LIFE SCIENCE TECHNICAL BULLETIN MODEL BASED DRUG DEVELOPMENT – WHAT IS IT GOOD FOR?AUTHOR: JANET R WADE, PHD, SENIOR CONSULTANT, SGS EXPRIMO The FDA ‘‘critical path'' document characterizes model-based drug development (MBDD) as the development and application of pharmaco-statistical models of drug efficacy and safety from preclinical and clinical data to improve both drug development knowledge management and decision-making (1), (2). A less formal description of MBDD would be the development and use of mathematical models to aid answer existing and future project team questions that arise during drug development. As an analogy, many of us probably played with Lego bricks during our childhood. We could make many different models out of those bricks, but we made what we wanted to make at that point in time. In MBDD, the Lego bricks represent pieces of information and the models they are used to create (castle, house, farm, etc.), depends on what is needed (a place to defend yourself from an attack, somewhere warm to sleep, somewhere to raise cows and chickens, respectively).
Privateessex.ac.ukRelating morphology to syntax Relating Morphology to Syntax
Louisa Sadler and Rachel Nordlinger Relatively little attention in theoretical work in LFG has focussed on the nature ofthe interface between morphology and syntax, or indeed on the role of morphologyproper.1 2 While the contribution of morphology to the definition of f-structures isfirmly established, and the separation of external structures by the principle of lexicalintegrity is the backbone of LFG's lexicalist outlook, the internal operation of the mor-phological component, and how words come to contribute the relevant f-descriptionshave not generally been at the forefront of theoretical work.
From a syntactic point of view this is unsurprising, for in the general case nothingmuch hangs on precisely how matters internal to inflectional morphology are dealtwith. In the typical case "pieces" of inflectional morphology contribute informa- tion to the f-structure of the word itself (e.g. ( TNS) = PAST) or to the f-structure of a dependent of the word (e.g. ( SUBJ PRED) = ‘PRO'), and thus the syntacticcontributions of discrete "pieces" of inflectional morphology do not interact in anycomplicated way. This means that a simple, word-syntactic, incremental view maybe taken of the syntactic contribution of inflectional morphological processes such asaffixation, in which f-descriptions are associated directly with morphological formsor features.
However, more complex data makes it evident that the simple incremental view canbe problematic. Difficulties may arise in several domains. For example, there is a con-siderable body of morphological data which suggests that an incremental approach isinsufficient or inappropriate on purely morphology-internal grounds of the adequacyof morphological description, although we will not be concerned with such evidencein this paper (see Stump 2001 and Spencer this volume for more discussion). Addi-tionally, there is a further type of complex data where the complexity relates to theinteraction between the syntax and the morphology, more particularly, the interac-tion between the pieces of syntactic information which are encoded morphologically.
Such data poses fundamental issues for the mapping between syntax and morphology,showing that the simple view, under which all that is required is to (incrementally)associate syntactic information with morphological features (or forms), is incorrect.
1Thanks for discussion of relevant material to Mary Dalrymple and Andrew Spencer. We are also grateful to Ryo Otuguro and two anonymous reviewers for comments on this paper. Remaining errorsare of course solely our own responsibility. Sadler is grateful to the University of Essex for a period ofsabbatical leave during which this work was completed, and Nordlinger for the support of the AustralianResearch Council, grant F9930026, held at the University of Melbourne.
2Existing work touching on, or having consequences for, these issues includes Ackerman 1990, Sadler 1997, Sells 2000 and this volume, and Kaplan and Butt 2002, amongst others, and in particularthe work on verbal periphrasis including Butt et al 1996, B¨orjars et al 1997, Sadler and Spencer 2001and Frank and Zaenen 2002.
Relating morphology to syntax This paper is concerned with data of this sort, and in particular with the phenomenonof case stacking, which shows in a clear fashion both that morphological structuredoes matter, and that there are interesting issues to be addressed in the morphology-syntax interface.
The phenomenon of case stacking, dramatically illustrated in (1) from the Australianlanguage Martuthunira, demonstrates in an extreme form the role that morphologycan have in building and constraining syntactic structures.
Ngayu nhawu-lha ngurnu that(ACC) euro-ACC joey-PROP-ACC thara-ngka-marta-a.
pouch-LOC-PROP-ACC‘I saw the euro with a joey in (its) pouch.' (Martuthunira, Dench 1995a:60,(3.15)) In this example the most deeply embedded nominal ‘pouch' carries three case mark-ers, each one relating to a successively higher syntactic relationship. First ‘pouch'is inflected with the locative case marking the f-structure function of ‘pouch', thenwith the proprietive case indicating that the locative nominal is embedded within theproprietive NP ‘joey in (its) pouch', and finally with the accusative case, marking thewhole proprietive NP as being contained within the object NP. Case stacking data suchas that in (1) poses some interesting challenges for morphological description becauseit demonstrates that morphosyntactic features may be iterated. More importantly, itcasts light on the nature of the interface between syntax (f-structure) and morphologybecause capturing these data necessitates a complex mapping between morphologicalsequencing and syntactic structure.
In earlier work, Nordlinger (1998) provides an incremental, morpheme-based accountof these data in LFG. The morphology (or lexical component) constructs fully in-flected wordforms with multiple case markers — for this Nordlinger adopts an essen-tially word-syntactic approach to inflectional morphology. Functional (f-structure) in-formation is associated directly with morphemes (which are conventionally thought ofas listed as (sub-)lexical entries). The role of morphology in defining or constrainingthe larger syntactic environment within which the word appears is straightforwardlycaptured by the use of so-called inside-out statements. For example, on a morphemicapproach the Martuthunira accusative case marker -yu can itself be associated with afunctional description which states that it specifies or defines an OBJ function. Thismodel of constructive morphology has been widely adopted in recent morphosyntac-tic research in LFG (Nordlinger 1998, Barron 1998, Sadler 1998, Sells 2000, Lee1999, Sharma 1999, Nordlinger 2000, Nordlinger and Sadler 2000, O'Connor 2002,Ørsnes 2002). To accommodate case stacking, Nordlinger formulates a combinatorialprinciple (the Principle of Morphological Composition (PMC)) which correctly con-strains the interaction of f-structure information associated with different morphemesin the inflected word. However an important issue which arises in this connection Relating morphology to syntax is that the PMC is not formalized within the LFG description language in that work.3As should become clear as we proceed, one reason why the mapping between mor-phemes (or morphological features) and syntactic functions is problematic to formal-ize on a word syntactic view is precisely because the incremental morphemic viewunder which affixes are added hierarchically by means of a binary X provides an inapprorpriate structure for the felicitious combination of f-descriptions.
The purpose of this paper is to explore more fully the mapping between morpholog-ical and syntactic descriptions, with primary reference to the case stacking data. Inparticular we aim to show how the insights of Nordlinger's (1998) Principle of Mor-phological Composition can be incorporated into a model of the morphology/syntaxinterface which is fully compatible with the description language of LFG, but on thebasis of different assumptions about the nature of the morphological representationitself. We will not be concerned here with actual morphological forms, nor with thetheory of inflectional morphology which generates the inflected word forms. In spec-ifying the mapping between morphology and syntax in this paper our starting pointwill be the sorts of structured representations delivered by the inferential-realizationalaccount of the morphology of case-stacking proposed in Sadler and Nordlinger (to ap-pear).4 The rest of this paper is structured as follows. Section 2 provides the background nec-essary to understand the problem we focus upon. It begins with a brief review of therelevant case stacking data and then illustrates the constructive morphology approachto this data which our analysis builds on. The section concludes with an evaluationof the Principle of Morphological Composition. With this background in place, sec-tion 3 outlines our proposal for the interface between morphological structures andf-descriptions and section 4 concludes.
3Note however that the appendix to Nordlinger (1998) suggests an approach to restating the PMC with standard LFG tools which prefigures in some respects the approach to formalization which weadopt here.
4Sadler and Nordlinger (to appear) propose a morphological analysis in the framework of Paradigm Function Morphology (PFM), which has several advantages over the morpheme-based account ofNordlinger (1998). In particular, it is quite straightforward in PFM to set up the morphology to ap-propriately constrain the interaction of different case functions (e.g. the relational, modal, associatingand complementizing case functions of Kayardild (Evans 1995a)), whereas in the original work byNordlinger, the morphology overgenerates on this front, with the syntax effectively playing a filteringrole. Additionally, the separation of function from exponence in a realizational framework permits var-ious exceptional forms, such as portmanteau affixes and case substitutions, to be correctly treated. SeeSadler and Nordlinger (to appear) for further discussion.
Relating morphology to syntax Composition and F-Descriptions
The following is a straightforward example of adnominal multiple case in the Aus-tralian language Thalanyji. Here the possessor is coded by the dative case marker -ku DAT, and also takes the case of the head that it modifies (ACC).
kupuju-lu kaparla-nha yanga-lkin wartirra-ku-nhachild-ERG dog-ACC chase-PRES woman-DAT-ACC ‘The child chases the woman's dog.' (Thalanyji, Austin 1995:372, (22)) The fully inflected word wartirra-ku-nha ‘woman-DAT-ACC' projects the functionalinformation shown in (3), in which is the f-structure of the nominal itself, and contains the dative case feature, while the accusative case feature belongs in a higherf-structure (namely, that of the head noun ‘dog').
A more complex case stacking example is the following from Martuthunira, repeatedfrom (1) above.
Ngayu nhawu-lha ngurnu that(ACC) euro-ACC joey-PROP-ACC thara-ngka-marta-a.
pouch-LOC-PROP-ACC‘I saw the euro with a joey in (its) pouch.' The information projected from the single inflected nominal thara-ngka-marta-a‘pouch-LOC-PROP-ACC' is shown diagrammatically in (5) — once again, the f-structure of the nominal itself is . In this example, the innermost (locative) case marks the locative adjunct ‘pouch'. The proprietive case signals the proprietive ad-junct relation between ‘joey' and ‘euro', and the outermost (accusative) case signalsthe relation between ‘euro' and the verb (the object relation).
Relating morphology to syntax The case system of the Tangkic language Kayardild (see Evans 1995a) is still morecomplex, additionally permitting the use of case markers in modal function (in whichcase morphology partially specifies temporal and modal information at the level of theclause) and case markers in complementizing function, where case markers are usedto mark interclausal relations on complementized clauses (Dench and Evans 1988,Evans 1995a). The word thabuju-karra-nguni-na in (6) illustrates the combination oftwo case markers in core function with a case marker in modal function. The modalablative case (M.ABL) marks the clause as having past tense. The instrumental casemarks ‘brother' as belonging to an instrumental argument of the verb and the genitivecase marks ‘brother' as the (adnominal) possessor argument within the instrumentalNP. The information projected from the nominal thabuju-karra-nguni-na is shown in(7)— again, the f-structure of the nominal itself is Ngada yalawu-jarra yakuri-na fish-M.ABL brother-GEN-INST-M.ABL net-INST-M.ABL ‘I caught the fish with brother's net.' (Kayardild, Evans 1995b: 400, (10)) As a further complication to the data, note that number marking may be interleavedwith case marking in these languages, with each instance of number marking modi-fying a different referent according to its position in the morphological structure, asshown in the Kayardild example (8), in which the ablative case marks the possessorfunction.
maku-yarr-nurru-naba-waladwoman-DU-ASSOC-ABL-MANY(NOM)‘the many belonging to (those) having two wives' (Kayardild, Evans1995a:123) Relating morphology to syntax Similarly, in the following Martuthunira noun phrase, the pronominal stem is SG, thegenitive case marks the possessor function and the subsequent dual number markingis interpreted with respect to the possessed noun pawulu- ‘child'.
1SG.OBL-GEN-DU-ACC child-DU-ACC‘my two children' (Dench 1995a:95, (4.154)) The fact that number marking interacts with the stacking of case markers in this man-ner is significant because it demonstrates that more is at issue here that a simple"quirk" of the case system of these languages. Rather it is evident that the morpho-logical structure itself is complex and that the successive levels of case marking definesyntactic structures which are referenced by other f-structure descriptions expressedword-internally, thereby providing additional support for the constructive view itself.
Constructive Morphology: Inside-Out Constraints
Such case stacking clearly demonstrates the fundamental role that morphology canplay in encoding complex syntactic relations. In order to account for such dataNordlinger (1998) develops the model of constructive case within LFG whereby mor-phological constituents/processes may actively define properties of their clausal envi-ronment independently of syntax (see also Simpson 1983, 1991 and Andrews 1996).
The model of constructive case consists essentially of two distinct ideas.
The first of these is the use of inside-out constraints (e.g. Halvorsen and Kaplan 1988,Dalrymple 1993, see also Andrews 1996:41-43) associated with the lexical elementsor morphological processes to enable nominal constituents to define the larger syn-tactic (f-structure) context in which they are embedded.5 In this way, case-markednominals can specify the grammatical function of the higher clause of which theirf-structure is the value. Thus the f-structure information associated with accusative 5Inside-out function application is well-established in LFG through work in such areas as quantifier scope (Halvorsen and Kaplan 1988), anaphoric binding (Dalrymple 1993), internally-headed relativeclauses (Culy 1990), Russian genitive of negation (King 1995), Urdu case (Butt 1995), and topicalization(Bresnan 2001).
Relating morphology to syntax case in an example such as the Martuthunira (4) is as in (11), and the accusative-casenominal (e.g. ‘euro-ACC') projects the f-structure in (12).
By virtue of the inside-out designator (OBJ ), the information associated with the accusative case constructs a higher f-structure ( ) which contains an OBJ to which the f-structure associated with the case-inflected nominal itself ( ) belongs. Thus, on this analysis, a nominal inserted into the syntax already defines its grammaticalfunction by virtue of the case marker attached to it.
While the use of the inside-out constraints enables nominals to construct informationabout the higher f-structure in which they are embedded (e.g. by specifying a gram-matical function for it), this alone does not provide an analysis of the case stackingdata presented above. The constructive case model also contains a second componentto compose the information contributed by multiple morphological elements, for eachcase marker contributes information about a successively higher f-structure. This isthe Principle of Morphological Composition, which we discuss in the following sub-section.
Interfacing Stacking Morphology with Syntax
On a standard LFG view of how the f-description associated with an inflectionallycomplex word comes about, the syntactic information associated with each morpho-logical element is simply conjoined. For a word with multiple case markers, suchas thara-ngka-marta-a ‘pouch-LOC-PROP-ACC' in (4), this essentially corresponds topositing the following sub-lexical annotated tree, in which each case marker intro-duces a CASE value and makes reference to a (different) grammatical function: Relating morphology to syntax But of course this will not give the desired results because it fails to embed the f-structures in the appopriate manner (and as a consequence it also assigns multiple inconsistent CASE values to the f-structure denoted throughout by (1998) observes that, informally speaking, each successive affix takes the outer f-structure (call it ) described by the previous affix and defines some properties of both it and the higher f-structure which immediately contains . If the process of affixation is constrained to have this syntactic consequence, then the iconic effectsexemplified in section 2.1 above are accounted for. This insight is captured in thePrinciple of Morphological Composition, which composes the information associ-ated with successive affixes. According to the PMC, the f-structure information theaffix actually defines depends on the information associated with the preceding mor-phological element (which could be the root or a more deeply embedded affix). Theidea is that context-sensitive substitutions to the f-descriptions in (sub-)lexical entries are carried out: every occurrence of in the lexical information associated with an affix is substituted with any expression of the form (GF ) on the preceding morpho- logical element. Nordlinger (1998) formulates this principle as follows: Principle of Morphological Composition:Where
is a string of attributes: In the case where the preceding morphological element is annotated simply with outside-in equations, such as ( TNS) = PAST, the intention is that substitution of will apply vacuously, while on the other hand if the previous element is anno- ) then every occurrence of on the current affix is replaced by (ADJ In this way, each affix defines information pertaining to a successively larger, con- Relating morphology to syntax taining f-structure. As an example, consider the fate of the sub-lexical entries for themorphemes listed in (15) in the Martuthunira nominal thara-ngka-marta-a in (4).
( PRED) = ‘pouch' As these entries show, the case morphology itself defines the grammatical functionof the nominal it marks, the LOCative case signals a locative ADJunct (ADJ ), the PROPrietive case signals a proprietive adjunct, (ADJ ), and the ACCusative case defines an OBJ function. From these entries the derived forms in (16) are outputfrom the process of substitution as formulated in the PMC. This approach permits amaximally general statement of the f-structure information associated with each affixin the lexicon.
Sub-Lexical Entry Entry Derived In Context ( PRED) = ‘POUCH' ( PRED) = ‘POUCH' With these substitutions to the f-descriptions associated with individual morphs, thesub-lexical tree is as follows: Relating morphology to syntax ( PRED) = POUCH ( CASE) = LOC The use of inside-out constraints and composition provides us with a simple accountof the use of nominals as heads or modifiers in many Australian Aboriginal languages,including Wambaya and Warlpiri. In these languages, nominal roots (that is, withoutany additional morphology) can themselves introduce syntactic functions, with con-sequences for the interpretation of the inflectional morphology which builds on thosestems, so that nominals can generally function either as NP heads or as modifiers.
Thus consider the Warlpiri and Wambaya examples in (18) and (19) respectively.
PRES-3.DU.SUBJ dog(ABS) chase-NPST small-DU-ERG ‘The two small children are chasing the dog.' (Warlpiri, Austin & Bresnan1996:225, (13)) Ngajbi ng-a ‘I saw his daughters.' (Wambaya, Nordlinger 1998:115, (42)) The Warlpiri nominal wita-jarra-rlu in (18) is an adjunct which agrees in number andcase with the nominal which it modifies. The f-structure corresponding to wita-jarra-rlu is shown in (20), in which the ADJ function is projected directly from the nominalstem (Nordlinger 1998), and contributes CASE and NUM features to the f-structure ofthe nominal which it modifies.
Relating morphology to syntax The information associated with the (sub-)lexical entries is as shown in the first col-umn of (21) and the f-descriptions derived by the operation of the PMC in the secondcolumn: Sub-Lexical Entry Entry Derived In Context ( PRED) = ‘small' ( PRED) = ‘small' In fact, the (ADJ ) annotation associated with nominal stems such as wita is optional.
General LFG principles of completeness and coherence will ensure that grammaticalf-structures only result if the ADJ function is present for a modifier use and absentwhen the nominal functions as the NP head.
Similarly, in (19) the possessive pronominal root is inflected for the case and numberof the possessed element, which is the head of the containing f-structure, while thepronominal root itself introduces the POSS function. The structure defined by the fullyinflected word nangi-marnda-rna is shown in (23).
( PRED) = ‘PRO' ( GEND) = ‘MASC' Notice that once the word formation component is set up to provide the right forms,the constructive morphology approach exemplified here immediately accounts, with-out further modification, for forms such as this which carry two number and gender Relating morphology to syntax values – one for the possessor and one agreeing with that of the possessed element.
The Principle of Morphological Composition, in this case in conjunction with theassumption that the stem introduces the POSS function, ensures that the values SGand MASC are in the f-structure of the possessor and the values PL and FEM in thef-structure of the governing nominal ‘daughter'.
Evaluating the PMC
The PMC straightforwardly captures the intuition that as they stack, the (case andnumber) affixes contribute information to the f-structure defined by the morphologi-cal structure to which they attach. This places a strong constraint on the relationshipbetween syntax and morphology, imposing a sort of isomorphism: morphologicalstructure and syntactic structure are required to match in the appropriate sense. Be-cause the principle essentially embeds the syntactic information associated with theprevious (more deeply embedded) affix into the syntactic information associated withthe next (higher) affix, it automatically accounts for the observed iconic behaviour ofcase stacking.
Despite this, the principle itself is not without problems. In particular, the statementof this principle does not fall within the mathematics which underpins the LFG for-malism. As we have seen, the operation of the PMC entails the substitution of paths inthe f-descriptions associated with affixes. Although the formulation of the principlein (14) might give the impression that these substitutions are local to a sub-tree ofdepth one, note that this is not actually the case — the substitution is not betweensisters in a local subtree. In fact, a crucial aspect of the principle is that the relevantsubstitutions are really performed at the level of the information lexically associatedwith the affixes, and not at the level of the derived word. As shown above, the word(and indeed the stem at each level of recursion within the word structure) is anno- = . This is crucial to ensuring that the word itself interacts correctly with the f-descriptions associated with the other nodes in the c-structure tree. What the princi-ple ensures is that the information associated in the lexicon with an affix is modified by substituting for the designation on the affix whatever inside-out path is eventu- ally associated with the preceding affix, once any substitutions at that level have beenperformed. This requires a form of pattern matching, which is not supported withinthe LFG formalism.
Because the approach to word internal structure in Nordlinger 1998 is basically mor-phemic, the PMC is formulated with reference to trees which reflect morphemic struc-ture. Once we move away from a morpheme-based morphology, however, we are ableto consider different structurings of morphological information which are not tied toexponence, and as a consequence the effect of the principle of morphological com-position can be captured directly without the need for any path substitutions. In therest of this paper, we take as our starting point the recent morphological treatment ofthe Kayardild case stacking data in Sadler and Nordlinger (to appear) and show how Relating morphology to syntax the mapping to syntax can be directly encoded on the basis of these morphologicalstructures.
The Morphology-Syntax Interface
We noted at the start of this paper that the interface between (inflectional) morphologyand syntax has received relatively little attention to date in LFG, the standard view be-ing a lexicalist, incremental one in which f-descriptions are associated with elementsof the morphology (for example, affixes or morphological features) and then com- bined straightforwardly by identifying word-internal instances of cases, of course, this is unproblematic, for the simple reason that the informationexpressed by a word is typically quite local to the f-structure of that word.
Conceptually, the interface between lexical representations and syntactic (f-) descrip-tions involves two distinct aspects. The first of these is the specification of a mappingbetween syntactic information and corresponding elements in the morphological do-main, that is, morphological features, and lexemes or roots. In very many cases,of course, this mapping is highly transparent, to such an extent that it is often tac-itly assumed that the syntax and the morphology involve one and the same set ofmorphosyntactic properties, but in fact there are good reasons to keep these featuresdistinct. For one thing, there are clearly morphology-internal features (such as con-jugation class), which have no place in syntactic representations of any sort, and foranother, there are well-known cases of mismatch between morphological and syntac-tic features, for example where an element is morphologically a member of categoryA but syntactically a member of category B (see Spencer to appear). The second as-pect of the interface between morphology and syntax is the specification of how thesyntactic information associated with the morphological "parts" is to be combined.
Here too, within an LFG context, simple concatenation of f-descriptions associated with morphological "parts" (with identification of instances of ) is generally appro- priate. However, as we have seen, this is not the case for the case stacking data, inwhich the functional information associated with morphological "parts" interacts ina more complex way. In the current section, we show how this interaction can besimply captured in the interface between a realizational morphology and the syntax.
Associating F-descriptions with M-features
In recent work, Sadler and Nordlinger (to appear) provide a morphological accountof case stacking within Paradigm Function Morphology (PFM) (Stump 2001). In sucha realizational approach, the morphological descriptions are paradigm cells, wherea paradigm cell is a pair consisting of a lexeme (or root) and a well-formed fea- Relating morphology to syntax ture bundle.6 For example, the morphological structures associated with fully in-flected wordforms in a case stacking language such as Kayardild (which has a modalcase function as well as core (adnominal or relational) case functions) are as shownin (24). The structure in (24 a) is associated with the word thabuju-karra-nguni-na ‘brother-GEN-INST-M.ABL' (see (6)), while the nominal maku-yarr-nurru-naba-walad ‘woman-DU-ASSOC-ABL-MANY(NOM)' (see (8)) is of the more complicatedform involving multiple number features, shown schematically in (24 b). These ex-amples are given in a notation for specifying paradigm cells in PFM (in what followswe will often abbreviate Core as C ).
b. LEX, Num:A, Case c. LEX, Num:A, Case Sadler and Nordlinger (to appear) is concerned essentially with morphology-internalmatters, rather than with the nature of the interface between morphological structuresand f-descriptions, and includes only a brief sketch of a relatively simple procedurefor correctly combining the syntactic information associated with each morpholog-ical feature (and the lexemic root). The current paper, on the other hand, takes asits starting point the sorts of structured morphological representations proposed inSadler and Nordlinger (to appear) and shows how the mapping between morphologi-cal stuctures and the syntax can be straightforwardly specified without any extensionto the LFG formalism (but with the addition of a minor notational extension), usingf-descriptions directly in the morphology-syntax interface.
As noted above, the first step is to specify the syntactic information correspondingto each morphological feature. This is quite trivial, and the syntactic information isprecisely that proposed in Nordlinger (1998), although of course in our realizationalapproach, this information is associated with morphological descriptions or featuresand not with morphemes. A mapping is specified between morphological A:V pairsand syntactic information, and between roots and syntactic information —- this maybe thought of as a lexicon or lexical transducer.7 We show below some examples of(constructive) case, number and nominal stems: 6That is, these structures are the output of morphological (inflectional) analysis, and the input to mor- phological (inflectional) generation. The rules of (inflectional) morphology relate well-formed paradigmcells to realizations.
7See Kaplan and Newman 1997 and Butt et al 1999 for discussion of a similar "lexicon" of morpho- logical formatives within the XLE computational environment.
Relating morphology to syntax ( CASE)=LOC, (ADJ ( CASE)=ABL, (ADJ ( CASE)=PROP, (ADJ ( CASE)=ERG, (SUBJ ( CASE)=NOM, (SUBJ ( PRED) = ‘WOMAN' The second step is to specify how the syntactic information, that is, the f-descriptions,are to combine. The lexical form, that is, in PFM the paradigm cell corresponding to afully inflected word, can be viewed as a simple tree structure in which each attribute isa preterminal node and each value a terminal node – this is captured in (26) where MFis a metavariable over feature labels Num, Case, and so on. For example, the paradigmcell in (24 a) would define a structure as shown schematically in (27) below.
To take an example, we consider the Martuthunira nominal thara-ngka-marta-a‘pouch-LOC-PROP-ACC' from example (4). The morphological description is as fol-lows: thara, Case :Loc, Case :Prop, Case :Acc and the interface tree is represented as in (29) in which morphological feature valuesare shown as terminal nodes with initial capitalisation.
Relating morphology to syntax The f-descriptions are associated with the terminal nodes, giving (30): It remains to specify the annotations associated with the pre-terminal tree nodes. Thegeneralization for a language with a constructive case feature, such as Kayardild orMartuthinira, is as follows: Annotation Principle: For node n, if the immediately preceding left sisternode is Case then annotate node n with = ( GF), otherwise annotate with appearing here is a notational innovation which we discuss below. Note that the interface grammar does not play a filtering role, rather it is the role of themorphology proper to ensure that only well-formed feature bundles are ever produced,for example by ensuring that Number is never directly embedded under Number, andso forth.
The two operations of the interface, namely lexical look-up and (re-)parsing of themorphological structure, together with the annotation principle, provide the annotatedtree-structure shown in (32).
The notational innovation left arrow ( ) denotes the f-structure of the immediate left sister of the node to which it is attached: that is, while denotes the f-structure of the mother node ( ( denotes the f-structure of the node to which it is annotated ( (*)), stands for a function which Relating morphology to syntax picks out an immediately preceding sister node. Note that is distinct from the function used in LFG to refer to the immediately containing f-structure in specifyingoff-path constraints (Dalrymple 1993),8 and for this reason we attach an s subscriptto the left arrow we use here, Substitution and Simplification
For clarity, we work through the process of constraint simplification and satisfactionfor (32) step by step to illustrate what does: since this involves multiple Case nodes we label them with subscripts in the tree fragments to improve comprehensi-bility. The annotations associated with the tree fragment in (33 a) define the partialf-structure also shown in (33 b).
( PRED) = ‘POUCH' Continuing through the tree left to right, consider the tree fragment in (34 a). Theannotation on the node Case specifies that the f-structure of the sister node (Case , of which the f-structure is ) is the value of some GF in the f-structure ( of the node Case . Since is the value of the path ADJ (from above), ADJ GF are equated, defining the structure in (34 a).
8Off-path constraints are used especially in the statement of conditions on long distance dependen- cies and anaphoric dependencies. In this context, associated with an attribute denotes the f-structure is an attribute (see Dalrymple 2001:151).
9It seems very possible that will be useful more generally in the description of syntactic phe- nomena. In recent computational work on projecting f-structure from chunk-based shallow trees, Frank(2003) independently proposes the addition of to refer to the f-structure of the (left) sister.
Relating morphology to syntax Substitutions in the rest of the f-descriptions operate in exactly the same fashion.
For example, for the next tree fragment, (35 a), we know that f-structure of theCase node is . The annotations on the terminal node specify that in a larger f-structure and define 's own CASE feature as PROP. The on the immediate right sister node Case specifies that the f-structure of the immediate left sister node (Case , f-structure ) is the value of some GF in the ) of the node Case . Since is the value of the path ADJ the Case annotations), ADJ and GF are equated (35 b.).
The annotations on the terminal node under Case specify that is the value of OBJ in some larger f-structure and define 's own CASE feature as ACC. Thus, the f- descriptions associated with the tree in (32) are satisfied by the following f-structurein the minimal model: Relating morphology to syntax Turning now to a second example, this time involving the interaction of case andnumber marking, the morphological description for the Kayardild nominal in (8) is asshown in (37).
The two operations of the interface, namely lexical look-up and (re-)parsing of theparadigm cell structure provide the annotated tree-structure (38).
These f-descriptions are satisfied by the structure in (39).
Constructive Stems Revisited
We turn now to the treatment of constructive stems. These are the cases, exemplifiedby (18) and (19), in which the root itself introduces a grammatical function. This Relating morphology to syntax is very frequently the ADJ function, as in (18), for there is generally no syntacticdistinction in Australian languages between nouns and adjectives, with most nom-inal elements functioning as either heads or modifiers. As noted above, we followNordlinger (1998) in assuming that such nominal roots in the languages we are con-cerned with optionally introduce an adjunct function. Other examples of constructivestems include Wambaya possessive pronouns, exemplified in (19), which introducethe POSS function. The lexical mappings which we propose treat such stems as op-tionally introducing a grammatical function, as shown in (40).
( PRED) = ‘SMALL'] [( PRED ) = ‘SMALL']] ( POSS) = , ( PRED) = ‘PRO' ( PERS) = 3, ( GEN) = MASC, ( NUM) = SG We illustrate the approach with the Warlpiri modifier wita-jarra-rlu ‘small-DU-ERG'from (18), in which the root constructs an ADJ function and the nominal contributes NUM and CASE features to the f-structure of the head which it modifies. The relevantstructures are shown below.
wita, Num:Du, Case :Erg Notice that the treatment of constructive stems under this proposal differs in one re-spect from the treatment proposed in Nordlinger (1998). In the earlier account, con-structive stems were associated with inside-out descriptions (and thus were treated ona par with constructive case morphology). The difference can be seen by comparing(43a) (from Nordlinger 1998) with (43b) (from the present analysis).
PRED) = ‘SMALL' ( PRED) = ‘SMALL' Relating morphology to syntax Under the proposal made here, therefore, the f-structure projected by the fully in-flected word wita-jarra-rlu is the f-structure of the head that wita- itself modifies.
As an alternative to the current proposal we might instead consider dealing with con-structive stems by introducing a morphological feature into the feature bundle with noexponent. For example, for the Warlpiri adjunct wita-jarra-rlu we would introduce aCase feature (with no corresponding exponent) at the top of the feature bundle, whichwould map to an ADJ function, and for the Wambaya possessive pronoun nangi-marnda-rna 3.SG.M.POSS-PL-II(ACC) we would introduce a Case feature (with nocorresponding exponent) which would map to a POSS function. This approach wouldcertainly reduce the set of constructive roots to instances of constructive inflectionalmorphology, but it seems otherwise to be incorrect. Firstly, the functional ambigu-ity of nominals in a language such as Warlpiri is quite systematic and is simply notdependent on morphological case. Secondly, this approach would make the incor-rect claim that those languages which have constructive roots necessarily permit casestacking — this claim is incorrect for some languages, including Wambaya. For thesereasons, we do not pursue here this alternative approach.10 This section has outlined a new proposal for associating f-descriptions with morpho-logical structures. The approach to the morphology-syntax interface involves deriv-ing a simple flat tree structure from the structured morphological representation. Thenodes of this morphological structure tree are annotated with f-descriptions in a fa-miliar fashion, and the resultant equations simplified. The major advantage of thisapproach over the morpheme-based PMC of Nordlinger (1998) (and the simplifiedthreading technique of Sadler and Nordlinger (to appear)) is that, with the exceptionof a modest notational extension to the language of f-descriptions, it uses the standard LFG formalism with no consequences for the formal power of the language. No pat-tern matching subsitutions are required because the morphological tree is not basedon incremental affixation in morphemic fashion.
From a linguistic point of view, however, the fundamental issue is the extent to which 10The approach that we take here to constructive stems shows some commonality with the treatment of derivational case morphology. It can be established that in some Australian languages some casemorphology is derivational rather than inflectional, producing an inflectional stem which defines its owngrammatical function (see, for example, Austin 1995, Nordlinger 1998). For example, in Wambaya,which does not permit inflectional case stacking, the cases PROP and PRIV are derivational while othercases are inflectional. In an example such as (1), the derivational morphology produces the root gijilu-lunguj, which is constructive, introducing an ADJ function.
Yandu ngi-n I'm waiting for the two old women with money (Nordlinger 1998:115 (41)) Relating morphology to syntax this proposal for the interface captures the basic intuition about constructive mor-phology. This intuition is the idea that (at least in these languages), morphologicaland syntactic structures (of the appropriate sorts) are nested or hierarchicalized iso-morphically; the syntactic contribution of a particular affix "builds" on that of the(perhaps complex) stem to which it attaches. This intuition is captured in the orig-inal PMC formulation by the incremental transformation or substitution into the f-description of a higher piece of morphological structure as a function of the (inputfrom) the f-description of the immediately lower or contained piece of morphologicalstructure/affix. Although not formalized, the substitution is stated in such a manneras to apply invariantly to both constructive and non-constructive morphological fea-tures (that is, irrespective of whether or not the f-description contains an inside-outstatement). Thus, the syntactic ramifications of a morphosyntactic feature followspurely from the f-descriptions associated with it (namely, whether or not it constructsa grammatical function), and not from the morphosyntactic structure (which remainsthe same irrespective).
In the current approach, however, a distinction between constructive and non-constructive features is also made in the Annotation Principle (31): the presenceof a constructive feature (Case) triggers the = ( GF) annotation, while a node following any other category is annotated = . Thus the distinction between con- structive and non-constructive features is made twice: in the f-descriptions introducedon terminal and on non-terminal nodes in the mapping structure. While this might bethought to be a disadvantage, it should be noted that the present proposal, which lim- its the permissible annotations to = ( GF), does rule out anti-iconic relations between morphological features and f-structures, as does Nordlinger's orig-inal proposal.11 Therefore, while the current approach may not have the generalityof Nordlinger's (1998) PMC it has the same empirical adequacy and, furthermore, isstraightforwardly integrated into the standard LFG architecture.
In most instances, the inflectional features of words define or reflect properties ofthe very local context — verbs express the tense, aspect and mood features of theclauses which they head, and encode agreement properties of their dependent corearguments, and nouns, adjectives and determiners inflect for properties such as thenumber, gender and definiteness of the nominal f-structure which they co-define. Thephenomenon of case stacking in Australian Aboriginal languages, however, showsthat inflectional morphology may express syntactic information pertaining to a muchlarger context, with words expressing functional information pertaining to f-structures 11It could be argued, however, that in any case a restriction to iconic ordering should be given a functional rather than a grammatical explanation, and therefore should not form a part of the grammar.
Whether or not this position is adopted, it remains a fact that the grammar must be able to accommodatethe complex contributions to relational structure that the case stacking data exemplifies.
Relating morphology to syntax within which their own f-structures are deeply embedded. Furthermore, the associa-tion of wider syntactic information with "pieces" of inflectional morphology comesabout in a highly structured manner. The importance of this data is that it provides acrucial window onto the nature of the interface between inflectional morphology andfunctional structure: the f-structure information associated with inflectional morphol-ogy must interact in a structured way. For these languages, associating f-descriptionswith the sort of morphological structure assumed by a word-syntactic, morphemicmodel gives the wrong result, because the f-descriptions interact incorrectly. On theother hand, given an approach to inflectional morphology which relates structuredproperty sets to exponents, the correct interaction between f-descriptions associatedwith morphological features can be obtained by representing morphological structuresin the interface as relatively flat trees, and associating and resolving f-descriptions as-sociated with tree nodes in the normal fashion, even for languages with complex casestacking morphology of this sort. The present proposal therefore permits us to inter-face a realizational approach to inflectional morphology with a standard LFG syntaxin a straightforward manner.
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