2.1 Lexical-Functional Grammar

LFG is a strongly lexicalist, constraint-based framework for grammatical analysis. A crucial feature of LFG is the representation of different types of grammatical information in different ‘projections’. The central levels of syntactic representation are c(onstituent)-structure, for surface constituency relations and grammatical category information, represented using the familiar ‘tree’ diagram, and f(unctional)-structure, represented as an attribute-value matrix, for more abstract syntactic relations such as grammatical subject and object, and unbounded dependencies (such as between a fronted question phrase and its corresponding gap). F-structure is ‘projected’ from c-structure via a projection function, $\unicode[STIX]{x1D719}$ , and c-structure nodes are annotated so as to constrain the formation of f-structure on the basis of c-structure. Example (3) shows the c-structure and f-structure for the sentence Henry likes trains, indicating the projection of f-structure from c-structure by means of the arrows between the two.

The symbols $\uparrow$ and $\downarrow$ in the c-structure annotations in (3) are metavariables, defined as in (4), where $\ast$ refers to the current c-structure node and $\hat{\ast }$ refers to the mother of the current c-structure node.

So the specification ( $\uparrow$  subj)  $=\downarrow$ on the specifier of IP in (3) constrains the formation of the f-structure such that the f-structure projected from the phrase in SpecIP ( $\downarrow$ ) must serve as the value of subj in the f-structure projected from the mother IP node ( $\uparrow$ ). Thus, the phrase in SpecIP serves as the subject of the main clausal predicate at f-structure, as shown in (3). The specification $\uparrow =\downarrow$ states that the f-structure corresponding to the current node is the same as the f-structure corresponding to the mother of the present node. Structural headedness is understood in these terms: a head or co-head node will necessarily have the specification $\uparrow =\downarrow$ .

This notion of headedness is crucial to the analysis of mixed projections in LFG. In (1), the adverb and object suggest verbal structure, but the possessive phrase implies nominal structure. The analysis proposed by Bresnan et al. (Reference Bresnan, Asudeh, Toivonen and Wechsler2016: 311–319), essentially identical to that of Bresnan (Reference Bresnan2001: 289–296), involves a ‘head-sharing’ construction, whereby a VP serves as co-head complement within a DP (the DP is the ‘extended head’ of VP):

The D head (the categorial head) itself is absent (indicated in parentheses) but would, if present, be marked with $\uparrow =\downarrow$ .Footnote ^[4] As a co-head, the VP has the same annotation. In (5) and the subsequent trees, I indicate headedness with ‘[(co-)head]’ for explicitness.

Kaplan (Reference Kaplan, Whitelock, Wood, Somers, Johnson and Bennett1987, Reference Kaplan, Huang and Chen1989) generalized the concept of projection functions, extending the scope of the framework to include additional projections representing different kinds of information, for example, s(emantic)-structure as an interface between syntax and semantics (Dalrymple et al. Reference Dalrymple, Lamping, Pereira, Saraswat, Kanazawa, Piñón and Henriette1996, Dalrymple Reference Dalrymple2001, Asudeh Reference Asudeh2012), p(rosodic)-structure for representing grammatically relevant prosodic information (Butt & King Reference Butt, King, Butt and King1998, Mycock Reference Mycock2006, Dalrymple & Mycock Reference Dalrymple, Mycock, Butt and King2011, Bögel Reference Bögel2015) and i(nformation)-structure for the representation of information structural properties of a sentence (Butt & King Reference Butt and King1997, King Reference King, Butt and King1997, Dalrymple & Nikolaeva Reference Dalrymple and Nikolaeva2011). In this paper, my primary concern is syntactic categories, for example, N (noun) and V (verb). LFG represents syntactic category information in the c-structure; c-structure nodes are labelled as, for example, NP or V $^{\prime }$ , according to category type and level of projection, based on a broadly X $^{\prime }$ -theoretic approach to phrase structure. Following Kaplan (Reference Kaplan, Huang and Chen1989), the relation between a c-structure node and its label is itself a projection, although it is not usually represented as such: the label of a particular node is projected from the node via a function  $\unicode[STIX]{x1D706}$ .Footnote ^[5] This means that c-structure models only surface constituency relations, while syntactic category status is represented separately.

An LFG grammatical architecture, therefore, would include at least the projections in (6); the ‘string’, from which the c-structure is projected, represents the linguistic signal parsed into syntactic units.

The crucial point for the present topic is that different types of grammatical information are represented separately; even syntactic information is not treated as an undifferentiated whole. The use of projection functions to separate out grammatical information in this way means that the different structures, and the information contained within them, are relatively encapsulated. Syntactic categorization is therefore treated as a distinct aspect of grammar, obviously related to other aspects of grammar, but not merely an epiphenomenon of the interaction of those aspects. This makes LFG an ideal framework within which to examine the definition of syntactic categorization.

Most work in LFG assumes a finite set of major categories. For example, Dalrymple (Reference Dalrymple2001: 52–54) assumes five major lexical categories, N(oun), V(erb), P(reposition), Adj(ective) and Adv(erb) as well as the functional categories I and C.Footnote ^[6] Other functional categories are sometimes assumed in LFG work, for example, D, K (case) and Q(uantifier), as well as a number of ‘minor’ categories which cannot project phrases, for example, ‘Part’ (particles), and one or more exocentric categories, for example, S, which can contain a predicate along with any or all of its arguments, including the subject.

2.2 Decomposing categories

In this work, the only categories of concern are the major lexical categories N, V, P and A(dj/dv). Bresnan et al. (Reference Bresnan, Asudeh, Toivonen and Wechsler2016: 103) propose that the major lexical categories N, V, P and A can be analysed according to the following categorial feature matrix:Footnote ^[7]

‘Predicative’ categories require an external subject of predication, while only ‘transitive’ categories may govern objects. In addition to this, for Bresnan et al. (Reference Bresnan, Asudeh, Toivonen and Wechsler2016), categories are specified for the level of projection, 0, 1 or 2 (corresponding to X, X $^{\prime }$ or XP) and as functional (with two levels, F1 and F2) or not functional, which permits the inclusion of the functional categories I, C and D: I is [ $+$ predicative, $+$ transitive] and F1, C is [ $+$ predicative, $+$ transitive] and F2, and D is [ $-$ predicative, $-$ transitive] and F1. Thus, I and C are functional categories corresponding to the lexical category V in terms of the feature matrix, and D is a functional category corresponding to the lexical category N in the same terms. This feature matrix permits Bresnan et al. (Reference Bresnan, Asudeh, Toivonen and Wechsler2016) to state constraints on the possible combinations of functional and lexical heads; for example, they propose that NP, AdjP and PP may not function as a complement to IP or CP.

This is a somewhat restricted decomposition of syntactic categories, leaving no room for a distinction between Adj and Adv (as argued for by Payne, Huddleston & Pullum Reference Payne, Huddleston and Pullum2010) and saying nothing about minor or exocentric categories. More important for the present purposes, however, is the fact that the feature matrix in (7) is not intended as a way of deconstructing syntactic categories but only as a way of cross-classifying them in order to state restrictions on the combination of lexical and functional categories or, more generally, as a way of permitting some categories to be grouped together in distinction from other categories. That is, N, V, P and A remain, but we are now able to state, should we so desire, that V and A pattern together in a certain respect in contrast to N and P by virtue of their having the feature [ $+$ predicative]. Underspecification in terms of the ‘F’ feature is not impossible: for example, English auxiliaries may appear either in I or C, and similarly Hristov (Reference Hristov2013) argues that some pronouns in English may be either N or D. However, underspecification in terms of the features distinguishing lexical categories is not admitted (and would in any case not be sufficient to deal with mixed projections).

2.3 Complex categories

Besides cross-classification across categories, there is another respect in which syntactic categories are not purely atomic in LFG. In any language, some members of a particular syntactic category are likely to differ from other members of the same category in respect of one or more properties. For example, category V in English is standardly assumed to contain both finite verb forms and nonfinite verb forms, for example, infinitives; it also contains intransitive, transitive and ditransitive verbs. The concept of complex categories (Butt et al. Reference Butt, King, Niño and Segond1999: 192) permits generalizations to be made over a subset of members of a category. For example, we might assume a phrase-structure rule, such as the following, for English:

Assume that at least all nonhead elements on the right-hand side of a phrase-structure rule are optional, that is, assume that this rule licenses either V NP or simply V as daughters of V $^{\prime }$ . If we have only an undifferentiated category V, then the rule in (8), besides licensing grammatical structures like VPs consisting only of an intransitive verb and VPs consisting of a transitive verb and an NP complement, also licenses VPs consisting of an intransitive verb followed by an NP object complement and VPs consisting of a transitive verb with no object complement. Of course, these ungrammatical possibilities can be ruled out at other levels of analysis: in LFG, the principles of completeness and coherence require that only and all subcategorized governable grammatical functions appear in an f-structure so that, for example, an NP object phrase could not appear if the governing verb does not subcategorize for one. Another possibility, however, is to distinguish different subcategories of category V, so as to distinguish transitive from intransitive verbs in the phrase-structure rules. Then, instead of (8), we can assume the following:

It is still possible to refer to category V as a whole in a phrase-structure rule, if required; but distinguishing subcategories of V in this way rules out ungrammatical structures such as an intransitive verb plus an object in the phrase structure, rather than requiring reference to another level of analysis. Maxwell & Kaplan (Reference Maxwell and Kaplan1994) investigate the relative merits of treating such phenomena either in terms of phrasal constraints, as in (9), or in terms of functional constraints resolved by unification in the f-structure. They show clearly that distinguishing mutually exclusive classes of some major categories in the c-structure, rather than in the f-structure, is considerably more efficient in terms of parsing time. That is, from a processing perspective, it is far better to eliminate major sets of impossible structures in the context-free phrase-structure rules than in the unification-based feature structure. Thus, it is preferable, for example, to distinguish between transitive and intransitive verbs in the phrase structure than to leave it to the f-structure to rule out sentences like *Bill sneezed Colin and *Bill devoured. It is important to note that this does not mean there is not also a functional difference between transitive and intransitive verbs; they retain the same functional and semantic differences in terms of subcategorization, but it is computationally more efficient to distinguish them also at the phrase-structure level. I assume henceforth that this approach is practically advantageous, given the importance of constraining the processing inefficiency of unification in a unification-based framework like LFG.Footnote ^[8]

Going beyond processing, however, there are important theoretical considerations when it comes to deciding whether particular phenomena should or should not be modelled in the phrase structure as well as at some other level of the grammar. Just because a particular phenomenon can be modelled in the f-structure or even semantics does not mean it should necessarily be modelled only at that level. For example, the fact that only nouns can take determiners could be given a purely semantic explanation: the semantic contribution of a determiner is such that it can occur only with a noun and not with a verb, adjective, etc. But this fact could also be given a featural syntactic explanation (the featural contribution of a determiner is only compatible with noun phrases) and even a structural explanation (the phrase-structure rules only license Ds with NPs). In fact, all three levels of explanation may be valid: a phrase structural constraint on determiners seems eminently reasonable, but this no doubt correlates with a featural properties of noun phrases and with the semantics. Ultimately, it is preferable to model a phenomenon at multiple levels unless there are good reasons not to: there is a methodological danger in, for example, assigning purely to the semantics phenomena which could reasonably have both a syntactic and semantic explanation since it could be (and often is) the case that such assignments are made primarily to avoid a difficulty in the syntactic analysis, rather than on principled grounds.

Once again, processing considerations aside, it remains conceptually useful to be able to distinguish subcategories of larger syntactic categories, allowing us to increase the differentiation of syntactic categories without losing the ability to make generalizations over larger categories (such as V). It is important to note, however, that complex categories permit subcategorization within fully defined and fully distinct categories, for example, subcategories of N or V, but do not permit any kind of intermediate status between N and V.

2.4 Dual categoriality

The central issue for any approach to mixed projections is how to deal with their apparent dual categoriality. As illustrated in (5), the standard LFG approach involves a ‘head-sharing’ structure in which a verbal projection is embedded within a nominal projection. By the feature specifications discussed in the preceding section, D is a functional version of N and differs in categorial features from V. The structure in (5) is therefore a ‘mixed’ construction in a sense that a VP complementing I (as in (3)) is not: in the latter case, both projections share the same category features ([ $+$ predicative, $+$ transitive]) and differ only in terms of the functionality feature; in this case, the two projections crucially differ in terms of category features. The phrase is therefore partly nominal and partly verbal.

The type of mixed construction seen in (5) involves a lexical category serving as a complement to a functional category. It is also possible, however, for a ‘mixed’ construction to involve a lexical category with a different lexical category as its extended head. Following Mugane (Reference Mugane1996) and Bresnan & Mugane (Reference Bresnan, Mugane, Butt, Dalrymple and King2006), nominalizations involve a VP with NP as its extended head:

In this example, the head of the phrase, ‘slaughterer’, is categorially a noun but also serves functionally as the head of the VP, which licenses the object phrase, here mbũri ‘goat’.

Other types of head-sharing construction have also been proposed. For example, Nikitina (Reference Nikitina2008) proposes that IP may take DP as an extended head, while Bresnan et al. (Reference Bresnan, Asudeh, Toivonen and Wechsler2016) allow the exocentric category S to take DP as extended head, and, similarly, Nikitina & Haug (Reference Nikitina and Haug2016) permit S to take NP as an extended head. These latter possibilities will be discussed below.

It is important to note that the LFG approach to mixed projections violates a strict approach to endocentricity, both in the fact that words may head phrases of different categories and in the fact that lexical phrases are permitted to lack an explicit head internal to the phrase. This is not to say that the approach is therefore not viable. Endocentricity is an important cross-linguistic tendency; in some grammatical theories, it is elevated to a syntactic universal but not within LFG. LFG adopts a relatively loose approach to X $^{\prime }$ theory, conforming wherever possible but treating X $^{\prime }$ theoretic principles as violable where a particular language does not conform.Footnote ^[9] But the fact that endocentricity is a strong cross-linguistic tendency means that its violation in the case of mixed projections should be treated as marked. For example, in the Optimality Theoretic approach to LFG developed by Bresnan (Reference Bresnan, Dekkers, Leeuw and Weijer2000), endocentricity derives from a set of universal syntactic constraints; exocentric structures may occur where competing constraints are more highly ranked, but it remains the case that all else being equal, nonendocentric structures are dispreferred in comparison with endocentric structures.Footnote ^[10] Thus, in principle (again, all else being equal), mixed projections should be admitted only where an alternative, X $^{\prime }$ theoretic, analysis accounts for the linguistic data less adequately.

Bresnan (Reference Bresnan, Butt and King1997) contrasts her exocentric ‘head-sharing’ approach, illustrated in (5), with the ‘indeterminate category projection theory’ and ‘projection-switching’ approaches. Under an ‘indeterminate’ approach, the head would be underspecified such that its phrase could display features of more than one category; under ‘projection-switching’ approaches, as proposed, for example, by Abney (Reference Abney1987), Lapointe (Reference Lapointe, Kathol and Bernstein1993), Wescoat (Reference Wescoat1994), Hudson (Reference Hudson2003) and Malouf (Reference Malouf2000), the head of a mixed projection is assumed to have an intermediate (rather than indeterminate) or dual category status, which enables it to project up to a certain level as if it were one category (e.g. a verb) and above that level as another category (e.g. a noun).

For example, Lapointe (Reference Lapointe, Kathol and Bernstein1993) proposes that category labels are bipartite, the first part determining external syntactic properties such as distribution (2b) and the second determining internal syntax (2a). So, Lapointe argues for an intermediate category (a ‘dual lexical category’) $\langle \text{N}|\text{V}\rangle$ to account for the English gerund, which projects verbally (ensuring verbal internal syntax), except for its top layer (ensuring it has the distribution of a noun phrase), and the -ing suffix has a morphological function in deriving a category $\langle \text{N}|\text{V}\rangle$ from a plain category $\langle \text{V}|\text{V}\rangle$ .

More sophisticated projection-switching approaches remain the standard approach to mixed projections within mainstream transformationalist grammar. For example, Alexiadou, Iordăchioaia & Schäfer (Reference Alexiadou, Iordăchioaia, Schäfer, Sleeman and Perridon2011) analyse nominalizations in Romance and Germanic in terms of DP projections which contain verbal functional projections; so for them, the English gerund of the type seen in (1) (their ‘English verbal gerund’) has the following structure:

Within such an approach, nominalizations may vary as to how much verbal, and indeed nominal, structure is included in the projection. More verbal nominalizations contain more verbal projections; for example, Alexiadou et al. (Reference Alexiadou, Iordăchioaia, Schäfer, Sleeman and Perridon2011) analyse ‘Spanish verbal infinitives’ as projecting also a tense phrase in addition to the verbal projections in (11), whereas the purely nominal English gerund (their ‘English nominal gerund’, shown in (25a)) projects only to the VoiceP in terms of verbal projections, while also containing additional nominal projections, such as NumberP and nP.

Within LFG, such a variation in terms of the abstract verbal/nominal features of nominalizations would not ordinarily play out in the phrase structure but would be captured at the level of f-structure, where tense, aspect and such features are represented. Moreover, the possibility of head movement within transformationalist approaches means that structures such as those in (11) may be proposed without necessitating the head to surface at the bottom of the projection; as discussed below, this is not the case in LFG, which Bresnan (Reference Bresnan, Butt and King1997) takes as evidence (within the assumptions of LFG) against a projection-switching approach.

In the Head-driven Phrase Structure Grammar analysis by Malouf (Reference Malouf1996, Reference Malouf2000), the mixed properties of the English gerund are accounted for by means of the multiple inheritance hierarchy for head values. The head value gerund is a subtype of both noun and relational. As a subtype of noun, its external distribution is that of an NP (it can ‘occur anywhere an NP is selected for’ (Malouf Reference Malouf1996: 262)) and does not necessarily correspond to the distribution of verbs (which are a separate subtype of relational). Adverbial modification applies to elements of category relational (which includes adjective). Since adjectives modify only c(ommon)-nouns, gerund phrases cannot be modified by adjectives. This is a sophisticated intermediate category analysis, the use of a multiple inheritance hierarchy permitting cross-classification across more than one grammatical category: it is possible to define a category that shares some features with nouns and some with verbs, without requiring it to be fully one or the other.

It would not be immediately possible to transfer Malouf’s proposal into LFG since LFG does not make use of multiple inheritance hierarchies and does not admit mixed categories in the sense of permitting categories which are partially of one superordinate category and partially of another superordinate category. On the other hand, it would conceivably be possible to model mixed projections using either a projection-switching approach similar to Alexiadou et al.’s (Reference Alexiadou, Iordăchioaia, Schäfer, Sleeman and Perridon2011) or an indeterminate approach. However, Bresnan (Reference Bresnan, Butt and King1997) argues strongly in favour of the ‘head-sharing’ approach on two grounds. First, there is strong evidence for the principle of ‘phrasal coherence’: in mixed projections, ‘the hybrid construction can be partitioned into two categorially uniform subtrees such that one is embedded as a constituent of the other’ (Bresnan Reference Bresnan, Butt and King1997: 4).Footnote ^[11] There are no clear counterexamples where, for example, a projection is mixed in such a way that no distinct verbal and nominal subtrees can be distinguished. This generalization rules out an approach to mixed categories involving an indeterminate, or underspecified, head.

Second, Bresnan (Reference Bresnan, Butt and King1997) argues that projection-switching, or intermediate, category approaches are inadequate because they require the head to be positioned in the lower projection (as in (5), where the head is in V, not D). It is important to note that this criticism applies only within the nontransformational assumptions of LFG. In a theory of phrase structure which permits movement, the surface position of the head may not correspond to its base position. But LFG assumes that constituent structure represents only the surface constituency. Thus, if we are dealing with a single projection, which at some point switches from one category to another or which displays some properties of one category and others of another while remaining a single projection, it is just a fact about phrase structure (so conceived) that the head must surface at the bottom of the projection concerned. Bresnan discusses a number of examples which show that in some languages, the head must surface in the higher projection of a head-sharing structure;Footnote ^[12] that is, the head cannot occur in the position expected under a projection-switching analysis. Thus, intermediate category analyses which require the head to be in the lower position are ruled out, and the head-sharing approach, which is in other respects largely equivalent, is in this respect preferable.

In this way, Bresnan’s head-sharing model could not unreasonably be seen as a nontransformational variant of the mainstream projection-switching approach. In both approaches, the phrase structure involves, for example, a verbal projection embedded within, for example, a nominal projection, with the lexical head serving as the head of both projections. Since in LFG the c-structure represents only the surface constituent structure, with no movement, this abstract headship must be represented at the level of f-structure (hence the definition of head and co-head in terms of the $\uparrow =\downarrow$ annotations), and the head must be permitted to appear (i.e. be generated) in the head of the higher phrase. The other main difference between the head-sharing model of Bresnan and a standard projection-switching approach is the larger inventory of functional heads assumed in mixed projections under the latter analysis; once again, this is due to the restriction of LFG’s c-structure to the representation of surface constituency relations, functional properties being represented at the level of f-structure. Thus, differences of framework aside, the head-sharing and projection-switching approaches are almost entirely equivalent.

In this paper, I adopt the head-sharing approach of Bresnan (Reference Bresnan, Butt and King1997). As noted also by Hudson (Reference Hudson2003: 585) and Panagiotidis (Reference Panagiotidis2015: 136), the majority of theoretical models share fundamental similarities, and the differences between head-sharing and projection-switching are not crucial to the concerns of this paper. Rather, what is of primary interest is the criteria used to determine dual categoriality however that is modelled. In almost all previous approaches, for example, distribution is taken as sufficient evidence for categorization, such that a phrase with verbal internal syntax but with the distribution of a noun phrase must have mixed categorization. The question at hand is whether this holds.

4.2 Distribution and the type B gerund

As discussed above, I take internal syntax to be crucial to categorization. Therefore, the fact that the type C gerund shows both nominal and verbal internal syntax means that it must be treated as a mixed projection, just like the Arabic masdar. I therefore accept Bresnan et al.’s analysis (27) for the type C gerund.

On the other hand, the type B gerund is consistently verbal in terms of its internal syntax as well as sharing the same verbal morphosyntactic properties as the type C gerund. The following table compares the relevant properties of the Arabic masdar and the type B and type C gerunds:

The type C gerund shows two distinct types of property ‘mixing’: first, the three criteria in (2) point in different directions, for example, distribution points towards nominal status and morphosyntax points towards verbal status; second, the criterion of internal syntax itself points in more than one direction. In this way, the type C gerund is similar to the Arabic masdar, the only difference being that with the former, the evidence points to NP-over-VP, while with the latter, the evidence points to VP-over-NP. In contrast to these constructions, the type B English gerund construction (25b) is more consistently verbal: it is morphologically verbal in exactly the same way as the type B gerund, and its internal syntax is purely verbal. Its only potentially nonverbal property is its distribution: it shows the same apparently nominal distribution as the type C gerund. Despite these differences, Bresnan et al. (Reference Bresnan, Asudeh, Toivonen and Wechsler2016: 318) treat the type B gerund via the same kind of head-sharing analysis as the type C construction (25c), the only difference being the category of the co-head phrase:

As with (5), the gerund appears in the head of a VP, with object complement like any transitive V, but in this case, the VP and accusative case subject phrase him together constitute a clausal phrase S, which serves as co-head complement of (absent) D in the higher DP. Thus, the phrase as a whole is a DP, headed by a V in an embedded VP, just as in (5). It is clear that the DP node and, therefore, the mixed projection analysis altogether depends entirely on the assumption that nominal distribution is sufficient evidence for a nominal projection in the phrase structure.

The S node in (29) is an exocentric category, often utilized within LFG for phrases containing a verb (phrase) and the verb’s subject. Thus, the analysis shown in (29) involves two instances of exocentricity: the exocentricity of S and the exocentricity of the extended head structure. The use of S is not strictly relevant for the present discussion, and it could be eliminated by licensing the subject phrase in SpecVP and thus having simply a VP complement of D. Under Bresnan et al.’s proposal, the S node is required only if there is an accusative case subject; if there is no subject, there is simply a VP with DP as extended head (ambiguous between the (25b) and (25c) types). Bresnan et al. (Reference Bresnan, Asudeh, Toivonen and Wechsler2016: 318) derive the S-less structure by Economy of Expression, a derivational process which effectively ‘prunes’ unnecessary nodes from trees. Given the rejection of Economy of Expression by Dalrymple, Kaplan & King (Reference Dalrymple, Kaplan and King2015), it is preferable to follow Seiss (Reference Seiss, Butt and King2008) in assuming that the daughter of DP in the type B gerund is consistently a VP, with the subject phrase appearing in SpecVP as in (30).

Nevertheless, the category of the verbal node is not the crucial point here. What matters is the top DP node: the internal syntax of the phrase is entirely verbal (or clausal): there can be no adjectival modifier, determiner or possessor phrase. Given that there are no explicit morphological properties of the gerund that require a DP node, it is clear that the DP node is assumed purely to account for the distribution of the phrase, that is, distribution is taken as a sufficient criterion for postulating a syntactic category.

There exist a number of similar proposals for mixed projection analyses that take distribution as a sufficient criterion for categorization. For example, as discussed in more detail below, Bresnan (Reference Bresnan, Butt and King1997) and Spencer (Reference Spencer, Butt and King2015) propose that attributive participle clauses, which show the internal syntax of a VP but the distribution and agreement features of an Adj, are best analysed via a mixed projection in which a VP functions as a complement to AdjP. Similarly, Haug & Nikitina (Reference Haug and Nikitina2016: 15) assume a head-sharing construction for a participle construction in Latin (the ‘dominant’ participle construction) which shows the external syntactic distribution of a noun but whose internal syntactic structure is that of an S.Footnote ^[24] Since Latin lacks a DP, they assume an S as a co-head complement of an NP:

The NP projection above S in (32) might predict that the phrase itself could contain nominal syntactic structure, but this is not the case. The dominant participle phrase as a whole, that is, what Nikitina & Haug (Reference Nikitina and Haug2016) and Haug & Nikitina (Reference Haug and Nikitina2016) demonstrate is an S, cannot be modified by an adjective, for example. Again, the only justification for the NP projection above S is the distribution of the phrase.

Distribution alone, then, is taken as sufficient evidence for categorization within LFG work on mixed projections. But as I have shown above, this assumption cannot be maintained in the case of the Arabic masdar. In that case, it appeared preferable to disregard the evidence of distribution, which can be accounted by other means, in favour of internal syntax as the primary criterion for categorization. The same argument can, in fact, be made for the English type B gerund.

A number of authors, including Abney (Reference Abney1987) and recently Pires (Reference Pires2007: 167–168), note certain differences between the type B and type C gerunds which bring into question the assumption that both involve a nominal projection at the top level. Specifically, the type B gerund shares certain properties with finite clauses which are not found with the type C gerund (poss-ing). For example, the type B gerund is compatible with wh-extraction, expletive subjects and certain adverbs, which are not possible with the type C gerund (examples from Pires Reference Pires2007):

Gerunds without an overt subject, which are superficially ambiguous between type B and type C, pattern with type B in all cases where the difference is not neutralized. None of this data can be accounted for under the proposals of Bresnan et al. (Reference Bresnan, Asudeh, Toivonen and Wechsler2016), according to which both types are mixed projections with the same top node. However, if we abandon the assumption that nominal distribution is sufficient evidence to require a nominal projection, it is possible to treat the type B gerund (including gerunds without overt subjects) as a purely verbal projection. Then the fact that the type C gerund is less clause-like than the type B gerund can follow from the fact that type C, but not type B, is at the top level a nominal projection. That is, instead of (30), I propose the following for the type B gerund:

Differences of theory aside, this is similar to the proposal of Pires (Reference Pires2001, Reference Pires2006, Reference Pires2007), according to which the type B gerund (his ‘clausal gerunds’) projects to a TP at the top level. What remains to be accounted for, under this proposal, is the identical distribution of gerunds and noun phrases. Under proposals where both type B and type C gerunds are mixed projections, nominal at the top level, their distribution falls out naturally. If this distribution is not accounted for by categorization, it must be accounted for in some other way. Within a minimalist framework, Pires (Reference Pires2007) assumes that the type B gerund, analysed as a TP, has the distribution of a noun phrase because it is assigned a case feature which requires checking.

A similar approach could be taken within the LFG framework adopted here; for example, type B gerunds could be lexically associated with a specification requiring the presence of a case feature at f-structure, which could only be supplied if the gerund phrase occurred in a relevant argument position. However, such an approach would not generalize to the analysis of participial clauses, discussed in the next section, which I analyse as verb phrases which share their distribution with adjectival and other modifying phrases.

I therefore adopt the same analysis proposed for the Arabic masdar above: if we distinguish the grammar, as a set of constraints on structures, from the structures themselves, then it is unproblematic to capture the identical distribution of type B gerund and noun phrases, by defining a metacategory which ranges over both phrase types, for example:

This constraint captures the nominal distribution of the type B gerund just as well as a mixed projection analysis involving a DP node, but has the advantage that it does not require that DP node to appear in the structure itself, accounting for the differences between the types B and C gerunds mentioned above. If both types have the same mixed projection structure, then these differences cannot easily be accounted for, but if the former is a mixed, partially nominal projection, while the latter is a purely verbal projection, the differences fall out naturally.

Of course, a set of phrase-structure rules which accurately models the distribution of noun phrases and gerunds is likely to require more than one metacategory which generalizes over these two types of phrase and one or more other phrase types. For example, one of the possible positions in which DPs and gerunds may appear, the subject position SpecIP, may also host phrases of other lexical categories, including APs, PPs and CPs:

Examples (36b, d, f) show that the position of the relevant phrases in (36a, c, e) is SpecIP, rather than a position further to the left.Footnote ^[25] Thus, the phrase-structure rule which makes generalizations over the SpecIP position will most appropriately be stated using a metacategory which ranges over at least the categories DP, AP, PP, CP and $\text{VP}_{[\text{ger}]}$ . In contrast, the phrase-structure rule which makes generalizations over the core direct object position (first complement of V) will most appropriately be stated using a metacategory which ranges over DP, CP and $\text{VP}_{[\text{ger}]}$ but not AP and PP.Footnote ^[26]

Thus, metacategory definitions have considerable use in grammar to model restrictions on phrase types in different positions, and, therefore, their use for mixed projections does not constitute an additional complication.

Besides the empirical evidence in favour of a structural distinction between type B and type C gerunds, there is also a theoretical argument. I argued above that exocentricity can be analysed as a marked possibility, cross-linguistically, which may be understood in terms of constraints which, all else being equal, rule out exocentric structures, including mixed projections.Footnote ^[27] Therefore, a grammar which necessitates fewer exocentric structures may be preferred, all else being equal. As there is no evidence specifically favouring the mixed (and therefore exocentric) analysis of the type B gerund, it seems fair to conclude that all else is equal and that the exocentric, mixed projection analysis of the type B gerund is to be dispreferred. This claim extends well beyond the analysis of the English gerund, of course. It entails that in all instances in which there is a difference between the distribution and the internal syntax of a particular phrase type, it is better not to analyse this in terms of a mixed projection, but rather assume an endocentric, internally consistent projection for the phrase itself, and to account for its distribution by other means.

To summarize my proposals for the English gerund, then: first, the type C gerund (poss-ing) is a true mixed projection, as evidenced by its mixed internal syntax. This can be modelled in LFG by means of a head-sharing structure, as proposed by Bresnan (Reference Bresnan, Butt and King1997) and shown in (37).

Second, the type B gerunds, under which heading I include both structures with an ‘accusative’ case subject (acc-ing) and those with no explicit subject, are not mixed projections, but pure verbal projections which share their distribution with that of noun phrases. They are formed like any other verb phrase, with the exception of the VP-internal subject, which is lexically licensed by the gerund form of the verb.

As a full illustration, I give the relevant phrase-structure rule, metacategory definition, lexical entry and c-structure/f-structure representation for the sentence in (25b).

5.1 Another mixed projection?

Spencer (Reference Spencer, Butt and King2015) discusses ‘Indo-European type’ participles in Sanskrit, as treated by Lowe (Reference Lowe2015), and also in Lithuanian, proposing an analysis that is, in many respects, the same as that proposed for German participles by Bresnan (Reference Bresnan, Butt and King1997: 2–3). All these participles are diachronically related and are of the same ‘subject-oriented’ type; that is, to the extent that an attributive participial clause can be treated as a reduced relative clause, it is necessarily the subject that is relativized on. The participle agrees with and attributively modifies a noun, which is identified with the gapped subject of the participial clause. Example (43) shows an attributive participle in Sanskrit, (44) one from Lithuanian and (45) one from German.

These participles can also have other uses. For example, as discussed by Lowe (Reference Lowe2015), Sanskrit participles can also be used predicatively, that is in ‘converbal’ or clausal adjunct use. The attributive use is the most canonically adjectival use of participles, but adjectives can also, to a slightly more limited extent, be used as clausal adjuncts; so in both uses, participles appear to display adjectival distribution. I focus on attributive participles here, following Spencer (Reference Spencer, Butt and King2015) and Bresnan (Reference Bresnan, Butt and King1997).

Morphologically, participles are mixed in the sense that they combine a verbal stem with an adjectival suffix. Distributionally, they are at least superficially most similar to adjectives. However, the internal syntax of the participle phrase is exclusively verbal. Participles to transitive verbal stems may take objects, in the same case as, and entirely indistinguishable from, the object of a corresponding finite verb form; accusative case objects appear in (43) and (45). Likewise, participles may be modified by adverbs but never by adjectives. Considering the three criteria defined in (2), the English type B gerund is purely verbal in respect of two of the three criteria, while attributive participles are purely verbal only in relation to one of the three:

Spencer (Reference Spencer, Butt and King2015) assumes that the adjectival distribution and mixed morphosyntactic properties of attributive participles justify a mixed projection analysis. Spencer notes that this could be formalized by means of the standard head-sharing approach seen with the type C English gerund above (i.e. in this case, a VP embedded within an AdjP), but he proposes an alternative, intermediate category analysis. Spencer (Reference Spencer, Butt and King2015) adopts the morphological model of Spencer (Reference Spencer2013), adapted to LFG, involving a semantic argument structure representation in the morphology of a word which maps to c-structure and f-structure and (among other things) determines the category of the word. The argument structure of a verb has an event semantic function (SF) role ev, while adjectives have a modifier SF role a-mod. The morphological process that derives (or inflects) a participle from a verb creates a composite SF role This composite SF role projects to c-structure and f-structure in such a way that participles display both adjectival and verbal morphosyntax. In terms of syntactic category, Spencer (Reference Spencer, Butt and King2015) proposes that the composite SF role maps to an intermediate category, which he labels ‘V2A’ (for ‘verb-to-adjective transposition’).

As it stands, this intermediate category approach is unsatisfactory within LFG since the specifically verbal and specifically adjectival features of the category must be stipulated. LFG has no equivalent to the multiple inheritance hierarchy utilized by Malouf (Reference Malouf2000) within HPSG to model a truly intermediate category gerund; thus, ‘V2A’ is not, formally, intermediate between V and Adj but is simply a third category, fully distinct from both. It must, therefore, be stipulated that V2A has the internal syntax of V and the distribution of Adj since it cannot fall out naturally from any principle of intermediate category formation. As Spencer (Reference Spencer, Butt and King2015) notes, however, the mixed projection analysis of attributive participles could equally be modelled in terms of head-sharing. The situation is therefore parallel to Bresnan et al.’s (Reference Bresnan, Asudeh, Toivonen and Wechsler2016) analysis of the English gerund: a phrase with purely verbal internal syntax is treated as a mixed projection because it shows nonverbal distribution and, in this case, nonverbal morphology.

5.2 Distribution

In Sanskrit, participle phrases used attributively have essentially the same distribution as adjective phrases used attributively. But this is because the two types of phrase share attributive functionality, not necessarily because they share the same syntactic category. Other types of phrase can also function as attributive modifiers in Sanskrit as well as in other languages with the same type of participle, for example, Lithuanian and German. Most obviously, CPs headed by relative pronouns can function as attributive modifiers:

It would theoretically be possible to treat even attributive CPs as mixed projections, projecting AdjP at the top level.Footnote ^[28] But then the same issues arise as with the English gerund discussed above: we can capture a distributional generalization in the rules of grammar in a way that licenses exocentric phrase structures, or we can capture the generalization equally well but in a way that licenses smaller and purely endocentric phrase structures.Footnote ^[29]

I therefore assume that the simplest analysis for participle phrases in languages like Sanskrit, English and Lithuanian is a plain VP, as proposed by Lowe (Reference Lowe2015), with no mixed projection required:

As with the English gerund VP, the participial VP can be treated as a subtype of VP, modelled by means of a complex category $\text{V}_{[\text{ptc}]}$ . The distribution of participial VPs will be constrained by metacategory definitions parallel to (23). However, Spencer’s (Reference Spencer, Butt and King2015) argument that participle phrases should be treated as at least partially categorially adjectival is not based on distribution alone but also on the third criterion used for categorial status in LFG: morphosyntactic agreement features.

5.3 Morphology and agreement

Superficially, it does not seem unreasonable to assume that agreement and similar morphosyntactic properties provide evidence of categoriality. In languages with rich morphological systems, some features are typically expressed on verbs and others on nouns and adjectives. Tense, aspect and mood are prototypically verbal features, while definiteness is prototypically nominal. In terms of agreement, many Indo-European languages, including those discussed in the previous section, typically mark person and number on verbs, and case, number and gender on nouns and adjectives: thus, person is a feature of verbal morphosyntax, and case and gender features of nominal and adjectival morphosyntax. However, while it is true that such patterns can be typical, even highly regular, in a language or even many languages, such patterns need not be absolute. Even cross-linguistically regular tendencies may have exceptions; for example, Nordlinger & Sadler (Reference Nordlinger and Sadler2004a, Reference Nordlinger and Sadlerb) discuss languages in which tense features can be marked on nominals.Footnote ^[30] But within languages too, there are often exceptions to the typical division of morphosyntactic labour between nouns and verbs. In fact, many such exceptions involve categories remarkably similar to the sorts of categories under discussion in this paper.

In particular, it is not uncommon for unequivocal finite verb categories to show ‘adjectival’ or ‘nominal’ agreement in some languages, in cases where nonfinite verbal categories such as participles or agent nominalizations have become grammaticalized and integrated into the finite verbal paradigm. For example, finite present and future verb forms in Russian and other Slavic languages mark person and number, but past tense verbs, marked with the formant -l-, agree rather in gender and number. The gender/number morphology of past tense verbs in Russian is more similar to that of nouns and adjectives than to the person/number marking on nonpast verbs. Diachronically, the reason for this is that the past tense in -l- derives from a construction involving a verbal adjective in *-lo-, which in the development of the Slavic languages replaced the inherited finite past tenses (which, like the present, marked person and number). At some point in the pre-history of Slavic, the forms in -l- must have been categorial adjectives, as they were in the ancestor of Slavic, Proto-Indo-European. Now, however, there is no justification for analysing the past tense formation in -l- as anything other than fully verbal. Many languages attest equivalent developments, including, for example, many Indo-Aryan languages, where the (often ergative) perfective aspect derives from what is in early Sanskrit a verbal adjective.

What phenomena like this show is that diachronic developments may lead to the recategorization of a particular formation, without necessitating any corresponding morphosyntactic reformation. When verbal adjectives are reanalysed as finite verbs, their adjectival agreement requirements need not immediately be replaced by verbal agreement. When a verbal adjective is integrated into a verbal paradigm, it will likely adopt some verbal feature marking, for example, tense or mood, but its existing agreement features may continue to exist alongside this. Over time, it may well be that analogical pressure results in changes to the paradigm which bring it more closely in line with the rest of the paradigm; an example of this is the integration of what was originally a noun into the verbal system as the ‘aorist passive’ formation in Sanskrit (Kümmel Reference Kümmel1996). Alternatively, the integrated formation may simply preserve its original paradigmatic oppositions (e.g. gender/number agreement), which therefore become oppositions relevant to the verbal system, rather than simply relevant to the nominal or adjectival system.Footnote ^[31] Thus, from a diachronic perspective, it is problematic to assume that morphosyntax necessarily tells us anything about the synchronic status of a formation. If a verb form happens to show adjectival agreement, this need not be because it is synchronically an adjective since it could equally be that it was adjectival at an earlier period and that its syntactic category has changed while its agreement features have not.

The example of the Russian past tense in -l- involves a verbal adjective being reanalysed as a finite verb. The course of development of the verbal adjective is too remote to trace, but *-lo- is not reconstructed as a participle for Proto-Indo-European since in other Indo-European languages, the descendants of *-lo- form not participles but lexical adjectival derivatives from verbal roots.Footnote ^[32] Thus, at some point, an Adj was reanalysed as a V. It is not necessarily the case, however, that the reanalysis as V was concomitant with the reanalysis as a finite verb form. It is equally possible that inherited *-lo- was first reanalysed as a participle, a nonfinite verbal form, and recategorized as V, and that the reanalysis as a finite formation was carried out later. In the case of participles of the type found in Sanskrit, German and Lithuanian, which are nonfinite verb forms with verbal internal syntax but adjectival agreement, we see forms that have undergone the first development but which have not undergone the second.Footnote ^[33] That is, if nonfinite verb categories such as participles, gerunds and infinitives are (or at least can be) of category V, it must be possible for adjectives and nouns which become reanalysed as part of a language’s nonfinite verb system to be recategorized as Vs, without necessarily losing their nominal or adjectival morphosyntax. In the case of Sanskrit, Lithuanian and German participles, comparative evidence suggests an ultimately adjectival origin, although the details are too remote to be secure (Lowe Reference Lowe2015: 311–316).

However, going beyond the fact that diachronic change can obscure otherwise neat correlations between category and morphosyntax, Spencer (Reference Spencer, Butt and King2015) argues that in purely synchronic morphological terms, it should not be an accident that in languages such as Sanskrit and Lithuanian, participles show exactly the same agreement features, and even paradigms, as lexical adjectives. This is a fair claim. However, in a grammatical framework like LFG, where different types of grammatical information are represented at different levels of structure, there is no reason why morphological patterns should necessarily be reflected in the constituent structure, which models primarily constituency relations. The morphological similarities between a finite verb showing, say, gender/number marking and a historically related noun or adjective category with gender/number marking may be relevant and could be modelled at the morphological level and may also be relevant at the level of functional structure since, for example, the feature gender may appear in all f-structures headed by a word which marks gender, whether verb or noun. But to further propagate morphological patterns into the representation of constituent structure is superfluous.

Spencer’s (Reference Spencer, Butt and King2015) argument that participles are categorially adjectival (at least in part) due to their adjectival morphosyntax depends on the assumption that the morphological feature(s) shared between adjectives and participles necessarily influence the syntactic category of a word. In Spencer’s model, this is true since it is the adjectival SF role a-mod in the argument structure representation of a lexeme that determines both agreement properties and syntactic category. However, there is no reason why this should necessarily be the case: it is perfectly conceivable that agreement properties and syntactic category be determined separately. In Lowe (Reference Lowe, Arnold, Butt, Crysmann, King and Müller2016), I provide a formal model of word formation within LFG which captures the morphological similarities between participles and adjectives in terms of shared properties at the morphological level, but which also permits participles and adjectives to be realized with distinct syntactic categories outside the morphological component.

For reasons of space, I omit the details of the morphological model here. However, it is worth considering the output of the morphology, that is, the syntactic similarities and differences between adjectives and participles, under my proposal.

Example (50) shows the lexical entry for the nom.sg.fem. participle ‘perfecting’, (51) shows the lexical entry for the finite 3sg. verb form sādháyati ‘perfects’ and (52) shows the lexical entry for the derived adjective ‘perfecting’ (nom.sg.fem.). As a part of the inflectional verbal paradigm, inherits the same pred value as the finite verb, including its subcategorization requirements, which accounts for its appearance with an object.Footnote ^[34] The participle also inherits verbal tense–aspect and voice features for the same reason. However, participles and finite verbs are specified as separate subtypes of the category verb, $\text{V}_{[\text{ptc}]}$ and $\text{V}_{[\text{fin}]}$ , respectively. The subcategory of participles inherits, alongside its verbal features, also the agreement features typical of adjectives, modelled here using an agr feature; thus, both the participle and adjective specify number, gender and case features. Both words also have a specification determining which element is agreed with; the participle, as a verb form, inherits the same specification as the finite verb, agreeing with its subject, while the adjective inherits the adjective-only specification that it agrees with the element it modifies.

In this way, the participle in (50) inherits and displays both verbal and adjectival properties, as we would expect. But crucially, the adjectival properties of the participle do not require a distinct Adj node in its c-structure projection; rather, it can be unproblematically treated as a subcategory of V, its distribution captured by means of a metacategory. As with the English gerund, this is a positive result because the analysis captures the data just as adequately as a mixed projection analysis would do but without the requirement for an exocentric structure.

In the default case, where distribution and internal syntax align, differences in agreement properties are not sufficient to justify separate categorization; for example, for imperfective and perfective verb forms in Hindi or nonpast and past forms in Russian, there is widespread agreement that these are all Vs and that the differences between the two types are relevant at the morphological and f-structure levels but not in the c-structure. Here, we have been considering a more complex case, where distribution and morphology pattern together in opposition to internal syntax. As argued in detail in the preceding sections, where internal syntax and distribution conflict, it is analytically problematic to privilege distribution over internal syntax. Thus, the logical conclusion is that morphosyntactic properties (or agreement properties, at least) must also be subordinate to internal syntax as a criterion for categorization.