Flat structure: a minimalist program for syntax

3.1 Heavy NP shift

Consider first Heavy NP Shift (HNPS).^[6] We review various ways in which HNPS might be viewed as movement, and argue that they are problematic at best. We conclude that the facts of HNPS are adequately captured under the assumptions that VP lacks internal syntactic structure, and that the order of constituents reflects ordering constraints stated over the flat structure.

In the analyses of Rochemont and Culicover (1990) and Culicover and Rochemont (1990), HNPS is ostensibly an A′ movement rule. One reason for this is that there is no canonical structure in the English VP that licenses an NP in final position.^[7] That is, the canonical order of English is (3a). But the VP-final NP is more acceptable when it is ‘heavy’, as in (3b) (Ross 1967: 51ff).^[8]

In a theory in which hierarchical structure determines linear order, there must be a derived syntactic structure corresponding to the order in (3b). If the canonical order is (3a), then one of the following holds.

1. The NP moves from the post-verbal position to the right (Ross 1967: 56).

2. The NP is higher than the VP, and the VP moves to the left of the NP (Larson 1988: 347; Wallenberg 2015: 337).

The first option is problematic for several reasons. First, if movements are structure preserving in the narrow sense, there must be a canonical NP position following the PP for the NP to move to. But then there is no motivation for movement.

The alternative is that rightward HNPS is not narrowly structure preserving, but an A′ movement to an empty specifier position analogous to topicalization. However, A′ movement is typically unbounded, and HNPS is radically clause-bound, as Ross (1967) noted – see (4).

The bounded nature of HNPS disfavors prima facie an A′ movement approach. We could state a principle that says that only leftward A′ movements are unbounded, but this would be a stipulation that does not follow from anything.

Moreover, taking A′ movement to be the product of (Internal) Merge, we should expect HNPS to exhibit reconstruction effects. For instance, a quantifier moved to the right should be able bind a pronoun that precedes it, but the examples in (5) show that the opposite is the case (Culicover and Jackendoff 2005: 119–120).

Finally, the idea that HNPS is rightward movement is difficult to reconcile with the view that movements check triggering features with an independently motivated functional head (Chomsky 2000, et seq.). The structure in VP-final position in (6) that could satisfy this requirement is not independently motivated.^[9]

(6)

Consider the second option. Rochemont and Culicover (1997) explored the possibility that HNPS is actually leftward movement, with subsequent leftward movement of the remnant to a position above it. Such a derivation is shown in (7).

(7)

But this option – which is entirely feasible in a derivational approach – also fails to capture the fact that HNPS is bounded, as in (4). Moreover, HNPS, unlike a true A′ construction, cannot apply to the complement of a preposition (8).

However, Rochemont and Culicover (1997) failed to notice that Larson’s (1988) proposal for HNPS avoids the problem of bounding and the problem of preposition stranding. On the assumption that the direct object is the specifier of the VP and does not itself move, either V′, which contains [V⁰-PP] raises to the left, yielding the order [V⁰-PP]-NP, or V⁰ does, yielding the order V⁰-[NP-PP], as in (9).

(9)

Although this analysis avoids the problems of bounding and no preposition stranding, there are a number of additional stipulations that have to be made in order for it to work properly. First, the higher V⁰ node has to be filled by something overt; it cannot be filled by an invisible element, otherwise the verb will not appear in the right position in the linear order. Second, the possibility of binding in (5d) poses further difficulties. Since the antecedent is embedded inside a VP, it would have covertly move to a position where it c-commands the pronoun.^[10]

Finally and most importantly, if the NP is not heavy, e.g., if it is a pronoun or a one word name, then raising of V′ yields an unacceptable sentence. So this derivation has to be filtered by a condition that licenses only heavy NPs in the position that is destined to be the final position. This filter renders the movement unnecessary if we allow free ordering of the complements of V⁰.

The situation is further complicated by the fact that the heavy NP need not be absolutely final in the VP; cf. (10).

These various orderings can be derived by adjusting the hierarchical position in the tree of [_NP the beer …] above the constituents that it precedes. Such variability of hierarchical structure undermines the assumption of a single canonical structure. But to derive all of the orderings from a single structure, it is also possible to assume that the underlying order is (11), and the verb picks up or leaves behind arbitrary adverbs and PPs as it moves up the tree. So, for example, (10) could be derived as shown in (11).

(11)

Another strategy would be to adapt Fanselow’s (2001; 2003 proposal for scrambling in German. On this proposal, complements and adjuncts of a verb can be merged into the VP in various orders, which derives the observed variation without movement. Again, deriving the linear order as a matter of syntactic structure leaves unresolved the problem that the order must be independently referred to in order to accommodate the heaviness condition on rightward shifted NPs.

Furthermore, the rightward placement of heavy constituents is not limited to NP, which further complicates the analysis. Clauses are preferred in VP-final position (12), as are PPs (13), adverbs (14) and adjective phrases (15).

It appears that we need constraints on order that are stated in terms of the relative weight of the constituents. We leave open the question of precisely what these constraints are. These may be complex, but they can be identified with some precision; see Büring (2013); Göbbel (2020); Hawkins (1994, 2004, 2014); Wasow (1997, 2002); Wasow and Arnold (2003), i.a. From our perspective, the main problem with any derivational analysis is this: if the XP is not heavy, e.g., if it is a pronoun, it cannot appear to the right in the VP. Such a derivation has to be filtered by a condition that licenses only heavy XPs in final position. This would be a filter constraining the relation between XPs and their position in the phonological string. But if this filter is necessary, there is no reason to derive linear order by movement – free ordering of the sisters of V⁰ in flat structure is sufficient.

Suppose, then, that the structure of the English VP is flat, following Culicover and Jackendoff (2005: Ch. 4). The basic syntactic constraint on order is that the phonological form of the verb must precede that of its complements. There are also ordering constraints or preferences connected to dependency, focus and constituent weight. Otherwise, the order of the constituents of VP is free. In this respect it resembles scrambling, a point to which we return below in Section 6.^[11]

An interesting consequence of the flat structure approach to linear order is that it rules out a derivational account of the fact that shifted constituents are ‘frozen’, as in (16) (Wexler and Culicover 1980).

Under a non-movement analysis, the apparent frozenness of HNPS must be accounted for outside of syntax proper, absent any other stipulations. A promising candidate is an account in terms of processing complexity (Culicover et al. 2022).

3.2 Extrapositions

We turn next to extraposition of relative clauses and result clauses. Examples are of the general form in (17). We refer to some people as the antecedent of the extraposed clause, and notate the relationship with subscripts.

Extraposition raises issues that are related to, but different from, those concerning HNPS. It is generally agreed that extraposition is not derived by syntactic movement; cf. Webelhuth et al. (2013); Rochemont (2015); Göbbel (2020). Still at issue, however, is whether there is a correspondence in the analysis of extraposition constructions between the linear order and hierarchical syntactic structure.

At the center of the analysis of extraposition are these four observations (Rochemont and Culicover 1990).

Observation 1. Extraposition is possible from NPs in a range of positions in the classical hierarchical structure: object, subject, and Spec,CP. In addition, there is result-clause extraposition. The examples in (18) illustrate:

Observation 2. The order of multiple extraposed clauses is the inverse of the order of their antecedents. The linear orders are illustrated in (19)–(22). We show only the more local relationships. While the examples are complex, the judgments appear to favor the inverse ordering.

Observation 3. It is possible to account for the order by attaching each type of extraposed clause at a different position in a hierarchical structure, along the lines of (24).

(24)

This structure accounts for the fact that the linear ordering is OX ≪ SX ≪ RX ≪ WX.^[12]

Observation 4. Assuming the structure in (24), ellipsis of VP should include OX but exclude SX, RX, and WX as in (25).

On the basis of these observations, the analysis proposed by Rochemont and Culicover (1990), closely following Guéron and May (1984), assumed ambiguity of attachment of extraposed clauses, as follows.

1. A clause extraposed from objects (OX) is adjoined to VP.

2. A clause extraposed from subjects (SX) is adjoined to IP or VP.

3. A result clause (RX) is adjoined to CP or TP or VP.

On this analysis, a constituent further to the right is attached higher in the tree.

However, the motivations for the structure hypothesized in (24) are open to question. Contrary to Observation 4, it seems that ellipsis can target all types of extraposition. This suggests that all extraposed clauses can be constituents of VP, regardless of the height of their antecedents. Example (26a) shows that SX may undergo ellipsis, and (26b) shows that RX may undergo elllipsis.^[13]

Moreover, the examples in (27) show that multiple extraposed clauses may undergo ellipsis.

So, contrary to what (24) might predict, ellipsis appears to treat both OX, SX and RX as constituents of VP.^[14]

Furthermore, the constructed examples in (28) show that a clause extraposed from a subject may precede a clausal complement in the VP; this suggests that such extraposed clauses may be VP-internal.

An alleged motivation for the rich structure in (24) is the fact that it predicts interactions between extraposition and binding (e.g. Göbbel 2020). Condition C of the binding theory rules out c-command of an r-expression by a coindexed pronoun. On this view, examples such as (29a) suggest that RX is higher than TP, since the pronominal subject could not c-command the r-expression. By the same logic, there should not be a Condition C violation when a pronominal object is coindexed with an NP in OX (29b). But a pronominal subject should produce Condition C violations with OX, a prediction that is contradicted by (30).

Given (30), non-flat accounts could stipulate that the NP containing the antecedent is covertly raised to a position above the antecedent, leaving behind a copy of itself with the r-expression replaced by a pronoun through vehicle change (see Göbbel 2020: 108–109). However, discussing naturally occurring examples similar to (30), Varaschin et al. (in press) propose an arguably simpler alternative that is compatible with flat structure in the VP (see also Sells 1987; Yashima 2015). They show that an r-expression can be c-commanded by a coindexed pronoun if it is in an anti-logophoric context (i.e. a context where its referent does not count as a perspective bearer). This is the case in the examples in (29). As (31) shows, when this condition is not met, coreference is not possible even when, according to (24), the pronoun does not c-command the r-expression.

Finally, the option of hierarchical attachment along with the possibility of uniform attachment to VP creates a paradox. While hierarchical attachment can account for linear ordering when there are multiple extraposed clauses, attachment to VP cannot. If we allow OX, SX and RX to be adjoined to VP, even optionally, we cannot use height of attachment to account for their ordering. We still have to impose an independent ordering condition on them, guaranteeing OX ≪ SX ≪ RX ≪ WX.^[15] But if we require this condition, then we do not also need hierarchical structure to induce linear order. As with HNPS, hierarchical structure is neither necessary nor sufficient; the structure may then be a flat non-recursive VP.^[16]

3.3 Asymmetry paradoxes

Our final argument for flat structure in the English VP is based on binding and coreference phenomena that have been claimed to require asymmetric c-command (Larson 1988, i.a.), but which, taken collectively, do not converge on a uniform structure. As a result, each phenomenon winds up entailing a different structural description for the same string (Barss and Lasnik 1986; Pesetsky 1995). This paradox undermines the binding-theoretic motivations for hierarchical structure. Upon closer examination, the asymmetries in question are better represented in linear order and semantics, which means that the syntactic structure itself can be flat.

We begin with quantifier binding. Assuming that binding is only sensitive to c-command, it has been suggested that the possibility of quantifier binding into adverbial clauses, as in (32), entails a right-branching structure where the object quantifier c-commands into the adjunct (Larson 1988, 1990, i.a.).

The traditional left-branching analysis of clausal adjuncts (Ernst 2002; Harley 2014; Jackendoff 1977; Lakoff and Ross 1976) makes the wrong predictions here because the PP would be higher than the QNP in object position. The right-branching analysis (Hale and Keyser 2002; Kayne 2004; Larson 1988) posits the correct c-command relations. However, as several authors note, right-branching creates a paradox in connection to Condition C (Bianchi 2001: 5, i.a.). If the QNP c-commands the pronoun in (32), then we should see a Condition C violation in (33), but we don’t (Solan 1983).^[17]

The paradox is that the object needs to asymmetrically c-command into the adverbial clause for the purposes of quantifier binding, but not for the purposes of coreference with an r-expression. Hornstein (1995: 110) attempts to resolve the paradox by assuming that the adverbial clause occupies a higher position in (33) and a lower position in (32). The problem with this view is that coreference and binding seem to be simultaneously possible in such structures; see (34).

There are other ways of averting this problem, but they raise difficulties of their own. On the basis of different facts, Culicover (1992) proposed that quantifiers within the VP undergo quantifier raising to a higher A′ position inside the VP, allowing them to bind into adverbial clauses (assuming, contra Reinhart (1983, 2006, that quantifier binding is licensed in LF). The structure in (35) illustrates.^[18]

A technical difficulty with this analysis is that it violates the typical constraints that rule out weak crossover in structures like (36). The QNP in (35) is simultaneously binding a trace and a pronoun with the former not c-commanding the latter. This is precisely the configuration invoked to exclude the LF of (36) after quantifier raising has taken place (Koopman and Sportiche 1983; Safir 1984, i.a.).

Therefore, structures like (35) overgenerate when it comes to predicting the anaphoric possibilities of QNPs. In addition, the operation of quantifier raising to VP, in contrast to quantifier raising to CP, lacks the motivation of being able to account for the fact that VP-internal QNPs can have wide scope over the subject.

Since the idea that anaphoric dependencies are solely governed by c-command leads to contradictory structures or to overgeneration, it is preferable to seek an alternative account. This point is reinforced by other counterexamples to c-command documented in Barker (2012). Following previous work, we hypothesize that, in addition to structural asymmetries (e.g. subject vs. object), binding and coreference are also sensitive to linear order and properties of the global discourse structure (Bruening 2014; Culicover 2013a; Varaschin 2021; Varaschin et al. in press, i.a.). These non-structural factors can explain why anaphoric dependencies are possible in structures like (34) while maintaining flat structure as a null hypothesis.

5.1 VP topicalization paradoxes

VP topicalization is exemplified by (45).

The standard analysis of VP topicalization involves movement of a VP projection to an initial A′ position (Huang 1993; Müller 1998; Zagona 1988). Accordingly, (46) points to the existence of a hierarchy of multiple VP projections, along the lines of [ _VP [ _VP [ _VP cook the potatoes] for fifteen minutes] in the morning].

Examples like those in (47) suggest that there is a further split in the English VP, with the verbal head also being able to move independently of its complements (Culicover and Winkler 2019: 184–5).

Furthermore, it is possible to strand not only PPs, complements CPs and heavy NPs, but also extraposed complements and adjuncts of NPs (48)–(49).

In the analysis of Culicover and Winkler (2019), which is partly motivated by data like (46)–(49), what moves is actually a V. Following Bare Phrase Structure (Chomsky 1995), they assume that there are no categorial distinctions between various projection levels of the same head. All of the projections in a VP are V, as in (50), and any of them, including the lexical head alone, may topicalize.^[27]

(50)

The assumption behind this analysis is that the initial VP is the same VP that is formed in the beginning of the derivation and subsequently fronted to the A′ position. Since the fronted VP is literally formed inside the VP in the base, this entails that hierarchical structure like (50) is possible for non-fronted VPs as well.

One prediction of this analysis is that no VP should be able to be fronted that is not able to appear in the ‘base’ position occupied by its trace/copy. Therefore, an initial problem for this analysis is the fact that it is possible to topicalize discontinuous portions of VPs, as shown in the variants of (45) in (51).

Examples such as these suggest one of two possibilities: (i) for VPs with many complements there are as many alternative structures of the form in (50) as there are possible combinations of verb+complement, or (ii) what is topicalized is not necessarily something that would be a constituent of VP, but an independently well-formed VP that corresponds to a coherent interpretation in cs and that can be matched with the remnant of the VP in situ (when there is one).^[28]

The second alternative is the one consistent with flat structure. It is further supported by the fact that topicalized VPs in English exhibit morphological autonomy with respect to their putative positions in the VP domain. This is incompatible with the assumption that the structure of the fronted VPs is determined by their base position (Thoms and Walkden 2019: 174).

If the ill-formedness of (52b) is related to the auxiliary’s selectional properties, then the gap in (52a) can’t have exactly the same structure as the fronted VP.

In some cases, the auxiliary can even be doubled in the fronted VP (53a). If the auxiliary appeared doubled in its base position, this would be evidently ill-formed, as (53b) shows (Thoms and Walkden 2019: 175).

In the next section we first sketch out a constructional approach to filler-gap constructions, of which VP topicalization is a special case, and then show how it applies specifically to VP topicalization, avoiding the problems we mentioned.^[29]

5.2 Licensing filler-gap configurations

We follow the standard approach of Zagona (1988), Huang (1993), Müller (1998), i.a. in treating VP fronting as an instance of a more general filler-gap structure which involves the extraction of a constituent to a clause-initial A′ position (Chomsky 1977; Levine and Hukari 2006; Pollard and Sag 1994). The fronting schema in (54) licenses any possible constituent (including a VP or any of its independently well-formed subparts) in clause-initial position, leaving behind the rest.

(54)

fronting schema [30]

The category symbol TP↾X stands for a TP which is missing a constituent of category X – a slash-category, in the sense of Categorial Grammar. The slash we use (↾) is the non-directional vertical slash of Kubota and Levine (2020). Unlike the complements of non-slashed categories, X need not be phrasal (i.e. XP). This allows us to capture cases like (47), where only V⁰ is fronted. As in HPSG, all categorial features (including a VP or any of its independently well-formed subparts) in clause-initial position, leaving behind the rest). valence information which distinguishes a head from its maximal projection) are required to be shared between the filler and the gap: i.e. the X in the slash and in the filler share all of their syntactic properties.

The general schema for licensing gaps is also common to all kinds of non-local dependency constructions in various languages. We follow early HPSG in treating gaps as ordinary lexical items as in (55) (Pollard and Sag 1994: 161):

(55)

The phon of a gap is the empty string (ɛ), its syn can be a slashed constituent of any category and its cs is a gap variable of the appropriate semantic type Z 1 gap .^[31] For VP fronting, the gap variable will typically be of type ⟨e, t⟩.

We also need a schema to license phrases containing slash categories. This schema should register the presence of the gap on the category of its mother by means of the slash feature. For this purpose, we assume (56), drawing from similar propagation mechanisms adopted in GPSG and HPSG (Borsley and Crysmann 2021: 539–543; Gazdar et al. 1985: 137–144; Pollard and Sag 1994: 159–164).

(56)

slash phrase schema

Along with (54), (56) ensures that information about the presence of a gap will be projected from the gap site upwards until a filler of the corresponding category is found. There is no restriction requiring X, Y and Z to be distinct: (56) only says that a phrase inherits the slash specification from its daughter. It is possible that the phrase and the daughter are projections of the same head. This is important for our account of partial VP topicalization, where we have a VP↾VP inside a VP.

Lastly, another schema is needed to accomplish the binding of gaps in cs. This is (57), where “/” is a term replacement function such that, for cs terms α, β of the same type, α/β is the result of replacing free variables in β by α.

(57)

gap binding schema

This schema guarantees that gaps are interpreted as λ-bound variables to be saturated by the meaning of the filler that the slashed phrase combines with.

Now we are ready to apply the filler-gap analysis to VP toplicalization, assuming flat structure. Let us start with a case where an entire VP is topicalized. For the second conjunct in (58a), our schemas license the structure in (58b).

(58)

a.	I knew Chris would cook the potato and cook the potato Chris did.

The fronted VP is directly licensed in initial position, given that it satisfies the independent licensing conditions for VPs in English: e.g. VP dominates V⁰, V⁰ is initial in phon. The syntactic connection between VP and the remainder of the clause is guaranteed by the slash feature and the semantic connection (i.e. “reconstruction”) is captured by the fact that the meaning of the slashed constituent is a functor over the meaning of the fronted VP in cs. This is ensured by (57), which establishes a correspondence between a phrase containing a gap and a function which results from λ-abstraction over the gap variable. The resulting β-reduced expression in cs is the same as the one we would get in a non-fronted structure. This analysis also accounts for V⁰ fronting cases like (47), with the only difference being that the filler and the gap are simple lexical items (i.e. V⁰).

Since this analysis does not assume that the topicalized VP is in situ at any stage, it avoids all of the movement paradoxes mentioned in connection to (52)–(53). The schemas only require that the fronted sequence be of the same syntactic category as the gap and that it correspond to a coherent interpretation that can be fed as an argument to the functor that results from λ-abstracting over the gap variable. Morphophonological properties – the kind of information that makes (52b) and (53b) bad – need not be shared among the filler and the gap, precisely because the filler is not derived from a VP in its base position.^[32]

Let us consider now cases of partial VP topicalization like (51). What we have so far is almost enough to license these, but one extra ingredient needs to be added. When a partial VP is fronted leaving behind a remnant, we want to license a phon/syn structure like (59), where an VP gap is contained inside an VP.^[33]

(59)

The head-complement schema in (41) licenses any sequence containing an X⁰ head plus a (possibly empty) subset of its complements as a constituent, with the mappings to phon and cs for this sequence subject to additional correspondence constraints. Any independently well-formed constituent can be the filler because the fronting schema in (54) imposes no categorial requirement on fronted elements. Therefore, any appropriately linearized and semantically coherent sequence including an initial V⁰ and a subset of its complements can be topicalized, including V⁰ alone. This is sufficient to license the fronted VP in (59).

The problem for us is the VP gap in situ. The head-complement schema does not license the combination between VP↾VP and its two complements in (59) because VP↾VP is not a lexical category like V⁰ (the category of a normal verb or a bare verb gap). Our solution, which is inspired by approaches to partial fronting in German (de Kuthy and Meurers 2001; Nerbonne 1994), is to say that partial VPs like those in (59) can only appear inside VPs as gaps. To account for the combination between a slashed constituent and its complements (the VP↾VP and the two PPs in (59)), we posit the following gap-complement schema.

(60)

gap-complement schema

Since the X variable in (60) need not be lexical, the gap complement schema in (60) licenses recursion of XPs with the same head. Thus, corresponding to each filler containing an initial V⁰, the mechanisms underlying filler-gap dependencies can license a VP gap inside the VP which combines with a proper subset of the verb’s complements. The head-complement schema, on the other hand, does not allow this, because any X phrase appearing inside an XP can only be a lexical X⁰ – this is precisely what rules out recursive XP projections and ensures flat structure in our system. Therefore, non-gap variants of partial VPs are never licensed inside VPs, only slashed VPs are. The only position in which non-gap variants of partial VPs can appear is the fronted position, where they are licensed as separate constituents and can bind their corresponding partial VP gaps in situ.

Since VP fronting results in a recursive VP projection in the extraction path, this analysis could potentially be seen as weakening the case for flat structure. However, we do not think that this is so. First, note that both the partial fronted phrases as well as the stranded remnants in (59) are flat constituents: all of the dependents of the head are sisters. Second, in our non-derivational approach, allowing for partial VPs in fronted positions does not automatically commit us to assuming that these partial VPs could also appear as partial VPs in situ (which would contradict flat structure). In fact, we have already seen reasons for not making the latter assumption: namely, the movement paradoxes in (52)–(53).

This entails that, if a sequence of constituents in the left-periphery includes V⁰ and satisfies the independent linear order, syntactic and semantic licensing conditions for VPs in English, it can be interpreted as a constituent even when it would not be a VP in situ. Hence all of the sequences in (61) are licensed as VPs in virtue of the fact that they are clause-initial and meet other constraints on English VPs.^[34]

It is of course possible to assume that for each of the different orders in (61) there is a different syntactic structure with corresponding VPs along the lines of (50). Assuming that alternative linear orderings of constituents are derived by movements from a canonical structure, such an approach entails that there is an underlying fixed ordering of the adjuncts. Furthermore, the idea that adjuncts are all specifiers of some functional head and that all movement must be leftward and triggered by agreement yields an analysis that is breathtaking in its complexity (Borsley and Müller 2021). Moreover, since pretty much any sequence starting with V⁰ can in principle be fronted (provided suitable discourse-conditions are met), this would entail spurious structural ambiguities for complex VPs (Pollard 1996b: 302–304). We will not attempt to sketch out the possibilities here – for some examples, see Cinque’s (1999) carefully worked out analysis, and for critical discussion, see Neeleman and van de Koot (2008) and the papers in Bailyn (2011).^[35]

7.1 Correspondences

Having demonstrated the feasibility of flat structure from the perspective of the syntax-phonology correspondence, we must deal with the question of how flat structure is interpreted, with an eye towards capturing the scope-related phenomena which have motivated more complex branching structures for both NPs and VPs (Andrews 1983; Cinque 2005, 2006; Levine 2003; Pesetsky 1995).

In standard approaches, each branching node in a syntactic structure corresponds to a rule of interpretation (Heim and Kratzer 1998; Klein and Sag 1985). If one assumes (as we do) a type theory in the semantic component, all such rules can be summarized in a single schema (65), which expresses the idea that the semantic contribution of a complex phrase is determined by the semantic contribution of its component parts.

(65)

compositionality schema

This schema employs a version of Klein and Sag’s (1985) Functional Realization operator (FR), which we define as follows (Sag et al. 2020: 17).

This allows us to say that the semantics of a mother node is the result of exhaustively applying the semantics of its daughters to each other in a manner fully-driven by their semantic types. In this way, both 1′(2′) and 2′(1′) are possible instances of the more general formula FR (1′, 2′). Which term is applied to the other is determined by their semantic types. The following two examples illustrate:

(67)

a.

b.

If syntactic structure is binary-branching, for any node n, the interpretation that (65) licenses for n can consist in applying the semantics of one of n’s daughters (typically the head) to the semantics of the other daughter. As a result, the cs of any phrase dominated by the daughter that is interpreted as a semantic argument will be under the scope of the cs of the daughter that is interpreted as a functor. In this way, the interpretation is essentially read off of the syntactic structure and semantic scope is fully determined by the height of attachment of phrases.

If, however, the syntactic structure is flat, type-driven compositionality will often underspecify the interpretation. This occurs because the functional realization of a multiset of cs formulae may contain more than one well-formed cs formula. This will happen, for instance, whenever a phrase has more than one daughter of the same semantic type.^[38] As an illustration, consider the case of a ditransitive verb like give, which takes three entity arguments: the agent, the theme and the goal. Assuming that the latter two combine with the verb at the same level (the VP) and that to is semantically vacuous, both of the interpretations in (68) are licensed by (65):

(68)

a.

b.

Further constraints will be needed in addition to (65) to guarantee that only (68a) is licensed as the correct interpretation for the string give the cake to Bob. One likely source of constraints is the hierarchy of grammatical functions. We could constrain (65) so that that less oblique elements (e.g. direct objects) are composed with the meaning of V⁰ before more oblique ones (PP arguments, datives) (Büring 2005; Dowty 1982; Keenan and Comrie 1977). This correctly rules out (68b).

Another possible source of constraints on type-driven functional realization is the linear order of complements: semantically dependent phrases tend to cluster together in linear order. In the next section, we provide a preliminary exploration of this idea, showing how some aspects of interpretation can be expressed in terms of direct correspondences between phonological form and semantic representation without reference to the syntactic structure internal to phrases. The only relevant structure is the head/projection relation.^[39] We look specifically at scopal interactions between modifiers of NPs (Section 7.2) and VPs (Section 7.3).

7.2 Flat NP

Culicover and Jackendoff (2005: 135–143) argue that the structure of NP is (69). A similar structure is proposed by Belk and Neeleman (2017).

(69)

This structure is completely flat: N⁰ and all of its dependents are in a symmetric relation with respect to each other. Scope, however, is intrinsically asymmetric: i.e., if a cs term α scopes over a cs term β, then β does not scope over α. To illustrate, consider the examples with intensional adjectives in (70). For the sake of simplicity, we ignore the representation of intensionality (i.e. the fact that former introduces a quantification over worlds/times) and assume that modifiers are always of type ⟨⟨e, t⟩, ⟨e, t⟩⟩ and nouns are of type ⟨e, t⟩.

In (70a), former ′ scopes over corrupt ′ ( officials ′): i.e. the NP refers to a set of individuals who used to be corrupt officials. In (70b), we have the opposite scopal interaction, with corrupt ′ scoping over former ′ ( officials ′): i.e. the reference is to a set of individuals who used to be officials but are (now) corrupt.^[40]

The standard approach is to encode the asymmetry of scopal interpretation in terms of the asymmetric c-command relation between constituents in syntax (May 1985; Panayidou 2013; Teodorescu 2006). However, in an approach adopting (69), these differences in scope cannot be defined syntactically by appealing to the different height of attachment of former and corrupt. It is necessary to invoke some other formal relation in terms of which the scopal asymmetries can be licensed.

Our proposal here is that, at least for scopal interactions between modifiers and nouns, this relation is the linear ordering of the phon realizations of subconstituents of NP. The basic idea is that a nominal modifier can scope over the cs corresponding to whatever is on its right or left edge, as long as the resulting interpretation is semantically well-defined – i.e. as long as the string whose semantics is scoped over corresponds to a semantic type that is defined as a possible argument for the function denoted by the modifier. We don’t need complex branching syntactic structure, because all of the information in the structure is contained in the phon-cs correspondence, plus constraints on semantic types.

We posit two schemas to account for the fact that modifiers can appear both before and after the noun in English. (71a) handles cases where the modifier precedes the head, and (71b) the cases where the modifier follows the head.

(71)

flat np modifier schemas

a.

b.

Note that there is no constituent in syn with a subscript 2 in either of these constructions. The way the modifiers are integrated into the semantics of the NP is determined directly by properties of phon. These schemas license correspondences where modifiers scope over the semantics of the strings which are (left or right) adjacent to them inside the NP, regardless of whatever else is inside the NP. To start with a simple case, consider the examples in (72).

The respective correspondences are given in (73).

(73)

a.

b.

We see that the correspondence in (73a) is licensed because it satisfies the conditions of (71a). The cs representation furry ′ scopes over dog ′, and the corresponding phon structure ‘furry’ precedes ’dog’. Similarly for (73b), ceteris paribus. Crucially there is no need to mention the head in the syntactic representation in the schema, although of course it plays a role in licensing the actual correspondence of the NP in virtue of independent constructions, like the head-complement schema, which ensures that XP must dominate an X⁰ (Jackendoff 1977).

The situation becomes more interesting when we consider the case of multiple modifiers in (70), repeated below:

The question is, when the cs representation is of the form A ′ 1 ( A ′ 2 ( N ′ 3 ) ) and the phon representation is 1⊕2⊕3, is the correspondence for the entire NP licensed by the schema in (71a)?

(75)

Consider first former. The string ‘former’ precedes ‘corrupt′⊕officials’ in phon and former ′ scopes over the corresponding corrupt ′(officials′) in cs. So this correspondence is licensed. Similarly, corrupt is licensed because ‘corrupt’ precedes ‘officials’ in phon and corrupt ′ scopes over officials ′ in cs. Notice that the interpretation of (74b), namely corrupt ′(former′(officials′) is not licensed for (74a), because the material in phon corresponding to the function with widest scope ( corrupt ′) does not precede a string that corresponds to what is in the scope of this function.

The other case of interest is where there is one modifier on either side of the head, and thus an opportunity for ambiguity depending on which one has wider scope. An example is given in (76).

On one reading, the former professor had pink hair when they were a professor. On the other reading, the former professor has pink hair at the present.

The two correspondences are given in (77).

(77)

a.

b.

In (77a), former scopes over professor with pink hair and precedes the corresponding phon. In (77b), former scopes over professor, and also precedes the corresponding form. Although it does not scope over the entire material that follows it, it satisfies (71) because the requirement is that it precede the material that it scopes over, not that it scope over everything that it precedes. Similarly for with pink hair. Thus, both (77a) and (77b) are licensed.^[41]

7.3 Flat VP

As in the case of the interpretation of adjectives that modify a noun, a VP adjunct scopes over the adjuncts that appear between it and the head. This gives us a possible way to derive some of the generalizations identified by Cinque (1999), without having to resort to rich branching VP structure and functional heads whose only motivation is to ensure the correspondence between linear order and scope. Consider Pesetsky’s (1995:233) example with VP-final PPs.

In (78a), the most natural interpretation is that Chris’s playing in foreign countries is restricted to weekends; in (78b), Chris’s activity of playing on weekends is restricted to foreign countries. Under the assumption that scope requires c-command, a left-branching analysis would be required to capture these readings. However, the only observable differences between (78a) and (78b) are: (i) the linear order between the PPs; and (ii) the fact that in (78a), on weekends scopes over in foreign countries and, in (78b), the opposite scopal relation holds.

As in the case of nominal modifiers discussed above, the difference in linear order in (78) correlates with the difference in scope. Therefore, in stating the principles determining the interpretation of VP modifiers, we also do not need to invoke anything beyond linear order in phon, assuming the semantic type-theory is sufficiently rich to constrain other unwanted readings (e.g. a reading where the cs of on weekends scopes over that of countries in (78a)).^[42] In other words, rather than taking the differences in scope between modifiers to be a reflection of differences in the height of attachment of the PPs, we can interpret these data as evidence that the interpretation of VP modifiers is subject to the direct linear order constraints in (79), which are exactly parallel to the correspondence constraints for NP modifiers proposed in Section 7.2.

(79)

flat vp modifier schemas

a.

b.

The constraint in (79a) licenses the correct interpretations for (78) exactly as discussed for the NPs in (74). Whenever we have a configuration with multiple modifiers where (79a) and (79b) can potentially apply, ambiguities analogous to the ones in (77) emerge. Consider the German examples from Müller (2023: 395):

Example (80a) has the negation scoping over the semantics of oft. The opposite scopal interpretation holds in (80b). This follows from (79b): oft and nicht are adverbs, which can scope over the semantics of the string to their right within the VP, given that the latter is a predicate and both oft and nicht are interpreted as functions that map predicates to predicates (i.e. ⟨⟨e, t⟩, ⟨e, t⟩⟩). Crucially, only one reading is possible because there is nothing to the right of liest. Example (80c) is ambiguous like (77) because now (79a) can apply to license a wide-scope reading for nicht, in addition to (79b) for oft. This is ambiguity follows from our account since both oft and nicht can be interpreted as functors over the semantics of strings that are adjacent to them (to the right and left, respectively). In (80a-b) only one possible reading is licensed because only the string to the right of the adjuncts inside the VP is of a semantic type that could be combined with the adjuncts.^[43]

This analysis also derives the observation that locative adjuncts only receive an object-oriented interpretation when there are no other event-scoping adjuncts (e.g. temporals) intervening between them and the head:

Only (81a) can be interpreted as situating the accident in the park (Koenig et al. 2003; Maienborn 2001; McInnerney 2022). This follows from the fact that, in virtue of (71b), in-the-park ′ can be combined directly with the semantic contribution of the accident. In the case of (81b), the presence of the intervening element yesterday forces an event locative interpretation for in the park because yesterday is also interpreted as an operator over the whole event. As a result, the semantic type of the string adjacent to in the park narrows the interpretation of the PP to that of an event operator. We do not attempt to spell out the formal details of this proposal, but merely point out that the scopal properties can be fully determined by the linear order of the locatives with respect to verbal heads.

All of these phenomena have been cited as motivations for enriched left-branching VP structures (Ernst 2002; Maienborn 2001; McInnerney 2022; Müller 2023). They are, therefore, in conflict with other phenomena like anaphor and quantifier binding, which, as we saw in Section 3.3, many interpret as favoring a right-branching analysis (Hale and Keyser 1993, 2002; Kayne 2004; Larson 1988).

What is useful about the linear-order based approach sketched above is that it derives the effects that both of these proposals try to model. Scope is represented by a right-branching structure in cs, but constraints like (79a) allow elements to the right in the linear order to scope over elements to the left in the linear order (see Jackendoff 1990a; Riezler 1995; Culicover 2013a for other semantic constraints invoking linear order). Our proposal is thus similar to the hybrid proposals in Pesetsky (1995), Schweikert (2005) and Cinque (2006). The difference is that, rather than having the linear and the scopal information be part of different syntactic representations, we encode them in terms of phon and cs, respectively.