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<Paper uid="P94-1021">
  <Title>Constraint-Based Categorial Grammar Gosse Bouma and Gertjan van Noord Alfa-informatica and Behavorial and Cognitive Neurosciences,</Title>
  <Section position="3" start_page="0" end_page="148" type="metho">
    <SectionTitle>
2 Recursive Constraints
</SectionTitle>
    <Paragraph position="0"> In cG, many grammatical concepts can only be defined recursively. Dowty (1982) defines grammatical functions such as subject and object as being the ultimate and penultimate 'argument-in' of a verbal category. Hoeksema (1984) defines verbs as exocentric categories reducible to s. Lexical rules frequently refer to such concepts. For instance, a categorial lexical rule of passive applies to verbs selecting an object and must remove the subject.</Paragraph>
    <Paragraph position="1"> In standard unification-based formalisms, these concepts and the rules referring to such concepts cannot be expressed directly.</Paragraph>
    <Section position="1" start_page="0" end_page="147" type="sub_section">
      <SectionTitle>
2.1 Subject-verb agreement
</SectionTitle>
      <Paragraph position="0"> Consider a categorial treatment of subject-verb agreement with intransitive ( NP\[NOM\]\S ) and transitive  Subject-verb agreement can be incorporated easily if one reduces agreement to a form of subcategorization.  If, however, one wishes to distinguish these two pieces of information (to avoid a proliferation of subcategorization types or for morphological reasons, for instance), it is not obvious how this could be done without recursive constraints. For intransitive verbs one needs the constraint that (arg agr) = Agr (where Agr is some agreement value), for transitive verbs that (val arg agr) = Agr, and for ditransitive verbs that (val val arg agr) = Agr. The generalization is captured using the recursive constraint sv_agreement (2). In (2) and below, we use definite clauses to define lexical entries and constraints. Note that lexical entries relate words to feature structures that are defined indirectly as a combination of simple constraints (evaluated by means of unification) and recursive constraints. 1 (2) lex(walks, X) :-</Paragraph>
      <Paragraph position="2"> Relational constraints can also be used to capture the effect of lexical rules. In a lexicalist theory such as cG, in which syntactic rules are considered to be universally valid scheme's of functor-argument combination, lexical rules are an essential tool for capturing language-specific generalizations. As Carpenter (1991) observes, some of the rules that have been proposed must be able to operate recursively. Predicative formation in English, for instance, uses a lexical rule turning a category reducible to vP into a category reducing to a vP-modifier (vP\vP). As a vP-modifier is reducible to vP, the rule can (and sometimes must) be applied recursively.</Paragraph>
    </Section>
    <Section position="2" start_page="147" end_page="148" type="sub_section">
      <SectionTitle>
2.2 Adjuncts as arguments
</SectionTitle>
      <Paragraph position="0"> Miller (1992) proposes a lexical rule for French nouns which adds an (modifying) adjective to the list of arguments that the noun subcategorizes for. Since a noun 1We use X/Y and Y\X as shorthand for dir '/' arg Y and dir ' , respectively and S, NP, and Adj as 'typed arg Y variables' of type \[ cats \], \[ cat np \], and \[ cat adj \], respectively.</Paragraph>
      <Paragraph position="1"> can be modified by any number of adjectives, the rule must be optional as well as recursive. The advantages of using a lexical rule in this case is that it simplifies accounting for agreement between nouns and adjectives and that it enables an account of word order constraints between arguments and modifiers of a noun in terms of obliqueness.</Paragraph>
      <Paragraph position="2"> The idea that modifiers are introduced by means of a lexical rule can be extended to verbs. That is, adjuncts could be introduced by means of a recursive rule that optionally adds these elements to verbal categories. Such a rule would be an alternative for the standard categorial analysis of adjuncts as (endocentric) functors. There is reason to consider this alternative.</Paragraph>
      <Paragraph position="3"> In Dutch, for instance, the position of verb modifiers is not fixed. Adjuncts can in principle occur anywhere to the left of the verb: 2 (3) a. dat Johan opzettelijk een ongeluk that J. deliberately an accident veroorzaakt causes that J. deliberately causes an accident b. dat Johan Marie opzettelijk that J. M. deliberately geen cadeau geeft no present gives that J. deliberately gave M. no present There are several ways to account for this fact. One can assign multiple categories to adjuncts or one can assign a polymorphic category x/x to adjuncts, with x restricted to 'verbal projections' (Bouma, 1988). Alternatively, one can assume that adjuncts are not functors, but arguments of the verb. Since adjuncts are optional, can be iterated, and can occur in several positions, this implies that verbs must be polymorphic. The constraint add_adjuncts has this effect, as it optionally adds one or more adjuncts as arguments to the 'initial' category of a verb:  (4) iex(veroorzaken, X):add_adjuncts(X, NP\(NP \S)).</Paragraph>
      <Paragraph position="4"> lex(geven, X) :add_adjuncts(X, NP\(NP\(NP\S))).</Paragraph>
      <Paragraph position="5"> add_adjuncts(S, S).</Paragraph>
      <Paragraph position="6">  add_adjuncts(Adj \X, Y) :add_adjuncts(X, Y).</Paragraph>
      <Paragraph position="7"> add_adjuncts( dir D , dir D ) :arg A arg A add_adjuncts(X, Y).</Paragraph>
      <Paragraph position="8">  This constraint captures the effect of applying the following (schematic) lexical rule recursively:</Paragraph>
      <Paragraph position="10"> The derivation of (3a) is given below (where X =~ Y indicates that add_adjuncts(Y,X) is satisfied, and IV ---- null An interesting implication of this analysis is that in a categorial setting the notion 'head' can be equated with the notion 'main functor'. This has been proposed by Barry and Pickering (1990), but they are forced to assign a category containing Kleene-star operators to verbal elements. The semantic counterpart of such category-assignments is unclear. The present proposal is an alternative for such assignments which avoids introducing new categorial operators and which does not lead to semantic complications (the semantics of add_adjuncts is presented in section 3.3). Below we argue that this analysis also allows for a straightforward explanation of the distribution and scope of adjuncts in verb phrases headed by a verbal complex.</Paragraph>
    </Section>
  </Section>
  <Section position="4" start_page="148" end_page="150" type="metho">
    <SectionTitle>
3 Cross-Serial Dependencies
</SectionTitle>
    <Paragraph position="0"> In Dutch, verbs selecting an infinitival complement (e.g.</Paragraph>
    <Paragraph position="1"> modals and perception verbs) give rise to so called cross-serial dependencies. The arguments of the verbs involved appear in the same order as the verbs in the  'verb cluster': (7) a.</Paragraph>
    <Paragraph position="2"> b.</Paragraph>
    <Paragraph position="3"> dat An1 Bea2 will kussen~.</Paragraph>
    <Paragraph position="4"> dat An Bea wants to kiss that An wants to kiss Bea</Paragraph>
    <Paragraph position="6"> dat An Bea Cor wants zien2 kussen3.</Paragraph>
    <Paragraph position="7"> to see kiss that An wants to see Bea kiss Cor The property of forming cross-serial dependencies is a lexical property of the matrix verb. If this verb is a 'trigger' for cross-serial word order, this order is obligatory, whereas if it is not, the infinitival complement will follow the verb:  (8) a. *dat An wil Bea kussen.</Paragraph>
    <Paragraph position="8"> b. dat An zich voornam Bea that An Refl. planned Bea te kussen.</Paragraph>
    <Paragraph position="9"> to kiss that An. planned to kiss Bea e. *dat An zich Bea voornam te kussen.</Paragraph>
    <Section position="1" start_page="148" end_page="149" type="sub_section">
      <SectionTitle>
3.1 Generalized Division
</SectionTitle>
      <Paragraph position="0"> Categorial accounts of cross-serial dependencies initially made use of a syntactic rule of composition (Steedman, 1985). Recognizing the lexical nature of the process, more recent proposals have used either a lexical rule of composition (Moortgat, 1988) or a lexical rule of 'division' (Hoeksema, 1991). Division is a rule which enables a functor to inherit the arguments of its  argument :3 X/Y ::C/, (X/Z, . . . IZ,,)I(Y/Z. . . IZ,) To generate cross-serial dependencies, a 'disharmonic' version of this rule is needed: (9) x/v (zA... z.\x)/(zA.., z.\Y) Hoeksema proposes that verbs which trigger cross-serial word order are subject to (9): (10) ...An Bea wil kussen</Paragraph>
      <Paragraph position="2"> In a framework using recursive constraints, generalized disharmonic division can be implemented as a recursive constraint connecting the initial category of such verbs with a derived category:</Paragraph>
      <Paragraph position="4"> cross_serial(X, (NP\(NPkS))/(NP\S)).</Paragraph>
      <Paragraph position="5"> lez(voornemen, (NPre fl \(NP\S))/(NP \S)).</Paragraph>
      <Paragraph position="6"> aArgument inheritance is used in HPSG to account for verb clustering in German (Hinrichs and Nakazawa, 1989). The rlPSG analysis is essentially equivalent to Hoeksema's account.</Paragraph>
      <Paragraph position="8"> Only verbs that trigger the cross-serial order are sub-ject to the division constraint. This accounts immediately for the fact that cross-serial orders do not arise with all verbs selecting infinitival complements.</Paragraph>
    </Section>
    <Section position="2" start_page="149" end_page="149" type="sub_section">
      <SectionTitle>
3.2 Verb Clusters
</SectionTitle>
      <Paragraph position="0"> The verb_cluster constraint ensures that cross-serial word order is obligatory for verbs subject to cross_serial. To rule out the ungrammatical (8a), for instance, we assume that Bea kussen is not a verb cluster. The verb kussen by itself, however, is unspecified for vc, and thus (7a) is not excluded.</Paragraph>
      <Paragraph position="1"> We do not assume that cross-serial verbs take lexical arguments (as has sometimes been suggested), as that would rule out the possibility of complex constituents to the right of cross-serial verbs altogether. If one assumes that a possible bracketing of the verb cluster in (7b) is \[wil \[zien kussen\]\] (coordination and fronting data have been used as arguments that this is indeed the case), a cross-serial verb must be able to combine with non-lexical verb clusters. Furthermore, if a verb selects a particle, the particle can optionally be included in the verb cluster, and thus can appear either to the right or to the left of a governing cross-serial verb. For a verb cluster containing two cross-serial verbs, for instance, we have the following possibilities:  (13) a. dat An Bea heeft durven aan that An Bea has dared part.</Paragraph>
      <Paragraph position="2"> te spreken to speak that An has dared to speak to Bea.</Paragraph>
      <Paragraph position="3"> b. dat An Bea heeft aan durven te spreken.</Paragraph>
      <Paragraph position="4"> c. dat An Bea aan heeft durven te spreken.</Paragraph>
      <Paragraph position="5">  A final piece of evidence for the the fact that cross-serial verbs may take complex phrases as argument stems from the observation that certain adjectival and prepositional arguments can also appear as part of the  verb cluster: (14) dat An dit aan Bea had duidelijk that An this to Bea has clear gemaakt made thai An had made this clear to Bea  Cross-serial verbs select a +vc argument. Therefore, all phrases that are not verb clusters must be marked vc. In general, in combining a (verbal) functor with its argument, it is the argument that determines whether the resulting phrase is -vc. For instance, NP-arguments always give rise to -VC phrases, whereas particles and verbal arguments do not give rise to -vc phrases. This suggests that NP's must be marked -vc, that particles and verbs can remain unspecified for this feature, and that in the syntactic rule for application the value of the feature vc must be reentrant between argument and resultant.</Paragraph>
    </Section>
    <Section position="3" start_page="149" end_page="150" type="sub_section">
      <SectionTitle>
3.3 The distribution and scope of
adjuncts
</SectionTitle>
      <Paragraph position="0"> The analysis of cross-serial dependencies in terms of argument inheritance interacts with the analysis of adjuncts presented in section 2.2. If a matrix verb inherits the arguments of the verb it governs, it should be possible to find modifiers of the matrix verb between this verb and one of its inherited arguments. This prediction is borne out (15a). However, we also find structurally similar examples in which the adjunct modifies the governed verb (15b). Finally, there are examples that are ambiguous between a wide and narrow scope reading (15c). We take it that the latter case is actually what needs to be accounted for, i.e. examples such as (15a) and (15b) are cases in which there is a strong preference for a wide and narrow scope reading, respectively, but we will remain silent about the (semantic) factors determining such preferences.</Paragraph>
      <Paragraph position="1"> (15) a. dat Frits Marie volgens mij lijkt that F. M. to me seems te ontwijken.</Paragraph>
      <Paragraph position="2"> to avoid It seems to me that F. avoids M.</Paragraph>
      <Paragraph position="3"> b. dat Frits Marie opzettelijk lijkt that F. M. deliberately seems te ontwijken.</Paragraph>
      <Paragraph position="4"> to avoid It seems that F. deliberately avoids M.</Paragraph>
      <Paragraph position="5"> c. dat Frits Marie de laatste tijd lijkt that F. M. lately seems te ontwijken.</Paragraph>
      <Paragraph position="6"> to avoid It seems lately as if F. avoids M.</Paragraph>
      <Paragraph position="7"> It seems as if F. avoids M. lately On the assumption that the lexical entries for lijken en ontwijken are as in (16), example (15c) has two possible derivations ((17) and (18)). Procedurally speaking, the rule that adds adjuncts can be applied either to the matrix verb (after division has taken place) or to the  governed verb. In the latter case, the adjunct is 'inherited' by the matrix verb. Assuming that adjuncts take scope over the verbs introducing them, this accounts for the ambiguity observed above.</Paragraph>
      <Paragraph position="8">  (16) lex(lijken, Verb):add_adjuncts(Verb, Verb'), cross_serial(Verb', (NP\S)/(NP\S)).</Paragraph>
      <Paragraph position="9"> lex(ontwijken, Verb):add_adjuncts(Verb, NP\(NP\S)).</Paragraph>
      <Paragraph position="10"> (17) ... de laatste tijd lijkt</Paragraph>
    </Section>
  </Section>
  <Section position="5" start_page="150" end_page="150" type="metho">
    <SectionTitle>
ADJ IV/IV
</SectionTitle>
    <Paragraph position="0"> The assumption that adjuncts scope over the verbs introducing them can be implemented as follows. We use a unification-based semantics in the spirit of Pereira and Shieber (1987). Furthermore, the semantics is head-driven, i.e. the semantics of a complex constituent is reetrant with the semantics of its head (i.e. the functor). The feature structure for a transitive verb including semantics (taking two NP's of the generalized quantifier type ((e, t), t} as argument and assigning wide scope to the subject) is:  Thus, a lexical entry for a transitive verb can be defined as follows (where TV refers to the feature structure in 19): (20)/ez(kussen, X) :add_adjuncts(X, TV).</Paragraph>
    <Paragraph position="1"> The lexical rule for adding adjuncts can now be extended with a semantics: (21) add_adjuncts(\[ sem Sx \]x' \[ sem Sy \]y) :-</Paragraph>
    <Paragraph position="3"> Each time an adjunct is added to the subcategorization frame of a verb, the semantics of the adjunct is 'applied' to the semantics as it has been built up so far (Sy), and the result (SA) is passed on. The final step in the recursion unifies the semantics that is constructed in this way with the semantics of the 'output' category.</Paragraph>
    <Paragraph position="4"> As an adjunct A1 that appears to the left of an adjunct A2 in the string will be added to the subcategorization frame of the governing verb after As is added, this orders the (sentential) scope of adjuncts according to left-to-right word order. Furthermore, since the scope of adjuncts is now part of a verb's lexical semantics, any functor taking such a verb as argument (e.g. verbs selecting for an infinitival complement) will have the semantics of these adjuncts in its scope.</Paragraph>
    <Paragraph position="5"> Note that the alternative treatments of adjuncts mentioned in section 2.2 cannot account for the distribution or scope of adjuncts in cross-serial dependency constructions. Multiple (i.e. a finite number of) categorizations cannot account for all possible word orders, since division implies that a trigger for cross-serial word order may have any number of arguments, and thus, that the number of 'subcategorization frames' for such verbs is not fixed. The polymorphic solution (assigning adjuncts the category x/x) does account for word order, but cannot account for narrow scope readings, as the adjunct will always modify the whole verb cluster (i.e the matrix verb) and cannot be made to modify an embedded verb only.</Paragraph>
  </Section>
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