() (a) p (b) * p wx wx y zzy So this constraint rules out crossing lines.3 It also rules out multiply mothered nodes such (2) when combined with the restriction that nodes cannot precede themselves (T14 from Ch. 3). () * a wx y Since y is dominated by w, which sister-precedes x, and y is also dominated by x, it follows that y precedes y; but such situations are ruled out by the independently required restriction that items cannot precede themselves. Given (A9) and (T1), multidominated trees will always result in a contradiction. This gives constituent structures a measure of explanatory power. It predicts the existence of constituency-based and structure-dependent phenomena. This insight is at the heart of Generative Grammar in most of its guises. Nevertheless, there are a number of attested phe- nomena which either escape explanation under these premises or are predicted not to occur without additional mechanisms added to the grammar. Chomsky (1957) used this observation to argue for trans- formations. He claimed that when you had phenomena that lay out- side the power of PSGs (and we can extend that to related formalisms), then a higher-order grammatical system, such as one that uses trans- formational rules, is in order. Take, for example, the phenomenon of wh-extraction without pied-piping of the preposition: (3) Who did you give the book to? The preposition to is separated from its complement who by the rest of the clause. There is no way to draw a tree for this sentence using a 3 The prohibition against crossing lines is also found in autosegmental phonology. See Goldsmith (1976), McCarthy (1979), Pulleyblank (1983), Clements (1985), Sagey (1986, 1988), and Hammond (1988, 2005) for discussion. 4 T1. PisirrreXexive:(8x 2 N) [:(x 0 x)]. 190 controversies simple PSG, maintaining the complement relation of to to who without crossing a line and violating (A9). In addition to traditional examples of movement such as wh- movement and raising constructions, McCawley (1982, 1989) observes that parentheticals, such as (4a), Right-Node Raising structures (4b) and other examples of non-constituent conjunction, relative clause extraposition (4c), and scrambling (4d) seem to exhibit discontinuous constituents (all examples from McCawley 1982): (4) (a) John [ VP talked, of course, about politics]. (b) Tom may [ VP be, and everyone is sure Mary is, a genius]. (c) [ NP A man entered who was wearing a black suit]. (d) [ NP Huic ego me bello] ducem proWteor. (Latin) this I myself war leader announce ‘‘For this war, I announce myself leader.’’ Blevins (1990) adds the case of VSO (verb–subject–object order) languages such as Irish, where the subject appears in the middle of the verb phrase: (e) [ VP Chonaic Sea ´ n an fear]. saw John the man ‘‘John saw the man.’’ In each case the underlined words appear in the middle of a string that otherwise passes tests for constituency (as marked by the brackets). Similar eVects were noted in Pike 1943; Wells 1947; Yngve 1960; and Speas 1985. A related but distinct problem are cases of linear order and hierarchical eVects, such as the binding conditions and negative polarity licensing, which seem to be in conXict. In mainstream generative grammar, the solution to these problems is either a transformational rule in the traditional sense or a movement rule in the Principles and Parameters or MP sense (see Ch. 8). An alternative to this approach suggests that we should relax our condition on line crossing and/or multidomination (McCawley 1982, 1987, 1988, 1989; Huck 1985; Speas 1985; Baltin 1987; Blevins 1990; among others). So, for example, we might allow a sentence such as (3) to be represented by a diagram like (5a) or (b), which are alternative representations of the same kind of diagram. multi-structures 191 () (a) S NP Aux did NP VP N who N John V give NP PP D the N book P to (b) S VP NP PP NP NP N who Aux did N John V give D the N book P to Let us call the views expressed in (5) ‘‘line-crossing approaches’’. Although there are no graphically represented line crossings in (5a), this diagram is equivalent to the line crossing form in (b) as the domination relations and linear orderings inside the two graphs are identical. It should be noted that in fact, structures such as (5)are entirely possible in ID/LP format grammars (Blevins 1990). A related alternative involves line crossing only in the limited cir- cumstance where a single node is dominated by more than one parent. Let us refer to the class of these proposals as ‘‘multidomination’’ approaches. Multidomination is most useful when an element simul- taneously satisWes the requirements of two diVerent positions in the tree. For example, if an NP is simultaneously the subject of both the embedded and the main clause (as in a raising construction), then it might be dominated by both the S nodes (Sampson 1975): ()S VP S NP VP V seems The man to be happy 192 controversies It should be noticed that line crossing is not a requirement of multi- domination, but merely a common consequence. Take for example a simple analysis of subject-to-object raising: ()S VP S NP NP VP V wants The man him to be happ y Here him is multidominated by VP (explaining the object case), and is simultaneous the logical subject/agent of the predicate to be happy. A constituent-sharing approach also provides a straightforward an- alysis of non-constituent coordination (see below for citations and discussion). For example, Right-Node Raising could be viewed as the sharing of the second VP’s object with the Wrst: ()S SS NP VP NP VP NP N Frank V loves Conj and N Susan V hates N tree-drawing Since the speech stream is linearly ordered in a single dimension (through time), and our written representations of language are typ- ically limited to two dimensions (up and down), linguists rarely consider the possibility that the hierarchical structure of language is not limited to two dimensions and instead branches into at least a third. Approaches with line crossing actually hint at such possibilities. Line crossing might be thought of extending the structure out into a third dimension. I hinted at such possibilities in the discussion of adjunction in Chapter 8, where the BPS interpretation of adjunction points towards the structures existing on separate planes which explains a wide variety of phenomena including restrictions on multi-structures 193 do-support and condition C-eVects in anti-reconstruction environ- ments. To schematize, we might hypothesize that simple constituent structure is represented on one plane, and the shared NP is in a third dimension: (9) basic clausal structure Shared constituent dimensio n sentence In this sort of approach, multiple dimensions hang oV of the single constituent tree. I will refer to this kind of analysis—a variant of the line-crossing approach—as ‘‘multidimensional.’’ I reserve this term for approaches where there is a single constituent-structure representation branching into three dimensions. There is another, more common, three-dimensional structure found in the literature. This is the view where we have fully formed inde- pendent planes of representation for diVerent kinds of information. This is distinguished from multidimensional approaches in that we have more than one representation of constituency. I will call this kind of approach ‘‘multiplanar’’ to distinguish it from the multidimensional approaches. There are two major versions of the multiplaner approach. The Wrst, which I call ‘‘wheel and spoke’’ syntax, involves diVerent constituents (and other relational structures) acting as spokes around a central linearized string of words: (10) words in the sentence planes of syntactic representation This is the approach taken by Autolexical Syntax (Sadock 1991), Role and Reference Grammar (Van Valin 1993, 2003), Pesetsky’s (1999) layers and cascades, and the Simpler Syntax Model (Culicover and JackendoV 2005). The other version of this we might call the ‘‘parallel-structures model.’’ This view of multiplanar structure has the various planes of syntactic structure, including constituent structure(s), developed in parallel and linked to one another by linking rules or related principles. Usually in such a system one of the planes contains the linear order: 194 controversies (11) linking principles syntactic planes We might call this the ‘‘parallel-planes’’ approach. Such a system is at least partly representative of traditional transformational grammar, Hale’s L-syntax model, Curry’s (1961) tecto- and phenogrammatical structures, as well as the Kathol (2000) and Reape’s (1994) implemen- tation of Curry’s distinction in HPSG, and the phase-theoretic version of MP. In this chapter, we will look Wrst at line crossing, multidomination, and multidimensional structures, and consider how they have been used to characterize mismatches between expected syntactic form and linear order; then we turn to multiplanar approaches in both their guises and look at the range of data that these account for. This will in turn lead us into the topic of the last chapter of this book—the contentful nature of categories and nodes in a constituent representation. 10.2 Line crossing and multidomination: axiomatic restrictions on form In Chapter 3, we looked at axiomatization of the basic structural properties of phrase structure trees. In this section, we consider what happens if we relax these axioms or replace them with others. 10.2.1 The non-tangling–exclusivity controversy Let us start with the arguments that we should allow line crossing, and leave multidomination for further discussion below. Recall the data given in (4): (4) (a) John [ VP talked, of course, about politics]. (b) Tom may [ VP be, and everyone is sure Mary is, a genius]. (c) [ NP A man entered who was wearing a black suit]. (d) [ NP Huic ego me bello] ducem proWteor. this I myself war leader announce ‘‘For this war, I announce myself leader’’ multi-structures 195 (e) [ VP Chonaic Sea ´ n an fear]. Saw John the man ‘‘John saw the man.’’ McCawley (1982)5 and Blevins (1990) claim that these kinds of sen- tences all involve trees like (47): () n w y o z m x In (10) some constituent crosses into and appears in the middle of its sister (or in the middle of one of the descendents of its sister). It goes without saying that this kind of tree cannot be represented in bracket notation. Recall the exclusivity condition (A8) from Chapter 3. A8. Exclusivity condition: (8xy 2 N) [((x 0 y) _ (y 0 x)) $:((x 3*y)_ (y 3* x))]. This condition states that if two nodes are in a precedence relation with each other then they may not be in a dominance relation as well. Tree (10) violates condition A8: o is ordered before z, but note that n meets all the conditions for being ordered before o (n sister precedes o). Since precedence is transitive, this means that n precedes z. But this is impossible, since n dominates z, and domination and precedence are mutually exclusive. McCawley6 suggests that such trees should be allowed by weakening the exclusivity condition, so that it is possible for two nodes to be unrelated by either dominance or precedence:7 A8’. Exclusivity condition: (8xy 2 N) [(x 3*y)!:((y 0 x) _ (x 0 y))].8 By doing this, n and o can be unordered with respect to one another (n doesn’t dominate o,andn doesn’t precede o). Therefore, n need not precede its daughter, which was the oVending situation. McCawley also 5 See also McCawley (1989). 6 Blevin’s solution is quite diVerent; we return to it below. 7 McCawley (1982: 93) phrases this as follows: ‘‘[these axioms] do not rule out the possibility of a node x 1 dominating nodes x 2 and x 4 without dominating a node x 3 , where x 2 0 x 3 and x 3 0 x 4 .’’ 8 I give here a slightly altered version of Huck’s (1985) formalization of the axiom, simply because it is more consistent with the notation I use in this chapter. 196 controversies weakens the non-tangling condition (A9’), so that it simply requires that daughter nodes be ordered relative to their mothers. He also adds a condition that ensures that all terminals are ordered (A10) with respect to one another. A9’. Non-tangling condition (McCawley): (8xywz 2 N) [(w 0 x) $ (( (w 3*y)&(x3* z)) ! (y 0 z)))]. A10.(8xy 2 N) [(:9z 2 N) [((x 3*z)_ (y 3* z)) ! ((y 0 z) _ (y 0 x))]]. This is an elegant solution to the problem, but I think McCawley is wrong about this. I believe there are at least two problems with this kind of analysis. First, even if we accept that McCawley is correct about the non-tangling constraint allowing structures such as (12), we have the problem that there is nothing in his system which forces such an order. That is, while the order y 0 o 0 z is allowed, there is nothing in the axioms that requires it. (A10 stipulates that all terminals be ordered, but it does not require that o be ordered before z.) For McCawley such orders are only ever derived transformationally, but it is not at all clear to me why they can not be base generated—as is argued by Blevins (1990). Second, observe that all9 of the constructions in (4) except (4e) involve constructions that today we identify as adjuncts (4a) or adjunctions (4b–d). As we discussed in Chapter 8, recent work on binding and reconstruction (Lebeaux 1988 and Speas 1990 ) have argued that adjuncts and adjunction structures like those in (4) are not present at all levels of representation, so they are not even clearly part of the constituent structure of the sentence10 or, alternately, exist on a distinct geometric plane. This may, in fact, be the eVect of McCawley’s proposal, but then a diVerent set of axioms is needed to force or license linearizations between planes. I do not know of any proposals to this eVect. Huck (1985) has also argued, however, that the non-tangling con- straint must be relaxed for diVerent kinds of constructions. Consider what happens when o is dominated by another node p which itself is ordered after n, as shown by the presence of r, which follows z: 9 See Van Valin (2001: 118) for examples in Serbian and Croatian that are not easily analyzed as adjunction. 10 This of course comes with its own set of problems, not the least of which is that at some levels of representation we will have constituent structures that are unconnected. multi-structures 197 (13) m n p w x y oz r This structure is excluded by McCawley’s versions of the axioms as o is not the sister of n (as it is in 10). However, this appears to be precisely the structure required for cross-serial dependencies such as the Dutch sentence in (14) (Huck 1985: 96) (see also the sentence from Zu ¨ ritu ¨ u ¨ tsh in Ch. 2): (14) . . . dat Jan Marie Piet zag helpen zwemmen. . . . that J. M. P. saw help-inf swim-inf ‘‘that Jan saw Marie help Piet swim.’’ . The structure of this sentence might be something like (15). () S¢ S 1 VP 1 S 2 VP 2 S 3 VP 3 NP 1 NP 2 NP 3 C that N 1 Jan N 2 Marie N 3 Piet V 1 zag V 2 helpen V 3 zwemmen In this sentence, N 1 is correctly linearly ordered with respect to V 1 ,N 2 with V 2 , and N 3 with V 3 . However, N 2 is not correctly ordered with respect to V 1 , because S 2 —which follows V 1 (as shown by the fact that its daughters V 2 and V 3 follow V 1 )—dominates NP 2 . A similar problem is found with NP 3 , but the problem is compounded by the fact that it is ordered before both V 1 and V 2 , in double violation of the non-tangling constraint. A similar example from English is seen in (16) (Huck 1985: 95): 198 controversies (16) Nancy called the fellow up she met at Jimmy’s last night. There are two interlocked discontinuous constituents here (call up and the fellow she met at Jimmy’s last night). In order to account for these kinds of sentence, Huck replaces the exclusivity condition with (A8’’), which he calls the ‘‘inclusivity condition’’. This condition requires that there be either a relation of precedence or dominance or both between any two nodes in the tree. A8’’. Inclusivity condition (Huck): (8xy 2 N) [(( x3*y)_ (y 3* x)) _ ((y 0 x) _ (x 0 y))]. However, he restricts the precedence relation by a revised version of the non-tangling condition based on the dependency or X-bar theoretic notion of head, where nodes may only be ordered in the same order as their heads. A9’’. Non-tangling condition (Huck’s Head-Order Condition): (8xw 2 N) [(w 0 x) $ (Hw 0 Hx)], where Hw ¼ head of w. Chametzky (1995) points out that this condition is of a very diVerent type than the axioms we have previously considered; notice that by referring to heads, it requires reference to syntactic (rather than graph- or set-theoretic) objects. Bunt (1996b) solves this problem by having the condition refer to leftmost daughter instead of head: A9’’’. Non-tangling condition (based on Bunt 1996b11): (8xw 2 N) [(w 0 x) $ (Lw 0 Lx)], where Lw ¼ the leftmost daughter of w. Needless to say, there is something vaguely circular in specifying that there is a condition that speciWes a Wt left to right order of the clause that is deWned in terms of a more basic notion of leftness. All of the approaches described above require that we abandon our notion of a precedence relation deWned in terms of sister precedence. For example, if we adopt a structure allowed by (A9’’’): 11 Bunt’s system is actually recursive rather than axiomatic. He uses a variety of Generalized Phrase Structure Grammar (Discontinuous Phrase Structure Grammar)— see Ch. 4 for more on GPSG. The deWnitions there are suYciently distinct from those here, so I simply recast Bunt’s deWnition of precedence (Bunt 1996b: 73) in axiomatic form here. See the original for a complete set of deWnitions; see also Bunt (1996a). multi-structures 199 . the ‘‘parallel-structures model.’’ This view of multiplanar structure has the various planes of syntactic structure, including constituent structure( s),. subject/agent of the predicate to be happy. A constituent- sharing approach also provides a straightforward an- alysis of non -constituent coordination (see below