wide Ellipsis in (32c), overt long-distance extraction of the from complement is also possible, thus the current account correctly predicts that QR is possible in this context, exactly as required to resolve ACD in (32b) and to derive the interpretation where DP1 and DP2 take separate scope. Lastly, to derive the wide scope of both quantifiers over want in (32b), the derivation is as in (30c).

Although, so far, the derivations in (30c,d) are compatible with the claim that overt and covert movement are subject to the same locality constraints, a problem could arise if scope splitting from subjects is also possible in Inverse Linking contexts. If this is the case, the current approach would need to resort to a different account of scope splitting (e.g., a non-scopal account of de re interpretations).²²,²³

4.3 The cost of QR

Recall the summary of the findings from the experimental results in (27), repeated in (33). In the previous section, I addressed the point in (33f). In this section, I provide a possible direction for further implementing the other observations.

The first step is to separate the question of the specifics of the cost of QR from the effects of the cost. In section 4.3.1, I summarize and present further data which show that the acceptability of inverse scope is only a reliable diagnostics for the cost of QR in sentences that are ambiguous (where there is a choice between a costly and a less costly interpretation). In cases where only the more costly interpretation is available (for whatever reason), the lack of choice makes inverse scope more or fully acceptable, while nevertheless remaining costly, which will confirm the hypothesis that every step of QR incurs a cost. Finally, in section 4.3.2, I formulate a possible algorithm for how to compute that cost.

4.3.2 Calculating costs

In the analysis presented so far, I have adopted and further specified the processing approach in Anderson (2004), with the additional part highlighted in (38).

(38)	Processing Scope Economy (based on Anderson 2004: 48, (46))
	The human sentence processing mechanism prefers to compute a scope configuration with the simplest syntactic representation (or derivation). Computing a more complex configuration is possible but incurs a processing cost of one penalty for each step of QR.

Within a cyclic movement approach, the further the distance between two quantifiers is, the more steps are necessary to derive inverse scope. Each step increases the processing burden up to a point where the inverse scope derivation becomes impossible to parse. The final question is whether there is more to these costs than just counting steps. In this section, I suggest a possible direction for how to formalize the cost computation in a copy theory approach to QR. It is not my aim to convey that this is the only approach to QR—I simply try to provide a possible way to further understand the reason for Processing Economy.

I follow a copy approach to movement where QR applies cyclically (not counter-cyclically at LF) and involves the PF pronunciation of the lowest copy. To derive inverse scope of the object over the subject, I assume that the subject can be interpreted in its base position within the vP (but more complex derivations are possible, too). To resolve copy choice at LF and to create the proper LF representation of quantificational phrases from multiple QP-copies, I adopt the process of Trace Conversion in (39).

(39)	Trace Conversion (Fox 2003: 111, (50))
	a.	Variable Insertion:	(Det) Pred ⇒ (Det) [Pred ly(y=himn)] [n is the index of the moved QNP]
	b.	Determiner Replacement:	(Det) [Pred ly(y= himn)] ⇒ the [Pred ly(y= himn)]

The scope-relevant derivation for a sentence such as (40a) is given in (40b). The object undergoes movement to the edge of vP above the base position of the subject. When the vP is complete, there are thus two copies of the object in the Θ-domain. The lower copy is transferred to and spelled out at PF and the higher copy is deleted for PF purposes. As part of transfer to LF, the lower copy undergoes trace conversion. As indicated in (40b), I propose that it is the operation of trace conversion that adds a cost (Ө) for processing. Although the subject QP undergoes further movement to TP, I follow approaches which regard the vP-internal subject position as the position relevant for LF. Thus the configuration in (40b) is what is sent to LF (either at the stage in (40b) or at a later stage after reconstruction).²⁵

(40)	a.	A technician tried to inspect every plane.	∀ »∃
	b.

Turning to Restructuring infinitives such as (41a), we have seen in section 4.1 that even the smallest complements involve at least an independent thematic domain. I propose that movement exiting a domain must proceed successive cyclically through the edge of each cyclic domain as depicted in (41b).²⁶ In a phasal approach, this would correspond to the Restructuring complement counting as a phase, either because it is a vP (see Wurmbrand 2015a; Wurmbrand & Shimamura 2017) or because it is the top extended projection of the embedded V (see Wurmbrand 2013; 2014a; 2015a; Bošković 2014). The first cycle in (41b) is identical to the derivation in (40b)—the lowest copy undergoes trace conversion at LF, incurring a processing cost, and is spelled out at PF (whether actual LF spell-out occurs at this point or, as in Cecchetto 2004, only at the end of the entire derivation is not relevant for our purposes, as long as LF spell-out occurs after trace conversion). After completion of the first cycle, PF and LF go separate ways (the moved QP is not visible for PF anymore, but it is still active in syntax). The QP-copy of the object undergoes a second step of movement and adjoins to the matrix vP, above the matrix subject. At the end of this cycle, copy choice occurs again since there are again two copies of the QP (minus the PF part). This can be achieved either via another application of trace conversion of the lower (now intermediate) copy or via deletion of the intermediate copy which is not interpreted in any way and hence is superfluos (as pointed out to me by B. Spector, p.c., since a trace converted definite description in this position would be vacuous, deletion may not be necessary). Either operation, I assume, is costly and hence the structure ends up with two Ө which make inverse scope less available in (41) than in (40).²⁷

(41)	a.	A technician tried to inspect every plane.	∀ »∃: less available than (40)
	b.

Lastly, the (simplified) derivation for inverse scope spanning a decide–type infinitive is given in (42). Since infinitives combining with verbs like decide involve a future interpretation, they project a tense/modal (Φ) domain (see Wurmbrand 2014c for motivation of a syntactic future element in infinitives). For an embedded object to take scope over a matrix quantifier, a QP originating in embedded object position has to cross two domains to reach a position above the matrix subject. As illustrated in (42b), this leads to two stop-overs and three applications of trace conversion, thus a processing cost of three Ө, which makes inverse scope more difficult than in try-type infinitives and simple predicates.

(42)	a.	A technician decided to inspect every plane.	%∀»∃
	b.

To ensure that movement proceeds as in (42b) in future infinitives, the embedded clause (e.g., TP or ModP) must count as a cyclic domain, which is the case under a contextual phase approach or a Grohmannian domain approach, but not under a phase approach in which only vP and CP are phases (Chomsky 2000; 2001). This finally brings us to QR from finite clauses. Interestingly, a phase approach and a domain approach make different predictions regarding the difficulty of QR from a finite clause compared to a future infinitive. The difference between phases and domains is the TP/Φ domain in contexts where that domain is not the top projection/domain of a clause. As shown in (43), an embedded finite clause involves three domains, (43b), but only two phases, (43c). A phase approach thus predicts that QR from finite clauses should be similar in difficulty to QR from future infinitives, whereas a domain approach predicts that QR from finite clauses should be harder than QR from future infinitives. To date, none of the experimental approaches has compared QR from finite complements and QR from future infinitives. Further psycholinguistic data will thus not only allow us to settle this data point but also contribute to the theoretical debate(s) of how to define cyclic domains.²⁸

(43)	a.	A technician decided that he would inspect every plane.	%∀»∃
	b.
	c.