DUTCH WORD ORDER AND BINDING

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1 Chapter 1 DUTCH WORD ORDER AND BINDING Glyn Morrill Abstract This paper offers a type-logical account of Dutch word order with special reference to quantifier binding in subordinate clauses. This paper offers a type-logical account of Dutch word order with special reference to quantifier binding in subordinate clauses. The word order of simple subordinate clauses is exemplified by the following: a. (:::dat) Jan zong (:::that) J. sang (:::that) Jan sang b. (:::dat) Jan boeken las (:::that) J. books read (:::that) Jan read books c. (:::dat) Jan boeken aan Marie gaf (:::that) J. books to M. gave (:::that) Jan gave books to Marie (1.1) We see that the finite tensed verb appears clause-finally. When the main verb is an infinitival complement of a modal or control verb, a so-called verb raising trigger, it appears after the verb raising trigger(s) in a clause-final verb cluster: a. (:::dat) Jan boeken kan lezen (:::that) J. books is able read (:::that) Jan is able to read books b. (:::dat) Jan boeken wil kunnen lezen (:::that) J. books wants be able read (:::that) Jan wants to be able to read books (1.2) Work partially supported by CICYT project PB C

2 2 The semantic form of (1.2a) is (able (read books)) and that of (1.2b) is (want (able (read books))). Thus we have a syntactic/semantic mismatch with the discontinuous constituent boeken:::lezen interpreted as a semantic unit (read books), with an indefinite number of verb raising triggers intervening. If such a subordinate clause contains a quantifier, there is scope ambiguity as to whether the quantifier takes scope within or outside of the verb raising trigger: (:::dat) Jan alles wil lezen (:::that) J. everything wants read (:::that) Jan wants to read everything (1.3) Main clause yes/no interrogative word order, V1 word order, is derived from subordinate clause word order by fronting the finite verb: Wil Jan boeken lezen. Does Jan want to read books? (1.4) Main clause declarative word order, V2 word order, is further derived by fronting a major constituent: Jan wil boeken lezen. Jan wants to read books. (1.5) In this paper we offer an account of these various facts of Dutch word order. 1. ASSOCIATIVE LAMBEK CALCULUS The associative D(AB)=fs1+s2js12D(A)&s22D(B)g D(AnB)=fsj8s02D(A);s0+s2D(B)g D(B=A)=fsj8s02D(A);s+s02D(B)g D(I)=fg F::=AjIjFnFjF=FjFF Lambek calculus with product unit (Lambek 1988) is the calculus of a monoid(l;+;)where+is seen as the associative operation of concatenation:s1+(s2+s3)=(s1+s2)+s3andis seen as the empty string: s+=+s=s. The category type formulasfare defined on the basis of a setaof atomic category type formulas by the type forming operators I (product unit),n( under ), / ( over ) and( product ) as follows: (1.6) Each category type formulaais interpreted as a setd(a)las follows: (1.7)

3 :A +:B :AnBnE :B=A a:a +:B :A=E a+:bnin :AnB 3 Where we write:ato indicate that expressionis in categoryathe following deduction rules are valid: :A+a:B=In :B=A a:a n +:AB :BI (1.8) :I II (1.9) (1.10) (1.11) The overline inni and /I indicates cancellation of a hypothesis with the coindexed rule. The rules fore and IE, which are more difficult to formulate, are excluded since they are not needed in this paper. D(AB)=fs1Ws2js12D(A)&s22D(B)g D(A#B)=fs2j8s12D(A);s1Ws22D(B)g D(B"A)=fs1j8s22D(B);s2Ws12D(A)gthat1hs1;s2i= 2. DISCONTINUITY Versmissen (1991) and Solias (1992, 1994, 1996) treat discontinuity in terms of split strings. Solias works with an algebra(l;+;h;i)where+is associative andh;iis strictly non-associative, i.e.(l;+)is a semigroup and(l;h;i)is a free groupoid. Wrap is derived as a parcial operation. This is made more explicit in Morrill and Solias (1993) where the algebra is augmented with projection functions,(l;+;h;i;1;2), such s1and2hs1;s2i=s2. Then wrapping,w, is defined as a total operation bys1ws2=df1s1+s2+2s1, whence infixation, extraction and discontinuous product operators are interpreted by: (1.12) However, these formulations encounter the technical difficulty of the incompleteness of the non-associative Lambek calculus for free groupoids (Venema 1994), therefore Morrill (1994, 1995) proposes wrap as a primitive operation

4 (B"C)#D)((AnB)"C)#(AnD) 4 in an algebra(l;+;(;);w)where(l;+)is a semigroup and(l;(;))and (L;W)are groupoids such that(s1;s2)ws=s1+s+s2. Nevertheless this does not assure all the expected behaviour of wrap, for example it does not validate the intuitively valid Geach-like shift: (1.13) Thus in D(A#B)=fsj8hs1;s2i2D(A);s1+s+s22D(B)g Morrill (1995, appendix) and Morrill and Merenciano (1996) an alternative tack D(B"A)=fhs1;s2ij8s2D(A);s1+s+s22D(B)g is taken which consists in sorting the categorial types. The concatenation adjunction has functionalityl;l!l. We further define an interpolation adjunctionwof functionalityl2;l!l:hs1;s2iws=s1+s+s2. We refer to sortlas sort string, and sortl2as sort split string. Les us assume that atomic formulasaare of sort string. The well-sorted category formulas or typesfof sort string andf2of sort split string are defined by mutual recursion (1;2):A 1++2:B :A#B#E n Each formulaaof sort string has an interpretationd(a)land each formula Aof sort split string has an interpretationd(a)l2: (1;2):B"A (a1;a2):a D(AB)=fs1+s+s2jhs1;s2i2D(A)&s2D(B)g(1.15) 1++2:B :A"E a1++a2:b#in :A#B Valid deduction rules are as follows: (1;2):A(1;2):B"A 1+a+2:B"In a:a n 1++2:AB :BI (1.16) (1.17) (1.18) thus:f::=ajijfnfjf=fjffjf2#fjf2f F2::=F"F (1.14)

5 John:Nthinks:(NnS)=N QUANTIFICATION John+thinks+someone+walks:S thinks+someone+walks:nnsne a:nwalks:nnsne (;walks):s"nsomeone:(s"n)#s#e a+walks:s"i1 someone+walks:s=e Quantification is derived by assigning quantifier phrases type (S"N)#S. Consider the narrow scope (non-specific) and wide scope (specific) readings of John someone walks. The narrow scope reading is derived by infixation at the level of the subordinate clause as follows: jthink1 (1.19) ((think9y(walky))j) (think9y(walky))ne x(walkx)x9y(xy)#e (walksx)"i1 xwalkne 9y(walky)=E Semantics is given by the Curry-Howard rendering of categorial deductions: functional application for rules of implicational use (elimination) and functional abstraction for rules of implicational proof (introduction); node for node with (1.19): John:Nthinks:(NnS)=S1 (1.20) (John+thinks;walks):S"N John+thinks+a+walks:S"I1 thinks+a+walks:nnsne John+thinks+someone+walks:S a:nwalks:nnsne a+walks:s=esomeone:(s"n)#s#e In the wide scope derivation on the other hand, infixation is at the level of the superordinate clause: (1.21)

6 x((think(walkx))j)x9y(xy)#e ((think(walkx))j)"i1 jthink1 (think(walkx))ne 9y((think(walky))j) xwalkne (walkx)=e 6 Node for node, the semantics is thus: that:r=((s"n)i)m::nsent:((nns)=pp)=n1 a:n=e (1.22) 4. FRONTING Fronting such as relativisation can be treated by assignment of the relative pronoun to (CNnCN)/((S"N)I). that+mary+sent+to+john:r (Mary+sent;to+John):S"N Mary+sent+a+to+John:S"I1 sent+a:(nns)=ppto+j::pp=e Mary+sent+to+John:(S"N)I=E sent+a+to+john:nnsne :II II For example (the book) that Mary sent to John is derived thus: the+book:n:(nns)=((s"n)i)mary+sent+to+john:(s"n)i=e (1.23) the+book+mary+sent+to+john:s Mary+sent+to+John:NnS Fronting such as topicalisation can be derived by assignment to the empty string of (XnS)/((S"X)I). For example The book, to John is derived thus: (1.24)

7 b:a3(b+a1;a2):b"a b+a1+c+a2:b"i2 (a1;a2):(anb)"c a1+c+a2:anb1c:c"e 2 :((AnB)"C)#(AnD) a1++a2:and#i1 b+a1++a2:dni3 :(B"C)#D#E 7 5. GEACH EFFECT The intuitively valid Geach-like shift (1.13) is derivable as follows: (1.25) 6. DUTCH VERB RAISING PLUS QUANTIFIER RAISING: MULTIPLE DISCONTINUITY Consider the following example with quantification in a subordinate clause: (:::dat) Jan alles aan Marie wil given (:::that) J. everything to M. wants give (:::that) Jan wants to give everything to Marie (1.26) A wide scope derivation is obtained on the following pattern: a. aan Marie geven b. aan Marie wil geven c. Jan aan Marie wil geven d. Jan alles aan Marie wil geven (1.27) A narrow scope derivation is obtained on the following pattern: a. aan Marie geven b. alles aan Marie geven c. alles aan Marie wil given d. Jan alles aan Marie wil given (1.28) The essential puzzle is the manageament of multiple points of discontinuity. We treat this by adding to the type language a logical constant J which is interpreted as a subsetjof the underlying algebraic field such that2j. We refer to this as the connection set. Intuitively, connections allow for hypothetical reasoning over discontinuous strings as if they were continuous, by supposing that they are connected; the connection set includesbecause the empty string always connects adjacent

8 :J JI 8 strings. Semantically, J is neutral, like I. It has the following rule of introduction: (1.29) 7. FINITE AND INFINITE VERBS For the generation of simple Dutch subordinate clauses let us assume the following assignments: aan+marie m := PP boeken books := N gaf gave := PPn(Nn(NnS)) Jan j := N las read := Nn(NnS) zong sang := NnS (1.30) These derive in a straightforward way the following: a. (:::dat) Jan zong (:::that) Jan sang b. (:::dat) Jan boeken las (:::that) Jan read books c. (:::dat) Jan boeken aan Marie gaf (:::that) Jan gave books to Marie (1.31) The possibility of verb-complement discontinuity will be accommodated by having infinite verbs combine with a connection to the left. Where a finite verb has categoryx, the corresponding infinite verb has categoryjnx: geven give := Jn(PPn(Nn(NnS))) lezen read := Jn(Nn(NnS)) zingen sing := Jn(NnS) (1.32)

9 Jan:Nboeken:NJI Jan:NJI Jan+zingen:S :Jzingen:Jn(NnS)nE zingen:nnsne 9 Note that this allows Jan+boeken+lezen:S boeken+lezen:nnsne :Jlezen:Jn(Nn(NnS))nE lezen:nn(nns)ne bare infinitival clauses to be generated as continuous strings: (1.33) (1.34) 8. FINITE AND INFINITE VERB RAISING TRIGGERS boeken:n1 a:jzingen:jn(nns)ne (;zingen):(nns)"jkan:((nns)"j)#(nns)#e a+zingen:nns"i1 1 kan+zingen:nns is-able := ((NnS)"J)#(NnS) (1.35) wil wants := ((NnS)"J)#(NnS) (boeken;lezen):(nns)"j boeken+a+lezen:nns"i1 a:jlezen:jn(nn(nns))ne a+lezen:nn(nns)ne boeken+kan+lezen:nns kan:((nns)"j)#(nns)#e (1.36) (1.37) A finite verb raising trigger is defined to infix at the connection site of a verb phrase: This situates the verb raising trigger at the left of an infinitival verb:

10 10b::Naan+M:1 (boeken+aan+marie;geven):(nns)"j boeken+aan+marie+a+geven:nns"i1 aan+marie+a+geven:nn(nns)ne a:jgeven:jn(ppn(nn(nns)))ne boeken+aan+marie+kan+geven:nns a+geven:ppn(nn(nns))nekan:((nns)"j)#(nns)#e(1.38) boeken:n1 (boeken;lezen):vp"j boeken+a+lezen:vp"i1 a:jlezen:jn(nnvp)ne a+lezen:nnvpne (boeken;kunnen+lezen):vp"j boeken+b+kunnen+lezen:vp"i2 b:jkunnen:jn((vp"j)#vp)ne boeken+wil+kunnen+lezen:vp b+kunnen:(vp"j)#vp#e 2 wil:jn((vp"j)#vp)#e(1.40) As was the case for ordinary verbs, so it is for verb raising triggers that where the finite verb has categoryx, the infinite verb has categoryjnx: kunnen be-able := Jn(((NnS)"J)#(NnS)) willen want := Jn(((NnS)"J)#(NnS)) (1.39) This accounts for multiple verb raising as in the following, where VP abbreviates NnS: 9. VERB RAISING PLUS QUANTIFIER RAISING Recall the following example: (:::dat) Jan alles wil lezen (:::that) J. everything wants read (:::that) Jan wants to read everything (1.41)

11 Jan:N2 b:n1 (b;lezen):(nns)"j a:jlezen:jn(nn(nns))ne 11 (Jan;wil+lezen):S"N b+a+lezen:nns"i1 a+lezen:nn(nns)ne Jan+a+wil+lezen:S"I2 b+wil+lezen:nnsne The wide scope reading for the Jan+alles+wil+lezen:S wil:((nns)"j)#(nns)#ealles:(s"n)#s#e quantifier is derived thus, where the quantifier joins the derivation after wil : (1.42) The narrrow scope reading is derived thus, where the quantifier joins the derivation before wil : Jan:N c:n2 b:n1 (c;a+lezen:s"n c+b+a+lezen:s"i2 b+a+lezen:nnsne a:jlezen:jn(nn(nns))ne a+lezen+nn(nns)ne Jan+alles+wil+lezen:S (alles;lezen):jn(nns) alles+a+lezen:nns c+alles+a+lezen:sni alles+wil+lezen:nns alles:(s"n)#n#ewil:((nns)"j)#(nns) (1.43) x(x):=m=((s"a)j) :=fva V1 10. V1 AND V2 For V1 yes/no interrogative order we assume lexical lifting of finite verbs (cf. Hepple 1990): (1.44)

12 wil:m=((s"x)j)jan:nboeken:n1 (boeken;lezen):(nns)"j boeken+a+lezen:nns"i1 a+lezen:nn(nns)ne a:jlezen:xne 2 12 Hence the following, wil+jan+boeken+lezen:m (Jan+boeken;lezen):S"X Jan+boeken+b+lezen:S"I2 boeken+b+lezen:nnsne Jan+boeken+lezen:(S"N)J=E b:((nns)"j)#(nns)#e:ji JI where X is Jn(Nn(NnS)). follows: xy(yx):=(xnt)=((m"x)j) (1.45) Jan+wil+boeken+lezen:T wil+boeken+lezen:nntne wil+boeken+lezen:(m"n)j=e :JI And for V2 declarative order we furthur assume assignment to the empty string as (1.46) (1.47) Thus:Jan:N:(NnT)=((M"N)J)(wil;boeken+lezen):M"NJI In this way the basic facts of Dutch subordinate and main clause word order are accommodated, including the case of quantifier binding.

13 O2::=pF2jF;O2jO2;Fj1pF2;O2;2pF2 Appendix A 13 2::=O2)pF2 O::=jF;OjO;Fj1pF2;O;2pF2 ::=O)F Appendix: Sequent calculus for sorted discontinuity In this appendix we present sequent calculus for sorted discontinuity (cf. Morrill 1998). The basic idea is to represent split strings by two formula occurrences at their two loci of action. These components are punctuated as roots. Sequents come in two sorts. A sort string sequenthas a sort string succedent on the right and a sort string configurationoon the left. A sort split string sequent2has a sort split string succedent the right and a sort split string 1pA;pA;2pA)pA A)A?)A(A))YCut (?))Y configurationo2on the left. The well-formed configurations and sequents of sort string and split string are defined as follows: (A.1) We have sort string and sort split string identity rules. The notation?() indicates a configuration?with a distinguished subconfiguration.yandz?)anb id2?(pa))pa(1pa;;2pa))ycut2 (?()))Y vary over formulas of?)a)br A;?)BnR?;A)B=R?)B=A)I IR?())YIL sort string and the roots of formulas of sort split string.?;)ab?)a(b))z=l?)a(b))znl (?;AnB))Z (B=A;?))Z?(I))Y?(AB))Z?(A;B))ZL (A.2) (A.3) The rules for the Lambek connectives are thus: (A.4)?(pB"A))pB"A 1pA;?;2pA)B#R?)A#B?(A))B"R?(pA))pA(B))Z#L )J (1pB"A;?;2pB"A))Z JR?)A(B))Z"L (?(A#B)))Z (A.5) (A.6) (A.7) J is like I but has no left rule: (A.8) The rules for the discontinuity connectives are as follows: (A.9) (A.10)

14 ?(pa))pa)br?())ab?(1pa;b;2pa))zl?(ab))z 14 (A.11) References Hepple, M. (1990) The Grammar and Processing of Order and Dependency: a categorial approach, Ph.D. thesis, Centre for Cognitive Science, University of Edinburgh. Lambek, J. (1988) Categorial and Categorical Grammars in Richard T. Oehrle, Emmon Bach and Deirdre Wheeler (eds.) Categorial Grammars and Natural Language Structures, D. Reidel, Dordrecht, pp Morrill, G. (1994) Type Logical Grammar: categorial logic of signs, Kluwer, Dordrecht. Morrill, G. (1995) Discontinuity in categorial grammar, Linguistics and Philosophy 18, Morrill, G. (1998) Proof syntax of discontinuity, in P. Dekker, M. Stokhof and Y. Venema (eds.), Proceedings of the 11th Amsterdam Colloquim, ILLC, Amsterdam, pp Morrill, G. and J.M. Merenciano (1996) Generalising Discontinuity, Traitement Automatique des Langues 37 2, pp Morrill, G. and T. Solias (1993) Tuples, Discontinuity and Gapping, in Proceedings of the European Chapter of the Association for Computational Linguistics, Utrecht, pp Solias, T. (1992) Gramáticas Categoriales, Coordinación Generalizada y Elisión, Ph.D. thesis, Departamento de Lingüística, Lógica, Lenguas Modernes y Fílosofia de la Ciencia, Universidad Autónoma de Madrid. Solias, T. (1994) Unassociativity, Sequence Product, Gapping and Multiple Wrapping, in M. Abrusci, C. Casadio and M. Moortgat (eds.) Linear Logic and Lambek Calculus, proceedings of the 1993 Rome Workshop, pp Solias, T. (1996) Gramática Categorial: modelos y aplicaciones, Editorial Sintesis, Madrid. Venema, Y. (1994) Tree models and (labeled) categorial grammar, in P. Dekker and M. Stokhof (eds.) Proceedings of the Ninth Amsterdam Colloquium, ILLC, Amsterdam, Versmissen, Koen (1991) Discontinuous Type Constructors in Categorial Grammar, ms. Onderzoeksinstituut voor Taal en Spraak, Rijksuniversiteit Utrecht.