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1 1 Resource Sensitivity in the Syntax-Semantics Interface and the German Split NP Construction Jonas Kuhn 1.1 Introduction The split NP (or split topicalization) construction of German (henceforth SNP) has received much attention in the literature, as a challenge for syntactic accounts of argument selection and of unbounded dependency constructions (Bayer 1987 van Riemsdijk 1989 Fanselow 1988 Fanselow 1993 Haider 1990 Hinrichs and Nakazawa 1994) and in the discussion of the semantic status of indenites (Diesing 1992 van Geenhoven 1996). 1 In this construction, the descriptive material about one underlying argument is not conned to a single NP as normal, but is spread over two nominal constituents: (1.1) B cher sieht Anna drei books sees Anna three `As for books, Anna can see three.' In terms of morphological marking of declension class (and similarly determiner selection), the two constituents behave like autonomous complete NPs (cf. the form of kein in (1.2a) vs. in (1.2b)), i.e., the lower NP, appearing in the German Mittelfeld, has the same form as elliptical NPs (1.2c). 1 I'd like to thank Judith Berman, Miriam Butt, Mary Dalrymple, Stefanie Dipper, Martin Emele, Christian Fortmann, Anette Frank, John Fry, Christian Rohrer, three anonymous reviewers and the audience at the ESSLLI 98 workshop in Saarbr cken for comments and discussion. Parts of this chapter (1.2, 1.3.1, 1.3.3, and 1.5) are revised sections of (Kuhn to appear). 1

2 2 / Jonas Kuhn (1.2) (van Riemsdijk 1989, p. 109, ex. (11)) a. Ein Schwimmbad hat er sich noch keins/*kein gebaut. a pool has he refl yet none/no built `As for a swimming pool, he hasn't yet built one.' b. Er hat sich noch*keins/kein Schwimmbad gebaut. `He hasn't yet built a swimming pool.' c. Er hat sich nochkeins gebaut. `He hasn't yet built one.' The SNP construction constitutes a problem in view of the widely assumed grammatical principle that the syntactic complement phrases of a head stand in a one-to-one correspondence to argument slots in an underlying conceptual representationformulated e.g. as the Theta Criterion of Government-and-Binding Theory (GB) and as Biuniqueness within LFG. In SNP apparently two NPs can realize a single underlying argument. 2 In previous accounts, dierent strategies have been pursued to avoid the problem, keeping up the Theta Criterion: van Riemsdijk (1989) argues for a movement accountthe NP in the topic position is a preposed part of the remnant NP in the Mittelfeld. The unexpected morphological autonomy of the two NPs is explained by positing that under certain circumstances, non-maximal projections that have been moved can regenerate some amount of structure to meet X-bar requirements applying at S-structure. Fanselow (1988) and Haider (1990) analyze both NPs as base-generated, but only the one in the Mittelfeld as an argument NP bearing a theta role the other phrase is a nonargument (semantically a predicate), further restricting the Mittelfeld NP through some mechanism of coindexation. Being a non-argument, it moves to the topic position. Van Geenhoven (1996) assumes both parts of SNP to be base-generated in the Mittelfeld as indenites of the semantic type of a property the referent that they restrict and that lls the argument slot is provided lexically by the verb, i.e., the NPs are semantically incorporated. Hinrichs and Nakazawa (1994) propose an analysis in Head-Driven Phrase Structure Grammar (HPSG), positing a construction-specic lexical rule. I'd like to argue that these accounts make unnecessary assumptions of some extra devices to deal with SNP and/or fail to explain the striking 2 Jackendo (1990, sec. 3.1) discusses two ways in which the Theta Criterion is empirically inadequate: (i) there are cases where an NP has more than one theta-role, and (ii) there are cases where multiple NPs hold a single theta-role. The English examples he cites for the latter case, referring to (Gruber 1965) and to talks by Richard Carter (1984), include The box has books in it and Bill carried some books with him. In the further discussion however, Jackendo says little more about the (ii) cases.

3 Resource Sensitivity and the Split NP Construction / 3 parallelism of the Mittelfeld NP and elliptical NPs. The recent version of Lexical-Functional Grammar (LFG) with a resource sensitive (linear logic-based) approach to semantic composition (cf. Dalrymple, Lamping, Pereira, and Saraswat 1997, henceforth DLPS97) provides the basis for an explanatory account without stipulation of construction-specic devices. In the semantic analysis of SNP, I assume that the Mittelfeld NP behaves like an elliptical NPs in that it picks up anaphorically the propertyintroduced by the topic NP. 3 Largely independent of the anaphorical relationship at the level of semantics, the two NPs behave as follows at the syntactic levels: at functional (f-)structure, both NPs are mapped to the same grammatical function (thus, one can speak of a unication analysis), contributing to the same argument slot in the underlying representation of the main predicate whereas locally at constituent (c-) structure, each of the NPs 4 has to independently satisfy constraints on determiner selection etc. The main objective of this paper is to motivate this particular division of labour in the architecture of grammar, assuming dierent formal devices to model the constraints on dierent structural levels. This methodology is fully in the LFG tradition, as well as central aspects of the unication analysis are. In a few details however, I'll argue either for modications of standard LFG assumptions containing redundancy, or for (conservative) extensions of an existing theory to cover a new type of data. In arguing for the division of labour, I will address resource-(in-)sensitivity of argument selection at the various structural levels. It should be noted that for the architectural point that I'd like to make, only certain aspects of each level are relevant. Iwillpoint out which aspects I think these are, and also whyitake other aspects to be orthogonal. The presentation of these orthogonal aspects follows practical considerations of simplicity rather than high standards of theoretical depth. In sec. 1.2, I give anoverview of the main empirical data discussed in the literature. Sec. 1.3 addresses the syntactic unication account in the LFG setting, and its implications for the character of the syntactic constraints. After briey introducing linear logic-based LFG semantics, sec. 1.4 presents the approach to semantic construction in SNP. Having presented myown account, I will discuss the mentioned approaches from the literature in some more detail (sec. 1.5), before concluding in sec Following (van Geenhoven 1996) I assume that under particular circumstances of semantic incorporation, indenites can denote just a property. 4 For simplicity, I will be using the label NP to refer to a maximal nominal projection, whenever internal details are irrelevant as will become clear in sec , the label DP would be more precise technically.

4 4 / Jonas Kuhn 1.2 Properties of the Split NP construction In addition to the morphological autonomy of the nominal projections involved in SNP, discussed already in the introduction, the following properties have been observed (for an extensive discussion, see van Riemsdijk 1989 this section is entirely based on his data): Determiner selection. Each of the two NPs has to locally satsify restrictions on determiner selection, i.e., a singular count noun is illformed without a determiner (1.3). (1.3) *(einen) neuen Wagen kann er sich noch keinen leisten a.acc new.acc car can he re yet none.acc aord `As for a new car, he can't aord one yet.' Agreement. The two NPs agree in number (and case and gender): Other than in the `as for... ' paraphrase in English, the SNP construction is ungrammatical when a mismatch in number occurs (1.4). (1.4) Ein Buch/*B cher ist erst eins von ihm erschienen a book/books has only one by him appeared `As for books, only one by him has appeared yet.' Indeniteness. The topic NP must be non-quanticational (cf. the ungrammatical manche `some' in (1.5)). Some dialects allow only a bare plural (like in (1.1)), others alternatively allow a singular indenite (cf. (1.4)). (1.5) (*Manche) some H user houses habe ich auch noch kleinere gesehen. have I also even smaller (ones) seen. Topic position. Other than in the oating quantier construction (1.6a), the higher NP in SNP is structurally conned to the (preverbal) topic position: (1.6b) is infelicitous. 5 (1.6) a. Er hat die Zigaretten gestern alle vier geraucht. he has the cigarettes yesterday all four smoked `Yesterday, he has smoked all four cigarettes.' b. *Er he hat has einen a Wagen sich car refl noch never nie before einen one leisten aord k nnen. been-able-to 5 Van Geenhoven (1996, p. 24, fn. 5) points out that example (i) (attributed to Fanselow, p.c.) shows that verb-nal (embedded) clauses may also contain SNP (note however that in this sentence, B cher needs to be pronounced with the prosodic characteristics of a topic: a rising pitch accent). (i)...weil...because man one B cher books damals then in to den the Osten East keine none mitbringen bring durfte was-allowed-to `because in the past it was not allowed to take books to East Germany. '

5 Resource Sensitivity and the Split NP Construction / 5 Headless remnant. The NP in the Mittelfeld may not contain an overt nominal head (1.7). 6 (1.7) *B cher books hat er noch keine Romane geschrieben. has he yet no novels written. Unbounded dependency. The standard diagnostics for an unbounded dependency construction apply (for instance, extraction out of a whclause is impossible: (1.8b)). (1.8) a. Unbesch digte undamaged auf in Vorrat stock habe. have b. *Unbesch digte undamaged Vorrat stock hat. has Exemplare copies glaube ich, da ich nur noch zwei believe I, that I only still two Exemplare wollte er wissen, wer noch zwei auf copies wanted he to-know who still two in VP topicalization. SNP can be part of (partial) VP topicalization: In (1.9), the (usually sentence-nal) participle appears in topicalized position, together with an indenite argument NP, and another NP realizing the same argument slot is left in the Mittelfeld. 7 (1.9) [Einen a Wagen gekauft] hat er sich noch car bought has he refl yet `As for cars, he has not yet bought one.' keinen. none 6 Fanselow (1993, 63) cites (i) (attributed to Santorini, p.c.) as a counterexample to this. To me, examples of this type are marginal, and I'd propose that their acceptability is due to a performance strategy dealing with duplication eects (cf. also fn. 35 below). (i) Raubv gel glaube ich kennt Gereon nur Bussarde. birds-of-prey believe I knows Gereon only buzzards `As for birds of prey, I believe that Gereon knows only buzzards.' 7 A further property van Riemsdijk (1989) discusses is the fact that restrictions on the serialization of multiple adjectives bear over to the split NP situation suggesting that the topic NP has to be reinserted into the remnant NP for checking this condition (examples (i)-(ii)). However, since very little is known about the formal character of this restriction, it is not unlikely that it applies on a more semantic level of representation, not requiring that there be some congurational level with a single unsplit NP. (i) a. ein neues amerikanisches Auto `a new American car' b. * ein amerikanisches neues Auto (ii) a. Ein amerikanisches Auto kann ich mir kein neues leisten. `As for an American car, I cannot aord a new one.' b. * Ein neues Auto kann ich mir kein amerikanisches leisten.

6 6 / Jonas Kuhn 1.3 Syntactic Analysis The architecture of LFG with its system of correspondence between parallel structuresconstituent (c-)structure, functional (f-)structure, argument (a-)structure and semantic structureturns out to provide the means for an explanatory analysis of the SNP construction that need not stipulate any construction-specic mechanisms. In subsection 1.3.1, I will present the core idea of the syntactic analysis, which centers on the mapping from c-structure to f-structure. This analysis has some implications for the character of c-structure and f- structure one has to assume. In the subsections and 1.3.3, I will address these issues and argue that the specic assumptions are fully compatible with independently developed recent LFG theories Unication in mapping from c-structure to f-structure The starting point for my analysis is the observation that on a low level, both parts of the SNP behave like autonomous NPs: the topic part has to satisfy standard requirements for determiner selection (singular mass nouns can stand without a determiner, while count nouns can't) the Mittelfeld NP surfaces exactly like an elliptical NP both parts must independently meet constraints on declension class. 8 This behaviour is precisely predicted under two independently established assumptions about the mapping from c-structure to f-structure: (1.10) In German, the same grammatical function can be assigned in different c-structure positions. (1.11) Under certain circumstances, more than one c-structure constituent can simultaneously contribute to the same grammatical function. Assumption (1.11) underlies, e.g., the unication analysis of clitic doubling by Andrews (1990). The conditions for compatibility in SNP will be discussed in detail in sec below. In the following, I will motivate assumption (1.10) and illustrate the basic SNP analysis. According to LFG theory, in a case-marking language like German the functional annotations in c-structure rules are underspecied as to the exact grammatical function (e.g., subj or obj) an NP bears not the congurational position, but case and agreement principles are decisive for function specication (cf. e.g., Bresnan 1996, 17 Bresnan 1995, ch. 5 Bresnan 1998 Berman 1998). Thus, on the basis of c-structure rules and case principles, an NP bearing a particular function (say, obj) can occur in dierent congurational positionse.g., in the Mittelfeld or in the preverbal position. Moreover, since the annotations are conned to 8 I will come back to the question which type of constraints regulate these NP-local restrictions in sec

7 Resource Sensitivity and the Split NP Construction / 7 local trees, nothing prevents the simultaneous occurrence of obj NPs in both these positions (provided their f-structures are compatible). The general mechanism of functional specication just laid out can be eshed out in dierent ways, the details of which are orthogonal to the matter of this chapter. One way to think of the case and agreement principles is as some kind of meta-constraints on the f-annotations of c-structure rules, like for example the functional specication for subj stated informally in (1.12) (cf. Bresnan 1995, ch. 5). (1.12) NP: (#case)=nom ^ ("subj agr)=(#agr) ) ("subj)=# Principle (1.12) says that if an NP is morphologically marked as nominative and agrees with the verb under which it is f-structurally embedded, then the grammatical function it bears is subj. Another possibility would be to follow Nordlinger's (1997) constructive case approach, according to which in languages with morphologically controlled functional specication, the case morphology comes with an inside-out designator (e.g., (obj ") for accusative case) specifying under which grammatical function the marked NP mustbeembedded. To avoid unneccessary complications in the following, I will present fully specied functional annotations in the c-structure trees, above the category symbols. If one assumes one of the mentioned generalized accounts, these annotations should not be seen as rule-specic stipulations, but the result of applying general morphological principles to underspeci- ed annotations (which again follow from an X-bar based general scheme of rule annotation, cf. (Bresnan 1995, ch. 5)). The general idea of the unication-based SNP analysis is illustrated by the simplied c-structure and f-structure analysis of (1.13) given in g (1.13) Einen Frosch sah er einen kleinen. a.acc frog saw he.nom a.acc small.acc `As for frogs, he could see a small one.' The NP nodes for einen Frosch and einen kleinen are both mapped to the same f-structure, as the obj of the verb sehen. 10 C-structurally, both NPs are treated as autonomous canonical NPs, under independent application of local constraints on determiner selection and morpholog- 9 The arrows (" and #) in the functional annotations (which interact to constrain the construction of the f-structure) are metavariables " refers to the f-structure projected from the mother node, # refers to the f-structure projected from the node itself. For more background information on the mechanisms of standard LFG, the reader is referred to the articles in (Dalrymple et al. 1995). 10 Since the merging of two constituents as a single underlying argument is captured by unication at the level of f-structure already, we can ignore the LFG level of argument (a-)structure in this study.

8 8 / Jonas Kuhn CP ("comp* obj)=# "=# NP C 0 H H einen Frosch "=# "=# C VP pred subj obj sah ("subj)=# ("obj)=# NP NP er `sehenhsubj obji' pred `er' 2 pred `Frosch' 4 spec adjuncts ein pred `klein' H H einen kleinen FIGURE 1 Unication analysis of (1.13) ical marking (declension class) to be discussed in sec Furthermore, the unbounded dependency behaviour of the construction is directly predicted, since the topic part is interrelated with its functional source by the same functional uncertainty equations (in g. 1, the optional comp* path for an embedded obj function) as in the standard case, where no Mittelfeld argument doubles its grammatical function. A relevant example would be (1.14), with f-structure analysis (1.15). (1.14) Einen Frosch glaube ich, da er einen kleinen sah. a.acc frog believe I that he.nom a.acc small.acc saw `As for frogs, I believe he could see a small one.' 2 pred `glaubenhsubj compi' 6 subj 6 pred 2 `ich' 6 pred `sehenhsubj obji' 6 (1.15) 6 6 subj 6 6 pred 2 `er' 6 6 comp 6 pred `Frosch' obj 4 spec ein adjuncts pred `klein' The unication analysis also carries over directly to the (partial) VP topicalization cases such as(1.9) like NPs, VPs can be introduced to the f-structure from dierent c-structure positions, provided their f-structures can be unied (i.e., if also f-structures embedded in their f-structuressay, under objcan be unied). So the SNP contained in (partial) VP topicalization is reduced to the same conditions as the stand-alone SNP

9 Resource Sensitivity and the Split NP Construction / Local categorial structure The above discussion of SNP assumed that the observed independence of the two NPs in terms of determiner selection and declension class can be captured at a local (i.e., pre-f-structure) level: if f-structure were involved to control, e.g., determiner selection, the unication account would predict that a single determiner could full the requirements of both NPsin one case locally, in the other case non-locally through uni- cation. The data contradict this prediction: (1.3) is ill-formed without a determiner. 11 This means that the classical LFG analysis of NPs, where the determiner and the noun simply map their contribution to the same f- structure and there is no more ne-grained distinction at the level of c-structure, has to be modied. However, taking into account more recent theories of c-structure regularities, the observed behaviour is not at all unexpected: Bresnan (1998, sec. 6.2) dispenses with the view of LFG category labels as simple, unanalyzed symbols, and introduces a feature system to classify category labels, drawing upon (and extending) concepts and ideas well-known from the generative literature: X-bar theory, lexical categorial features, the lexical/functional distinction. 12 The determiner and declension class requirements within NPs have often been regarded as intimately connected with conditions on functional completion of the lexical category NP as a DP (cf. e.g. in the constraint-based setting Netter's (1993) DP analysis in HPSG). One (Netter-style) way to put the requirement of a determiner with singular count nouns in the category format of recent LFG would be the following: (i) only functional projections (i.e., DPs) are allowed in argument position (e.g., with verbs) and (ii) singular count nouns are lexically 11 In certain dialects, examples like (i), with a determiner-less singular count noun, are reported to be acceptable (cf. Fanselow 1988, 103). (i) Hemd tr gt er keines. shirt wears he none `As for a shirt, he doesn't wear one.' However, to account for the standard German data, a local explanation is indispensable the (i) data on the other hand can just as well be explained in a local account: in these dialects, there is no strict syntactic requirement of a determiner, not even with singular count nouns. Thus, when the semantics doesn't make a determiner necessary (i.e., in cases where the singular indenite denotes a property, as I will argue below in sec. 1.4), we can nd a bare singular count noun. 12 Formally, such a categorial feature system can be captured by a GPSG-style multiplication of c-structure rules, since the values are atomic and the set of possible values is nite. The LFG implementation of the Xerox Linguistic Environment(XLE) provides this mechanism of complex category symbols, which has been used successfully for generalizations over rules in the Parallel Grammar Development project (Kuhn 1998).

10 10 / Jonas Kuhn marked as non-functional (whereas plurals and mass nouns are optionally marked as functionalor possibly underspecied). The eect is thatindependently of the question whether there are any other nominal projections contributing to the same grammatical function in the sentenceeach singular count noun has to go together with a determiner else, the analysis would fail already at the level of c-structure. 13 Note furthermore, that with this purely syntactic and very local account of determiner selection with singular count nouns, we expect there to be determiners even in situations where they wouldn't be required semantically. One situation where no determiner is semantically required is when an indenite NP is used to denote a mere property (without introducing and quantifying over a variable) as I will argue at length in sec. 1.4, the topic part of SNP is exactly such a property-denoting indenite. 14 And indeed we nd the indenite article ein(en) to be obligatory with singular count nouns in the topic NP of the SNP construction: example (1.3)which we can now explain as an eect of the local syntactic constraints just laid out. 15 This observation about the occurrence of the determiner ein is quite revealing about its semantic status. As we just saw, there is at least one usage in which ein occurs for purely syntactic reasons (as a default determiner), and is semantically empty. It is not strictly compelling to assume a second, semantic, version of ein to account for the use in existential NPs: bare plurals and mass nouns can have an existential reading without there being an overt determiner, so some other device has to be assumed anyway. Dynamic semantic theories such as Discourse Representation Theory (DRT Kamp and Reyle 1993) explain the existential interpretation indenites to be a discourse level eect rather than a lexical one. In the exposition of a linear logic-based semantics for SNP in sec. 1.4 below, I will nevertheless follow anestablished generalizedquantier analysis of the semantic variant of the indenite article to 13 Another way to express the pre-f-structure constraints, which is equally feasible for the present purposes, and which is also independently motivated, would be the assumption of a special projection level distinct from f-structure, projected locally from c-structure (cf. the so-called m(orphological)-structure of (Butt, Ni o, and Segond 1996 Butt, Fortmann, and Rohrer 1996)). 14 Another context where according to (Zimmermann 1993) we can nd propertydenoting NPs is as the (de dicto) object of intensional verbs like seek: (i) Hans Hans sucht seeks ein a Einhorn. unicorn 15 Note that using the plural in the topic NP instead, (which does not come with the syntactic requirement of a determiner) is no viable alternative, since the number feature does get projected to f-structure, and thus must unify with the partner NP in SNP (cf. example (1.4)).

11 Resource Sensitivity and the Split NP Construction / 11 avoid additional complications of this heavily formal section this forces me to assume an extra lexical entry for the syntactically triggered ein discussed in the present section. Consequently, as an example the two occurrences of ein(en) in (1.13) have to be analyzed as two dierent readings. A dynamic reconstruction of the account should be able to do with just a single entry for ein. Summing up this subsection on local syntactic constraints in SNP: Even though I could not go into much detail as to the exact c-structure constraints regulating local restrictions in German nominal projections, I hope the character of such constraints has become clear. For the overall picture that arises we can note that the SNP data support a division of labour between local c-structure constraints on the one hand, formulated using categorial features with a limited expressive power (they can be compiled out as a context-free grammar) and independent unication at f-structure on the other hand The role of pred values Coming back to f-structure, the general idea of the unication analysis outlined in sec is fairly straightforward. However, it remains to be shown that there are independent principles constraining the mechanism inaway that explains the data. 16 Given the mechanism of f-structure unicationwhy cannot simply any canoncial NP dissociate and spread its contribution to the sentence over various c-structure NPs? The constraints on morphological marking following from autonomy ofthenps at the level of c-structure do not explain the indeniteness and topichood restrictions observed in sec. 1.2 moreover the question arises whether assumption (1.11) from abovethat the f-structures of the two NPsin SNP unifyis tenable without an undermining of the key concepts regulating subcategorization in LFG. Classically, a central role of f-structure is to constrain the great freedom at c-structure (especially in non-congurational languagescf. assumption (1.10) above), by excluding that two canonical NPs are assigned the same grammatical function. This is achieved by functional uniqueness (which disallows two distinct appearences of the same grammatical function within a single f-structure), combined with the fact that the pred values of the NPs will fail to unify. Even if the pred values are of the same form, standard LFG interprets them as instantiated symbols, i.e., as semantically distinct from any other symbol (Kaplan and 16 It would be certainly possible to explicitly state restrictions on the rules that ensure the empirical generalizationsimilarly as in the lexical rule of (Hinrichs and Nakazawa 1994)but as will be shown, these restrictions follow from independent properties of the elements involved.

12 12 / Jonas Kuhn Bresnan 1995, 77). Doubling of a functionas in the ungrammatical example (1.16)is thus ruled out as shown in g. 2. (1.16) *den Peter sieht der Karl den Peter. the.acc Peter sees the.nom Karl the.acc Peter. ("...obj)=#... ("obj)=# NP NP DET N DET N ("pred)=`peter' 27 ("pred)=`peter' pred `sehenhsubj obji' subj pred `Karl' obj pred? 3 5 den Peter den Peter FIGURE 2 Eect of instantiated symbols (cf. (1.16)) It has been observed however (Andrews 1990) that to a limited degree, some languages allow for exceptions to this rule. While in French, the presence of an object clitic on the verb makes the appearence of a full NP with the same function impossible, Spanish does allow clitic doubling (1.17) (Andrews 1990, sec. 3.1). (1.17) Lo him vimos we saw a l. him `We sawhim.' Keeping up the standard pred mechanism, Andrews formally models the construction by making the introduction of the clitic's pred value optional. This has certainly the desired eect and is plausible as far as the instantiated symbol character of the pred value is concerned, but it seems somehow ad hoc to give an otherwise referential item the option of being semantically empty. My claim here is that the observations are due to more general principles of resource sensitivity in the syntax-semantics interface that become clearer when a more ne-grained view is taken on what standard LFG bundles up in the semantic forms under the pred feature. Already Dalrymple et al. (1995, 14) note that of the four types of information that semantic forms classically encoded, three 17 are now covered by new mechanisms like argument structure with linking theory, and the linear logic-based account of semantics. The only remaining type of information still encoded in the pred values, they argue, is instantiation to mark predicate uniqueness These are: specication of the semantic relation, mapping of grammatical functions to semantic roles, and subcategorization information (the governed grammatical functions). 18 In their analysis of complex predicate constructions, they assume that the light

13 Resource Sensitivity and the Split NP Construction / 13 As it turns out, even instantiation can be taken over by resource sensitivity in the linear logic-based account of semantics (see sec below). Thus, the pred feature can be removed entirely from the f- structure representation. This means that one can get a very clear-cut formal division in the architecture of grammar, with resource accounting exclusively on the semantic side, and feature unication (without any exceptional value types like the old pred values) for functional syntax Modelling resource sensitivity in Split NPs with pred values? Before going into the linear logic formalism in sec. 1.4, let us clarify the polarity of resource sensitivity in the SNP data. A consideration how this could be modelled with the classical pred values will give additional support for the revision. Contrary to the excluded doubling of canonical NPs as in (1.16), one of the NPs in the German SNP construction must resemble Spanish clitics in that it tolerates c-structurally distinct material contributing to the same grammatical function as itself. The following question will help to judge which part of the SNP has this nature: Can there be even more than two NPs, and if so, which ofthetwo NPtypes in SNP can be iterated? It turns out that it is the topic part of SNP the attempt to iterate the lower NP (which introduces and quanties over the variable/referent) leads to ungrammaticality (1.18), while in a context providing appropriate contrast, it is in fact possible to havetwo (property-denoting) topic parts (1.19): the NP politische, in the Mittelfeld, clearly bears the intonational marking of atopic(a rising pitch accent, cf. example (i) in fn. 5). (1.18) *Bilder haben wir welche im Museum einige gesehen. paintings have we some in-the museum several seen (1.19) B cher books durfte was-allowed man one politische political damals then in to den the Osten East keine none mitbringen. bring `Talking about booksas for political ones, one wasn't allowed to bring any toeastgermany.' If one wanted to capture this behaviour within the standard account of pred values, one way would be to have the topic NP introduce its contribution under an embedded set-valued feature like adjuncts,while the Mittelfeld NP, although noun-less, introduces an ordinary (pronominal) pred value. (1.21) sketches this analysis for (1.20). verb diyaa `permit' (in Urdu) lacks a pred value, and can thus unify f-structurally with a full verb to form a complex predicate.

14 14 / Jonas Kuhn (1.20) Fr sche sieht Karl kleine. frogs sees Karl small `As for frogs, Karl can see small ones.' (1.21) Fr sche: ("...obj adjuncts 3 pred) =`Frosch' kleine: ("obj pred) =`pro' ("obj adjuncts 3 pred) = `klein' 2 pred `sehenhsubj obji' 6 4 subj pred 2 pred 4 adjuncts `Karl' `pro' 3 5 obj pred `Frosch' pred `klein' Due to the (instantiated) pred value it introduces (here called `pro', quite arbitrarily), the Mittelfeld NP cannot be repeated, whereas there could be more of the adjunct-introducing topic NPs. Note that this way of enforcing the right restrictions with the standard pred mechanism leads to a picture that is almost the opposite of the naive way ofputting the pred's together, shown in g. 1. The confusion is caused by the dierent rolespred's play, which diverge in the SNP construction. This brief consideration should be enough to motivate a formally separated approach to the resource-sensitive aspects in the SNP construction The Syntax-Semantics Interface This section contains a fair amount of formalism however, the general ideas should become clear even if one doesn't follow the linear logic derivation in every detail Linear logic-based semantic construction In the introduction, a close parallel between the Mittelfeld NP of the SNP construction and elliptical NPs has been observed. Based on the c- and f-structural analysis from the previous section, I will argue here that underlying both NP usages is a common anaphoric behaviour requiring an antecedent of the semantic type of a property (Fanselow 1988, 105 van Geenhoven 1996). Again, the formal modelling relies mainly on established assumptions, in this case from the linear logic-based framework of semantic construction within LFG, established by Dalrymple and colleagues in a series of papers (among others Dalrymple et al Dalrymple et al. 1995, DLPS97). This approach builds on LFG's projection architecture, assuming a level of semantic representation, projected from 19 See (Kuhn to appear) for more discussion. A similar set of issues is also discussed in (Berman, Dipper, Fortmann, and Kuhn 1998), for the empirical domain of the correlative pronouns co-occurring with nite argument clauses

15 Resource Sensitivity and the Split NP Construction / 15 f-structure, that is associated with a meaning. Meaning association is expressed by the predicate symbol. Constraints on the meaning associated with a semantic structure are called meaning constructors and are expressed in the lexical entries, like intheentry (1.22) for the proper name Anna. 20 (1.22) Anna NP ("pred) = `Anna' " Anna The central insight of the linear logic approach is that the semantic contribution of lexical items can be viewed as resources that are being subsequently consumed, as the meaning for larger expressions is built up. At the end of a successful derivation, all resources will be used up and only the meaning for the entire sentence will be left, which has to be of type t. This intuition cannot be modelled by a derivation in classical logic, since there, a premise may be used arbitrarily many times in a derivation. Linear logic, with its connectives (multiplicative conjunction) and ( (linear implication), captures the resource consciousness of natural language semantics: deducing B from A (A ( B) by modus ponens will consume A i.e., A B is not derivable from just this formula. The meaning constructors for transitive verbs like sieht `sees' make use of these connectives: 21 (1.23) sieht NP ("pred) = `sehen' 8X Y:(" subj) X (" obj) Y (" sehen (X Y ) The logic language containing both meaning associations and linear logic expressions that control their processing is called the glue language. (1.24) (weil) Anna Otto sieht because Anna Otto sees Now, the linear logic derivation of a sentence like `Anna sees Otto' (1.24) starts out with a c-, f- and semantic structure analysis, as given in g. 3, with arrows illustrating the projection functions. The premises for the linear logic derivation originating from the lexical entries are given 20 Entry (1.22) has the following eects: (i) it introduces the string Anna under the c-structure category NP, (ii)it introduces the feature pred with value `Anna' in the f-structure projected from the NP node (referred to by the metavariable "), and (iii) it associates the semantic structure projected from that f-structure (which is mathematically the result of applying the projection function to the f-structure that " refers to) with the meaning language constant Anna. 21 Intuitively, the meaning constructor in this entry says: for any meaning language terms X and Y,suchthat("subj) the semantic structure projected from the value of subjis associated with X, and("obj) is associated with Y, a new meaning can be associated with (the semantic structure " projected from) the verb itself, which has the shape of a meaning language predicate sehen, applied to X and Y.

16 16 / Jonas Kuhn VP NP NP V Anna Otto sieht f : `sehen' pred subj pred g : case obj h : pred case `Anna' nom `Otto' acc g : [ ] f : [ ] h : [ ] FIGURE 3 LFG projections for (1.24) in (1.25). Here, the metavariables (", #) from the lexical entries have been instantiated to the f-structure labels from g. 3: (1.25) Anna: g Anna Otto: h Otto sieht: 8X Y: g X h Y ( f sehen (X Y ) Looking at the premises Anna and sieht, the meaning language constant Anna can be substituted for X in sieht, producing (1.26) as an intermediate result nally the constant Otto can likewise be substituted for Y, generating the meaning association (1.27) for the complete sentence. Since all premises have been used, leaving just an association for the entire sentence with a meaning language term of type t, the derivation has been successful. 22 (1.26) Anna-sieht: 8Y: h Y ( f sehen (Anna Y) (1.27) Anna-Otto-sieht: f sehen (Anna Otto ) Had there been an additional NP, not subcategorized for by theverb, like in the ungrammatical sentence (1.16) above, there would have been no derivation using up all premises, predicting ill-formedness. The instantiated symbols as values of pred are thus no longer needed to exclude illicit doubling. (As briey mentioned in sec , Dalrymple and colleagues point out that the glue language semantics replaces the Completeness and Coherence conditions of standard LFG, but to my knowledge, the observation that even instantiated symbols are made redundant has not been stated in the literature. 23 ) The f-structure in g. 3 can thus be reduced to (1.28). (1.28) f : subj g : case nom obj h : case acc To be able to address the SNP, weneedtobrieylookatthegeneralized quantier analysis in the linear logic framework (DLPS97, 234). As the representation at semantic structure for an NP like ein Kaninchen, an object with some internal structurea var(iable) and a restr(iction) featureis assumed. So, for (1.29), the LFG projections 22 For a more detailed introduction the reader is referred to DLPS It should be noted however that Johnson (1997, 1998) proposes a variant oflfg (R-LFG) that uses linear logic even as a replacement for f-descriptions.

17 look as in g. 4. (1.29) (weil) because Resource Sensitivity and the Split NP Construction / 17 Anna Anna VP ein a Kaninchen rabbit NP NP V sieht sees DET N Anna ein Kaninchen sieht f : subj g : obj h : case case nom acc g : [ ] f : [ ] var [ ] h : restr [ ] FIGURE 4 LFG projections for (1.29) In (1.30), the lexical entries with meaning constructors for the determiner ein `a' (R and S are property type variables, mnemonic for the restrictor and scope in the generalized quantier), 24 and for the common noun Kaninchen `rabbit' are given. (1.30) ein DET 8H R S:(8x(" var) x ( (" restr) R(x)) (8x " x ( H S (x)) ( H ein(r S) Kaninchen N 8X:(" var) X ( (" restr) Kaninchen (X ) Combining the two in the concrete example of g. 4, with the metavariables instantiated to h, and furthermore instantiating R in ein as Kaninchen will yield (1.31) as the meaning constructor for the NP. (1.31) ein-kaninchen: 8H S:(8x:h x ( H S (x)) ( H ein (Kaninchen S ) The antecedent of this linear implication is matched by the subjectverb semantics Anna-sieht of (1.26) above, which isidentical for this sentence, so instantiating H with the semantic structure f of the complete sentence, and S with the property z:sehen(anna z ) (by higherorder unication), we end up with the meaning association (1.32): (1.32) Anna-ein-Kaninchen-sieht: f ein (Kaninchen z :sehen (Anna z )) 24 Recall the discussion of the indenite article in sec above. I assume a generalized quantier analysis for the indenite article merely for ease of presentation, paying the price of having to assume two dierent lexicon entries for ein.

18 18 / Jonas Kuhn Anaphora In order to model the observed interplay between compositionality and anaphoricity in SNP in the linear logic framework, at least a simple analysis of anaphora is required. It is obvious that some adjustment of the basic mechanism is required, since intuitively anaphoricity allows to refer back to the meaning of an expression that is already involved as a resource in some independent derivation. DLPS97 (sec. 3.8) discuss two alternatives of a linear logic-based account of (E-type) anaphora. The rst one is to provide the anaphoric element (e.g. the pronoun himself ) with a meaning constructor that takes in some other meaning (from its antecedent) to generate its own meaning, but simultaneously outputs an identical copy of the antecedent's meaning, cf. the lexical entry in (1.33). 25 (1.33) himself NP ("pred) = `pro' (DLPS97, p. 249 (55)) 8X:(" ant) X ( (" ant) X " X This account is however problematic when dealing with extrasentential antecedents, as it requires for the anaphor to access the antecedent's meaning before this has been consumed. 26 The other alternative DLPS97 discuss avoids this problem by shifting the copying task from the anaphors to the (potential) antecedents. The meaning constructor for himself will then be simply the consumer (1.34) 8X:(" ant) X (" Y and the entry for a name, for instance, will supply arbitrarily many (including zero) extra copies of its meaning. Formally, thisisachieved with the of course connective of linear logic `!', which provides a reusable resource: (1.35) Anna: " Anna!(" Anna ) A problem that DLPS97 note for this account is that modications made to the meaning of an antecedent cannot be taken into account by the E-type anaphor. 27 A further problem may arise when the linear logic derivation is to replace the function of pred values completely, as argued in sec above. With the antecedent of an anaphor providing arbitrarily many, including zero, extra copies of its meaning for external 25 Like DLPS97, I assume that anaphora have been resolved (taking into account discourse factors such as salience, topichood, and focus). The choice of an antecedent is marked for simplicity within semantic structure, by a feature ant, which has as its value the antecedent's semantic structure. 26 If the linear logic derivation is not at all taken to model aspects of linguistic derivation, this may not be a problem. 27 This problem leads Crouch and van Genabith (1998) to propose yet another linear logic-based analysis of anaphoricity, assuming a context assignment,! for every expression besides the meaning assignment under.

19 Resource Sensitivity and the Split NP Construction / 19 use, an illicit NP doubling conguration like (1.36) might become possible: an NP (here den Peter) occurs exclusively to provide its meaning as an antecedent for an anaphor (ihn), without actually contributing to a local derivation. However, it is possible that such congurations are always ruled out by syntactic binding principles here, more research is required. (1.36) *den Peter sieht der Karl ihn. the.acc Peter sees the.nom Karl him I leave the question of anaphor-based vs. antecedent-based provision of extra resources open for now, temporarily adopting the second variant for practical reasons (dealing with extra-sentential antecedents in the following exposition of elliptical NPs) I'll briey come back tothe question in sec below Elliptical NPs The second key assumption I make for the overall SNP analysis, besides f-structure unication of the participating NPs, is anaphoricity of the Mittelfeld NP, completely parallel to elliptical NPs with an extrasentential antecedent. For elliptical NPs, it should be uncontroversial to assume anaphoric behaviour, in the sense that they take up a property that is salient in the context. In English, this anaphoricitycaneven be lexically tied to the item one (as in a new one). 28 In the corresponding cases in German, no overt element is required. (1.37) Ottos Auto ist kaputt gegangen. Er will sich Otto's car has broken gone he wants refl ein a neues new kaufen. buy `Otto's car has broken down. He wants to buy a new one.' I won't go into the question whether the eect should be captured by an empty nominal head like thepro that Fanselow (1988) assumes, or by category change, or at the level of the construction, since this is orthogonal to the main point under discussion. 29 For illustration I will simply use the indenite pronoun welche `some' as in (1.38) and assume (i) 28 However, where no adjective appears in the elliptical NP, one is not required: Isawsome/two/many/none. 29 Depending on this decision, the glue language expression marking anaphoricity (which gets introduced lexically in the case of (1.39) below) will be introduced in dierent ways for an example like einen kleinen `a small (one)': if an empty element is assumed, this will contribute the anaphorial expression lexically if one works with category change of the adjective, the lexical rule performing this change will add the anaphorial expression nally, if a construction-level treatment of headless NPs is assumed, we would have to deal with a glue language expression introduced by the construction. All this is possible technically.

20 20 / Jonas Kuhn that it is lexically anaphoric to a property, as expressed by the meaning constructor in (1.39). (1.38) Gestern wollten wir Kaninchen beobachten. Aber nur Anna hat yesterday wanted we rabbits watch but only Anna has welche some gesehen. seen `Yesterday, we wanted to watch rabbits. But only Anna could see any.' (1.39) welche NP 8H R S:(8x:(" ant var) x ( (" ant restr) R(x)) (8x: " x ( H S (x)) ( H welche (R S) Note that the meaning constructor is like the one for a determiner (cf. (1.30)), except that the rst implication (for the property that ends up as the generalized quantiers's restrictor) is based on the anaphor's antecedent rather than on the locally available noun semantics. Following the account for anaphora based on reusable resources on the side of the antecedents, we can assume that the common noun Kaninchen `rabbits' from the rst sentence of (1.38) supplies (on demand) additional copies of its meaning constructor under the of course connective: (1.40) Kaninchen: 8X:(" var) X ( (" restr) Kaninchen (X )!(8X:(" var) X ( (" restr) Kaninchen (X )) Thus, even after the derivation of the rst sentence has consumed the semantics of Kaninchen, another copy will be available for welche, which we can assume to mark the semantic structure projected from Kaninchen as its antecedent (i.e., as the value of the ant feature), as sketched in the f- and semantic structures for (1.38) given in g. 5 (the curved line without arrowheads signies identity).. VP NP... NP NP V f : subj g : obj h : case case nom acc Kaninchen Anna welche gesehen 2 4 ::: gf i : ::: ::: 3 5 f : [ ] g : [ ] 2 h 4 var [ ] : restr [ ] ant 3 5 i : [ ] FIGURE 5 Elliptical NP Analysis (cf. (1.38))

21 Resource Sensitivity and the Split NP Construction / 21 Instantiating the metavariables from (1.39) with the labels from g. 5, furthermore inserting i for (h ant), the premise for welche looks as follows: (1.41) welche: 8H R S:(8x:(ivar) x ( (irestr) R(x)) (8x:h x ( H S (x)) ( H welche (R S) The antecedent's left over semantics at i (cf. (1.42)) will match the rst implication in (1.41), so after anaphora resolution we getwelche 0 (1.43). (1.42) Kaninchen: 8X:(ivar) X ( (irestr) Kaninchen (X ) (1.43) welche 0 : 8H S:(8x:h x ( H S (x)) ( H welche (Kaninchen S ) Note that this is of identical form as ein-kaninchen in (1.31) above. The remainder of the derivation for the second sentence in (1.38) will thus go through as above The semantics of the Split NP construction Now, when welche is used as part of an SNP like in (1.44), my claim is that exactly the same lexicon entry is used as with an extrasentential antecedent. Although in this case, its f-structure happens to be unied with the f-structure projected from the NP Kaninchen under a single grammatical function (as discussed in sec ), welche still introduces an anaphorically dependent meaning constructor. (1.44) Kaninchen hat Anna welche gesehen. rabbits has Anna some seen `As for rabbits, Anna could see some.' The choice of a possible antecedent for the property-type anaphor is heavily restricted by thediscourse functions. 30 The antecedent has to be the topic of the sentence, i.e., in the concrete case the NP Kaninchen. For the standard mechanisms involved in this reasoning, it is a matter of coincidence that at f-structure, the chosen antecedentisidentical with the anaphor 31 the resources will nevertheless interact as usual. Essential for this to work is the circumstance that in the course of a glue-language derivation, the meanings associated with a particular semantic structure can change (this dierence from a unication account is also central for the analysis of adjuncts and complex predicates, cf. Dalrymple et al Dalrymple et al. 1995). 30 For a full understanding of the impact and interpretation of discourse functions in this context, further research is required. 31 As far as I can see, cyclic semantic structures of the form [1][ANT [1]] should pose no problem for the linear logic-based interpretation.

22 22 / Jonas Kuhn CP f : subj g : obj h : case nom NP C 0 Kaninchen C VP hat NP NP V Anna welche gesehen g : [ ] f : [ 2 ] h 4 var [ ] : restr [ ] ant 3 5 FIGURE 6 Projections of split NP analysis (cf. (1.44)) Based on the f- and semantic structure analysis of (1.44) in g. 6, the premises for the linear logic derivation are as follows. (1.45) Kaninchen: 8X:(hvar) X ( (hrestr) Kaninchen (X )!(8X:(hvar) X ( (hrestr) Kaninchen (X )) gesehen: 8X Y:g X h Y ( f sehen (X Y ) Anna: welche: g Anna 8H R S:(8x:(hant var) x ( (hant restr) R(x)) (8x:h x ( H S (x)) ( H welche (R S) First of all, Anna matches the rst conjunct in gesehen, yielding (1.46). (1.46) Anna-gesehen: 8Y:h Y ( f sehen (Anna Y ) Furthermore, since Kaninchen is the antecedent forwelche ((h ant) = h ), a copy ofkaninchen matches the rst conjunct in the antecedent of welche, substituting Kaninchen for R: (1.47) Kaninchen-welche: 8H S:(8x:h x ( H S (x)) ( H welche (Kaninchen S ) Finally, substituting z:sehen(anna z ) for S, (1.46) matches the antecedent of (1.47), and we get a meaning association for the complete sentence: (1.48) Kaninchen-Anna-welche-gesehen: f welche (Kaninchen z :sehen (Anna z )) Now, we have to see if all premises have been consumedto make this a successful derivation. This brings us back to the question which anaphoric mechanism to assume (sec ). Adopting the antecedentbased provision of extra resources, as we just did, there is a linear logic derivation that indeed consumes all premises: the of course operator