Reflexives in the Correspondence Architecture

Reﬂexives in the Correspondence Architecture

Ash Asudeh Carleton University

University of Iceland July 2, 2009

1 Introduction

• The standard LFG theory of the syntax of anaphora (Dalrymple 1993) is rather unique:

• Highly lexicalized: binding behaviour driven by reﬂexives, etc.

• The superiority condition on binding (f-command) does not need to be separately stated: consequence of ‘inside-out’ formalization

• No separate binding principles per se: a set of general (universal) constraints and parameters

2 Introduction

• Parameters (lexicalized): • Positive vs. negative binding equation • Domain: coargument (PRED), minimal complete nucleus (SUBJ), minimal ﬁnite domain (TENSE), root S • Antecedent: SUBJ vs. non-SUBJ • Universal constraints: • Locality Condition on constraints (uninterrupted binding domains) • Noncontainment Condition on antecedents (not equiv. to i-within-i) • Primacy of positive constraints • Thematic hierarchy

3 Goals

1. Review Dalrymple’s theory

2. Update the theory in light of some subsequent developments; in particular, variable-free binding in a resource-sensitive compositional semantics (Glue Semantics)

3. Augment the theory to formally capture interactions with logophoricity

Throughout:

1. Integration with LFG’s ‘Correspondence Architecture’

2. Reference to Icelandic data (from Þráinsson, Maling, Strahan)

4 Touchstone Quote 1

This indicates, I believe, that there is a close relationship between BT and lexical content of NPs but BT is nevertheless autonomous in the sense that not all binding properties of NPs follow from their lexical content. If they did, it would be difﬁcult to imagine how non-overt NPs could have different binding properties. (Þráinsson 1991: 70)

5 Touchstone Quote 2

But it is important to note that the semantic conditions for these syntactically unbound cases of long-distance reflexives in Icelandic (and Faroese) seem to be the same as those for the ones where a reflexive inside a finite (subordinate) clause is syntactically bound by the subject of a higher clause in the same sentence. This is shown in some detail in Sigurðsson (1986) and it indicates that we do not want a special account of the syntactically unbound long-distance reflexives in these languages. What we need is rather an account that takes care of both the more familiar instances of reflexives inside finite (subjunctive) clauses bound by (subject) antecedents in a higher clause and the intersentential, unbound reflexives just observed. That seems to make any attempt to extend the syntactic binding domain beyond finite-clause boundaries in languages like Icelandic and Faroese, for instance, a dubious enterprise. (Þráinsson 1991: 59)

6 Overview

• Icelandic data

• Background on LFG and Glue Semantics

• Correspondence Architecture

• Anaphora in LFG-Glue

• Binding constraints

• Variable-free binding

• Anaphoric Structure

• Logophoricity

7 Mig langar að fara till Islands... ✈

8 Icelandic

9 Icelandic sig

• Binding out of inﬁnitive

(1) Péturi bað Jensj um [PROj að raka sigi/j] • Subject orientation

(2) * Egi lofaði Önnuj [PROi að kyssa sigj] • Binding and the subjunctive

(3) Jóni sagði [að ég hefði svikið sigi]

(4) Jóni segir [að María telji [að Haraldur vilji [að Billi heimsæki sigi]]]

(5) * Jóni lýkur þessu ekki [nema þú hjálpir séri]

(6) Jóni segir [að hann ljúki þessu ekki [nema þú hjálpir séri]

(7) Húni sagði [að sigi vantaði peninga]

(8) Jóni upplýsti hver hefði/*hafði barið sigi

10 LFG

11 Lexical-Functional Grammar

• Lexical-Functional Grammar (Kaplan and Bresnan 1982, Bresnan 1982, Dalrymple et al. 1995, Bresnan 2001, Dalrymple 2001) is a constraint-based, model-theoretic theory of grammar. • Structural descriptions are constraints — statements that can be evaluated for truth (true or false) — that must be satisﬁed by structures (models). • LFG postulates multiple structures, each having properties relevant to the linguistic aspect it models.

12 Lexical-Functional Grammar

• For example, constituency, dominance, and word order are described by phrase structure rules that define tree structures. This level of structure is called ‘constituent structure’ or ‘c-structure’ for short. • Other, more abstract aspects of syntax — such as grammatical functions, predication, agreement, unbounded dependencies, local dependencies, case, binding, etc. — are described by quantifier- free equality statements and define attribute value matrices, a.k.a. feature structures. This level of structure is called ‘functional structure’ or ‘f-structure’ for short.

13 Lexical-Functional Grammar

• Structures are presented in parallel and elements of one structure ‘are projected to’ or ‘correspond to’ elements of other structures according to ‘projection functions’, which are also called ‘correspondence functions’. For example, the function relating c-structure to f-structure is the ϕ function. • This was subsequently generalized to a ‘Correspondence Architecture’ (Kaplan 1987, 1989, Halvorsen & Kaplan 1988, Asudeh 2006, Asudeh & Toivonen 2009). • Another term used in the literature is ‘Parallel Projection Architecture’, but this is perhaps best avoided to prevent confusion with Jackendoff’s recent proposals (e.g., Jackendoff 1997, 2002, 2007).

14 f ! f $ " f % " % # f & LFG:[ that A [ Simplee] . . . ], unless ExampleS or its trace is in the context: [ NP ...] s NP NP

IP1 f1 PRED ‘see#SUBJ,OBJ$’ Φ (↑ SUBJ) = ↓ ↑ = ↓ f3 SUBJ f2 PRED ‘John’ !   NP2 I3 Φ f4 OBJ f7$PRED ‘Bill’ % f5   = =   ↑ ↓ ↑ ↓ f6 TENSEFUTURE$ %  John   I4 VP5   Φ will ↑ = ↓ (↑ OBJ) = ↓ ! V6 NP7

see Bill

φ(1) = f1 −1 φ (f1)={1, 3, 4, 5, 6} .

1 “festschrift” 2006/6/5 page 366

366 / Ash Asudeh

Kaplan 1989). According to this architecture, there are various levels of linguistic representation (not just syntactic ones) called projections that are present in parallel and are related by structural correspondences (i.e., projection functions) which map elements of one projection onto elements of another. C-structure and f-structure are still the best-understood projections, but they are now two among several levels of representation and the projection function φ is now one of many. For example, f-structures are mapped onto s(emantic)-structures by the σ-function (Halvorsen 1983, Dalrymple 1993, Dalrymple et al. 1999b, Dalrymple 2001). Kaplan (1987, 1989) gives (3) as a hypothetical example of the pro- Correspondencejection architecture, representing Architecture: the decomposition Programmatic of a single mapping, Γ, from form to meaning. (3) Kaplan’s hypothetical parallel projection architecture: anaphoric structure α • Form π φ σ Meaning • • • • • string c-structure f-structure semantic structure δ • discourse structure

Two of the projections proposed in (3) — anaphoric structure and discourse structure — never received much further attentio(Kaplan 1987,n in 1989) the LFG literature, at least not in the way that Kaplan originally suggested. Anaphors have been handled at semantic structure (Dalrymple 1993, 2001), and discourse structure has been pursued instead as information structure (i-structure; Butt and King 2000), which encodes notions like discourse topic and focus and old and new information. Importantly, the correspondence functions between levels can be composed (see below for details), since the domain of each successive function is the range of the previous one. This is summarized in the 16 following passage from Kaplan (1987:363): Although the structures related by multiple correspondences might be descriptively or linguistically motivated levels of representation, justi- ﬁed by sound theoretical argumentation, they are formally and math- ematically, and also computationally, eliminable . . . Obviously there is a structural correspondence that goes from the word string to the f-structure, namely the composition of π with φ. ...So as a kind of formal, mathematical trick, you can say ‘Those intermediate levels of representation are not real, they are just linguistic ﬁctions, useful for stating the necessary constraints’. “festschrift” 2006/6/5 page 369

Direct Compositionality and the Architecture of LFG / 369 17 • model Meaning ψ • -structure s ain recent proposals) σ (Asudeh 2006, Asudeh & Toivonen 2009) & Toivonen (Asudeh 2006, Asudeh • σ σ ι ρ λ • α φ • • p-structure i-structure • The parallel projection architecture (incorporating cert ι ρ 1 µ • FIGURE π

• string c-structure m-structure a-structure f-structure

Form Correspondence Architecture: A Recent Synthesis A Recent Architecture: Correspondence Reﬂexives in the Correspondence Architecture Ash Asudeh Institute of Cognitive Science & School of Linguistics and Language Studies Carleton University

Lexical-Functional Grammar (LFG; Kaplan and Bresnan 1982, Bresnan 2001, Dalrymple 2001) is a constraint-based theory of grammar in which lexical items constitute key loci for grammatical information and for cross-linguistic variation. LFG posits two syntactic representations: c(onstituent)-structure and f(unctional)-structure. C-structure represents word order, dominance and constituency, as modelled by a standard (non-tangled) tree — i.e., a phrase- structural parse of the phonological string; see the left side of (1). F-structure models more abstract aspects of syntax, such as predication and grammatical functions, null pronominals, local and unbounded dependencies, etc. F-structure is modelled as a feature structure; see the Unboundedright side of (1). The Dependencies:φ correspondence function maps Example elements of c-structure to elements of f-structure, as exempliﬁed in (1).

(1) CP φ PRED ‘say!SUBJ,COMP"’ DP C!  PRED ‘pro’  FOCUS C IP φ  $PRONTYPEWH %  who   did DP I!  PRED ‘pro’  SUBJ   PERSON 2  VP  $ %  you    PRED SUBJ OBJ  !  ‘injure! , "’  V    SUBJ     V CP φ     PRED ‘pro’  !    say C   PRONTYPE REFL     COMP OBJ PERSON 3  IP           NUMBERSING  I!  φ      GENDERMASC  φ        VP  TENSE PAST     !  MOOD DECLARATIVE  V      TENSE PAST  V DP   MOOD INTERROGATIVE  injured   himself  

18 It is perhaps not widely known that c-structure and f-structure have been understood for more than twenty years as just two components of a larger grammatical architecture, the Corre- spondence Architecture (Kaplan 1987, 1989, Halvorsen and Kaplan 1988, Asudeh 2004, 2006, Asudeh and Toivonen 2008), which divides the form-meaning mapping into a series of simultaneously-present, discrete modules, each of which represents distinct linguistic information. One recent version of the architecture is shown in Figure 1. The various correspondence functions thus allow a single lexical entry to simultaneously specify constraints about a variety of grammatical information. Relative Clauses:Syntax of Long-Distance ExampleDependencies 401

(26) a man who Chris saw PRED ‘MAN’

SPEC PRED ‘A’

PRED ‘PRO’ TOPIC PRONTYPE REL

RELPRO ADJ PRED ‘SEE SUBJ,OBJ ’

NP SUBJ PRED ‘CHRIS’

Det N OBJ

a N CP

N NP C

man N IP

who NP I

N VP

Chris V Note: The examples on this and the next saw slide are from Dalrymple (2001: ch. 14).

In (26), the relative pronoun appears in initial position in the relative clause, and its f-structure is both the TOPIC and the RELPRO of the relative clause.

Example (27) shows that the relative pronoun can also appear as a subcon- 19 stituent of the initial phrase. Here the relative pronoun whose is a subconstituent of the fronted phrase whose book: Relative Clauses: Pied Piping Example 402 14. Long-Distance Dependencies

(27) a man whose book Chris read PRED ‘MAN’

SPEC PRED ‘A’

PRED ‘PRO’ SPEC TOPIC PRONTYPE REL

PRED ‘BOOK’

ADJ RELPRO PRED ‘READ SUBJ,OBJ ’

SUBJ PRED ‘CHRIS’

OBJ NP

Det N

a N CP

N NP C

man Det N IP

whose N NP I

book N VP

Chris V read

In (27), the value of the TOPIC attribute is the f-structure of the fronted phrase whose book, and the value of the RELPRO attribute is the f-structure of the relative 20 pronoun whose. We examine syntactic constraints on both of these dependencies in the following. We propose the phrase structure rules in (28–29) for the analysis of these examples:

(28) N N CP = ( ADJ) lexeme

HEAD ARGUMENT STRUCTURE AGREEMENT

agreeing non-agreeing lexeme verb noun . . . intrans trans . . . person number gender HEAD ARGUMENT STRUCTURE AGREEMENT pers-1-2 pers-3 sing plur masc fem agreeing non-agreeing 1 2 verb noun . . . intrans trans . . . person number gender intr-verb-lxm 3-sing-lxm pers-1-2 pers-3 sing plur masc fem

walks 1 2 yawns . . . intr-verb-lxm 3-sing-lxm

verb HEAD verbwalks PRD  yawns . . . ⇒ $ −% INDEX ref      verb HEAD verb  PRD  ⇒ intrans $ ARG−-S%T [] ⇒ # $ INDEX ref   )  *  

intrans ARG-ST [] index ⇒pers-3 I#ND$EX ) ⇒ * $PERS 3%   index pers-3 INDEX ⇒ $PERS 3inde% x Outside-In and Inside-Outsing equationsINDEX  ⇒ $NUM sing% • Outside-in equations with respect to an f-structure f make  speciﬁcations about paths leading in frominde fx: sing INDEX ( COMPTENSE⇒ ) =NUPRESENTM sing  ↑ (( COM$P) TENSE) %= PRESENT ↑ • Inside-out equations with respect to an f-structure f make speciﬁcations about paths leading out from f: (( COMP()(CTEONMSPE) =) TPERNESEEN) T= PRESENT ↑ ↑ • The two kinds of equation can be combined:

((COMP ) TENSE) = PRESENT ↑

1 Outside-In and Inside-Out equations

• Outside-in equations with respect to an f-structure f make speciﬁcations about paths leading in from f: (f COMPTENSE) = PRESENT

• Inside-out equations with respect to an f-structure f make speciﬁcations about paths leading out from f: (COMP f )

• The two kinds of equation can be combined:

((COMP f ) TENSE) = PRESENT

22 lexeme

HEAD ARGUMENT STRUCTURE AGREEMENT

agreeing non-agreeing

lexeme verb noun . . . intrans trans . . . lexemeperson number gender

HEAD ARGUMENT STRUCTURE AGREEMENT HEAD ARGUMENT STRUCTURE pers-1-2 pers-3 singAGREplurEMENTmasc fem agreeing non-agreeing 1 2 agreeing non-agreeing verbintr-verb-lxmnoun . . . intrans trans . . . person 3-sing-lxmnumber gender verb noun . . . intrans trans . . . person number gender pers-1-2 pers-3 sing plur masc fem pers-1-2 pers-3 sing plur masc fem walks yawns . . . 1 2 1 2 intr-verb-lxm 3-sing-lxm intr-verb-lxm 3-sing-lxm verb HEAD verb  PRD  ⇒ $ −% INDwalksEX ref  yawns . . .  walks  yawns . . .   verb intrans HEAARDG-STverb[] verb ⇒HEAD $PRD# $ % verb ⇒ ) $PRD −*% ⇒INDEX ref −  INDEX ref     index  intrpers-3ans AINRDGE-SXT [] intrans⇒⇒ARG-ST $#P[E]$RS 3% ⇒) # $* ) *  index pers-3 INDEX index pers-3 ⇒INDEX $indePERxS 3% sing INDEX PERS 3 ⇒ $NUM sing% ⇒ $ %   index sing INDEX index sing(( C⇒OMIPN)DTEEXNSE$)N=UMPREsingSEN%T ↑ ⇒ $NUM sing% Functional Uncertainty    ((COCMOMP P)) TTEENNSSEE))==PPRREESSEENNTT ((↑ COMP) TENSE) = PRESENT • Simple↑ or ↑limited functional uncertainty can be expressed by deﬁning abbreviatory symbols disjunctively: ((COMP ) TENSE) = PRESENT (G(FCO=MP S↑U) BTJENOSEB)J =OPBRJESEONBTL COMP XCOMP ADJ XADJ { ↑ | | θ | | | | | } • UnlimitedGF = S functionalUBJ OBJ uncertaintyOBJθ OBL canCO beM PexpressedXCOMP withADJ KleeneXADJ star (*)G orF =Kleene{ SUB plusJ | O B(+J), |whereOBJθ |X*O BmeansL | CO M‘0P or| XmoreCOM X’P | andAD JX|+ XmeansADJ } { | | | | | | | } ‘1 or more X’: ( FOCUS) = ( XCOMP COMP ∗ GF) (↑ FOCUS) = (↑ {XCOMP | COMP}∗ GF)1 ↑ ↑ { | } ( INDEX) = ((GF+ ) SUBJ INDEX) (↑ INDEX) = ((GF+ ↑) SUBJ INDEX) • Note↑ that f-descriptions↑ are therefore written in a regular language, as is also the case for the right-hand side of c-structure rules. 1 1

23 SubsequentSubsequentwork withinwork withinHPSGHPSGhas builthasonbuiltthisonviewthis. Linguisticview. Linguisticgeneralizationsgeneralizationsin in HPSGHPSGare capturedare capturedby a tybype haietyrpearchhieyr,awithrchymore, withspecificmore specifictypes inheritingtypes inheritinginformationinformation from lessfromspecificless specificbut relatedbut relatedtypes. types.ConstructionConstructionGrammarGrammar(Kay, 1998)(Kay, assumes1998) assumesa sim-a similar hierarchyilar hierarchy, the constructional, the constructionalhierarchyhierarchy. On the. OnHPSGthe HPSGview, lexicalview, lexicalgeneralizationsgeneralizations are statableare statableas relationsas relationsbetweenbetweenelementselementsin the intypethelattice,type lattice,wherewheredifferentdifferentsubtypessubtypes representrepresentalternatives,alternatives,and a typeand acantypebelongcan belongto multipleto multiplesupertypes.supertypes.For example,For example,Mal- Mal- ouf (1998)ouf (1998)providesprovidesthe followingthe followingdepictiondepictionof a partialof a partialtype hierarchytype hierarchyof HEAofD Hvalues:EAD values:

(1) (1) HEAD HEAD

NOUNNOUN RELATRIOELNAATLIONAL

C-NOUCN-NOUGNERUNGDERUNVDERB VERB This diagramThis diagramrepresentsrepresentsan ANDan/OARNlattice:D/OR lattice:the alternativethe alternativetypes NtypesOUNNandOURNEandLATRIOELNAATLIONAL are disjunctivelyare disjunctivelyspecifiedspecifiedas differentas differentsubtypessubtypesof the oftypetheHtypeEAD.HTheEADtype. TheGtypeERUNGDERUND inheritsinheritsfrom twofromsupertypes,two supertypes,NOUNNandOUNREandLATRIOELNAATLI,OandNALthe, andinformationthe informationinheritedinherited from allfromsupertypesall supertypesis conjoined.is conjoined. Work withinWork withinLFG, onLFG,theonotherthehand,other hashand,nothasappealednot appealedto typedto featuretyped featurestructuresstructures to encodeto encodelinguisticlinguisticgeneralizations.generalizations.Instead,Instead,LFG encodesLFG encodeslexicallexicalgeneralizationsgeneralizationsnot not in termsin oftermsformalof formalinheritanceinheritancerelationsrelationsbetweenbetweentypes, types,but in buttermsin oftermsinclusionof inclusionrela- rela- tions betweentions betweendescriptdeioscrnsiptofiostructures.ns of structures.An LFGAnfunctionalLFG functionaldescriptiondescription– a collection– a collection of equationsof equations– can be– cangivenbe agivenname,a name,and thisandnamethiscannamebecanusedbetousedstandtoforstandthoseforequa-those equations intionsotherinlinguisticother linguisticdescriptions.descriptions.In computationalIn computationaltreatments,treatments,these namedthese nameddescrip-descriptions aretionsreferredare referredto as tetomplasatteempls. Aatdescriptiones. A descriptioncontainingcontaininga referencea referenceto a templateto a templateis is equivalentequivalentto thattosamethatdescriptionsame descriptionwith thewithnamedthe namedequations,equations,the template’the template’s definition,s definition, substitutedsubstitutedfor thefortemplatethe templatereference.reference. TemplateTemplatedefinitionsdefinitionscan refercantoreferothertotemplates;other templates;thus, athus,templatea templatehierarchyhierarchysimilarsimilar to the typeto thehierarchytype hierarchyof HPSGof HPSGor Constructionor ConstructionGrammarGrammarcan becandrawnbe drawnto representto representthe the inclusioninclusionrelationsrelationsbetweenbetweenthese namedthese namedLFG descriptions.LFG descriptions.ImportantlyImportantly, however, however, the , the relationrelationdepicteddepictedin suchinasuchdiagrama diagramshowsshowsonly howonlypieceshow piecesof descriptionsof descriptionsare factoredare factored into patternsinto patternsthat recurthatacrossrecur acrossthe lexiconthe lexiconand doesandnotdoesindicatenot indicatethe formalthe formalmode ofmodecom-of com- binationbinationof thoseofpieces.those pieces.The contextThe contextof the templateof the templatereferencereferenceis whatisdetermineswhat determineshow how the templatethe templatedefinitiondefinitioncombinescombineswith otherwithpartsotherofpartsa larofgera lardescription.ger description. In the Infollowing,the following,we willwepresentwill presentseveralseveralsmall templatesmall templatehierarchieshierarchiesand showandhowshow how they cantheybecanusedbeinusedthe definitionin the definitionof linguisticof linguisticconstraints.constraints.For moreFordiscussionmore discussionof com-of com- putationalputationalissues issuesrelatedrelatedto the tousetheofusetemplatesof templatesin grammaticalin grammaticaldescription,description,see Kingsee King et al. (2004).et al. (2004).

2 Templ2 Taetempldeaﬁtneidtieoﬁnsnitions Lexical Generalizations in LFG We beginWe withbeginawithsimplea simplelexicallexicalentry forentrytheforverbtheyaverbwns:yawns:

(2) ya(2)wnsyawV(ns PRE(D)=‘yawnPRED)=‘yawnSUBJ ’SUBJ ’ ( VFO( RMV)=FOFIRNMI)=TEFINITE ( TEN( SET)=ENPRSE)=S PRES ( SUB( J PSEURBSJ)=3PERS)=3 ( SUB( J NSUUMBJ)=NSUGM)=SG

A lot of this information is shared by other verbs.

24 201 201 Subsequent work within HPSG has built on this view. Linguistic generalizations in HPSG are captured by a type hierarchy, with more speciﬁc types inheriting information from less speciﬁc but related types. Construction Grammar (Kay, 1998) assumes a similar hierarchy, the constructional hierarchy. On the HPSG view, lexical generalizations are statable as relations between elements in the type lattice, where different subtypes represent alternatives, and a type can belong to multiple supertypes. For example, Mal- ouf (1998) provides the following depiction of a partial type hierarchy of HEAD values:

(1) HEAD

NOUN RELATIONAL

C-NOUN GERUND VERB This diagram represents an AND/OR lattice: the alternative types NOUN and RELATIONAL are disjunctively specified as different subtypes of the type HEAD. The type GERUND inherits from two supertypes, NOUN and RELATIONAL, and the information inherited from all supertypes is conjoined. Work within LFG, on the other hand, has not appealed to typed feature structures to encode linguistic generalizations. Instead, LFG encodes lexical generalizations not in terms of formal inheritance relations between types, but in terms of inclusion relations between descriptions of structures. An LFG functional description – a collection of equations – can be given a name, and this name can be used to stand for those equations in other linguistic descriptions. In computational treatments, these named descriptions are referred to as templates. A description containing a reference to a template is equivalent to that same description with the named equations, the template’s definition, substituted for the template reference. Template definitions can refer to other templates; thus, a template hierarchy similar to the type hierarchy of HPSG or Construction Grammar can be drawn to represent the inclusion relations between these named LFG descriptions. Importantly, however, the relation depicted in such a diagram shows only how pieces of descriptions are factored into patterns that recur across the lexicon and does not indicate the formal mode of combination of those pieces. The context of the template reference is what determines how the template definition combines with other parts of a larger description. In the following, we will present several small template hierarchies and show how they can be used in the definition of linguistic constraints. For more discussion of computational issues related to the use of templates in grammatical description, see King et al. (2004).

2ThisTelexicalmplatentrye deficontainsnitions information that is shared by other verbs. We can define the templatesLFGPR ETemplates:SENT and 3SG to Relationsencode this common betweeninformation: Descriptions We begin with a simple lexical entry for ThistheThisverblexicallexicalyawentrynentrys: containscontainsinformationinformationthatthatis sharedis sharedby otherby otherverbs.verbs.WeWcane candefinedefinethe the (3) PRESENT = ( VFORM)=FINITtemplatesE templatesPRPERSEESNETNandT and3SG3StoG encodeto encodethisthiscommoncommoninformation:information: (2) yawns ( PRE( D)=‘yawnTENSE)=SPUREBSJ ’ ( VFORM)=FINITE (3)(3)PRPERSEESNETNT= =( (VFVOFROMR)=MFI)=NFIITNEITE 3SG (= T(ENSSUE)=BJPPREERSS)=3 ( (TETNESNE)=SEP)=REPSRES S(UBSJUPBEJRNS UM)=SG ( )=3 3S3GSG = =( (SUSBUJ BPJERPES)=3RS)=3 ( SUBJ NUM)=SG ( SUBJ NUM)=SG

The template name PRESENT names the functional description( consistingSUBJ NUMof)=StheG two equations ( VFORM)=⇧FINITE and ( TENSE)=PRES, and similarly for 3SG. With these TheThetemplatetemplatenamenamePRPERSENSETNnamesT namesthethefunctionalfunctionaldescriptiondescriptionconsistingconsistingof theof thetwotwo definitions the entry for yawns can be rewritten as equationsequations( (VFVOFROMR)=MFI)=NFIITNEITandE and( (TENTESEN)=SEP)=REPSR,EandS, andsimilarlysimilarlyfor for3SG3.SWG.ithWtheseith these definitions the entry for yawns can be rewritten as (4) yawns ( PRED)=‘yawn SUBJ ’ definitions the entry for yawns can be rewritten as @PRESENT Dalrymple, KaplanPR E&D King (2004)SUBJ (4)(4)yaywanwsns ( ( PRE)=‘yawnD)=‘yawn SUB’J ’ @3SG Asudeh, Dalrymple@PRE S&E ToivonenNT (2008) @PRESENT @3SG 201 SG A template reference (or invocation) in a lexical entry or @in3the definition of another template, as in ((5) below), is marked byAaAtemplateprecedingtemplatereferencereferenceat-sign (or“@”.(orinvocation)invocation)The present-tensein ainlexicala lexicalentryentryor inor thein thedefinitiondefinitionof anotherof another and third-singular templates will be invokedtemplate,template,by allassimilarlyasin in((5)((5)below),inflectedbelow),isverbs,markedis markedsobythatbya precedingthea precedingat-signat-sign“@”.“@”.TheThepresent-tensepresent-tense and third-singular templates will be invoked by25 all similarly inflected verbs, so that the details of these subdescriptions are specifiedandinthird-singularone place buttemplateseffectivewillin manybe invoked. by all similarly inflected verbs, so that the details of these subdescriptions are specified in one place but effective in many. We can further subdivide the functionaldetailsdescriptionof thesenamedsubdescriptionsby PRESEareNT specifiedinto twoin one place but effective in many. We can further subdivide the functional description named by PRESENT into two more primitive template definitions: We can further subdivide the functional description named by PRESENT into two more primitive template definitions: more primitive template definitions: (5) FINITE = ( VFORM)=FINITE (5) FINITE = ( VFORM)=FINITE PRES-TENSE = ( TENSE)=PRES (5) FINITE = ( VFORM)=FINITE PRES-TENSE = ( TENSE)=PRES PRES-TENSE = ( TENSE)=PRES PRESENT = @FINITE PRESENT = @FINITE @PRES-TENSE PRESENT = @FINITE @PRES-TENSE @PRES-TENSE These template definitions can be arrangedThesein atemplatesimple hierarchydefinitionsthatcanindicatesbe arrangedtheirinin-a simple hierarchy that indicates their in- terdependencies: terdependencies:These template definitions can be arranged in a simple hierarchy that indicates their in- terdependencies: (6) PRES-TENSE FINITE (6) PRES-TENSE FINITE (6) PRES-TENSE FINITE PRESENT PRESENT PRESENT This diagram records the fact that the PREThisS-TEdiagramNSE andrecordsFINITEthetemplatesfact thatarethebothPRESrefer-TEN-SE and FINITE templates are both refer- enced in (or inherited by) the definition ofencedThisPREinSdiagramE(orNT.inheritedSimilarlyrecordsby),thewethefactcandefinitionthatalsothesubdividePofREPSR-ETSEENNSTE. andSimilarlyFINIT,Ewetemplatescan alsoaresubdivideboth refer- the 3SG template as follows: theenced3SG templatein (or inheritedas follows:by) the definition of PRESENT. Similarly, we can also subdivide the 3SG template as follows: (7) 3PERSONSUBJ = ( SUBJ PERS)=3(7) 3PERSONSUBJ = ( SUBJ PERS)=3 (7) 3PERSONSUBJ = ( SUBJ PERS)=3 SINGSUBJ = ( SUBJ NUM)=SG SINGSUBJ = ( SUBJ NUM)=SG SINGSUBJ = ( SUBJ NUM)=SG 3SG = @3PERSONSUBJ 3SG = @3PERSONSUBJ 3SG = @3PERSONSUBJ @SINGSUBJ @SINGSUBJ @SINGSUBJ This information can also be representedThisas ainformationtemplate hierarchy:can also be represented as a template hierarchy: This information can also be represented as a template hierarchy:

202 202 202 This lexical entry contains information that is shared by other verbs. We can deﬁne the templates PRESENT and 3SG to encode this common information:

(3) PRESENT = ( VFORM)=FINITE ( TENSE)=PRES This lexical entry contains information that is shared by other verbs. We can deﬁne the 3SG = ( SUBJ PERS)=3 templates PRESENT and 3SG to encode this common( SUBinformation:J NUM)=SG

(3) PRESENT = ( VFORM)=TheFINtemplateITE name PRESENT names the functional description consisting of the two equations ( VFORM)=FINITE and ( TENSE)=PRES, and similarly for 3SG. With these ( TENSE)=deﬁnitionsPRES the entry for yawns can be rewritten as

3SG = ( SUBJ PERS)=3(4) yawns ( PRED)=‘yawn SUBJ ’ @PRESENT ( SUBJ NUM)=SG @3SG This lexical entry contains information that is shared by other verbs. We can define the A template reference (or invocation) in a lexical entry or in the definition of another ThetemplatestemplatePRESENnameT and 3SPGRtoEencodeSENTthisnamescommontheinformation:functional description consisting of the two template, as in ((5) below), is marked by a preceding at-sign “@”. The present-tense equations ( VFORM)=FINITE andand( third-singularTENSE)=PtemplatesRES, andwillsimilarlybe invoked byforall3similarlySG. Winflectedith theseverbs, so that the (3) PRESENT = ( VFORM)=FINITE details of these subdescriptions are specified in one place but effective in many. definitions the entry( TEforNSEy)=aPwRnESs can be rewritten as We can further subdivide the functional description named by PRESENT into two 3SG = ( SUBJ PERS)=3 more primitive template definitions: PRED SUBJ (4) yawns (( SUBJ NUM)=‘yawn)=SG ’ @PRESENT (5) FINITE = ( VFORM)=FINITE The template name PRESENT names the functional description consisting of the two @3SG PRES-TENSE = ( TENSE)=PRES equations ( VFORM)=FINITE and ( TENSE)=PRES, and similarly for 3SG. With these definitions the entry for yawns can be rewritten as PRESENT = @FINITE A template reference (or invocation) in a lexical @entryPRES-orTENinSE the definition of another template,(4) yawnsas (in P((5)RED)=‘yawnbelow),SUisBJ marked’ by a preceding at-sign “@”. The present-tense @PRESENT These template definitions can be arranged in a simple hierarchy that indicates their in- and third-singular@3SG templates will beterdependencies:invoked by all similarly inflected verbs, so that the details of these subdescriptions are specified in one place but effective in many. A template reference (or invocation) in a lexical(6)entryPREorS-TinENtheSEdefinitionFINITE of another template,We canas in further((5) below),subdivideis marked bythea precedingfunctionalat-signdescription“@”. The present-tensenamed by PRESENT into two PRESENT moreand third-singularprimitivetemplatestemplatewilldefinitions:be invoked by all similarly inflected verbs, so that the details of these subdescriptions are specified inThisonediagramplace butrecordseffectivethe factin manythat the. PRES-TENSE and FINITE templates are both refer- WTemplates:e can further subdivide Factorizationthe functional descriptionenced andin (ornamed inheritedHierarchiesbyby)PREtheSEdefinitionNT into twoof PRESENT. Similarly, we can also subdivide (5) FINITE = ( VFORM)=FINITE more primitive template definitions: the 3SG template as follows: PRES TENSE TENSE PRES (5) FINITE - = ( VFOR=M)=FI( NITE (7))= 3PERSONSUBJ = ( SUBJ PERS)=3 PRES-TENSE = ( TENSE)=PRES SINGSUBJ = ( SUBJ NUM)=SG PRESENT = @FINITE PRESENT = @FINIT@E PRES-TENSE 3SG = @3PERSONSUBJ @PRES-TENSE @SINGSUBJ

This information can also be represented as a template hierarchy: ⇧ TheseThese templatetemplatedefinitionsdefinitions⇧ can be arrangedcan beinarrangeda simple hierarchyin a simplethat indicateshierarchytheir in-that indicates their in- terdependencies:terdependencies: (6) PRES-TENSE FINITE (8) 3PERSONSUBJ SINGSUBJ (6) PREPSR-ETSEENNTSE FINITE 3SG This diagram recordsPRtheESfactENthatT the PRES-TENSE and FINITE templates are both refer- enced in (or inherited by) the definition of PRESENT. Similarly, we can also subdivide Finally, we can define a template 202PRES3SG that combines both tense and agreement Thisthe 3SdiagramG templaterecordsas follows:the fact that the PRES-TENSE and FINITE templates are both refer- features: enced(7) 3inPER(orSONinheritedSUBJ = (by)SUBtheJ PEdefinitionRS)=3 of PRESENT. Similarly, we can also subdivide the 3SG template as follows: SINGSUBJ = ( SUBJ NUM)=SG (9) PRES3SG = @PRESENT 26 @3SG (7) 33SGPERS=ON@S3UPBERJSON=SUB(J SUBJ PERS)=3 @SINGSUBJ Putting all these definitions together, our template hierarchy becomes SINGSUBJ = ( SUBJ NUM)=SG This information can also be represented as a template hierarchy: (10) PRES-TENSE FINITE 3PERSONSUBJ SINGSUBJ 3SG = @3PERSONSUBJ PRESENT 3SG @SINGSUBJ PRES3SG This information can also be represented as a template hierarchy: and the lexical entry for yawns further reduces to 202 (11) yawns ( PRED)=‘yawn SUBJ ’ @PRES3SG

Thus we see that a number of hierarchically arranged generalizations can be expressed through a simple set of template deﬁnitions. The use of parameterized templates allows for further generalizations to be captured by factoring out information provided as an argument to the template. These are discussed next. 202 3 Parameterized templates

All intransitive verbs in LFG carry a semantic form that indicates the relation denoted by the verb and also the fact that the verb must appear in f-structures containing the single governable grammatical function SUBJ. The predicate, of course, differs from verb to verb, but the SUBJ subcategorization frame is common to all intransitives. We can deﬁne INTRANSITIVE as a parameterized template that expresses the common subcategorization. The predicate itself can be provided as an argument that is speciﬁed differently in different lexical entries. This template can be used with all intransitive verbs:

(12) INTRANSITIVE(P) = ( PRED)=‘P SUBJ ’

Whatever argument is provided in an invocation of this template will be substituted for the parameter to create the description that replaces the template reference. Thus the description in the original entry for the verb yawns can be equivalently speciﬁed as follows:

(13) yawns @INTRANSITIVE(yawn) @PRES3SG

203 Arguments to parameterized templates can represent any part of an f-structure description: attributes as well as values and even whole subdescriptions can be parameterized. Templates can also take multiple arguments. For example, the template for a particle verb might take the verbal predicate as one argument and the form of the particle as another: Arguments to parameterized templates can represent any part of an f-structure descrip- (14) VERB-PRT(P PRT) = ( PREtion:D)=‘attributesP SUBJ, asOBwellJ ’ as values and even whole subdescriptions can be parameterized. ( PRTT-emplatesFORM)=ccanPRTalso take multiple arguments. For example, the template for a particle verb might take the verbal predicate as one argument and the form of the particle as The few templates we have definedanother:serve to demonstrate the point that templates interpreted only by simple substitution allow commonalities between lexical entries to Argumentsbe representedto parameterizedsuccinctlytemplatesand forcanlinguisticrepresent(14)anygeneralizationsVEpartRB-PofRTan(Pf-structurePRTto) be=expresseddescrip-( PREDin)=‘aPtheoret-SUBJ, OBJ ’ tion: icallyattributesmotivatedas well asmannervalues and. Theevenparameterizedwhole subdescriptionstemplatecanINbeTparameterized.RANSIT(IVEP(RTP)-FisORsharedM)=c PbyRT Templatesverbscanlikealsosnetakeeze,multiplearrive, arandguments.many Forothers.example,The PtheREtemplateS3SG templatefor a particleis shared by verbs verb might take the verbal predicate as one argumentTheandfewthetemplatesform of thewe particlehave definedas serve to demonstrate the point that templates like appears, goes, cooks, and many others. The template PRESENT, used in defining another: interpreted only by simple substitution allow commonalities between lexical entries to the PRES3SG template, is also used bybeverbsrepresentedlike basuccinctlyke, are, andandmanyfor linguisticothers.generalizations to be expressed in a theoret- (14) VERB-PRT(P PRT) = ( PRED)=‘P SUicallyBJ, OBmotivatedJ ’ manner. The parameterized template INTRANSITIVE(P) is shared by 4 Templates and Bo(olePaRTn -oFpeORrMa)=ctoverbsrsPRT like sneeze, arrive, and many others. The PRES3SG template is shared by verbs like appears, goes, cooks, and many others. The template PRESENT, used in defining The few templates we have defined serve to demonstrate the point that templates the PRES3SG template, is also used by verbs like bake, are, and many others. interpretedIn LFG,onlycomplexby simpledescriptionssubstitution allowcan becommonalitiesconjoined, disjoined,between lexicalor negated.entries toSince templates be representedare just namessuccinctlyforanddescriptions,for linguisticwegeneralizationscan also useto betheseexpressedoperatorsin a theoret-with templates. For icallyinstance,motivatedwemannercould. Thedefineparameterizeda templatetemplate4PRETSemplNINOTTaR3tAeSNsGSaInbyTdIVBonegatingE(Po)leisansharedotheperaby3tSoGrstemplate, as verbsfollows:like sneeze, arrive, and many others. The PRES3SG template is shared by verbs like appears, goes, cooks, and many others. TheIn templateLFG, complexPRESENdescriptionsT, used in definingcan be conjoined, disjoined, or negated. Since templates the PR(15)ES3SGPRtemplate,ESNOT3isSalsoG used= @byPverbsRESElikeNareT bajustke, anamesre, andformanydescriptions,others. we can also use these operators with templates. For @3SG instance, we could define a template PRESNOT3SG by negating the 3SG template, as 4 Templates and Boolean operators follows: The substitutions specified by these invocations produce the following description: In LFG, complex descriptions can be conjoined, (15)disjoined,PRESorNnegated.OT3SG Since= @templatesPRESENT are just(16)names( forVFOdescriptions,RM)=FINITweE can also use these operators with templates.@3SForG instance, we could define a template PRESNOT3SG by negating the 3SG template, as Templates:( TENSE)= BooleanPRES Operators follows: The substitutions specified by these invocations produce the following description: ( SUBJ PERS)=3 (15) PRESNOT(3SSGUB=J N@UMPR)=ESSEGNT (16) ( VFORM)=FINITE ⇧ @3SG ( TENSE)=PRES The first two lines are the result of expanding the PRESENT template, and the third and ( SUBJ PERS)=3 The substitutions specified by these invocations produce the following description: fourth lines are theNegationnegation of the expansion of( theSU3BSJGNUtemplate.M)=SG This template can be used in the lexical entry of verbs which are present tense but whose subject is not third (16) ( VFORM)=FINITE The first two lines are the result of expanding the PRESENT template, and the third and person( TENsingularSE)=PRES(yawn, bake, appear, etc.). (WithSUBthisJ PEadditionRS)=3 we have the followingfourth linestemplateare thehierarchy:negation of the expansion of the 3SG template. This template can be ( SUBJ NUM)=SG used in the lexical entry of verbs which are present tense but whose subject is not third (17) PRES-TENSE FINITE 3PpersonERSONsingularSUBJ (ySawINnG, baSUkeB,Jappear, etc.). The first two lines are the result of expanding the PRWESithENthisT template,additionandwethehavethirdtheandfollowing template hierarchy: PRESENT SG fourth lines are the negation of the expansion of the 3SG template.3 This template can be used in the lexical entry of verbs which are present(17)tensePbutRESwhose-TENSsubjectE FIisNnotITEthird3PERSONSUBJ SINGSUBJ person singularPR(yEaSwNn,ObaT3keS,Gappear, etc.). PRES3SG PRESENT 3SG With this addition we have the following template hierarchy: This indicates that PRESNOT3SG includes (“inherits”) descriptions from both of its an- PRESNOT3SG PRES3SG (17)cestors.PRES-HoweverTENSE ,FIunlikeNITE an3PHPSGERSONtypeSUBJhierarchySINGSU, thisBJ does not entail that the inherited

PRESENT This3SG indicates that PRESNOT3SG includes27 (“inherits”) descriptions from both of its an- cestors. However, unlike an HPSG type hierarchy, this does not entail that the inherited PRESNOT3SG PRES3SG

This indicates that PRESNOT3SG includes (“inherits”) descriptions from both of its an- cestors. However, unlike an HPSG type hierarchy, this does not entail that the inherited

204 204

204 Subsequent work within HPSG has built on this view. Linguistic generalizations in HPSG are captured by a type hierarchy, with more speciﬁc types inheriting information from less speciﬁc but related types. Construction Grammar (Kay, 1998) assumes a similar hierarchy, the constructional hierarchy. On the HPSG view, lexical generalizations Hierarchies: Templatesare statable vs. asTypesrelations between elements in the type lattice, where different subtypes represent alternatives, and a type can belong to multiple supertypes. For example, Mal- ouf (1998) provides the following depiction of a partial type hierarchy of HEAD values: • Type hierarchies are and/or lattices: (1) HEAD • Motherhood: or NOUN RELATIONAL

• Multiple Dominance: and C-NOUN GERUND VERB

• Type hierarchies encode inclusion/inheritanceThis diagram andrepresents place constraintsan AND/OR lattice: on howthe thealternative types NOUN and RELATIONAL are disjunctively specified as different subtypes of the type HEAD. The type GERUND inheritance is interpreted. inherits from two supertypes, NOUN and RELATIONAL, and the information inherited • LFG template hierarchies encode onlyfrom inclusion:all supertypes multipleis conjoined. dominance not interpreted as conjunction, no real status for motherhood.Work within LFG, on the other hand, has not appealed to typed feature structures to encode linguistic generalizations. Instead, LFG encodes lexical generalizations not • LFG hierarchies relate descriptions inonly:terms modeof formal of combinationinheritance (logicalrelations operators)between types, is but in terms of inclusion rela- determined contextually at invocationtions or betweenis built intodescr theipt iotemplate.ns of structures. An LFG functional description – a collection of equations – can be given a name, and this name can be used to stand for those equa- • HPSG hierarchies relate first-class ontologicaltions in other objectslinguistic ofdescriptions. the theory. In computational treatments, these named descriptions are referred to as templates. A description containing a reference to a template is • LFG hierarchies are abbreviatory onlyequivalent and haveto thatno realsame ontologicaldescription status.with the named equations, the template’s definition, substituted for the template reference. Template definitions can refer to other templates; thus, a template hierarchy similar to the type hierarchy of HPSG or Construction Grammar can be drawn to represent the inclusion relations between these named LFG descriptions.28 Importantly, however, the relation depicted in such a diagram shows only how pieces of descriptions are factored into patterns that recur across the lexicon and does not indicate the formal mode of combination of those pieces. The context of the template reference is what determines how the template definition combines with other parts of a larger description. In the following, we will present several small template hierarchies and show how they can be used in the definition of linguistic constraints. For more discussion of computational issues related to the use of templates in grammatical description, see King et al. (2004).

2 Template deﬁ nitions

We begin with a simple lexical entry for the verb yawns:

(2) yawns ( PRED)=‘yawn SUBJ ’ ( VFORM)=FINITE ( TENSE)=PRES ( SUBJ PERS)=3 ( SUBJ NUM)=SG

201 (8) 3PERSONSUBJ SINGSUBJ 3SG

Finally, we can deﬁne a template PRES3SG that combines both tense and agreement features:

(9) PRES3SG = @PRESENT @3SG

Putting all these deﬁnitions together, our template hierarchy becomes

(10) PRES-TENSE FINITE 3PERSONSUBJ SINGSUBJ PRESENT 3SG

PRES3SG (8) 3PERSONSUBJ SINGSUBJ and the lexical entry for yawns further3SG reduces to

Finally, we can define a template PRES3SG that combines both tense and agreement (11) yawns ( PRfeatures:ED)=‘yawn SUBJ ’ @PRES3SG (9) PRES3SG = @PRESENT @3SG Thus we see that a number of hierarchically arranged generalizations can be ex- Putting all these definitions together, our template hierarchy becomes pressed through a simple set of template definitions. The use of parameterized templates allows for further generalizations(10) PRES-TENtoSE beFINcapturedITE 3PERSbyONSfactoringUBJ SINGSoutUBJ information provided PRESENT 3SG as an argument to the template. These are discussed next. (8) 3PERSONSUBJ SINGSUBJ PRES3SG and the lexical entry for yawns further reduces to 3 P3aSGrameterized templates (11) yawns ( PRED)=‘yawn SUBJ ’ Finally, we can define a template PRES3SG that combines@PRES3bothSG tense and agreement features: All intransitive verbs in LFG carry a semantic form that indicates the relation denoted Thus we see that a number of hierarchically arranged generalizations can be ex- by the verb and also thepressedfactthroughthata simplethe setverbof templatemustdefinitions.appearTheinusef-structuresof parameterizedcontainingtemplates the (9) PRES3SGsingle= @governablePRESENT grammaticalallows for furtherfunctiongeneralizationsSUBtoJbe. capturedThe predicate,by factoring outofinformationcourse,provideddiffers from @3SG as an argument to the template. These are discussed next. verb to verb, but the SUBJ subcategorization frame is common to all intransitives. We Putting all thesecandefinitionsdefine togetherINTRAN, ourSIT3templateIVPEarasameathierarchyeparameterizedrized templbecomesates template that expresses the common subcategorization. The predicate itself can be provided as an argument that is specified All intransitive verbs in LFG carry a semantic form that indicates the relation denoted PRES TENSE FINITE ERSON UBJ ING UBJ (10) - differently in dif3ferentP bylexicaltheS verb andentries.Salso theS factThisthattemplatethe verb mustcanappearbein usedf-structureswithcontainingall intransitivethe Pverbs:RESENT single governable3SG grammatical function SUBJ. The predicate, of course, differs from verb to verb, but the SUBJ subcategorization frame is common to all intransitives. We PRES3SG can define INTRANSITIVE as a parameterized template that expresses the common sub- (12) INTRANSITIVE(categorization.P) = ( ThePpredicateRED)=‘itselfP ScanUBbeJ provided’ as an argument that is specified Parametrized Templatesdifferently in different lexical entries. This template can be used with all intransitive and the lexical entry for yawns further reducesverbs: to Whatever argument is provided in an invocation of this template will be substituted for (11) yawns the( PparameterRED)=‘yawntoScreateUBJ ’(12)theINTdescriptionRANSITIVE(P) that= ( replacesPRED)=‘P SUtheBJ ’ template reference. Thus the description@PRES3SG in the originalWhateverentryargumentfor istheprovidedverbinyanawinvocationns canofbethisequivalentlytemplate will be substitutedspecifiedfor as fol-

the parameter to create the description that replaces the template reference. Thus the Thus we seelows:that a number of hierarchicallydescription⇧ inarrangedthe originalgeneralizationsentry for the verb yacanwns canbe beex-equivalently speciﬁed as fol- pressed through a simple set of template deﬁnitions.lows: The use of parameterized templates allows for further(13)generalizationsyawns to@beINcapturedT(13)RANyaSwIbynTs IfactoringV@E(yawn)INTRANoutSITIVinformationE(yawn) provided as an argument to the template. These@PareRESdiscussed3SG next.@PRES3SG

3 Parameterized templates

All intransitive verbs in LFG carry a semantic form that indicates the relation denoted by the verb and also the fact that the verb must appear in f-structures containing the single governable grammatical function SUBJ. The predicate, of course, differs from verb to verb, but the SUBJ subcategorization frame is common to all intransitives.203 We can deﬁne INTRANSITIVE as a parameterized template that expresses the common subcategorization. The predicate itself can be provided as an argument that is speciﬁed 29 differently in different lexical entries. This template can be used with all intransitive verbs: 203

(12) INTRANSITIVE(P) = ( PRED)=‘P SUBJ ’

(13) yawns @INTRANSITIVE(yawn) @PRES3SG

203 information is conjoined. For example, in (15) PRESNOT3SG invokes 3SG via negation. Template sharing is distinct from the mode of combination, which is determined by the context of the invocation. For another illustration of this point, suppose that we have deﬁned a parameterized TRANSITIVE template to be used for verbs like devour:

(18) TRANSITIVE(P) = ( PRED)=‘P SUBJ, OBJ ’

This can be combined disjunctively with the INTRANSITIVE template to deﬁne a subcategorization template for verbs that can appear either with or without an object (eat, cook, bake, etc.):

(19) TRANS-OR-INTRANS(P) = @TRANSITIVE(P) @INTRANSITIVE(P)

Notice that the parameter for TRANS-OR-INTRANS appears as an argument in the invocations of both INTRANSITIVE and TRANSITIVE. The reference @TRANS-OR-INTRANS(eat) thus expands ultimately to the disjunction

(20) ( PRED)=‘eat SUBJ, OBJ ’ ( PRED)=‘eat SUBJ ’

Finally, we can extend the hierarchical template inclusion diagram so that it bottoms out in particular lexical items, thus showing how generalizations are captured not only among the templates but also across the lexicon:

(21) 3PERSONSUBJ SINGSUBJ

PRESENT 3SG INTRANSITIVE TRANSITIVE

PRES3SG TRANS-OR-INTRANS

falls bakes cooked

5 Expressing defaults

Default values can be expressed in LFG by means of existential constraints and disjunction. An existential constraint asserts that a feature must be present in an f-structure but it does not deﬁne the value that the feature must have. Thus the existential constraint in (22) is satisﬁed only if the f-structure denoted by has some value for the feature CASE:

(22) ( CASE)

ThisThe firstassertspartthatof thesomedisjunction(unspecified)is satisfiedvalue mustif hasbe providedsome valuebyfora definingCASE providedequationbyfor thea definingf-structureequation. Otherwise,elsewherethein theexistentialfunctionalconstraintdescriptionis not(thesatisfied.existential constraint in the WleftDefaultse candisjunctdisjunctivelyThe isinsatisfied). LFGfirstcombinepartTheof secondthethisdisjunctionspecificationpart of theisdisjunctionwithsatisfieda definingifis satisfiedequationhas someif statingvaluehas thethatfor CASE provided by thevaluef-structureNOM for CaAhasdefiningSE the(thefeaturedefiningequationCAequationSelsewhereE withinvaluetheinrightNtheOMfunctionaldisjunct: is satisfied).descriptionThe(theeffectexistential constraint in is that NOM is thethedefaultleft disjunctvalue foris satisfied).CASE: if noTheothersecondvalue partis definedof thefordisjunctionthat feature,is satisfied if has the the(23)value( CNAOSME)willvalue(beNinstalled.COAMSEfor)=NCOAMSE (theThe f-structuredefining equationmust havein casethe andright disjunct is satisfied). The effect This techniqueis thatfor specifyingNOM is thea defaultdefaultif nothingvaluevalue elseVforfor providesCaAdesignatorSE: itsif case,no otherD can valuebe encapsu-is defined for that feature, then its case is nominative. lated in a parameterizedthe valuetemplate:NOM will be installed. This technique for specifying a default value V for a designator D can be encapsu- (24) DEFAULT(D V) = D D=V Parametrized template for defaults. lated in a parameterized template: and we can use this to make more obviousAlsothe illustratesfact that thatNO Mparameterizedis the default value of CASE: (24) DEFAULT(D V)templates= D canD have=V multiple arguments

(25) @DEFAULT(( CASE) NOM) and we can use this to⇧make205 more obvious the fact that NOM is the default value of CASE: An invocation of this default CASE assignment template could then be a part of the lexical description for(25)a noun@DEinFAaUlanguageLT(( CAwithSE)caseNOMclitics.) If there is no case clitic to specify a particular case for the noun, the default NOM case will appear. An invocation of this default CASE assignment template could then be a part of the lex- 6 Templates aicalnd Pdescriptionhrase StrucfortureaAnnounnotaintioanlanguages with case clitics.30 If there is no case clitic to specify a particular case for the noun, the default NOM case will appear. Since templates simply stand for pieces of functional descriptions, it is also possible to use templates6in Tannotationsemplates aonndphrasePhrasstructuree Structrules,ure Antoncaptureotationrecurrings generalizations in the specification of the relation between c-structure configurations and f- structures. ThereSinceis no diftemplatesference insimplythe waystandtemplatesfor piecesare definedof functionalor invokeddescriptions,when they it is also possible are used in phraseto usestructuretemplatesrules; infunctionalannotationsannotationson phrasein phrasestructurestructurerules,rulesto capturecan recurring gener- simply be replaced with a template reference. alizations in the specification of the relation between c-structure configurations and f- To take an example, suppose that every adjunct in the grammar must be annotated structures. There is no difference in the way templates are defined or invoked when they with both its grammatical function and an ADJUNCT-TYPE feature, e.g., (26). are used in phrase structure rules; functional annotations in phrase structure rules can (26) VP simplyV be replacedADVP*with a template reference. =To take an example,( ADJUsupposeNCT) that every adjunct in the grammar must be annotated with both( itsADgrammaticalJUNCT-TYPEfunction)=VP-ADJand an ADJUNCT-TYPE feature, e.g., (26).

This can be rewritten(26) usingVPa parameterizedV template: ADVP* = ( ADJUNCT) (27) VP V ADVP* ( ADJUNCT-TYPE)=VP-ADJ = @ADJUNCT(VP-ADJ) where the ADJUThisNCT templatecan be rewrittenexpands to:using a parameterized template:

(28) a. ADJUN(27)CT(P) VP= ( AVDJUNCT) ADVP* @ADJU=NCT-T@YPAED(PJ)UNCT(VP-ADJ)

b. ADJUNwhereCT-TYthePE(PA)DJU=NC(T AtemplateDJUNCT-expandsTYPE)=Pto:

(28) a. ADJUNCT(P) = ( ADJUNCT) @ADJUNCT-TYPE(P)

b. ADJUNCT-TYPE(P) = ( ADJUNCT-TYPE)=P

206

206 Glue Semantics

31 Glue Semantics

• Glue Semantics is a type-logical semantics that can be tied to any syntactic formalism that supports a notion of headedness. • Glue Semantics can be thought of as categorial semantics without categorial syntax. • The independent syntax assumed in Glue Semantics means that the logic of composition is commutative, unlike in Categorial Grammar. • Selected works: Dalrymple (1999, 2001), Crouch & van Genabith (2000), Asudeh (2004, 2005a,b, 2006, in prep.), Lev (2007), Kokkonidis (2008)

32 Copy Raising and Perception June 9, 2007 32

copy raising is like a case of resumption, where resumptive pronouns can also be understood essentially as a problem of semantic composition. In both cases, there is a pronoun saturating a semantic argument position that must be left open in order to properly compose the subject (for copy raising) or the top of the resumptive long- disCtoapnycReaisdinegpaennddPerncecpiteiosn(for resumptiveJupnero9,n2o0u07ns in unbounded dependencies). T3h2e removal of the pronoun from semantic composition is carried out by a lexically specified manager resource. Thus, both types of resumption copy raising is like a case of resumption, where resumptive pronouns can also be understood essentially as a areprolibcleemnosfesdemthanrtoicucgomhploesxitiiocna. lInspboethcicfiasceas,ttihoenre.isIna ptrhoenocunassaetuoraftincgoapsyemraanistiicnagrg,uimteinst ptohseitisonpethcaitfication of a manager resource thamtuslticbee nlesfteosptehneincoordpeyr torapirsoipnerglyscuombjpeocset tahensdubtjhecet c(foorpcyopryariasiisningg)roerltahteitoonp .ofAthnearpeshumorpiticveblionngd-ing of the copy pronoun by the sudbisjteacnctesdyepnetnadcetniccieasl(lfyorirdeseunmtpitfiiveesprtohneounpsrionnuonbuonuntdhedatdeipsencdaenucsieins)g. Tthheeremsaotvualroaftithoenprponroubnlferomm for semantic composition and semantic composition is carried out by a lexically specified manager resource. Thus, both types of resumption thearemlicaennasegdethrroreugsholuexricceal espfefceificctastiiotns. Irnetmheocvasaelodf cuorpiynrgaiscinogm, itpisotshietsipoenci.fiTcahtioenkofeaymdainfafgeerrerensocuercbeetween copy raising verbs and petrhcatelpicteunsaelsrtheesceompybrlaaisnincgesuvbejercbt sanidsththe econpyreradisuincgerdelattoioan. sAinmapphloericlebxinidcinaglodfitfhfeecroepnycpreo:nocuonpbyy trhaeising verbs contribute manager subject syntactically identifies the pronoun that is causing the saturation problem for semantic composition and resthoeumracneasge,rpreesrocuercpeteuffaelctrseitsseremmbovlaalndcureinvgecrobmspodsiotionno. Tt.he key difference between copy raising verbs and perTcehpetuatel rremsemmblaanncaegveerrbsriessthoeun rrecdeucietdsetolfa ssitmepmleslefxricoaml difGfelreuneceS: ceompyarnaitsiincgsv(eDrbas clroyntmribputleem1a9na9g9er, 2001), a theory of the syntax– sermesaounrtciecs,speirncteeptrufaalcreeseamnbdlansce mverabns dtiocnocto. mposition. In Glue Semantics, the logic of semantic composition is linear The term manager resource itself stems from Glue Semantics (Dalrymple 1999, 2001), a theory of the syntax– logseimcan(tGicsiriantredrfa1ce9a8n7d)s,emwanhticchcomispoasitiroens. oIun rGcleuelSoegmiacn,ticas,sthdeislocguicsosfesdemianntimc coormepodseititoanilisblieneloarw. Each lexically contributed meloagnicin(Ggiracrodn1s98is7t)s, wohficah itsearmresofurrocme loagicm, aesadnisicnugsseldaningmuoargeedeatasisl obeclioawt.edEacwhiltehxicaalltyercmontroibfutleidnear logic. These paired terms Glue Semanticsmeaning consists of a term from a meaning language associated with a term of linear logic. These paired terms areareccaalllleeddmmeaenainngicnongstcruocntosrtsraundctaorerrseparnesdenaterdeasrefopllroewsse: nted as follows: • Lexically-contributed meaning constructors := (127) M : G Meaning language(12 7term) M : G Composition language term • Meaning languageM :=is somethe m lambdaeanin gcalculuslanguage term and G is the linear logic term (the colon is an uninterpreted pairing symbol). • Model-theoretic • CompositionM languageThieslitn :=hea elinearr lmog eilogiccasnerivnegs alsaan‘gluuealganeguteagrem’ thaatnrdelaGtes siysnttahxetolsienmeaanrticlsoagndicspteecrifimes h(tohwesecmoalnotinc teirsmas nareuninterpreted pairing symbol). • Proof-theoreticThtoebleicnoemaprosleodg. iTchesmerevaneinsgacsonastr‘ugctloursealrae nusgeduasgpere’mtihseastinreal(alitneesarsloygnict)apxrotoof thsaetmcoansnutmices thaenldexiscpalecifies how semantic terms are • Curry Howard Isomorphismpremises to betweenproduc formulase a sen t(meanings)ential me aandnin typesg. A successful Glue proof proves a conclusion of the following form (proof terms) to be composed. The meaning constructorsGtare used as prte1m8 ises in a (linear logic) proof that consumes the lexical • Successful Glue( fSemanticsollowing proof:Crouch and van Genabith 2000: 117), where is a term of type : premises to produce a sentential meaning. A successful Glue proof proves a conclusion of the following form (128) Γ ! M : Gt (following Crouch and van Genabith 2000: 117), where Gt is a term of type t:18 Each step in the linear logic proof of semantics corresponds to an operation in the meaning language via the

Curry-Howard isomorphism between formulas and33 types (Curry and Feys 1958, Howard 1980). This means that Gt (1t2h8e )syntacticΓw!ell-Mform:edness of the proof can be calculated using standard proof-theoretic methods on G while simultaneously constructing meaning terms in the meaning language M. The meaning language M itself is Easctahndasrtdelypinitnerptrheteedlminoedaelr-thleoogreitcicapllyr,oaosfisothfe sceasme iannthtiiscspapceor.rrTehsups,oanlthdosugthoseamnanotipc ecormatpioosnitioinnisthe meaning language via the Cudrirvyen-Hprooowf-athredoriestiocamllyo, rinptehripsremtatibonetiws meoednel-ftoheromreuticl.asThains dhastythpeeasdv(aCntuagrerythatnmdeaFneinygsco1n9st5ru8c,tioHnoward 1980). This means that is sensitive only to the linear logic types of the meaning constructors and not to the actual meanings in M. the syntactic well-formedness of the proof can be calculated using standard proof-theoretic methods on G while Compositionality is therefore guaranteed, since no assumptions are made about the content of meaning terms siminualstsaemnbeloinugsmlyeanciongnss(tDrualcrytminpgle emt ael.a1n9i9n9ag: 2t6e2r–m26s3)i.nTthhe elinmearealongicnpgroloafnthguus asegrevesMas .theTsyhnetaxmeaning language M itself is staonf dseamradnltiyc cionmtepropsirtieonte, dwhmichordeevela-ltshaecoleraertircelaatliloyn,shaips biestwteheen lcinaesareloignicttheirms spianpGelur.e STemhaunsti,csaaltnhdough semantic composition is categories in Categorial Grammar (Ajdukiewicz 1935, Bar-Hillel 1953, Lambek 1958, Ades and Steedman 1982, drSivteeednmpanro19o9f6-,t2h0e0o0,rBeutsizckaolwlysk,i ient atle. r1p98r8e,tOaetihorlne eitsal.m19o8d8,eMl-otrhriello1r9e94ti,cC.arpTenhteisr 1h99a7s, Mthooertgaadt v19a9n7t),age that meaning construction is assednissciutsisvede inondeltyailtboy Dthaelrymlipnleeaetrall.o(g19i9c9at)y. pAensothoefr ptehrsepemctiveeanoninthgis creolantisotnrsuhicptoisrtshaat nlindearnlootgicto the actual meanings in M. is essentially equivalent to the commutative Lambek Calculus (Moortgat 1997, Asudeh 2004, Ja¨ger 2005). In Cohims dpisocsusistioonnoafldietysiraibsletphreoprerftioesreofg“Luaamrbaenkt-seteylde,CastiengocreialnGoramasmsaur”m, Jpa¨gteior (n2s00a5:riex)mnoatedsethaatb“[oTu]htethe content of meaning terms inCausrrsye-Hmowbalirdngcormresepaonndienngces. .(.Dsuapplrliyesmthpelteypeetloagli.ca1l 9sy9n9taax:w2ith62an–e2x6tre3m).elyTelhegeanltiannedainrdelopegnidcenptlyroof thus serves as the syntax ofmsoetimvataend tinictercfaocemtopmoosdietil-othne,orwetihc iscemhanrteicvse.”aTlhsisacocmlmeaenrt erqeulaaltlyioanppslhieisptobGelutewSeemenantliicns.ear logic terms in Glue Semantics and Let us consider a simple Glue derivation. Syntactic analysis of the sentence in (129) yields the meaning cactoengsotrurcietosrsiinn (C13a0t)e. gNoorteiathlaGt wreamassmignarth(eAlinjedaur kloigeicwteircmzs1in9t3he5,mBeaanirn-gHciolnlsetrluc1t9or5s 3m,neLmaomnicbneakm1es9, 58, Ades and Steedman 1982,

Stee18dThme taypning1in9t9he6li,ne2ar0lo0g0ic,siBde uGsizs ikndoepwensdekntioef,tbuat lre.la1te9d 8to,8th,eOtypeinhgrinletheemteaanli.ng1la9ng8u8ag,e MM.oTrhreirlellat1io9ns9hip4c,anCbae rpenter 1997, Moortgat 1997), stated simply: type t in G corresponds to the propositional type t in M; type e in G corresponds to the individual type e in M; type ε in G ascodrriespconudsstoethde eivnentudaleitytatyiple εbinyMD(saeelrseyctmionp6.l4efoer ttypainlg.of(M19).99a). Another perspective on this relationship is that linear logic is essentially equivalent to the commutative Lambek Calculus (Moortgat 1997, Asudeh 2004, Ja¨ger 2005). In his discussion of desirable properties of “Lambek-style Categorial Grammar”, Ja¨ger (2005: ix) notes that “[T]he Curry-Howard correspondence . . . supplies the type logical syntax with an extremely elegant and independently motivated interface to model-theoretic semantics.” This comment equally applies to Glue Semantics. Let us consider a simple Glue derivation. Syntactic analysis of the sentence in (129) yields the meaning constructors in (130). Note that we assign the linear logic terms in the meaning constructors mnemonic names,

18The typing in the linear logic side G is independent of, but related to, the typing in the meaning language M. The relationship can be stated simply: type t in G corresponds to the propositional type t in M; type e in G corresponds to the individual type e in M; type ε in G corresponds to the eventuality type ε in M (see section 6.4 for typing of M). 56 CHAPTER 2. AN OVERVIEW OF LFG AND GLUE SEMANTICS

(2.56) a. Application : Implication Elimination · · · · · · 56 CHAPTER 2. AN OVERVIEWa :OAF LFG Af N: AD !GLBUE SEMANTICS !E Key Glue Proof Rules with Curry-Howardf (a) : B Terms

(2.56) a. Application : Implication Elimination b. Abstraction : Implication Introduction · · 1 · · [x : A] · · · · a : A f : A ! B · !E f : B f (a) : B !I,1 λx.f : A ! B b. Abstraction : Implication Introduction Pairwise 1 Conjunction c. Pairwise substitution : Conjunction Elimination Subs[txitu:tiAon] : Elimination · [x : A]1 [y : B]2 · 1 2 · [x : A] [y : B] Beta re· duction for let: · f : B · · · · let a · b be x y in f · β f [a/x, b/y] · !I·,1 a : A×⊗ B × f : C⇒ aλx: A.f· : AB ! B f :·C ⊗ ⊗E,1,2 ,1,2 let a be x y in f C let a be x y in f : C ⊗E × : × c. Pairwise substitution : ConjuAnsctnioonteEdlaimboinvaet,ioimnplication elimination corresponds to functional application, and implication in- [x : A]1 [y : B]t2roduction corresponds to abstraction. The assumed premise in the introduction rule is associated · · · · let · · with a variable that is abstracted over when the assumpti34on is discharged. The term constructor a A B f C : ⊗ : A B a b ⊗E 1is2possibly less familiar. A multiplicative conjunction ⊗ corresponds to a tensor product × , let be in , , a x × y f : C where a is the proof term of A and b is the proof term of B (see the rule for conjunction introduction

As noted above, implication elimination cor(r⊗esIp)oinnds(2t.o62fu)nbcetlioowna)l. aHpopwliceavteiro,nl,etanpdreivmepnltiscaptrioojnecitnio-n into the individual elements of the tensor troduction corresponds to abstraction. The apsasiurmanedd tphreermefiosreeienntfhoercienstrpoadiurwctisoensruublestiitsutaisosnoc(iAatberdamsky 1993, Benton et al. 1993, Crouch and with a variable that is abstracted over when vthaenaGsseunmabpittihon20i0s0d:i8s8c)h,asrugcehd.thTahteatleertmexcpornesstsriuocntoβr-lreetduces as follows: is possibly less familiar. A multiplicative conjunction A ⊗ B corresponds to a tensor product a × b, (2.57) let a × b be x × y in f ⇒β f [a/x, b/y] where a is the proof term of A and b is the proof term of B (see the rule for conjunction introduction

(⊗I) in (2.62) below). However, let preventTshperosjuebcsttiiotnutiionntootfhethiendpiaviridiusaslimeluemltaennetosuosfatnhde tdeonessornot involve projection into the members. So pair and therefore enforces pairwise substitulteitonis(nAobtrfaomrbsikdydi1n9g9a3n,dBiesnjtuosnt eatsalilg. h1t9ly93m, oCrreosutcrhucatnudred form of functional application. van Genabith 2000:88), such that a let expressioInt βis-rtehdeuCceusrrays-Hfoollwowarsd: term assignments that determine operations in the meaning language. I use the locution “operations in the meaning language” purposefully. The term assignments con- (2.57) let a × b be x × y in f ⇒β f [a/x, b/y] structed by rules of proof for linear logic result in linear lambdas (Abramsky 1993); these are The substitution of the pair is simultaneous laanmdbddoaetsernmots iinnvwolhviechpreovjercytiolanmibndtoa-tbhoeumndemvabreirasb.leSoccurs exactly once (i.e. no vacuous abstrac- let is not forbidding and is just a slightly motrieonstrauncdtunroedmfuolrtmiploefafbusntcraticotnioanl )a.pTplhiceaptiroono.f terms therefore satisfy resource sensitivity. However, It is the Curry-Howard term assignmentlsextihcaatlldyecteornmtriinbeutoepdemraetiaonnisngins ntheeedmneoatncinogntlaaingounalgye.linear lambdas (for a similar point about the I use the locution “operations in the meaning language” purposefully. The term assignments con- structed by rules of proof for linear logic result in linear lambdas (Abramsky 1993); these are lambda terms in which every lambda-bound variable occurs exactly once (i.e. no vacuous abstraction and no multiple abstraction). The proof terms therefore satisfy resource sensitivity. However, lexically contributed meanings need not contain only linear lambdas (for a similar point about the Example: Mary laughed

1. mary : σe PRED ‘laugh SUBJ ’ ↑ ! " 2. laugh : ( SUBJ) f ↑ σe ! ↑σt SUBJ g PRED ‘Mary’   # $

1!. mary : gσe 1!!. mary : m

2!. laugh : gσe ! fσt 2!!. laugh : m ! l

Proof Proof 1. mary : m Lex. Mary mary : m laugh : m ! l 2. laugh : m l Lex. laughed ≡ ! !E 3. laugh(mary) : l E !, 1, 2 laugh(mary) : l

35 Example: Most presidents speak

1. λRλS.most(R, S) : (v r) X .[(p X ) X ] Lex. most ! ! ∀ ! ! 2. president ∗ : v ! r Lex. presidents 3. speak : p ! s Lex. speak

λRλS.most(R, S) : president ∗ : (v r) X .[(p X ) X ] v r ! ! ∀ ! ! ! λS.most(president ∗, S) : speak : X .[(p ! X ) ! X ] p ! s ∀ , [s/X] !E most(president ∗, speak) : s

36 Example: Most presidents speak at least one language

PRED ‘speak SUBJ, OBJ ’ ! " Single parse  PRED ‘president’  SUBJ ➡  SPEC PRED ‘most’      $ %  Multiple scope possibilities  PRED ‘language’     (Underspeciﬁcation through OBJ   SPEC PRED ‘at-least-one’    quantiﬁcation)     $ % 1. λRλS.most(R, S) : Lex. most (v1 r1) X .[(p X ) X ] ! ! ∀ ! ! 2. president ∗ : v1 ! r1 Lex. presidents 3. speak : p ! l ! s Lex. speak 4. λPλQ.at-least-one(P, Q) : Lex. at least one (v2 r2) Y .[(l Y ) Y ] ! ! ∀ ! ! 5. language : v2 ! r2 Lex. language

37 Most presidents speak at least one language Subject wide scope

λPλQ.a-l-o(P, Q) : lang : λxλy.speak(x, y) : (v2 r2) Y .[(l Y ) Y ] v2 r2 p l s [z : p]1 ! ! ∀ ! ! ! ! ! λQ.a-l-o(lang, Q) : λy.speak(z, y) : λRλS.most(R, S) : president ∗ : (v1 r1) X .[(p X ) X ] v1 r1 Y .[(l ! Y ) ! Y ] l ! s ! ! ∀ ! ! ! ∀ [s/Y ] a-l-o(lang, λy.speak(z, y)) : s λS.most(president ∗, S) : ! ,1 X .[(p ! X ) ! X ] λz.a-l-o(lang, λy.speak(z, y)) : p ! s I ∀ [s/X] most(president ∗, λz.a-l-o(lang, λy.speak(z, y))) : s

38 Most presidents speak at least one language Object wide scope

λRλS.most(R, S) : president ∗ : λyλx.speak(x, y) : (v1 r1) X .[(p X ) X ] v1 r1 l p s [z : l]1 ! ! ∀ ! ! ! ! ! λPλQ.a-l-o(P, Q) : lang : λS.most(president ∗, S) : λx.speak(x, z) : (v2 r2) Y .[(l Y ) Y ] v2 r2 X .[(p ! X ) ! X ] p ! s ! ! ∀ ! ! ! ∀ [s/X] most(president ∗, λx.speak(x, z)) : s λQ.a-l-o(lang, Q) : ,1 !I Y .[(l ! Y ) ! Y ] λz.most(president ∗, λx.speak(x, z)) : l ! s ∀ [s/Y ] a-l-o(lang, λz.most(president ∗, λx.speak(x, z))) : s

39 Further Points of Interest

• Glue Semantics can be understood as a representationalist semantic theory (cf. Kamp & Reyle 1993, Cann et al. 2005)

• Proofs can be reasoned about as representations (Asudeh & Crouch 2002a,b).

• Proofs have strong identity criteria: normalization, comparison

• Glue Semantics allows recovery of a non-representationalist notion of direct compositionality (Asudeh 2005, 2006).

➡ Flexible framework with lots of scope for exploration of questions of compositionality and semantic representation

40 Anaphoric Binding in the Correspondence Architecture

41 Binding Constraints ca. Dalrymple (1993)

Positive binding constraint (schema): ((DomainPath GF ) AntecedentPath)σ = σ ( X) ↑ ↑ ¬ →

Negative binding constraint (schema): ((DomainPath GF ) AntecedentPath)σ = σ ( X) ↑ # ↑ ¬ →

Example: herself (( GF∗ GF ) GF) = ↑ σ ↑σ ( SUBJ) ¬ → . .

Example: sig (( GF∗ GF ) SUBJ) = ↑ σ ↑σ ( TENSE) ¬ → . .

42 Equality in LFG is Token Identity: A Nice Consequence

• Notice that there are no indices in this theory: the antecedent and the anaphor are equated in semantic structure.

• This formally represents the fact that the two things denote the same entity in the semantics.

• Like coindexation, equality as token identity is transitive: If A = B and B = C then A = C, just as if A is coindexed with B and B is coindexed with C, the A is coindexed with C.

• This avoids the problem for asymmetric linking/dependency accounts (Higginbotham 1993, Saﬁr 2004) with circumvention of illicit binding conﬁgurations (requires stipulation re. obviation): (1) John said he saw him.

43 Binding Constraints ca. Dalrymple (2001), Asudeh (2004)

((DomainPath GF ) AntecedentPath)σ = ( σ ANTECEDENT) ( X) ↑ ↑ ¬ → • Problem: Now the relation is asymmetric; same problem as for linking/ dependency accounts arises • Why the change? • Glue Semantics: resource-sensitive semantic composition • Formally models without extra stipulations that the pronoun and its antecedent are satisfying separate compositional requirements (Asudeh 2004). • If the anaphor and its antecedent were token identical, there would be a resource deﬁcit. • Beneﬁt: Account of non-resumptive behaviour of relational nouns (Asudeh 2005)

44 Anaphora in Glue Semantics

• Variable-free: pronouns are functions on their antecedents (Jacobson 1999, among others)

• Commutative logic of composition allows pronouns to compose directly with their antecedents.

• No need for otherwise unmotivated additional type shifting (e.g. Jacobson’s z-shift)

45 Anaphora in Glue Semantics

(1) Joe said he bowls.

• Pronominal meaning constructor: λz.z z : A (A P) × ! ⊗

λuλq.say(u, q) : λv.bowl(v) : 1 2 [x : j ] j ! b ! s [y : p] p ! b joe : λz.z z : λq.say(x, q) : bowl(y) : j j (×j p) b s b ! ⊗ ! joe joe : j p say(x, bowl(y)) : s × ⊗ ,1,2 let joe joe be x y in say(x, bowl(y)) : s ⊗E × × β say(joe, bowl(joe)) : s ⇒

46 A Solution

• The essential problem of the new system is that we would like the feature ANTECEDENT to play contrary roles: we want the pronoun and its antecedent to be equated for computation of binding constraints, but we want the antecedent and the anaphor to be distinguished for computation of Glue semantic proofs.

• Solution: Resuscitate anaphoric structure, an original component of Kaplan’s programmatic Correspondence Architecture.

• However, this is only a good solution if the move solves some other problems, too.

• It does: logophoricity of Icelandic/Faroese long-distance reﬂexive

47 Adding Anaphoric Structure to the Architecture

i-structure ana-structure •• p-structure $ ι ισ $σ • ρ φ σ Form ρ Meaning π µ α λ σ ψ string• c-structure• m-structure• a-structure• f-structure• s-structure• model•

herself (( GF∗ GF ) GF) = Mar´ıa ( ID) = maria ↑ ! ↑! ↑! ( SUBJ) maria : ¬ → ↑σ

λz.z z :(!)!σ ! (( !)!σ σ) × ↑ . ↑ ⊗↑ .

48 Strahan’s Observation

• In work in progress, Strahan (2009) observes that the logophoricity of Icelandic/Faroese sig/seg raises a problem for LFG’s inside-out theory of anaphoric constraints.

• She contrasts the following examples:

(1) * Hanni kemur ekki nema þú bjóðir séri

(2) Jóni segir að hann komi ekki nema þú bjóðir séri

• The problem is: If logophoricity is a property of the long-distance reﬂexive, what allows it to acquire the feature in (2) but not in (1)?

• She proposes instead that the logocentre introduced by segir (i.e. Jón) should instead issue a downward (outside-in) search for something to bind.

49 Logophoricity

• We now have a symmetric relation between the anaphor and its antecedent at anaphoric structure and an asymmetric relation between the anaphor and its antecedent in the semantics (because the anaphor is a function that takes its antecedent as an argument). • What remains is to capture the logophoricity of sig using our theoretical innovation.

• Intuitions (Þráinsson, Maling, Strahan, others): 1. Logophoricity is a property introduced by certain lexical items.

2. The property can ‘drip’ down (Þráinsson via Maling). 3. The long-distance reﬂexive is conditioned by this property, not by mood. 4. The LDR must bind to the logocentre (Strahan).

50 Introduction of Logophoricity and Making it Drip segir, etc. ( PRED) = ‘say SUBJ, COMP ’ ↑ " # λpλx.say(x, p):( COMP) ( SUBJ) ↑ σ ! ↑ σ ! ↑σ (( SUBJ) LOGOCENTRE) =+ ↑ " ( LOGOPHORIC) =+ Introduction  ↑  ( GF+ ) ↑  ( MOOD) =c SUBJUNCTIVE   →   ( LOGOPHORIC) = ( LOGOPHORIC)  Drip  ↑ →   λPλx.perspective-of (x, P(x)) : [( SUBJ)σ σ] [( SUBJ)σ σ]   ↑ ! ↑ ! ↑ ! ↑   .  .

(( GF∗ GF ) SUBJ ) = ↑ ! ↑! ( LOGOPHORIC) ( LOGOCENTRE) = +  → →! c  Somewhat over-simplistic     (should use templates!)  ∨    sig    (( GF∗ GF ) SUBJ)! = !   ↑ ↑   ( TENSE)  ¬ →      (( GF∗ GF ) SUBJ)! = !   ↑ $ ↑   ( PRED)   ¬ →      λz.z z :( !)!σ ! (( !)!σ σ) × ↑ ↑ ⊗↑ . . 51 Back to the Icelandic Data

• Binding out of inﬁnitive

(1) Péturi bað Jensj um [PROj að raka sigi/j] • Subject orientation

(2) * Egi lofaði Önnuj [PROi að kyssa sigj] • Binding and the subjunctive

(3) Jóni sagði [að ég hefði svikið sigi]

(4) Jóni segir [að María telji [að Haraldur vilji [að Billi heimsæki sigi]]]

(5) * Jóni lýkur þessu ekki [nema þú hjálpir séri]

(6) Jóni segir [að hann ljúki þessu ekki [nema þú hjálpir séri]

(7) Húni sagði [að sigi vantaði peninga]

(8) Jóni upplýsti hver hefði/*hafði barið sigi

52 Prospects for Intrasentential Logophors?

• Maling (1984), Sigurðsson (1986), Þráinsson (1991) have observed that sig can be bound from outside the clause, though it must have an antecedent in discourse (Þráinsson 1991: 62).

(1) María var alltaf svo andstyggileg. Þegar Ólafurj kæmi segði hún séri/*j áreiðanlega að fara …

• We now have the structure we need to deal with logocentres that are introduced by discourse, but the discourse rules that govern this process need further investigation.

53 Another Apparent Puzzle Solved?

• Maling (1984: 235) struggles with the following relative clause data:

(1) Jón segir að Ólafuri haﬁ ekki enn fundið vinnu, sem séri líki.

• Initially this seems problematic, because it would seem to complicate our generalizations about logophoric sig, because it is embedded in an object and it is not referring to the logocentre.

• However, Ólafur is the ﬁrst subject outside of the coargument domain of the reﬂexive.

• This case is in fact covered by the non-logophoric generalization about sig; i.e. it seems to be a case of narrow syntactic binding.

• A potentially troubling fact remains: the subjunctive marking on the relative clause.

54 Conclusion

• In light of recent developments in LFG, particularly the addition of Glue Semantics to the Correspondence Architecture, we had to reconsider classical LFG binding constraints (Dalrymple 1993). • We revived the notion of anaphoric structure (Kaplan 1987, 1989) and put it to good use. • Not only do we recapture what was lost, we have made progress in tying the notion of logophoricity to the notion of syntactic binding explicitly, rather than treating logophoricity as an unanalyzed concept or a concept analyzable only purely orthogonally to non-logophoric uses (Sells 1987). • There are some stipulations that remain and that can hopefully be eliminated.

55 Research supported by: Social Sciences and Humanities Research Council of Canada Standard Research Grant 410-2006-1650 & Natural Sciences and Engineering Research Council of Canada Discovery Grant 371969

http://www.carleton.ca/~asudeh/