Extraction from NP, frequency, and minimalist gradient harmonic grammar

2.1 ΔP

In what follows, we will pursue the hypothesis that frequency is the decisive factor in establishing a natural predicate, i.e., an entrenched V–N dependency, in the cases of extraction from NP that we are interested in. A basic premise is that the absolute frequencies of individual lexical items in corpora will not be particularly informative in this context, and that the same goes for the absolute frequencies of V–N collocations. Rather, what is needed is a more fine-grained approach to frequency that is based on how well the two lexical items in a V–N dependency predict each other. One such measure that has been proposed is collostructional strength (see Gries et al. 2005; Gries and Stefanowitsch 2004; Stefanowitsch 2009). More recently, Gries (2013) has suggested to employ the measure of ΔP, and it is this concept that we will make use of in what follows.^[7] ΔP _X|Y measures how well the presence of some item Y predicts the presence or absence of some other item X. ΔP is defined as in (11).

Here, p(X|Y = present) captures the probability of the outcome X in the presence of the cue Y; p(X|Y = absent) is the probability of the outcome X in the absence of the cue Y; and to determine ΔP _X|Y , the latter is subtracted from the former. The values of ΔP range from −1.0 to 1.0; they are interpreted as follows:

1. ΔP _X|Y approaching 1.0: Y is a good cue for the presence of X

2. ΔP _X|Y approaching −1.0: Y is a good cue for the absence of X

3. ΔP _X|Y approaching 0.0: Y is not a good cue for the presence or absence of X

Note that this relationship is asymmetric. An element predicting another element well is not necessarily well-predicted by that element. This means that for every pair of X and Y, there are two values ΔP _X|Y and ΔP _Y|X . As an illustration, let us look at how ΔPs are determined for a V–N dependency involving kaufen ‘buy’ and Buch (‘book’) on the basis of the frequencies of the co-occurrences. To calculate ΔP _X|Y , we first search the corpus for the number of all cases where X and Y co-occur, where only one of the elements occurs, and where none of the elements occur. (12) shows such a co-occurrence table for the pair Buch kaufen ‘book buy’.^[8]

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Co-occurrences of Buch ‘book’ and kaufen ‘buy’

This kind of information can be used to calculate ΔP _X|Y by taking the difference between the probability of X given the presence of Y and the probability of X given the absence of Y. Suppose that X = Buch and Y = kaufen. ΔP _X|Y (= ΔP _Buch|kaufen) is then determined as shown in (13); it shows how well kaufen predicts Buch in the corpus.

In the same way, ΔP _Y|X (= ΔP _kaufen|Buch) based on the data in (12) is calculated as shown in (14). The resulting value indicates how well Buch predicts kaufen.

By comparing the two ΔPs, it becomes evident that kaufen is a somewhat better predictor for Buch than Buch is for kaufen: The likelihood of a buying event involving books (rather than, say, bikes or guitars) is greater (ΔP = 0.01186) than the likelihood that a book is involved in a buying event (rather than, say, a reading or burning event, or some other scenario in which books may show up; ΔP = 0.00381).^[9]

2.2 Corpus

The data in our survey come from the core corpus of Digitales Wörterbuch der deutschen Sprache (DWDS; see Geyken 2007). The DWDS is a freely searchable corpus consisting of about 5.8 m sentences in the German language. It contains a balanced mix of fictional, scientific, functional, and newspaper texts from the twentieth century.

The list in (15) shows the queries used to elicit the counts for nouns, verbs, and noun–verb pairs. Ideally, one would like to query the corpus for every instance where a given noun is the direct object of a given verb (recall that this is the only environment in which extraction from NP can be possible, given our characterization of the empirical evidence in the previous section). However, while the corpus is lemmatised and tagged for part-of-speech, it does not encode dependencies. Hence, without an additional step of dependency parsing applied to corpora, the queries can only ever be approximations.

The query in (15c) attempts to find noun-verb pairs by looking for sentences where the noun and the verb are close to each other. This avoids false positives as in (16a) (where Buch ‘book’ and gekauft ‘bought’ are clause-mates in a VP coordination construction, but Buch is the (head of the) object of gelesen ‘read’, not of gekauft). However, it also introduces false negatives as in (16b), where Buch is the (head of the) object of gelesen, but is separated from it by more than three items as a consequence of having undergone topicalization to the clause-initial (‘Vorfeld’) position.

Cases like (16b) can only pose a potential problem if there is reason to assume that object topicalization also (i.e., like extraction from NP) shows asymmetries depending on how close the relation between the verb and the object’s head noun is, such that, e.g., an object headed by Buch ‘book’ tends to undergo topicalization more often, or more easily (or, in fact, less often, or less easily) in the presence of lesen ‘read’ than in the presence of stehlen ‘steal’. We are not aware of any claims in the literature that would go in this direction, and will assume, here and henceforth, that there is no such effect. Thus, false negatives like (16b) generated by object movement can be ignored, assuming that they affect all kinds of V–N dependencies in the same way.^[10]

2.3 Results

We have determined both ΔP values for every V–N pair where N is a noun in (17a) and V is a verb in (17b) (see the Appendix for the raw data). This results in high-frequency collocations like Buch lesen ‘book read’, combinations of low-frequency pairs where this intuitively seems to be ‘the noun’s fault’, like Verlautbarung lesen ‘official.statement read’, and combinations where it is the verb that is responsible for the low frequency, as in Buch werfen ‘book throw’.

As shown in (19), the ΔPs for Buch lesen are both higher than the ΔPs for Buch stehlen.

This is in full accordance with the fact that the V–N dependency Buch lesen permits extraction from the NP whereas the V–N dependency Buch stehlen does not; recall the examples in (7a) and (7b) above. As shown by the ΔPs for some other V–N combinations in (19), this result can be generalized: The higher a ΔP is, the more likely it is that extraction is possible.

These data also shed some light on which ΔP value may be most relevant for establishing the strength of a V–N dependency (and, consequently, for determining the option of extraction from NP). A priori, three options suggest themselves: ΔP _V|N , ΔP _N|V , and the arithmetic mean of these two values. Closer inspection reveals that ΔP _N|V is not fully reliable. On the one hand, there are cases like Buch weglegen ‘book put.away’ where ΔP _N|V is fairly high (i.e., weglegen ‘put.away’ is a reasonably good predictor for the presence of Buch ‘book’), but extraction is not straightforwardly possible in this environment (cf. *Worüber hat der Fritz ein Buch weggelegt? ‘about.what has the Fritz _nom a book _acc put.away’). On the other hand, there are also cases like Bericht schreiben ‘report write’ where ΔP _N|V is quite low (i.e., schreiben ‘write’ is not a good predictor for the presence of Bericht ‘report’), but extraction is easily possible (cf. Worüber hat der Fritz einen Bericht geschrieben? ‘about.what has the Fritz _nom a report _acc filed’). In contrast, ΔP _V|N makes the right predictions in these cases: Bericht ‘report’ is a good predictor for schreiben ‘write’, and Buch ‘book’ is not such a good predictor for weglegen ‘put.away’. This leaves ΔP _V|N and the arithmetic mean of the values as the remaining options. In what follows, we will settle for ΔP _V|N alone. Note that this introduces an asymmetry: Whether a V–N dependency qualifies as a natural predicte or not depends on how well the noun can predict the verb.^[11]

2.4 Scaling

In the next section, we will implement the frequency-based approach to extraction from NP in German in a version of Gradient Harmonic Grammar (see Smolensky and Goldrick 2016). Standardly, numerical strength values assigned to linguistic objects in this grammatical theory are taken to be within the interval [0, 1].^[12] We will therefore scale up numerical values of the type found for ΔP in (18) and (19), by min-max normalization (feature scaling), so that they end up squarely in the [0, 1] interval. Thus, the data can be normalized into a range of [0, 1] using the formula X ′ = X − min ( X ) ( max ( X ) − min ( X ) ) . For the V–N dependencies in (18) and (19), this produces the values in (20). We will adopt these normalized values for the theoretical modelling in the next section.

(20) shows that there is a correlation between a higher normalized ΔP value and the option of extraction. In addition, the plot in (21) reveals that the cut-off point with respect to extraction is not so much between high-frequency and low-frequency pairs of N and V, but rather within the low-frequency area, at a strength of 0.14 (or thereabout). This picture persists when the complete set of data is taken into account (cf. the Appendix).

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3.1 The gist of the analysis

In this section, we show how the different strength values of V–N dependencies correctly predict the options of extraction from direct object NPs in German, assuming (i) a gradient harmonic grammar approach where both violable syntactic constraints and linguistic expressions (like V–N dependencies) are associated with weights, (ii) a minimalist approach to syntactic derivations in which both intermediate and final movement steps target the left edge of a verbal phase (a specifier of v), and (iii) an approach to iterative optimization based on harmonic serialism, where optimization domains are small and the amount of information that can be taken into account during each optimization is limited. However, before we address these issues in detail, let us focus on the gist of the analysis.

In all cases of extraction from NP, there is a dependency between a verbal head X and a noun Y that intervenes between the base position (α _i+1) and (what is typically) the target position (intermediate or final) at the left edge of the verbal phase (α _i ); see (22).

At the heart of the analysis is a well-established locality constraint, the Condition on Extraction Domain (CED), which we take to be violable and weighted. If YP (the maximal projection of Y) is not a complement of X, ungrammaticality will invariably arise with extraction from NP (because of a violation of the CED that will always emerge as fatal); this covers the structural restrictions discussed in Section 1. If, however, YP is a complement of X, the CED can be satisfied, and it is at this point that the weight of the X–Y dependency becomes crucial: CED satisfaction can bring about a reward, and this reward is required by each case of extraction from NP because the general constraint blocking movement (Economy Condition) as such has slightly more weight than the general constraint forcing movement (Merge Condition), so for the scales to be tipped in favor of the movement candidate, the derivation cannot do without a reward from the CED – and only if the reward for CED satisfaction generated by the X–Y dependency’s weight is sufficiently high will extraction from NP (i.e., movement from α _i+1 to α _i ) be legitimate. This covers the lexical variation with extraction from NP, i.e., the natural predicate effect. In what follows, we flesh out this analysis, starting with Gradient Harmonic Grammar.

3.2 Gradient Harmonic Grammar

Harmonic Grammar (see Smolensky and Legendre 2006; Pater 2016) is a version of Optimality Theory (see Prince and Smolensky 1993) that abandons the strict domination property (according to which no number of violations of lower-ranked constraints can outweigh a single violation of a higher-ranked constraint) and replaces harmony evaluation by constraint ranking with harmony evaluation based on weight assignment to constraints. The central concept of harmony is defined in (23) (see Pater 2009).

According to (23), the weight of a constraint is multiplied with the violation score of a candidate for that constraint, and all the resulting numbers are added up, thereby determining the harmony score of a candidate. An output qualifies as optimal if it is the candidate with maximal harmony in its candidate set; i.e., if it has the highest harmony value.

Gradient Harmonic Grammar (see Smolensky and Goldrick 2016), in turn, is an extension of Harmonic Grammar where it is not just the constraints that are given weights; rather, symbols in linguistic representations are also assigned weights (between 0 and 1). This gives rise to a very straightforward way of associating strength with linguistic objects. So far, most of the work on Gradient Harmonic Grammar has been in phonology; but cf. Smolensky (2017), Putnam and Schwarz (2017), Lee (2018), Müller (2019), and Schwarz (2020) for recent applications in syntax.^[13]

3.3 Minimalist derivations

We adopt a minimalist setting (cf. Chomsky 2001), according to which syntactic structure is created incrementally by external and internal Merge operations, where the former are responsible for basic structure-building and the latter bring about structure-building by movement. We assume that syntactic movement is restricted by the inviolable Phase Impenetrability Condition (PIC; cf. Chomsky 2001, 2008) in (24).^[14]

This implies that movement must take place successive-cyclically, via intermediate edge domains (i.e., specifiers) of phases, where the clausal spine is composed of CP, TP, vP, and VP, of which CP and vP qualify as phases. (We follow Chomsky in assuming that NP/DP is not a phase). Next, suppose that all Merge operations, including movement steps to intermediate phase edges, are triggered by designated features (cf. Chomsky 1995, 2001; Collins and Stabler 2016; Georgi 2017; Pesetsky and Torrego 2006; Urk 2015); this can be enforced by the Merge Condition (MC) in (25) (see Heck and Müller (2013) for the [•F•] notation for features that trigger external or internal Merge), which we assume to be a violable, weighted constraint (in contrast to the PIC).

Next, there is a counteracting constraint that prohibits structure-building; for present purposes, it can be assumed that this role is played by the Economy Condition (EC) in (26) (see Grimshaw 1997; Legendre et al. 2006; also see Grimshaw (2006) for an attempt at a yet more principled approach). Like MC, EC is violable, and associated with a weight.

Given this state of affairs, for now it looks as though the relative weights of MC and EC decide on whether Merge can apply or not. In a pure Harmonic Grammar approach, this may indeed be true (abstracting away from the potential influence of other constraints for the time being). However, in Gradient Harmonic Grammar, things are somewhat more flexible since the varying strength of the [•F•] features that MC is formulated as a restriction for lead to different degrees of violation of this constraint. A [•F•] feature with a weight of 0.2 will trigger a less severe violation of MC in an output where movement does not take place than a [•F•] feature with a weight of 0.6, and this may distinguish between a violation of MC (in a candidate that does not carry out movement) that is optimal and one that is not. As shown in Müller (2019), asymmetries between different kinds of Merge operations – in particular, between different types of movement – can be derived in such an MC/EC-based approach by postulating different weights (like 0.2 vs. 0.6) of the individual [•F•] features that trigger the operations. With stronger features, an MC violation may become fatal that may be tolerable with weaker features; stronger features may thus ensure that structure-building (or movement) takes place where weaker features do not. This way, it can be derived that, e.g., wh-movement (with a strong trigger [•wh•] on C) can leave a CP in German whereas scrambling (with a weak trigger [•Σ•] on v) cannot do so. That said, as shown in Section 1, extraction from NP in German does not distinguish between wh-movement and scrambling (or, for that matter, topicalization, relativization, or others movement types that exist in German); cf. Webelhuth (1992), Müller (1995). For this reason, to keep things simple, we will postulate in what follows that a violation of MC is always of strength −1.0, independently of which movement type is involved.

Against this background, two questions need to be answered to provide an account of extraction from NP in German. First, how does optimization of Merge operations proceed technically? And second, how can the (frequency-based) weights assigned to V–N dependencies be integrated as a factor that may enable or block extraction from NP in the presence of MC and EC? We address the two issues in turn.

3.4 Optimization

There are two general possibilities to model the interaction of minimalist derivations and harmony evaluation. A first option is that all syntactic operations (which, by assumption, take place in the Gen component of the grammar) precede a single, parallel step of harmony evaluation (H-Eval). This then qualifies as a standard case of harmonic parallelism (see Prince and Smolensky 2004), and it has been explicitly pursued by, e.g., Broekhuis (2006) and Broekhuis and Woolford (2013). Another option is that Merge operations (Gen) and harmony evaluation (H-Eval) alternate constantly. On this view, syntactic operations and selection of the most harmonic (optimal) output are intertwined. This model is an instance of harmonic serialism (see Prince and Smolensky 2004). It has been adopted in, e.g., Heck and Müller (2013) and Murphy (2017) (also see McCarthy [2010] and contributions in McCarthy and Pater [2016] for some applications in phonology). In what follows, we adopt an approach based on harmonic serialism. Harmonic serialism in syntax can be viewed as a procedure that is actually little more than a reasonably precise specification of standard minimalist approaches that incorporate a concept of the best next step at any given stage of the derivation (see, e.g., Chomsky [1995, 2001] on Merge over Move). The mechanics of harmonic serialism are laid out in (27).

In the present context, the main reason for adopting a harmonic serialist approach is that, in interaction with the PIC, it directly implements strict locality of constraint interaction: Since all competing outputs are separated from the input by at most one elementary operation, it can be ensured that there is no danger that processes taking place in potentially radically different areas of the sentence can interact with the process at issue in unwanted and unforeseen ways; in line with this, harmony evaluation based on weights assigned to constraints and to linguistic expressions remains feasible throughout since the number of interacting weights remains small.

3.5 Integrating dependencies

Finally, it needs to be clarified how the optimization of structures involving extraction from NP can be made sensitive to ΔP _V|N -based weight assignments to V–N dependencies. To this end, we postulate that X–Y dependencies relating two heads can function as syntactic primitives that constraints can refer to (and that they can restrict). This assumption has been made earlier in a number of otherwise quite different approaches, and sometimes with a different label attached to X–Y (like chains, catenae, or selections instead of dependencies); see, e.g., O’Grady (1998), Osborne et al. (2012), Manzini (1995), Bowers (2017), and Bruening (2020a, 2020b). For present purposes, we assume that dependencies (in this technical sense) are always two-membered (X–Y), and that they are characterized by a selection relation (X selects Y).^[15] As detailed above, we assume that ΔP _X|Y determines the strength of an X–Y dependency. And we would like to suggest that the constraint where strength of dependencies plays a crucial role in the theory of extraction is the Condition on Extraction Domain (CED; see Huang 1982; Chomsky 1986; Cinque 1990) in (28).

According to earlier versions of the CED, an XP blocks movement across it if it is not governed (see Huang 1982), or not L(exically)-marked (see Chomsky 1986), or not a complement (Cinque 1990). It is this latter version that we adopt in (28). Furthermore, (28) formulates the CED as a constraint on X–Y dependencies intervening in a movement chain (rather than as a constraint on movement, or on adjacent members of movement chains, as in the original versions). This is so as to ensure that it is the strength of the intervening X–Y dependency (rather than, say, the strength of the moved item, or of the movement chain that it is a part of) that determines CED satisfaction. Assuming the concept of intervention in (29), this change is innocuous.

Given (29), all but the most local instances of movement to either intermediate phase edges or final landing sites will cross an X–Y dependency. Let us illustrate the concept of intervention in 3.5 by looking at some of the relevant configurations. Consider first the case of extraction from a direct object NP to the Specv position; cf. (30).

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Dependency intervention with extraction from direct object NP to Specv:

There are three relevant X–Y dependencies to be considered in (30), viz., V–N₂ (V selects the head of a direct object NP₂), v-V (v selects the head of its complement VP), and v-N₁ (the head of the external argument NP₁ is selected by v). Of these, only the V–N₂ dependency intervenes between α _i and α _i+1: α _i m-commands V; N₂ m-commands α _i+1; and it is not the case that V both m-commands α _i and c-commands α _i+1 (the latter is true but the former is not). In contrast, the v-V dependency does not intervene between α _i and α _i+1: α _i m-commands v; V m-commands α _i+1; but it is the case that v both m-commands α _i and c-commands α _i+1.^[17] Third, the v-N₁ dependency does not intervene either: α _i m-commands v; but N₁ does not m-command α _i+1; furthermore, as we have just seen, v as an X makes clause (c) of (29) false. There are further dependencies that eventually need to be taken into account, but they will fail to intervene between α _i and α _i+1 because one of their members is too deeply embedded to carry out m-command (for instance, this holds for the D head of DP, assuming that N selects D); so we can conclude that there is a unique intervening V–N₂ dependency with extraction from a direct object NP.

Consider next extraction from a subject NP in Specv, to a higher Specv, as in (31).^[18]

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Dependency intervention with extraction from subject NP to Specv:

Let us focus again on the three X–Y dependencies V–N₂, v-V, and v-N₁. This time, the V–N₂ dependency does not intervene between α _i and α _i+1; the reason is that N₂ does not m-command α _i+1. As before, the v-V dependency does not intervene: α _i m-commands v; and v fails to simultaneously m-command α _i and c-command α _i+1, as required for intervention. However, V does not m-command α _i+1. Still, there is again a unique intervening dependency, viz., v-N₁: α _i m-commands v; N₁ m-commands α _i+1, and, as we have just seen, v m-commands α _i but does not c-command α _i+1 (whereas v m-commands α _i+1, thus supporting the use of c-command rather than m-command in the second subclause of (29c)).

For present purposes, (30) and (31) are the core contexts of extraction from NP. However, more generally, it can be verified that there is an intervening X–Y dependency (often a unique one) in other extraction from NP scenarios as well. For instance, with extraction from an indirect object NP in SpecV, there is a unique intervening V–N₃ dependency; see (32a). With extraction from a direct object NP scrambled to Specv, there will be two intervening dependencies, viz., v-N₂ and V–N₂; cf. (32b).

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a.

Dependency intervention with extraction from indirect object NP to Specv:

b.

Dependency intervention with extraction to Specv from direct object NP scrambled to Specv:

Thus, we can conclude that in all these scenarios where extraction takes place from an NP in a specifier or complement position, there is a dependency intervening between the moved item and its base position.^[19]

Based on these assumptions, we postulate that the CED, as a constraint on X–Y dependencies, plays a dual role in harmony evaluation. On the one hand, it is a negative constraint, just like MC and EC are: The CED registers a violation if it is violated by an output (and the strength of the violation depends on the strength of the X–Y dependency that gives rise to it). On the other hand, however, the CED is also a positive constraint, unlike MC and EC: It assigns a reward if it is satisfied. Positive constraints of this type are difficult to implement in standard parallel optimality theory (because of an Infinite Goodness problem arising according to which one could in principle carry out an infinite number of processes yielding rewards from a given constraint), but as noted by Kimper (2016), this problem vanishes under harmonic serialism, where input and output can be separated by at most one operation. Kimper observes that adopting positive constraint evaluation is empirically advantageous in the area of autosegmental spreading in phonology; and it turns out to also give rise to a much simpler account of the natural predicate effect with extraction from NP than would otherwise be available. Positive evaluation of the CED has the consequence that if an X–Y dependency satisfies the constraint, it can yield an additional reward, depending on the weight assigned to the X–Y dependency via ΔP _X|Y .

3.6 Analyses

Let us look at some consequences. Suppose that MC is associated with a weight of 4.0, and EC with a weight of 5.0. Based on just these two constraints, the default consequence is that movement (or, in fact, any other kind of structure-building) is not possible: An output that carries out movement (in the presence of a designated feature [•F•]) will incur a violation (−1) of EC, and end up with a harmony value of −5.0. In contrast, a competing output that fails to apply movement will only trigger a violation (−1) of MC, therefore has an overall harmony value of −4.0 (other things being equal), and will thus always be selected. On this view, to bring about movement (i.e., to make the output with movement optimal), it is necessary to get a reward from the remaining constraint, CED.^[20] We take the CED to be associated with a weight of 7.5.

Under these assumptions, a first prediction is that NP specifiers (subjects, indirect objects, and moved NPs) are invariably islands. Movement from a position within NP to the next edge of a phase will always violate the CED, and thus the bias against the movement-inducing MC will actually be strengthened. As we have seen, there are intervening dependencies in these environments: There is an intervening v-N dependency with extraction from subject NPs (see (31)), there is an intervening V–N dependency with extraction from indirect object NPs (see (32a)), and there is an intervening v-N dependency (plus an intervening V–N dependency) with extraction from scrambled objects (see (32b)). Consequently, the CED springs into action here, and rules out extraction. This is shown for the case of extraction from a subject NP in (33).

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Optimization of extraction from subject NP:

In (33), output O₂ leaves XP₁ in situ, within the subject NP in Specv, even though, by assumption, there is a featural trigger for it. This gives rise to a −1 violation of the MC with weight 4.0, and to a harmony score of −4.0. On the other hand, O₁ extracts XP₁ out of the subject NP in Specv, to an outer Specv position, as required by MC (and ultimately by the PIC). This violates EC, yielding a violation score of −5.0. However, in addition, the CED is also violated since there is an intervening v-N dependency, and NP is not a sister of v. It is clear that, whatever the weight of the v-N dependency is, the constraint profile of the output that employs movement is thereby further worsened. For the sake of concreteness, we have registered a −1 violation of CED with O₁, yielding an overall harmony score of −12.5; but essentially the same result would have been obtained if the v-N dependency had a weight of, say, 0,01 (with −5,075 as the overall harmony score). The fact that the in-situ candidate O₂ wins this competition is, as such, not yet fatal. However, it is clear that XP₁ movement to the eventual target position later in the derivation (unless this already is the final landing site, as with local scrambling) will now eventually give rise to a fatal violation of the inviolable PIC.

Consider next the consequences that arise for extractions from NPs that are complements of V, i.e., direct objects. In this scenario, the CED is not violated. However, this does not yet suffice to permit extraction from the complement domain of N to the phase edge of v; in addition, there must be a sufficient reward from the CED (with weight 7.5) generated by an intervening V–N dependency. This reward may then render fatal the MC violation incurred by the output that does not apply movement, by lessening the EC violation incurred by the output that does. The reward is big enough in the well-formed cases of extraction from NP (i.e., where a natural predicate is involved, with a strength >0.133), and too small in the ill-formed cases of extraction from NP (where V and N do not enter a tight relation, with a strength <0.133).^[21]

To illustrate this, we will focus on two weights assigned to V–N dependencies that are close to the dividing line between V–N dependencies that permit extraction and V–N dependencies that do not permit extraction; recall (20). Suppose first that the V–N dependency is equipped with a numerical value of 0.12 (roughly the strength associated with Buch stehlen (‘book steal’)). As shown in (34), this leads to a reward of 0.9 provided by the CED. Thus, the harmony score of the output that employs movement (i.e., O₁) is improved. However, (34) also shows that this does not yet suffice to license movement; the EC violation incurred by movement is still too strong, and leaving XP₁ in situ, as in O₂, remains the most harmonic strategy.

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Optimization of extraction from direct object, ΔP V|N  → 0.12:

Things are different when the V–N dependency has a weight of 0.15, though (approximately the strength associated with Bericht schreiben ‘report write’). As shown in (35), in this case the reduction effect brought about by the 1.125 reward for CED satisfaction is sufficiently large to permit the unavoidable violation of EC in the movement candidate O₁; and the MC violation incurred by the in-situ candidate O₂ becomes fatal.

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Optimization of extraction from direct object, ΔP V|N  → 0.15:

It is clear that all V–N dependencies with a weight higher than 0.15 (i.e., with higher ΔP _V|N values, as with, e.g., Buch lesen ‘book read’ or Buch schreiben ‘book write’, which have normalized ΔP values in the 0.5, 0.6 area) will ceteris paribus also permit extraction from a complement NP, and that all V–N dependencies with a weight smaller than 0.12 will invariably block it. Thus, by assuming frequency-based ΔP values to act as weights associated with V–N dependencies, the concept of a natural predicate can be given a precise characterization, and asymmetries arising with extractions from NP in German can be derived.

3.7 Consequences

Needless to say, the present analysis makes a lot of further predictions, and raises several new questions. One obvious consequence is that not just extraction from NP, but in fact all instances of movement that are not extremely local will depend on an intervening head-head dependency giving rise to a CED reward that sufficiently reduces the negative harmony value incurred by the EC violation inherent to movement, so as to make the output that carries out movement more harmonic than the output that does not (and that thereby violates MC). For instance, given (29), a movement step from Specv to SpecC (as in standard cases of wh-movement) crosses an intervening T-v dependency: In (36), α _i m-commands T, v m-commands α _i+1, and whereas T c-commands α _i+1, it is not the case that T m-commands α _i .

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In contrast, the C-T dependency does not intervene in (36) since C m-commands α _i and c-commands α _i+1. If nothing more is said, this dependency must be strong enough to bring about a sufficient CED reward to license the movement step, i.e., T-v must be associated with a weight >0.133. We will assume that, more generally, when a head-head dependency involves two functional categories, or one functional category and one lexical category, the weight associated with it is typically very high; this follows naturally by determining the ΔP values: A category like v is an extremely good predictor for a category like T, even if it is assumed that the particular phonological realizations of v and T are taken to be decisive (rather than the abstract functional category labels); the reason is that the number of different manifestations of both v and T is very small (and v and T usually co-occur).

A further consequence of the analysis concerns EPP-driven movement of subject NPs to SpecT, which we take to be optional in German. Given a clause structure as in (37), there is no head-head dependency intervening between two members of a movement chain α _i and α _i+1 (T m-commands α _i and c-commands α _i+1).

Consequently, the CED cannot be violated in (37), but there is also no reward since there is no dependency that satisfies the constraint non-trivially (in general, trivial constraint satisfaction by dependencies must not be able to generate a reward). This means that movement should ceteris paribus be blocked in (37) (with the in-situ candidate violating MC being more harmonic than the movement candidate violating the constraint EC, which has a greater weight than MC). Several options suggest themselves to solve this problem. A simple solution would be that the EPP feature triggering (internal or external) Merge with T has more strength than other features triggering movement.^[22]

Next, recall that varieties of German allow for the option of moving an R-pronoun wo (‘where’) or da (‘there’) as the pronominal argument of a preposition, and this may also further involve extraction from an object NP, as in (1b) and (1d). R-pronoun extraction from NP is determined by exactly the same structural and lexical factors that PP extraction from NP is determined by; in the present context, this implies that the N-P dependency does not directly interact with the V–N dependency in the same optimization, neither by contributing additional weight, nor by reducing weight. The facts fall into place if it is assumed (i) that PP is accompanied by a functional projection pP on top of it, (ii) that pP qualifies as a phase, and (iii) that N continues to select P (deviating from strict locality in this environment; see Foonote 1) but does not select p (cf. Riemsdijk 1978; Koopman 2000, and Abels (2012) for discussion of relevant proposals); cf. (38) (compare (30)).

(38)

Under these assumptions, an R-pronoun needs to reach Specp before moving on; and since there is no N-p dependency and the P item of the N-P dependency fails to m-command α _i+1 in the specifier of pP, there is no additional intervening dependency to consider.

Finally, it can be noted that the present approach opens up the possibility of implementing Featherston’s (2004) findings regarding the role of frequency in extraction from CPs in German in a very direct way. In German (and many other languages), the legitimacy of extraction from an embedded declarative clause headed by dass (‘that’) depends both on the grammatical function (direct object: yes, subject: no) and, more importantly in the present context, on the choice of matrix verb; only bridge verbs allow extraction. Two examples illustrating this are given in (39a) (with bridge verbs) versus (39b) (with non-bridge verbs).

Featherston’s (2004) observation is that bridge verbs are more frequent than non-bridge verbs. Thus, the mean log frequencies of CP-embedding verbs that can be derived by collecting the absolute frequencies of these verbs in four different corpora, converting the numbers by applying a logarithm function, summing the four individual resulting numbers for each verb, and finally dividing them by four strongly correlate with the option of extraction from CP (which was determined by experiments involving grammaticality judgements). This is shown for the verbs sagen ‘say’, glauben ‘believe’, and bezweifeln ‘regret’ in (40).

(40)

Interestingly, even though Featherston (2004) has, in our view, convincingly identified frequency of the matrix verb as a factor determining the option of extraction from CP in German, the grammatical theory he employs (the Decathlon Model; see Featherston 2005, 2019), while designed to predict frequencies in outputs, does in fact not incorporate frequency as a grammatical building block that may interact with other building blocks (like MC, EC, or CED in the present approach) to license or block extraction. Accordingly, Featherston (2004) remains silent on how to actually account for the frequency effect with the bridge verb phenomenon in grammatical theory. In contrast, it seems clear how the effect of frequency on extraction from CP could be modelled in the present approach. First, instead of bare V frequencies, ΔP _V|C values for V–C dependencies that intervene between a movement chain member α _i+1 in SpecC and its immediate chain antecedent α _i in the matrix Specv have to be determined (we have not done this but are reasonably confident that the results will be very similar to Featherston’s results). And second, normalized versions of these numbers are then predicted to bring about CED-based rewards that permit extraction from CP with highly frequent V–C dependencies (i.e., V–C dependencies that form a bridge).