Friday, November 21, 2014

The 2nd Hilbert Question: Barbara Citko on Diagnostics for Multidominance

What are the Diagnostics of a Multidominant Structure?
Multidominant structures (doubly rooted structures of the kind given in (1)) have been invoked as a solution to a number of both empirical and theoretical puzzles.

(1)    XP          YP
                       /       \       /        \
    X           ZP           Y

The idea that such structures exist spans several decades and frameworks, going back at least to the seventies and the work of Sampson (1975) on raising and control and Williams (1978) on Across-the-Board wh-questions. Since then, many different mechanisms have been proposed to generate such structures, including (but not limited to): factorization of Williams (1978), Parallel Merge of Citko (2005), behindance-Merge of De Vries 2005, grafting of Van Riemsdijk (2000, 2006a,b), banyan trees of Svenonius (2005), sharing of Gračanin-Yuksek (2007), union of phrase markers of Goodall (1987), node contraction of Chen-Main (2006) and tree linking of Gärtner (2002). Interestingly, while the issue of linearization and interpretation of multidominant structures has received a fair amount of attention in the literature, the very fundamental issue of how to diagnose a multidominant structure has not. We have reliable ways to diagnose A versus A-bar positions, heads versus phrases, specifiers versus complements, covert versus overt movement; what still seems to be lacking is an adequate diagnostic (or set of diagnostics) of multidominance, something akin to crossover as a diagnostic of A-bar dependencies.   

The landscape of multidominance is quite diverse and includes both coordinate and non-coordinate structures, as evidenced by the far from complete list of constructions (coordinate ones in (2) and non-coordinate ones in (3)) that have been analyzed in a multidominant fashion. For the purpose of the question of how to diagnose multidominance, it is immaterial whether a multidominant analysis is the correct one for all of them or just a subset thereof; all that matters is that the grammar allows such structures. Simply put, if they exist, we need to know how to find them.
(2)  a.   Across-the-board wh-questions (Williams 1978, Goodall 1987, Citko 2005,
2011, De Vries 2009, among others)
b.         Right Node Raising (Citko 2011, McCawley 1982, Goodall 1987, Wilder 1999, De Vries 2009, Kluck 2009, Johnson 2007, among many, many others)
            c.         gapping (and determiner sharing) (Kasai 2007, Citko 2006, 2011, 2012)
d.         Questions with coordinated wh-pronouns (Gracanin-Yuksek 2007, Citko 2013,
Citko and Gracanin-Yuksek 2013, among others)
(3)        a.         Serial verb constructions (Hiraiwa and Bodomo 2008)
b.         Free relatives (Haider 1988, Citko 2000, Van Riemsdijk 1998, 2000, 2006)
c.         Parasitic Gaps (Kasai 2007)
d.         Amalgams (De Vries 2013)
e.         Parentheticals (McCawley 1982, De Vries 2005)  
f.          Appositives (McCawley 1982, Heringa 2009)
g.         Comparatives (Moltmann 1992)
h.         Discontinuous idioms (Svenonius 2005)
i.          movement in general (Chomsky 2004, Gärtner 2002, among others)
A natural way to proceed in the search for a reliable multidominant diagnostic (or set of diagnostics) is to ask what property (or set of properties) characterizes these constructions to the exclusion of others. Let us thus look at some that at various times been associated with multidominance. Intuitively, coordination might seem like a plausible candidate. After all, the two conjuncts in a coordinate structure are parallel. Thus perhaps multidominance is a way to capture this parallelism. However, it is clear that it cannot be one due to the simple the fact that there do exist non-coordinate multidominant structures, i.e. the ones given in (3). Likewise, ellipsis cannot be the right diagnostic, in spite of the intuitive appeal of the idea that perhaps what (some) cases of ellipsis involve is the non-pronunciation of one occurrence of the multiply dominated element. While movement is sometimes analyzed in a multidominant fashion, not all of the constructions in (2-3) involve movement. Similarly, while parentheticals of various types (appositives, amalgams) have been claimed to involve multidominance, there exist enough multidominant yet non-parenthetical constructions to be doubtful of a one-to-one correlation between the two.
What the multidominant constructions listed in (2-3) seem to have in common is the idea (or intuition) that a single element has to simultaneously fulfill the requirements imposed on it by the two elements between which it is shared. In other words, it has to match them in some relevant sense. If so, could matching be a diagnostic we are after? In order to answer this question, we need to further ask what kind of matching multidominant structures require, and what kinds of mismatches they tolerate (if they tolerate mismatches at all). If we limit our attention to constructions in which a nominal element is shared between two nodes, the question becomes whether this shared nominal has to match both in morphological case, Abstract case, thematic role, or (relative) thematic prominence. Logically speaking, mismatches could be due to syncretism effects, proximity effects (or the reverse, anti-proximity effects) or hierarchy effects. The ameliorating effects of case syncretism have been documented pretty well in the relevant literature. However, it is not the case that mismatches due to factors other than syncretism are never tolerated. Citko (2011), for example, points out that in Polish ATB wh-questions tolerate mismatches only with syncretic forms, whereas Right Node Raising tolerate mismatches that suggest proximity is at issue, as shown by the contrast between the ATB question in (4a) and the RNR construction in (5b). In both of them, the verbs inside the two conjuncts impose different case requirements on their objects: the verb lubić ‘like’ requires accusative case whereas the verb ufać ‘trust’ requires dative case. Furthermore, in both of them the object of these two verbs (bolded in (4a-b)) is shared between the two clauses. Interestingly, in the ATB case, neither the accusative nor the dative form of the shared (fronted) wh-pronoun yields a grammatical result, whereas in the RNR case, the dative form of the shared object is possible.
(4) a.         *Kogo/*komu                   Jan       lubi     a           Maria  ufa? [Polish]                         
who.acc/who.dat      Jan       likes       and      Maria  trusts
            ‘Who does Jan like and Maria trust?’                                                  atb question
      b.   Jan       lubi       a     Maria ufa      tej          koleżance/*tȩ koleżankȩ z pracy.                 
Jan       likes     and Maria trusts   this.dat friend.dat/this friend.acc from work
‘Jan liked and everyone avoided this friend from work.’                RNR
The fact that not all multidominant constructions are subject to the same kind of case matching requirement casts doubt on the correlation between multidominance and matching, and, consequently, on matching as a multidominance diagnostic. Thus, the search for a reliable diagnostic of a multidominant structure continues.

Chen-Main, Joan. 2006. On the Generation and Linearization of Multi-Dominance Structures. Ph.D. dissertation, Johns Hopkins University.
Chomsky, Noam. 2004. ‘Beyond Explanatory Adequacy.’ In Structures and Beyond: The Cartography of Syntactic Structures, ed. by A. Belletti, 104-131. Oxford: Oxford University Press.
Citko, Barbara. 2000. Parallel Merge and the Syntax of Free Relatives. Ph.D. thesis. Stony Brook University.
Citko, Barbara. 2005. On the Nature of Merge: External Merge, External Merge, and Parallel Merge,” Linguistic Inquiry 36: 475497.
Citko, Barbara. 2011. Symmetry in Syntax: Merge, Move and Labels. Cambridge: CUP. 
Citko, Barbara. 2012. ‘A Parallel Merge Solution to the Merchant/Johnson Paradox,’ In Ways of Structure Building, ed. by M. Uribe-Etxebarria and V. Valmala. Oxford: Oxford University Press.
Citko, Barbara. 2013. ‘The Puzzles of Wh-Questions with Coordinated Wh-Pronouns,’ In Principles of Linearization, ed. by T. Biberaurer and I. Roberts. Berlin: Mouton de Gruyter.
Citko, Barbara and Martina Gračanin-Yuksek. 2013. ‘Towards a New Typology of Wh-Questions with Coordinated Wh-Pronouns.’ Journal of Linguistics 49-1-32.
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Haider, Hubert 1988. ‘Matching Projections.’ In Constituent Structure: Papers from the 1987 GLOW Conference, ed. by A. Cardinaletti, G. Cinque and G. Giusti, 101-123. Dordrecht: Foris.
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Johnson, Kyle.  2007. ‘LCA+Alignment=RNR,’ Handout of a talk presented at the Workshop on Coordination, Subordination and Ellipsis, Tubingen, June 2007.
Kasai, Hironobu. 2007. Multidominance in Syntax. PhD thesis, Harvard University.
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Moltmann, Frederike. 1992. Coordination and comparatives. Ph.D. thesis. MIT.
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Riemsdijk, Henk van 2000. ‘Free relatives inside out: transparent free relatives as grafts.’ Proceedings of the 8th Annual Conference of the Polish Association for the Study of English.
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Riemsdijk, Henk van 2006b. Grafts Follow from Merge.’ in Frascarelli (ed.), pp. 1744.
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  1. I'd like to amend your question with some technical observiations. This post got way longer than I anticipated and meanders quite a little bit, so if you want to get the overall gist just go down all the way to the last paragraph.

    The implicit assumption is that multi-dominant structures can be distinguished from traces or copies with chain formation, yet all formal results on this issue point in the other direction. Marcus Kracht's 2001 L&P paper showed in great detail that the three representation formats are interchangeable. This can also be seen with MGs, where all information is already present in the derivation trees --- which have neither chains, nor copies, nor multi-dominance arcs --- and the mapping to the desired type of phrase structure tree can be switched in and out as one sees fit.

    I don't mean to imply that these technical results render the problem vacuous, but they show that the way we formulate this Hilbert question needs to be sharpened. Here's two issues that detractors could raise:

    1) Why not be 100% multi-dominant?
    The Hilbert question as stated is about multi-dominant (MD) structures in an otherwise non-MD theory. So the first question is, is there any reason to have a non-MD theory in the first place? Kracht's result show us that there isn't, but there are reasons to prefer MD over copies, mostly related to space usage --- programming languages, for example, share identical objects where possible in order to save memory. So shouldn't the question rather be, what are tests for non-md status?

    2) What are your parameters? Why should those be the right parameters?
    The whole driving point of the MD literature is that an MD structure behaves differently (or at least seems to) from a non-MD structure in their assumed theory, which operates with specific definitions of c-command, constituency, locality domains, and so on. But it's unclear why these parameters should have to be fixed, and if so, how the Hilbert question could be turned into a concrete research program given the lack of consensus when it comes to technical details. Minor differences in the definition of c-command (e.g. lowest dominating node VS all dominating nodes) give very different results in MD-structures.

    In my opinion, the issue you worry about is completely independent of MD, and adding it to the picture only muddies the water. You ask whether there are tests to identify MD-structures, but that is a little bit like asking whether there are tests to identify the arrows in the lines of a Feynman diagram. MD is a technical analysis, it is not a term refering to specific constructions. I'm sure that this point is completely obvious to you and you're using the style of analysis as a shorthand for the empirical objects the analysis is applied to. The reason I point out this duality, though, is that only certain phenomena seem natural candidates for an MD-analysis. So I would say a more direct paraphrase of your Hilbert question is the following:

    - Is there a property P that all the structures that are analyzed in MD-terms have in common?
    - If so, how can we express P in a fashion that is independent of the specifics of the formalism?
    - Finally, is there representation format that allows for a more succinct formulation of P?

    PS: Sorry for the necro, the last few weeks have been very busy but I'm slowly working my way backwards through all the posts I missed.

    1. From my reading of the multi-dominance (MD) literature, what does most of the work is not the MD assumption but a further assumption about how MD structures can be derived. In particular, the assumption that the structure in (1) above is derivable by simultaneously merging ZP with X and Y. In other words, ZP is not FIRST merged with X (say) and then merged with Y but is merged in ONE step with BOTH. This distinguishes MD approaches to RNR, for example, with Nunes style sidewards movement analysis. What's the reason for this? Mainly, I believe, to allow such derivations to escape island constraints. The evidence seems to be that RNR, for example, is not subject to bounding effects, which would be odd if this were a species of movement. So, here's a question for you Thomas: does Kracht's formulation of copies vs MDs have anything to say about the derivational history of these structures? And if it does can it distinguish between those MDs which are products of Movment and this that are products of Merge? This is what is required. The issue has been case as a question of MD vs copy, but I suspect that there is at least one more dimension to the problem: "copies" via merge or via move? If one wants simultaneous merge then it looks like one will want MD (or MD seems very natural). And that's what I believe is driving a lot of the discussion. Is this right Barbara?

      One more question once I'm at it: how do structures like (1) translate into BPS. It can't be something like {a,[b},x] ('[' used to disambiguate the brackets) as this makes not set theoretical sense. So is it {a,b} {b,x}? If so, then if one allows sidewards movement, this will be structurally indistinguishable from a Nunes style derivation. The issue really coming down to a question of derivational history not derived object.

    2. I think this is once again an instance of 2: the MD derivation via simultaneous Merge yields certain effects given certain assumptions. You can get those effects in a variety of ways without a simultaneous Merge representation. Your second paragraph already points in this direction: we can simply model these cases with sideward movement, and as long as we distinguish these cases from Nunes' sideward movement, the two can be made to behave differently. We could even go meta-derivational and have a non-MD derivation tree that produces an MD-derivation tree that then produces an output structure. Only if you fix certain parameters of the theory do these emulation strategies become difficult or impossible, and Kracht does not fix these parameters.

      You might object now that the emulation strategy makes the theory less elegant, but that's actually not obvious because it solves e.g. the BPS problem you notice right away. But I really don't want to argue that point in great detail because I think that's exactly the wrong way to approach the issue: MD structures are not the object of interest, it's the phenomena that are analyzed in those terms. They seem to have some property that makes them particularly amenable to such an analysis, so we need to figure out what that property is (or develop a convincing argument that the phenomena above are just a historical accident of the development of the field because every random sample of phenomena can be made to form a natural MD-class). Discussing how MD structures can be reencoded without multi-dominance doesn't strike me as particulary fruitful because there is just way too much wiggle room.

    3. @Thomas:
      this may surprise you, but I agree. I just wanted to point out what I took to actually like behind Barbara's MD proposal. I have no doubt that we can arrange things so that things work out. The question is what makes the two different kinds of cases tick. I also wanted to observe, and you have verified my hunch, that I don't think that the Kracht stuff was actually particularly relevant. Thx.

  2. I am confused by something. If (3i) is part of the game -- that is, the assumption that literally every movement operation results in multidominance (let's add Zhang 2004 to the list of references, btw) -- then I'm not sure there's anything that wouldn't fall under the heading of a "multidominance structure." For one thing, it is not completely clear that there is a single linguistic utterance where literally every single sub-constituent remains in situ (maybe certain fragment answers?). And even if there is, the question of how to identify a "multidominance structure" becomes very close to the question of how to identify a "structure in which movement has occurred."

    So if the Hilbert Question is along the lines of "is (3i) correct?" (i.e., does every movement operation result in multidominance), then I understand the question. (Though the answer might still be something like, "it's a notational choice" -- see the discussion above -- though the details of that discussion are above my pay grade.)

    But if the Hilbert Question is "how do we diagnose multidominance given that something like (3i) is true, then I guess I just don't understand the question.