Lexical-Functional Grammar

Ash Asudeh Carleton University

University of Iceland July 3, 2009

1 Architecture and Structures

2 “festschrift” 2006/6/5 page 365

Direct Compositionality and the Architecture of LFG / 365

17.2 The Parallel Projection Architecture The original architecture of LFG (Kaplan and Bresnan 1982) consisted of two syntactic levels: constituent structure (c-structure) and functional structure (f-structure). C-structures are represented as trees, which are described in the usual manner (with a set of nodes, a la- beling on the set, and functions for dominance and precedence). The level of c-structure represents syntactic information about precedence, dominance, and constituency. F-structures are represented as feature structures (attribute-value matrices), described by a set of recursive functional equations on a set of symbols. The level of f-structure is another aspect of syntactic representation — it is not a semantic rep- resBasicentatio nSyntactic. However, Architecturef-structure rep rofes eLFGnts more abstract aspects of syntax, such as grammatical functions, predication, subcategorization, and local and non-local dependencies. C-structure and f-structure are pro•jTwoecte basic,d fro msimultaneouslexical ite mrepresentationss, which sp eofci syntax:fy their c-structure category and •f-C(onstituent)-structurestructure feature con: tconstituency,ributions. V dominance,ariables i nwordlex iorder,cal it ems are in- stantiphraseated b structurey the c-structure parse. The two syntactic representations are prAnnotatedesent sim utreesltaneously, in parallel. They are related by the φ pro- jecti•onF(unctional)-structurefunction, also know: abstractn as a cgrammaticalorrespond erelations/functionsnce function. T he φ function m(subject,aps c-s tobject,ructu retc.),e no tense,des ( icase,.e., t ragreement,ee nodes) predication,to f-struct localure nodes (i.e., featurande s tnon-localructures dependencies). The original grammatical architecture of LFG is shownFeatureschem structures/attribute-valueatically in (2). matrices (2)• KaplanThe & oBresnanriginal (1982):LFG architecture: φ constituent structure functional structure An LFG representation of an expression on this view is a triple consisting of a c-structure, an f-structure and a φ projection functi3on that maps the c-structure to the f-structure: !c, f , φ". C-structures and f-structures are constructed by simultaneous constraint satisfaction. LFG is a declarative, non-transformational theory. The fact that c-structure and f-structure are represented using distinct data structures (trees and feature structures) distinguishes LFG from both transformational theories such as P&P, which represents all syntactic information in a tree, and non-transformational theories such as Head-Driven Phrase Structure Grammar (Pollard and Sag 1987, 1994), which represents all grammatical information, whether syntactic or not, in a directed acyclic graph. LFG uses mixed data structures related by structural correspondences, rather than a single monolithic data structure. The LFG architecture was subsequently further generalized to a parallel projection architecture (Kaplan 1987, Halvorsen and Kaplan 1988, “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). LFG’sKaplan Parallel(1987, 198 9Projection) gives (3) as a Architecturehypothetical example of the projection architecture, representing the decomposition of a single mapping, Γ, from form to meaning. • Kaplan (1987,1989): (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 attention in 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. 4 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 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’. LFG’s Parallel Projection Architecture D i re c t

• Asudeh (2006): C o m p o

i-structure s i t

• i o n a l i

p-structure t ι • ισ y a n

ρ d φ ρσ t

Form Meaning h • π • µ • α • λ • σ • ψ • e string c-structure m-structure a-structure f-structure s-structure model A r c h i t e

FIGURE 1 The parallel projection architecture (incorporating certain recent proposals) c t u re o f L F G / 3 6 9

5 p 2 “ 0 f a e 0 g s 6 e t / s 3 c 6 6 h / 9 r 5 i f t ” Design Principles

• Principle I: Variability External structures (modelled by LFG c-structures) vary across languages.

• Principle II: Universality Internal structures (modelled by LFG f-structures) are largely invariant across languages.

• Principle III: Monotonicity The mapping from c-structure to f-structure is not one-to-one, but it is monotonic (information-preserving).

6 Nonconﬁgurationality

• Two fundamental ways for language to realize underlying concepts:

• Phrase structure (groups)

• Morphology (shapes)

• Bresnan (1998, 2001): ‘Morphology competes with syntax’

• English: phrase structure strategy (conﬁgurational)

• Warlpiri: morphological strategy (nonconﬁgurational)

7 English

• Underlying meaning: That of ‘the two small children are chasing that dog’

S NP Aux VP are V NP the two small children chasing that dog

8 NP Aux V NP NP NP

wita-jarra-rlu ka-pala wajili-pi-nyi yalumpu kurdu-jarra-rlu maliki small-DUAL-ERG pres-3duSUBJ chase-NPAST that-ABS child-DUAL-ERG dog-ABS English and Warlpiri

• English:

(1) a. The two small children are chasing that dog. b. * The two small are chasing that children dog. c. * The two small are dog chasing children that. d. * Chasing are the two small that dog children. e. * That are children chasing the two small dog.

• Warlpiri:

• All of the permutations in (1) are grammatical ways to express the same underlying concept of ‘the two small children are chasing that dog’

• Even more permutations than this are possible

• Only restriction: Aux must be in second position (Note: this is a slight simpliﬁcation)

9 Warlpiri S NP Aux VP • Underlying meaning:are V NP the two small children That of ‘the twoch asmallsing t hchildrenat dog are chasing that dog’

NP Aux V NP NP NP

wita-jarra-rlu ka-pala wajili-pi-nyi yalumpu kurdu-jarra-rlu maliki small-DUAL-ERG pres-3duSUBJ chase-NPAST that-ABS child-DUAL-ERG dog-ABS

10 Abstract Syntax

• Despite the striking structural differences between English and Warlpiri, there are nevertheless common syntactic constraints on the two languages.

• Example: a subject can bind an object reﬂexive, but not vice versa

(1) a. Lucy is hitting herself. b. * Herself is hitting Lucy.

(2) a. Napaljarri-rli ka-nyanu paka-rni Napaljarri-ERG PRES-REFL hit-NONPAST ‘Napaljarri is hitting herself.’

b. * Napaljarri ka-nyanu paka-rni Napaljarri.ABS PRES-REFL hit-NONPAST ‘Herself is hitting Napaljarri.’

➡ How should abstract grammatical relations be captured? Transformational Grammar: conﬁgurationally, using a uniform syntactic representation

LFG: non-conﬁgurationally, using a separate syntactic representation

11 C-structure

• Language variation in phrasal expression:

• Basic word order:

• SVO (English), SOV (Japanese), VSO (Irish), VOS (Malagasy)

• Constituency:

• Grouping of verb and complements,

• Grouping of noun and modiﬁers

• Strict vs. free word order:

• conﬁgurational languages vs. case-marking languages

12 84 Lexical Functional Grammar

Unlike many theories, LFG assumes that daughters Constraints on C-structures: of all phrasal categories are optional. In particular, Phrase Structure Rules the head of a maximal phrase need not appear. In many languages, for example, tensed verbs appear 84 Lexical Functional Grammar • LFG distinguishes between the objects in the model and descriptions of those objects (i.e. constraints on the objects). in I (King,841995;LexicalSells,Functional2001).GrammarA Swedish sentence such as (3), with a tensed verb and noUnlikenontensemany theoriesd , LFGTheassum•esrightC-structurethat dau-handghters treesside areof constrainedan LFG byphrase phrase structurestructure rules.rule of all phrasal categories are optional. In particular, verbs, has a VUnlP ikethatmanydoestheoriesnot co, LFGntainassumatheVes.headthatofdaua maximalghters phraseis needa regularnot appearexpres. In sion, allowing for disjunction, op- of all phrasal categories are optionamanyl. languagIn particules, forarexample,, tionatensedlityverbs, andappeararbitrary repetition of a node or se- (3) Anna sa˚g boken in I (King, 1995; Sells, 2001). A Swedish sentence the head of a maximal phrase needsuch notas (3),appearwith a. tensedIn verbquenceand no ofnontensenoded s.TheTheright-handV andside ofNPan LFGdaphraseughtersstructureinrulethe Anna saw book.DEF many languages, for example, tensedverbs, hasverbsa VPappearthat does not contain• Right-handa V. side isofa LFGregular phraseexpres structuresion, allowing rulesfor aredisjunct regularion, op- ‘Anna saw the book.’ rule inexpressions(6) are optiona: tionalityl,, andandarbitrartheyKleenerepetition starof a node(*)oranno-se- in I (King, 1995; Sells, 2001). A Swe(3) Annadish sentencesa˚g boken quence of nodes. The V and NP daughters in the such as (3), with a tensed verb and noAnnanontensesaw book.d DEF tationThe righton-handthe sidePP indicateof an LFGs phrasethat astructuresequencrulee of zero or ‘Anna saw the book.’ ➡disjunction, optionality,rule in (6) arearbitraryoptiona repetitionl, and the Kleene (Kleenestar plus(*) anno- [+] and verbs, has a VP that does not contain a V. moreis a regularPPstarco expres[*])nstituentssion,tationallowingonmaythe PPappearforindicatedisjuncts.that aion,sequencop-e of zero or tionality, and arbitrarmorey repetPP constituentsition ofmaya nodeappear. or se- (3) Anna sa˚g boken (6) V (V) (NP) PP* quence of0 nodes. The(6)VVand0 (V)NP(NP) PP*daughters in the Anna saw book.DEF ! ! ‘Anna saw the book.’ rule in (6) are optional, and the Kleene star (*) annotation on the PP indicateFunctionals that aStructuresequence of zero or 13 Functionalmore PP constituentsStructureSynmaytacticappearanalyses. in traditional grammatical descriptions are stated in terms of abstract syntactic functions (6) V (V) (NP) PP* Syntactic0 ! analysessuchin astraditiosubject, objecnalt, gramand complmaticaement. Thel descrse func-iptions are represented at LFG’s functional structure. tions are stated in F-strutermctures orepref abstrsents actabstractsyntacgrammaticatic functionsl functions Functional Structuresuch as subject and object, as well as features such as such as subject, objectense, case,t, andperson,compland numberement.. These func- Nonhead daughters are also onltionsSyny optactictionaarellyanalysprerepresent.esIn sentedin traditioatnalLFG’gramsmaticafunctionall descrip-structure. Japanese and other so-calledF-strutions‘prodroarepcture’ lastatednguagrepreesin, atermsentsGrammaticals of abstrabstractactFunctionssyntacgramandticTheirmaticafunctionsRepresentationl functions verb can appear with no overt arguments. If no overt arguments of a verb are presesuchsuchnt, theasasc-stsubject,rusuctbjecture trobjecee anInt,d aandobject,sentcomplence sasucement.h wellas DaviTheasd dfeatesevoufunc-reuresd a sandsuchwich, as contains only the verb: tions are representedDaatvidLFG’is the subfunctionalject and a sandstrucwich isture.the object. This tense, case, person,infoandrmationumbern is represen.ted by an attribute-value struc- (4) koware-ta F-structure representstuabstractre, the f-strugramcture,maticain whiclhfunctionsthe value of the SUBJ Nonhead daughters are also only optionally pbreak-PreseASTnt. In such as subject and object,feature isasthewellf-struascturfeate foruresthe subsuchject anasd the value of ‘[it/something] broke.’ tense, case, person, andthe OnumberBJ featur.e is the f-structure for the object. Japanese and other so-called ‘prodrop’ languages, a Grammatical Functions and Their Representation verb can apNopeanhreawdidtauh ghnoteorsvareretalarsoguonlmey ontptis.onaIfllynopreovsenert.tIn (7) David devoured a sandwich. arguments Jaofpaanevese rbandaroetherpresose-cnaltle, dth‘eprodc-strorup’ ctlaungrueatgrees,ea InGrammaticala sentencFunctionse such aands DaTheirvidRepresentationdevoured a sandwich, verb can appear with no overt arguments. If no overt David is the subject and a sandwich is the object. This contains onarlyguthmeentvesrobf:a verb are present, the c-structure tree In a sentence such as David devoured a sandwich, C-structure does not contain subparts of words or contains only the verb: inDafovirmd isatthioe nsubisjerctepanredsea nsatneddwbyich anis thate otrbibjecutt.eTh-visalue struc- (4) koware-ta unpronounced features, nor does it contain null pro- nominals in prodrop languagtuinesforesuchrm, tathasioe nJapanesf-ists rruepe.ctreseurForne,tedclarityinbywh,anmanyatictrhiboftuhtthee-vvafeataluluurese estroanducf- tvaluehe sSUin BJ break-P(4)ASTkoware-ta Rather, it reflects the structurefetuatandre,urtgroupingheeisf-tsthruofectf-theurste,ruthisinctuwhf-strucreicfhoturerththehaevaveslubeueenbjoeomifctthtted,ane SUda practicetBhJe vaofteluen of ‘[it/something]break-Pbroke.’AST full syntactic units – the wordsfeatandurphrasese is the–f-insttheructufollowre foredthine sLFGubjeprctesentationand thes.vaTheluefullof f-structure ‘[it/something] broke.’ sentence. the OBJ feature iscontaithe nsf-sttense,ructaspecture, fperson,or thenumberobjec, at.nd other the OBJ feature is thefunctf-struionalcturfeate ures.for the object. Every content word in a sentence contributes a Phrase Structure Rules (7)(7) DavidDaviddevoureddevouredvaluea sandwich.fora sandwich.the feature PRED. These values are called LFG draws a strong distinction between the formal semantic forms. In the functional structure, semantic objects of the theory – constituent structure trees and forms are surrounded by single quotes: the semantic functional structures – and the constraints or descrip- form contributed by the word David is ‘DAVID.’ tions involving those objects. C-structure trees are An important property of semantic forms is that constrained by phrase structure rules, which license they are uniquely instantiated for each instance of C-structure does not contain subpartslocal treeofconwordsfigurationors. The phrase structure rule in their use, reflecting the unique semantic contribution (5a) licenses the c-structure in (5b): of each word within the sentence. This is occasionally C-structureunprodoesnouncednot cofeaturesntain, norsubpartsdoes it contaiof wordsn null pro-or unpronouncednominalsfeaturesin prodrop, nor doelanguags it contaies suchnasnullJapanespro-e. For clarity, many of the features and values in Rather, it reflects the structure and grouping of the Forthis f-strucclarityture, manyhave beenofomithetted,feata practiceures andoftenvalues in nominals in prodrop languages such as Japanese. followed in LFG presentations. The full f-structure full syntactic units – the words and phrases – in the this f-structure have been omitted, a practice often Rather, it reflecsententsce. the structure and grouping of the contains tense, aspect, person, number, and other full syntactic units – the words and phrases – in the followfunctionaled featin ures.LFG presentations. The full f-structure contaiEverynscontenttense,wordaspectin ,a person,sentence contributenumber,s and other sentence. Phrase Structure Rules functvalue ionalfor thefeatfeatureures.PRED. These values are called LFG draws a strong distinction between the formal semanEverytic forms.contentIn thewordfunctionalin astructuresentence, semcontributeantic s a Phrase Structureobjects ofRulesthe theory – constituent structure trees and forms are surrounded by single quotes: the semantic functional structures – and the constraints or descrip- valueform contributefor the dfeatureby the wordPRED.DavidTheseis ‘DAVID.’values are called LFG drawstionsa stronginvolvingdistinctithose objecon betwts. C-structureen thee formaltrees are semanAn importanttic forms.propertIn they ofunf semanctionaltic formsstructureis that, semantic objects of theconstrtheoryained –byconphrasestituentstructurestructurerules, whitreesch licenseand formsthey areareuniquelysurrouninstandedtiatedby singlefor eachquotes:instancetheof semantic functional structurelocal tree cons –figurationand thes.constrThe phraintsase structureor descrruleip-in formtheir use,contributereflectingdthebyuniquthe ewordsemantiDavidc contributiis ‘DAonVID.’ (5a) licenses the c-structure in (5b): of each word within the sentence. This is occasionally tions involving those objects. C-structure trees are An important property of semantic forms is that constrained by phrase structure rules, which license they are uniquely instantiated for each instance of local tree configurations. The phrase structure rule in their use, reflecting the unique semantic contribution (5a) licenses the c-structure in (5b): of each word within the sentence. This is occasionally 84 Lexical Functional Grammar

Unlike many theories, LFG assumes that daughters of all phrasal categories are optional. In particular, the head of a maximal phrase need not appear. In many languages, for example, tensed verbs appear in I (King, 1995; Sells, 2001). A Swedish sentence such as (3), with a tensed verb and no nontensed The right-hand side of an LFG phrase structure rule verbs, has a VP that does not contain a V. is a regular expression, allowing for disjunction, optionality, and arbitrary repetition of a node or se- (3) Anna sa˚g boken quence of nodes. The V and NP daughters in the Anna saw book.DEF ‘Anna saw the book.’ rule in (6) are optional, and the Kleene star (*) annotation on the PP indicates that a sequence of zero or more PP constituents may appear. (6) V (V) (NP) PP* 0 !

Functional Structure Syntactic analyses in traditional grammatical descriptions are stated in terms of abstract syntactic functions such as subject, object, and complement. These functions are represented at LFG’s functional structure. F-structure represents abstract grammatical functions such as subject and object, as well as features such as tense, case, person, and number. Nonhead daughters are also only optionally present. In Japanese and other so-called ‘prodrop’ languages, a Grammatical Functions and Their Representation verb can appear with no overt arguments. If no overt In a sentence such as David devoured a sandwich, arguments of a verb are present, the c-structure treF-structurese contains only the verb: David is the subject and a sandwich is the object. This information is represented by an attribute-value struc- (4) koware-ta • F-structuresture, trepresenthe f-stru abstractcture, grammaticalin which th functionse value o(subject,f the SU BJ object, etc.), grammatical features (tense, case, person, number, break-PAST feature is the f-structure for the subject and the value of ‘[it/something] broke.’ etc.), and grammatical dependencies (raising, control, unboundedthe O dependencies)BJ feature is the f-structure for the object. (1)David devoured(7) David a sandwich.devoured a sandwich.

C-structure does not contain subparts of words or unpronounced features, nor does it contain null pro- nominals in prodrop languages such as Japanese. For clarity, many of the features and values in Rather, it reflects the structure and grouping of the this f-structure have been omitted, a practice often full syntactic units – the words and phrases – in the followed in LFG presentations. The full f-structure14 sentence. contains tense, aspect, person, number, and other functional features. Every content word in a sentence contributes a Phrase Structure Rules value for the feature PRED. These values are called LFG draws a strong distinction between the formal semantic forms. In the functional structure, semantic objects of the theory – constituent structure trees and forms are surrounded by single quotes: the semantic functional structures – and the constraints or descrip- form contributed by the word David is ‘DAVID.’ tions involving those objects. C-structure trees are An important property of semantic forms is that constrained by phrase structure rules, which license they are uniquely instantiated for each instance of local tree configurations. The phrase structure rule in their use, reflecting the unique semantic contribution (5a) licenses the c-structure in (5b): of each word within the sentence. This is occasionally 84 Lexical Functional Grammar

Functional Structure Syntactic analyses in traditional grammatical descriptions are stated in terms of abstract syntactic functions such as subject, object, and complement. These functions are represented at LFG’s functional structure. F-structure represents abstract grammatical functions such as subject and object, as well as features such as tense, case, person, and number. Nonhead daughters are also only optionally present. In Japanese and other so-called ‘prodrop’ languages, a Grammatical Functions and Their Representation verb can appear with no overt arguments. If no overt arguments of a verb are present, the c-structure tree In a sentence such as David devoured a sandwich, contains only the verb: David is the subject and a sandwich is the object. This information is represented by an attribute-value struc- (4) koware-ta Anatomyture, th ofe f- anstru ctF-structureure, in which the value of the SUBJ break-PAST feature is the f-structure for the subject and the value of ‘[it/something] broke.’ the OBJ feature is the f-structure for the object. Feature Value: complex (semantic form) (7) David devoured a sandwich. Feature Value: simple (semantic form) Value: complex (feature structure) Feature Value: complex Feature (feature structure)

C-structure does not contain subparts of words or Value: simple unpronounced features, nor does it contain null pro- nominals in prodrop languages such as Japanese. For clarity, many of the features and values in this f-strucFeatureture have been omitted, a practice often Rather, it reflects the structure and grouping of the Value: simple (semantic form) full syntactic units – the words and phrases – in the followedFeaturein LFG presentations. The full f-structure sentence. contains tense, aspect, person, number, and other functional features. Every content word in a sentence contributes a Phrase Structure Rules

value for the feature PRED. These values are called 15 LFG draws a strong distinction between the formal semantic forms. In the functional structure, semantic objects of the theory – constituent structure trees and forms are surrounded by single quotes: the semantic functional structures – and the constraints or descrip- form contributed by the word David is ‘DAVID.’ tions involving those objects. C-structure trees are An important property of semantic forms is that constrained by phrase structure rules, which license they are uniquely instantiated for each instance of local tree configurations. The phrase structure rule in their use, reflecting the unique semantic contribution (5a) licenses the c-structure in (5b): of each word within the sentence. This is occasionally General Constraints on F-structures: Completeness, Coherence, Uniqueness

• Completeness: All the grammatical functions subcategorized by a predicate must be present in the f-structure.

(1)* David devoured.

Devour

• Coherence: Only the grammatical functions subcategorized by a predicate may be present in the f-structure.

(2)* David devoured a sandwich that it was raining.

• Uniqueness: No attribute may have more than one value.

16 Lexical Functional Grammar 85

Uniquenessindicate andd by associSemanticating a unique Formsnumerical identifier Table 1 Governable grammatical functions with each instance of a semantic form, as in (8): SUBJ Subject • Semantic forms(8) David(valuesdevoured of PREDa sandwich.features) are unique. OBJ Object COMP Sentential or closed (nonpredicative) infinitival complement XCOMP An open (predicative) complement, often infinitival, whose SUBJ function is externally controlled

OBJy A family of secondary OBJ functions associated with a particular, language-specific set of thematic roles;

in English, only OBJTHEME is allowed, while other languages allow more than one thematically restricted secondary object In (8), the particular occurrence of the semantic form OBL A family of thematically restricted oblique functions ➡Multiple instances of semantic forms cannot unify, even if the y for the word David as it is used in this sentence is such as OBL or OBL , often corresponding semantic forms are otherwise compatible. GOAL AGENT represented as ‘DAVID42.’ Another use of David will to adpositional phrases at c-structure (1) * Davidbe devouredassociat eda sandwichwith a differen a sandwich.t unique identifier, perhaps ‘DAVID73.’ Representing semantic forms with explicit numerical identifiers clearly shows that each word makes a unique contribution to the f-structure. The grammatical functions that a predicate can However, the identifiers also add unnecessary clut- 17 ter to the f-structure and, therefore, are usually not govern are called governable grammatical functions. displayed. The inventory of universally available governable A verb or other predicate generally requires a par- grammatical functions is given in Table 1. Languages ticular set of arguments: for example, the verb differ as to which of these functions are relevant, but devoured requires a subject (SUBJ) and an object in many languages, including English, all of these (OBJ). These arguments are said to be governed by functions are used. the predicate; equivalently, the predicate is said Not all phrases fill argument positions of a predi- to subcategorize for its arguments. The semantic cate. Modifying adjunct phrases are not required by a form contributed by a verb or other predicate con- predicate and hence are not governable. In (11), the tains information about the arguments it governs. phrase yesterday bears the nongovernable grammatical As shown in (8), the governed arguments appear in function ADJ (unct): angled brackets: ‘DEVOUR SUBJ,OBJ .’ (11) David devoured a sandwich yesterday. The LFG requirements ofhcompleteneiss and coherence ensure that all and only the grammatical functions There are two nongovernable grammatical functions. governed by a predicate are found in the structure of a The function ADJ is the grammatical function of grammatically acceptable sentence. For example, the modifiers such as in the park, with a hammer, and unacceptability of example (9) shows that the verb yesterday. The function XADJ is the grammatical devoured cannot appear without an OBJ: function of open predicative adjuncts whose subject is externally controlled; as with the governable gram- (9) *David devoured. matical function XCOMP, the X in the name of the This sentence violates the principle of complete- function indicates that it is an open function whose ness, according to which every grammatical function SUBJ is supplied externally. The phrase filling the governed by a predicate must be filled. Here, the OBJ XADJ role is in boldface in (12). is not present, and the sentence is incomplete. (12a) Having opened the window, David took a deep Furthermore, devour cannot appear with other breath. functions than the grammatical functions SUBJ and (12b) David ate the celery naked. OBJ that it governs. Example (10) shows that it can- (12c) David ate the celery raw. not appear with a sentential complement in addition In (12a) and (12b), the open adjunct XADJ is con- to its object: trolled by the subject of the main clause: It is David (10) *David devoured a sandwich that it was raining. who opened the window, and it is David who is naked. In (12c), the XADJ is controlled by the object: This sentence violates the principle of coherence, It is the celery that is raw. according to which only the grammatical functions Unlike governable grammatical functions, more that are governed by a predicate can appear. Because than one adjunct function can appear in a sentence: the sentence contains a grammatical function that the verb devour does not govern, it is incoherent. (13) David devoured a sandwich at noon yesterday. Features and the Lexicon in LFG

18 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 Entries 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

F(unctional)-description, made up of functional schemata

19 201 201 Lexical Functional Grammar 87

(21) David sneezed (24a) (f PRED) ‘SNEEZE SUBJ ’ (f TENSE)¼ PRES h i (f SUBJ) g¼ (g PRED)¼ ‘DAVID’ (g NUM) ¼SG (f SUBJ NUM)¼ SG ¼ c Notice, however, that the f-description also holds of (24b) the f-structure in (22), which also contains all the attributes and values that are mentioned in the f-description in (20):

Here, the value SG for the NUM feature for g is specified in the second-to-last line of the functional description. Thus, the f-structure in (24b) satisfies the defining constraints given in the first five lines of (24a). Moreover, it satisfies the constraining equation given in the last line of (24a). We can also place other requirements on the minimal solution to the defining equations in some f-description. The expression in (25a) requires f not However, the f-structure in (22) is not the minimal to have the value PRESENT for the feature TENSE, or smallest solution to the f-description in (20) be- which can happen if f has no TENSE feature or if f cause it contains additional attributes and values has a TENSE feature with some value other than that do not appear in the f-description. We require PRESENT. When it appears in a functional descrip- the f-structure solution for a particular f-description tion, the expression in (25b) is an existential con- to be the minimal solution to the f-description: straint, requiring f to contain the feature TENSE, no additional attributes or values that are not men- but not requiring any particular value for this feature. tioned in the f-description are included. Thus, the We can also use a negative existential constraint to correct solution to the f-description in (20) is the require an f-structure not to contain an feature, as in f-structure in (21), not the larger one in (22). Formally, (25c), which requires f not to contain the feature the solution to an f-description is the most general TENSE with any value whatsoever. f-structure that satisfies the f-description, which sub- Two Main Kinds of F-structure Constraints: (25a) Negative equation: (f TENSE) PRESENT Definingsu Equationsmes all otandhe Constrainingr (larger) fEquations-structures that satisfy the 6¼ f-description. (25b) Existential constraint: (f TENSE) (25c) Negative existential constraint: (f TENSE) • Functional Inschemataaddit andion functionalto descriptionsthe defining are often referredconstraint to as s just de- equations. This is a little inaccurate, because equality is not always the : relevantscribed, relation, butLFG it is certainlyalso theallows most commonelement way of specifyings of the f-description Functional descriptions can also be stated in terms constraintsto checkon f-structuresthe inpropert LFG. So theies termof hasthe stuck.minimal solution to the of the Boolean operations of conjunction, disjunction, • There aredefining two main classesequati of f-structureons. The constraintsexp inression LFG: in (23) is a con- and negation. In the f-descriptions just given, we im- 1.Defining Equations Thesestraini equationsng defineequ the ation,f-structure bydistingui specifying whichshed featuresfrom a defining plicitly assume that the constraints in the f-description haveequati which values.on Theyby ‘makethe itc so’.subscr Definingipt equationson the are statedequals sign in the are interpreted conjunctively; if an f-description con- with a simple equality (or other relation symbol). expression: tains more than one requirement, each requirement must hold. LFG also allows disjunctions and negations (23) (f SUBJ NUM) SG ¼ c of sets of requirements. For example, a verb like When this expression appears, the f-structure f that is sneeze contributes the following f-description: the minimal solution to the defining equatio20 ns must (26) sneeze contain the feature SUBJ whose value has an feature NUM with value SG. The constraining equation in (23) does not hold of the f-structure in (21) because in that f-structure the value of the NUM feature has been left unspecified and the SUBJ of f does not have a NUM feature with value SG. Disjunction is indicated by curly brackets, with the In contrast, the functional description in (24a) alternatives separated by a vertical bar |. Negation for for the sentence David sneezes has a well-formed a set of requirements is represented by prefixing , and solution, the f-structure in (24b): the scope of negation is indicated by curly bra:ckets. Lexical Functional Grammar 87

Here, the value SG for the NUM feature for g is specified in the second-to-last line of the functional description. Thus, the f-structure in (24b) satisfies the defining constraints given in the first five lines of (24a). Moreover, it satisfies the constraining equation given in the last line of (24a). We can also place other requirements on the minimal solution to the defining equations in some f-description. The expression in (25a) requires f not However, the f-structure in (22) is not the minimal to have the value PRESENT for the feature TENSE, or smallest solution to the f-description in (20) be- which can happen if f has no TENSE feature or if f cause it contains additional attributes and values has a TENSE feature with some value other than that do not appear in the f-description. We require PRESENT. When it appears in a functional descrip- the f-structure solution for a particular f-description tion, the expression in (25b) is an existential con- to be the minimal solution to the f-description: straint, requiring f to contain the feature TENSE, no additional attributes or values that are not men- but not requiring any particular value for this feature. tioned in the f-description are included. Thus, the We can also use a negative existential constraint to correct solution to the f-description in (20) is the require an f-structure not to contain an feature, as in f-structure in (21), not the larger one in (22). Formally, Two Main Kinds of F-structure Constraints: (25c), which requires f not to contain the feature the solution to an f-description is the most general Deﬁning Equations and Constraining Equations TENSE with any value whatsoever. f-structure that satisfies the f-description, which sub- (25a) Negative equation: (f TENSE) PRESENT • There are twosu mainme sclassesall otof f-structureher (la rconstraintsger) f-s intr LFG:uctures that satisfy the 6¼ f-description. (25b) Existential constraint: (f TENSE) 2.Constraining Equations (25c) Negative existential constraint: (f TENSE) These equationsIn furtheraddit constrainion to the thef-structuredefining once it hasconstraint been s just de- : constructed.scribed, LFG also allows elements of the f-description Functional descriptions can also be stated in terms In other words:to check the properties of the minimal solution to the of the Boolean operations of conjunction, disjunction, 1. Satisfy definingdeﬁning equations,equati settingons. asideThe constrainingexpression equations,in to(23 get ) is a con- and negation. In the f-descriptions just given, we im- minimal model. 2. Satisfy strainiconstrainingng equations.equation, distinguished from a defining plicitly assume that the constraints in the f-description equation by the c subscript on the equals sign in the There are a number of different kinds of constraining equations, but the are interpreted conjunctively; if an f-description con- ones thatexpres check feature-valuesion: pairs are written with a subscript c on the tains more than one requirement, each requirement equality like this: must hold. LFG also allows disjunctions and negations (23) (f SUBJ NUM) SG ¼ c of sets of requirements. For example, a verb like When this expression appears, the f-structure f that is sneeze contributes the following f-description:

the minimal solution to the defining equations21 must (26) sneeze contain the feature SUBJ whose value has an feature NUM with value SG. The constraining equation in (23) does not hold of the f-structure in (21) because in that f-structure the value of the NUM feature has been left unspecified and the SUBJ of f does not have a NUM feature with value SG. Disjunction is indicated by curly brackets, with the In contrast, the functional description in (24a) alternatives separated by a vertical bar |. Negation for for the sentence David sneezes has a well-formed a set of requirements is represented by prefixing , and solution, the f-structure in (24b): the scope of negation is indicated by curly bra:ckets. LexicalLexicalFunctionalFunctionalGrammarGrammar87 87

(21)(21)DavidDavidsneezedsneezed (24a)(24a) ((ff PRED) ‘‘SNEEZESNEEZESUBJSUBJ’ ’ ¼ Lexicalh Functionali Grammar 87 ((ff TENSE)¼ PRESPRES h i ¼ ((ff SUBJ) gg¼ ¼¼ (21) David sneezed (24a) (((ggf PRED)PRED) ‘‘‘DASNEEZEDAVIDVID’ ’ SUBJ ’ ¼¼ (((ggf TENSE)NUM) ¼SGSGPRES h i ¼¼ (((fff SUBJSUBJ)NUM)NUM)g¼ c SGSG ¼¼ c NoticeNotice, howev, however, erthat, thatthethef-descripf-descriptiontionalsoalsoholdsholdsofof (24b) (g PRED)¼ ‘DAVID’ (24b) ¼ the thef-structuref-structurein in(22),(22),whiwhichchalsoalsoconcontainstainsallallthethe (g NUM) SG attributes and values that are mentioned in the ¼ attributes and values that are mentioned in the (f SUBJ NUM) c SG f-description in (20): ¼ f-descriNotiception, howevin (20):er, that the f-description also holds of (24b) the f-structure in (22), which also contains all the attributes and values that are mentioned in the Here, the value SG for the NUM feature for g is f-description in (20): Here,specifiedtheinvaluethe secondSG for-to-lastthe NUMline of featurethe functforionalg is specifidescription.ed in Thusthe second, the f-struc-to-lastturelinein (24bof )thesatisfiesfuncttheional description. Thus, the f-structure in (24b) satisfies the Here,definingtheconstraintvalue SGs givefor nthein NUMthe firstfeaturefive lifornes gofis defining constraints given in the first five lines of specifi(24a). Moreoveed in ther,secondit satisfies-to-lastthe constrainiline of thengfunctequatiionalon (24a). Moreover, it satisfies the constraining equation descrgiveniption.in the lastThusline, theoff-struc(24a).ture in (24b) satisfies the givenWeincanthealsolastplaceline othof (24er requirema). ents on the mini- defining constraints given in the first five lines of mal solution to the defining equations in some (24a).We canMoreovealso placer, it satiothsfieser requiremthe constrainients ngonequatithe mionni- f-description. The expression in (25a) requires f not malgivensolutionin the lasttolinetheof defining(24a). equations in some However, the f-structure in (22) is not the minimal to have the value PRESENT for the feature TENSE, f-descriWe canption.alsoTheplaceexothpressioner requiremin (25a)entsrequion theresmif ni-not Howeveror small, theestf-strucsolutionturetointhe(22f-descrip) is nottiontheinminimal(20) be- towhichhavecanthehavalueppenPRESENif f has noT forTENtheSEfeaturefeature TENSE,or if f cause it contains additional attributes and values mal solution to the defining equations in some or smallest solution to the f-description in (20) be- whichhas a canTENSEhappenfeatureif f withhas nosomeTENvalueSE featureother thanor if f that do not appear in the f-description. We require f-description. The expression in (25a) requires f not causeHoweverit contains, the f-strucaddittureionalin (22attribut) is notes andthe minimalvalues hasPRESENa TENSET. Whenfeatureit appearswithinsomea funvaluectionalotherdescrip-than the f-structure solution for a particular f-description totion,havethetheexpressionvalue PRESENin (25bT)foris athen exisfeaturetentialTENSE,con- thator dosmallnotestappearsolutionin tothethef-def-descripscriptiontion. Wine (20)requirebe- PRESENT. When it appears in a functional descrip- to be the minimal solution to the f-description: whichstraint,canrequiringhappenf iftof containhas no TENthe featSE featureure TENSE,or if f thecausef-strucitturecontainssolutionadditforionala particulattributaresf-descriptiand valueons tion, the expression in (25b) is an existential con- no additional attributes or values that are not men- hasbut nota TENSErequiringfeatureany particularwith somevaluevaluefor thisotherfeature.than tothatbe dothenotminappearimal soinlutionthe f-detoscriptionthe f-descrip. We requiretion: straint, requiring f to contain the feature TENSE, tioned in the f-description are included. Thus, the PRESENWe can alsoT. Whenuse aitnegativeappearsexistentialin a functionalconstraintdescrtoip- notheaddf-strucitionaltureattributsolutiones orforvaluea particuls thatararef-descriptinot men-on correct solution to the f-description in (20) is the buttion,requinotretherequanexf-struciringpressiontureany notinparticular(25bto con) itainsvalueananexisforfeature,tentialthis featascon-inure. tionedto beinthethe minf-descriptiimal soonlutionare incluto theded.f-descripThus, tion:the f-structure in (21), not the larger one in (22). Formally, Wstraint(25c)e can, ,whichalsorequiringuserequiafresnegativetofcontainnot toexistentialcontainthe featureconstraintthe featureTENSE,to correct solution to the f-description in (20) is the Other Kinds of Constraining Equations nothadde soitionallution tattributo an f-esdesorcripvaluetion sisthatthe aremosnott gemen-neral requibutTENSEnotre anrequwithf-struciringany valuetureany panotwhatrticulartosoeverconvaluetain. anforfeature,this feature.as in f-sttionedruf-ctstruurcteinuinrthee(2th1a)f-descripti,t nsoattistfihese laonthrgeearefr-doesnincluecrinipti(2ded.o2n),. wFThusohricmha, sulthelyb,- (25c)We can, whichalso userequia resnegativef notexistentialto containconstraintthe featureto thecorresusomelucttsiosoanlllutoottionhaenr tof(-ladrthesgecrer)ifp-fdt-iseotsrncurciisptutirthonese tinmhaot(s2ts0agt)iesnifsyertthahlee TENSErequi(25a)re anwithNegativef-strucanyequation:turevaluenotwhat(tof TENSE)consoevertain. anPRESENTfeature, as in (25b) Existential constraint: ( TENSE)6¼ f-stf-rustf-ctdrueuctscruerirptehtiiaontn.(s2a1t)is, finoest tthheelaf-rdgesercronipetiinon(2, 2w).hFicohrmsuablly-, (25c), which requires f not fto contain the feature (25a)(25c) NegativeNegative existentialequation: constraint:(f TENSE) (fPRESENTTENSE) sumethesInsaollluaddittotiohneionrto(laatonrgfethe-rd)esfdefiningcr-stirputicotnureisconstraints ththeatmsoasttisjustgfyenthede-real TENSE with any value whatsoever. :6¼ f-df-estsscribed,cruripcttuiorn.eLFGthatalsosatisallowsfies thelemente f-descrs ipoftitheon,f-descriptiwhich suonb- (25b)FunctionalExistentialdescriptionsconstraint:can(alsof TENSE)be stated in terms (25c)(25a) NegativeNegative existentialequation: (fconstraint:TENSE) PRESENT(f TENSE) Insutomeadditchecks alionl theothtoproperter the(largiesdefininger)off-thestruminimalcconstrainttures thsolutatssaionjusttisftoyde-ththee of the Boolean operations of conjunction,: disjunction, (25b) Existential constraint: ( TENSE)6¼ f-ddefiningescriptioequatin. ons. The expression in (23) is a con- and negation. In the f-descriptifons just given, we im- scribed, LFG also allows elements of the f-description Func(25c)tionalNegativedescrexistentialiptions canconstraint:also be (statf TENSE)ed in terms to checkstrainiIn addittheng propertionequation,to iestheofdistinguidefiningthe minimalshedconstraintfromsolutionas justdefiningto thede- ofplicitlythe Booleanassume opethatrationsthe constraintof consjunction,in the: f-descripdisjuncttionion, definingscribed,equatiequationLFGbyons.alsothe callowsThesubscrexpelementiptressionon thes oinfequalsthe(23f-descripti) signis a incon-theon andareFuncinegatintetionalrpron.eteddescrIncothenjiptionsunf-descriptictivelcany; ifalsoanonsf-bejustdestatscgiven,riptedioinn wectermsonim-- strainitoexprescheckng sion:equtheation,propertdistinguiies of theshedminimalfromsoluta iondefiningto the plicitlyoftainthes mBooleanassumore theanopethatonrationsethereconstraintquiofremconenjunction,t,seainchtheref-descripdisjunctquiremeion,ntiont defining equations. The expression in (23) is a con- andmustnegatihold. on.LFGInaltheso alf-descriptilows disjunonsctiojustns angiven,d negawetionim-s equation(23)by(f theSUBJcNUM)subscriptc SGon the equals sign in the are interpreted conjunctively; if an f-description con- 22 expresstrainision:ng equation, distingui¼ shed from a defining taplicitlyofinsetss moassumofre requiremtheanthatontheeents.reconstraintquForiremexamplenst,ineathee,chaf-descripreverbquirelikemtionent When this expression appears, the f-structure f that is sneeze contributes the following f-description: equation by the c subscript on the equals sign in the muarestinhtoelrdp.reLtFGed coalsonjunalctloivwels y;disifjuannctiof-dnsesancridptnioengactoionn-s expres(23)the (minimalfsion:SUBJ NUM)solutionc SGto the defining equations must tains more than one requirement, each requirement ¼ of (26)sets sneezeof requirements. For example, a verb like contain the feature SUBJ whose value has an feature must hold. LFG also allows disjunctions and negations WhenNUM(23)this(fwithexpresSUBJvalueNUM)sionSG.appears,c TheSG constrathe f-struciningtureequationf that isin sneeze contributes the following f-description: the minimal solution to¼ the defining equations must of sets of requirements. For example, a verb like When(23) doethissexpresnot holdsionofapthepears,f-structurethe f-strucin (21)turebecausef that inis sneez(26)e cosneezentributes the following f-description: contain the feature SUBJ whose value has an feature thethatminimalf-structuresolutionthe valueto theofdefiningthe NUMequatiofeaturens musthas NUM with value SG. The constraining equation in (26) sneeze contaibeennleftthe unsfeaturepecifiedSUBJandwhosethe valueSUBJ hasof fandoefeatures not (23) does not hold of the f-structure in (21) because in NUMhave awithNUMvaluefeatuSG.re withThe valueconstraSG.ining equation in Disjunction is indicated by curly brackets, with the that f-structure the value of the NUM feature has (23)Indoecons nottrast,holdtheof thefunctf-structureional descriniption(21) becausein (24a)in alternatives separated by a vertical bar |. Negation for beenthatforleftf-sthetructureunssentencepecifiedtheDavidvalueand thesneezesof theSUBJNUMhasofa fwellfeaturedoe-formeds nothas a set of requirements is represented by prefixing , and solution, the f-structure in (24b): : havebeena NUMleft unsfeatupecifiedre withandvaluetheSG.SUBJ of f does not Dithsje unscoctpeionofisneignadtiioncateisdinbydiccuaterldybbyracuckrlety s,brawickthetsth. e Inhavecona NUMtrast, featuthe functre withionalvaluedescrSG.iption in (24a) alDitesjrnunatctivioesnseispainradteicadtebdy bya vecurtrlicyalbbararck|.etNs,egwiatthionthfoer for the sentence David sneezes has a well-formed a set of requirements is represented by prefixing , and In contrast, the functional description in (24a) alternatives separated by a vertical bar |. Negatio:n for solution,for thethesentencef-structureDavidin (24b):sneezes has a well-formed thaesestcoofpereqofuirnemegeanttsionis reispirnedsiecnateteddbbyyprecufirxilynbgra,caknetds. solution, the f-structure in (24b): the scope of negation is indicated by curly bra:ckets. Lexical Functional Grammar 87

Here, the value SG for the NUM feature for g is specified in the second-to-last line of the functional description. Thus, the f-structure in (24b) satisfies the defining constraints given in the first five lines of (24a). Moreover, it satisfies the constraining equation given in the last line of (24a). We can also place other requirements on the minimal solution to the defining equations in some f-description. The expression in (25a) requires f not However, the f-structure in (22) is not the minimal to have the value PRESENT for the feature TENSE, or smallest solution to the f-description in (20) be- which can happen if f has no TENSE feature or if f cause it contains additional attributes and values has a TENSE feature with some value other than that do not appear in the f-description. We require PRESENT. When it appears in a functional descrip- the f-structure solution for a particular f-description tion, the expression in (25b) is an existential con- to be the minimal solution to theFunf-descripctionation:l Consstrainttraint,srequiring f to contain the feature TENSE, 109 no additional attributes or values that are not men- but not requiring any particular value for this feature. tioned in the f-description are included. Thus, the We can also use a negative existential constraint to correct solution to the f-description in (20) is the require an f-structure not to contain an feature, as in f-structure in (21), not the larger one2in.4(2.2). FOormpatlilyo, na(25c)lity, which requires f not to contain the feature the solution to an f-description is the most general TENSE with any value whatsoever. f-structure that satisfies the f-description, which sub- An f-descriptio(25a)n caNegativen alsoequation:be op(ftiTENSE)onal. WPRESENThen this happens, the f-description sumes all other (larger) f-structures that satisfy the 6¼ f-description. may but need not (25b)be saExistentialtisfied.constraint: (f TENSE) (25c) Negative existential constraint: (f TENSE) In addition to the defining constraints just de- : scribed, LFG also allows elements of theBf-descriptiresnanonand MFuncchotionalmbodescr(19iptions87) scanhoalsow tbehastatt vederinbstermsin Chichewaˆ optionally carry to check the properties of the minimalinfsolutormionattoiothen aboofuthet thBooleaneir suopebjerationscts; iofn cona Cjunction,hichedisjunctwaˆ seion,ntence, a subject noun phrase defining equations. The expression in (23) is a con- and negation. In the f-descriptions just given, we im- straining equation, distinguished mfromay abedefiningeither prplicitlyesentassumor aebthatsenthet: constraints in the f-description equation by the c subscript on the equals sign in the are interpreted conjunctively; if an f-description con- expression: (64) a. njuˆchtaiinzsim-noaré-ltuhám-n oane requirement, each reaqlueinrejmeent must hold. LFG also allows disjunctions and negations (23) (f SUBJ NUM) SG bees SUBJ-PAST-bite-INDICATIVE hunters ¼ c of setsOptionality,of requirem Disjunction,ents. For exampl Conjunction,e, a verb like Negation When this expression appears, the f-structure f that‘isThesneezbeeescobntributesit the htheunfollowters.ing’ f-description: the minimal solution to the defining equations must (26) sneeze contain the feature SUBJ whose value has anbfeature. zi-na´-lu´m-a alenje Conjunction (implicit) NUM with value SG. The constraining equation in SUBJ PAST INDICATIVE (23) does not hold of the f-structure in (21) because in - -bite- hunters Negation ¬ A or ¬{ ... } that f-structure the value of the NUM feature has‘They bit the hunters.’ been left unspecified and the SUBJ of f does not Disjunction { A | B } have a NUM feature with value SG. Disjunction is indicated by curly brackets, with the Bresnan and Mcho•mThebo lexicalpr oentrypo forse ‘sneeze’that (fromth eDalrympleverb 2001:87)zi-n a´says-lu ´them- following:a ‘b it’ optionally con- In contrast, the functional description in (24a) alternatTheives PREDsepa ofra ‘sneeze’ted by isa ‘SNEEZE’.vertical bar |. N Alsoegat (conjunction):ion for Either (disjunction) the for the sentence David sneezes hastriabuwelltes-formedan f-desacsreitpotfiVFORMreoqnuicre oism nBASEenststr i(i.e.asiren it’spirn ae sgnon-finiteenttehdebv yform)aplreu fiorexi ito nhasgf tpresenth, aendP RtenseED andat itt risi notbu thete caseof its subject. that (negation) its subject has third person singular: agreement features (cf. She sneeze.) solution, the f-structure in (24b): This optional f-dtheessccorpeiptofionnegiastionenicsliondsiecadteidnbpy acurerlyntbhraecskeetss:.

(65) zi-na´-lu´m-a: (( SUBJ PRED) = ‘PRO’) Optionality ( A )

Since the equation ( Hint:SU B‘pro-drop’J PRED) = in‘P LFG!RO’ is optional, it may but need not contribute to the minimal solution to the f-description for the sentence. If an overt 23 subject noun phrase does not contribute its own PRED value, the f-structure for this sentence is incomplete unless this equation is satisfied, and the wellformed f-structure for the SUBJ contains the pair PRED ‘PRO’ . If an overt subject noun phrase appears, the equation may not be satisfied, since the PRED value of the overt subject would produce a clash; instead, the PRED value for the SUBJ is the one specified by the subject noun phrase: (66) a. njuˆchi zi-na´-lu´m-a alenje bees SUBJ-PAST-bite-INDICATIVE hunters ‘The bees bit the hunters.’ PRED ‘BITE SUBJ,OBJ ’

PRED ‘BEES’ SUBJ NOUNCLASS 10

PRED ‘HUNTERS’ OBJ NOUNCLASS 2 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

25 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

26 160 6. Syntactic Relations and Syntactic Constraints

of a reﬂexive pronoun like himself must f-command the pronoun. The contrast in acceptability between examples (67a) and (67b) is due to the fact that in example (67a), the antecedent of the reﬂexive pronoun himself f-commands the f-structure of the pronoun, while the f-command relation does not hold in (67b): (67) a. David saw himself .

PRED ‘SEE SUBJ,OBJ ’

SUBJ PRED ‘DAVID’

PRED ‘PRO’ OBJ PRONTYPE REFL b. *David ’s mother saw himself .

PRED ‘SEE SUBJ,OBJ ’

PRED ‘MOTHER’ SUBJ SPEC PRED ‘DAVID’

PRED ‘PRO’ OBJ PRONTYPE REFL

Chapter 11 provides a fuller discussion of constraints on anaphoric binding; there, we will see that the f-command condition for antecedents of reflexive pronouns follows as a corollary from the binding requirements for reflexives, along the lines Functionalof the definitio nDescriptionsin (66). and Subsumption

3.2. Subsumption • F-descriptions are true of not just the smallest, ‘intuitively intended’ f-structure, but also any larger f-structureSubsumpti othatn is containsa relation thethat sameholds binformation.*etween two f-structures and if is compatible with but perhaps has more structure than . In other words, subsumes if and are the same, or if is the same as except that it contains * Thisso mrelationshipe additional isst rcalleducture tsubsumptionhat does not app: ear in . For example, the f-structure In general,labeled ain structure(68) subsu Am subsumeses the f-stru catu structurere labeled B: if and only if A and B are identical or B contains A and additional information not included in A. (68) subsumes :

PRED ‘GO SUBJ ’ TENSE FUTURE PRED ‘GO SUBJ ’ PRED ‘PRO’ f subsumes g SUBJ NUM SG SUBJ CASE NOM NUM SG

• An f-description is therefore true of not just the minimal f-structure that satisﬁes the description: the f-description is also true of the inﬁnitely many other f-structures that the intended, minimal f-structure subsumes.

27 86 Lexical Functional Grammar

Because the ADJ function can be multiply filled, its the CASE feature to allow for case indeterminacy. value is a set of f-structures: Some studies assume a PCASE feature whose value specifies the grammatical function of its phrase. In (14) David devoured a sandwich at noon yesterday. more recent work, Nordlinger (1998) provided a theory of constructive case, according to which a case marked phrase places constraints on its f-structure environment that determine its grammatical function in the sentence. This treatment supplants the traditional treatment of obliques in terms of the PCASE feature.

Functional Descriptions As with c-structures, we draw a sharp distinction between f-structures and their descriptions. The set The same is true of XADJ; more than one XADJ of f-structure constraints associated with the analysis phrase can appear in a single sentence: of some sentence is called a functional description or f-description. (15) Having opened the window, David ate the To refer to the value of a feature, say, TENSE, in celery naked. some f-structure, we use an expression like the Hence, the value of the XADJ feature is also a set following: of f-structures. (16) (f TENSE) The f-structures that have been presented so far have included only a subset of their functional fea- This expression refers to the value of the TENSE tures. In fact, it is common in LFG literature to display feature in the f-structure f. If we want to specify the only those features that are relevant to the analysis value of that feature, we use an expression such as: under discussion because a full representation is often (17) (f TENSE) PAST too unwieldy. A full f-structure for these sentences ¼ contains at least the features and values listed in This defining equation specifies that the feature Table 2 and probably other language-specific features TENSE in the f-structure f has the value PAST. and values as well. The values given in this chart are We can also specify that an feature has a particu- the ones that are most often assumed, but some lar f-structure as its value. The expression in (18) authors have argued for a different representation of specifies that the value of the SUBJ feature in f is the the values of some features. For example, Dalrymple f-structure g: and Kaplan (2000) argue for a set-based representa- (18) (f SUBJ) g tion of the PERS and GEND features to allow for an Minimization¼ account of feature resolution in coordination and of Some features take as their value a set of functional structures. For example, because any number of adjuncts can appear in a sentence, the value of the Lexical Functional Grammar 87 Table 2 f-Structure features • There is a general requirement on LFG’s solution algorithm that it yield the minimal solution: feature ADJ is a set. We can specify that an f-structure Lexical Functional Grammar 87 h is anomem featuresber of thatthe areADJ notset mentionedwith the folloin thewing f-description may be included. Feature Value (21) David sneezed (24a) (f PRED) ‘SNEEZE SUBJ ’ constraint, using the set-membership symbol : ¼ h i 2 (f TENSE) PRES Person PERS 1, 2, 3 • Let’s look at an example from Dalrymple (2001). (21) David sneezed (f SUBJ) (24a)g¼ (f PRED) ‘SNEEZE SUBJ ’ Gender GEND MASC, FEM, . . . (19) h (f ADJ) ¼ ¼ h i 2 (g PRED) ‘DAVID(f TENSE)’ PRES Number NUM SG, DUAL, PL, . . . (g NUM) ¼SG ¼ Case CASE NOM, ACC, . . . The co(1)nsDavidtraints sneezed.discussed so far are called defining ¼ (f SUBJ) g (f SUBJ NUM) c SG ¼ Surface form FORM Surface word form constraints because they define the required properties ¼ (g PRED) ‘DAVID’ Notice, however, that the f-description also holds of (24b) Verb form VFORM PASTPART, PRESPART, . . . of a functional structure. An abbreviated f-description (g NUM) ¼SG • F-description: the f-structure in (22), which also contains all the Complementizer COMPFORM Surface form of subsumes ¼ for a sentence such as David sneezed is: attributes and values that are mentioned in the (f SUBJ NUM) c SG form complementizer: THAT, Minimal consistent f-structure ¼ f-descriNotiception, howevin (20):er, that the f-description also holds of WHETHER, . . . (20) (f PRED) ‘SNEEZE SUBJ ’ (24b) Tense TENSE PRES, PAST, . . . (f TENSE)¼ PAST h i the f-structure in (22), which also contains all the Aspect ASPECT F-structure representing ¼ (f SUBJ) g attributes and values that are mentioned Here,in thethe value SG for the NUM feature for g is complex description of ¼ (g PRED) ‘DAVID’ f-description in (20): specified in the second-to-last line of the functional sentential aspect; ¼ sometimes abbreviated, Consistent but non-minimal f-structure description. Thus, the f-structure in (24b) satisfies the This f-description holds of the following f-structure, defining constraints given in the first five lines of e.g., PRES.IMPERFECT where the f-structures are annotated with the names Pronoun type PRONTYPE REL, WH, PERS, . . . (24a). MoreoveHere,r, it satithesfiesvaluethe constrainiSG forng equatithe onNUM feature for g is used in the f-description (20): given in the last line of (24a). We can alsospecifiplace othederinrequiremthe secondents on-to-lastthe mini-line of the functional mal solution descrto theiption.definingThusequations, the f-strucin someture in (24b) satisfies the f-description. definingThe expressionconstraintin (25a)s requigiveresn finnotthe first five lines of However, the f-structure in (22) is not the minimal to have the value(24a).PRESENMoreoveT for rthe, itfeaturesatisfiesTENSE,the constraining equation or smallest solution to the f-description in (20) be- which can happengivenif inf hasthenolastTENlineSE featureof (24a).or if f cause it contains additional attributes and values has a TENSE feature with some value other than that do not appear in the f-description. We require PRESEN28 T. WhenWiteappearscan alsoin aplacefunctionalotherdescrrequiremip- ents on the mini- the f-structure solution for a particular f-description tion, the expressionmal solutionin (25b) istoan theexistentialdefiningcon- equations in some to be the minimal solution to the f-description: straint, requiringf-descrif to ption.containThethe featexpressionure TENSE,in (25a) requires f not noHoweveradditional, theattributf-struces orturevalueins that(22are) isnotnotmen-the minimalbut not requiringto haveany patherticularvaluevaluePRESENfor this featTure.for the feature TENSE, tionedor smallin theestf-descriptisolutionontoaretheincluf-descripded. Thustion, thein (20)We canbe-also use a negative existential constraint to correct solution to the f-description in (20) is the require an f-strucwhichture notcantohaconppentain anif feature,f has noas inTENSE feature or if f f-causestructureitincontains(21), not theadditlargerionalone in (2attribut2). Formesallyand, (25c)value, whichs hasrequiaresTENSEf not to featurecontain thewithfeaturesome value other than ththate soludotionnotto aappearn f-descriniptiothen isf-dethe scriptionmost gene.raWl e TENSErequirewith anyPRESENvalue whatT. Whensoever. it appears in a functional descrip- f-thestructf-strucure thaturet satissolutfies thione f-dforescripatiparticulon, whicharsuf-descriptib- on (25a) Negativetion,equation:the ex(f TENSE)pressionPRESENTin (25b) is an existential con- sutomesbeall theothermin(largimaler) f-stsorulutionctures thatot sathetisfy f-descripthe tion: 6¼ f-description. (25b) Existentialstraintconstraint:, requiring(f TENSE)f to contain the feature TENSE, (25c) Negative existential constraint: (f TENSE) noIn addaddititionalion to theattributdefininges orconstraintvaluessthatjust arede- not men- but not requiring any: particular value for this feature. scribed,tionedLFGin alsotheallowsf-descriptielementons ofarethe f-descriptiincluded.on ThusFunc, thetional descrWe iptionscan alsocan usealso bea negativestated in termsexistential constraint to tocorrecheckctthesopropertlutioniestoof thetheminimalf-descsolutriptiionontointhe(20)ofisthethBooleane requioperationsre anoff-strucconjunction,ture notdisjunctto conion, tain an feature, as in defining equations. The expression in (23) is a con- f-structure in (21), not the larger one in (22). Foandrmanegatilly, on.(25c)In the,f-descriptiwhich onsrequijustresgiven,f notwe im-to contain the feature strainithe sngoluequtioation,n to adistinguin f-desshedcriptfromion isa definingthe most plicitlygeneraassuml e that the constraints in the f-description equation by the c subscript on the equals sign in the are interpretedTENSEconjunctwithively; ifanyan valuef-descriptwhation csoeveron- . expresf-strusion:cture that satisfies the f-description, whictahinsus mbo-re than one requirement, each requirement sumes all other (larger) f-structures that satimusfystthhoeld. LFG al(25a)so allowNegatives disjunctioequation:ns and neg(fatTENSE)ions PRESENT (23) (f SUBJ NUM) SG 6¼ f-description. ¼ c of sets of requirem(25b)ents.ExistentialFor examplconstraint:e, a verb like(f TENSE) When this expression appears, the f-structure f that is sneeze contributes(25c)the followNegativeing f-descriptiexistentialon: constraint: (f TENSE) In addition to the defining constraints just de- : the minimal solution to the defining equations must (26) sneeze contaiscribed,n theLFGfeaturealsoSUBJallowswhoseelementvalue hass oanf thefeaturef-description Functional descriptions can also be stated in terms NUMto checkwith thevaluepropertSG. Theiesconstraof theiningminimalequationsolutin ion to the of the Boolean operations of conjunction, disjunction, (23)definingdoes notequatihold ofons.the f-structureThe expinression(21) becausein (23in) is a con- and negation. In the f-descriptions just given, we im- thatstrainif-structureng equtheation,value distinguiof the NUMshedfeaturefromhasa defining plicitly assume that the constraints in the f-description been left unspecified and the SUBJ of f does not haveequatia NUMon byfeatuthere withc subscrvalueiptSG.on the equals signDiinsjunthection isarinediicnateedrpbyretcuedrlycobnjracunketcts,ivwielthy; thife an f-description con- expresIn consion:trast, the functional description in (24a) alternatives sepatainrates dmbyoraevetrthicaaln baonr e|. Nreegqatuiiorenmfoernt, each requirement for the sentence David sneezes has a well-formed a set of requiremumensttshisoreldpr.eLseFGntedalbsoy prealfiloxiwngs d,iasnjudnctions and negations (23) (f SUBJ NUM) SG : solution, the f-structure in (24b):¼ c the scope of nofegatsetsion isofindrequiremicated by cents.urly brForacketsexampl. e, a verb like When this expression appears, the f-structure f that is sneeze contributes the following f-description: the minimal solution to the defining equations must (26) sneeze contain the feature SUBJ whose value has an feature NUM with value SG. The constraining equation in (23) does not hold of the f-structure in (21) because in that f-structure the value of the NUM feature has been left unspecified and the SUBJ of f does not have a NUM feature with value SG. Disjunction is indicated by curly brackets, with the In contrast, the functional description in (24a) alternatives separated by a vertical bar |. Negation for for the sentence David sneezes has a well-formed a set of requirements is represented by prefixing , and solution, the f-structure in (24b): the scope of negation is indicated by curly bra:ckets. 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

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 f-description is shared by other verbs.

29 201 201 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 PRED SUBJ (4)(4)yaywanwsns ( ( PRE)=‘yawnD)=‘yawn SUB’J ’ @3SG @PRESENT @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 by30 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-ETSENNTSE 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 template202PRES3SG 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 31 @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 (8) 3PERSONSUBJ SINGSUBJ This lexical entry contains information that is shared by other verbs. We can deﬁne the templates PRESENT and 3SG to encode this3SGcommon information:

(3) PRESENT =Finally( V,FweORMcan)=FIdeﬁneNITE a template PRES3SG that combines both tense and agreement features:( TENSE)=PRES

3SG = ( (9)SUPBRJ EPSE3RSSG)=3 = @PR(8)ESEN3TPERSONSUBJ SINGSUBJ ( SUBJ NUM)=SG @3SG 3SG The template namePuttingPRESENallT thesenamesdefinitionsthe functionaltogetherdescription, our templateconsistinghierarchyof thebecomestwo equations ( VFORM)=FINITE and ( TENSEFinally)=PRES,, andwe cansimilarlydefinefora3templateSG. With PtheseRES3SG that combines both tense and agreement Templates:(8) 3PERSON FactorizationSUBJ SINGSUBJ and Hierarchies definitions the entry (10)for yawPnRsEcanS-TEbeNSrewrittenE FIfeatures:NIasTE 3PERSONSUBJ SINGSUBJ 3SG PRESENT 3SG (4) yawns ( PRED)=‘yawn SUBJ ’ (9) PRES3SG = @PRESENT Finally, we@canPRESdefineENT a template PRES3SPGREthatS3SGcombines@both3SG tense and agreement

features: @3SG and the lexical entry for⇧yPuttingawns furtherall thesereducesdefinitionsto together, our template hierarchy becomes A template(9) referencePRES3SG(or =invocation)@PRESinENaTlexical entry or in the definition of another template, as in ((5) below),(11) yawisn@markeds 3SG( byPREaDpreceding)=‘yawn(10) PRSat-signEUSB-JT’EN“@”.SE TheFINpresent-tenseITE 3PERSONSUBJ SINGSUBJ and third-singular templates will be invoked by all similarly inflected verbs, so that the @PRES3SG PRESENT 3SG detailsPuttingof theseallsubdescriptionsthese definitionsare specifiedtogether,inouronetemplateplace buthierarchyeffectivebecomesin many. We can further subdivideThus wetheseefunctionalthat a numberdescriptionof hierarchicallynamed by PRarrangedESENTPintoRgeneralizationsES3twoSG can be ex- more primitive(10) PRtemplateESpressed-TENdefinitions:SEthroughFINITaEsimple3PsetERofSOtemplateNSUBJ definitions.SINGSUBTheJ use of parameterized templates allows for further generalizationsand the lexicalto be capturedentry forbyyafactoringwns furtherout informationreduces to provided (5) FINITE = as(PanRVEFarSOEgumentRNMT)=FINtoITtheE template. These3SGare discussed next. (11) yawns ( PRED)=‘yawn SUBJ ’ PRES-TENSE = ( TENSE)=PPRREESS3SG 3 Parameterized templates @PRES3SG andPREtheSENlexicalT = entry@FINforITE yawns further reduces to Thus we see that a number of hierarchically arranged generalizations can be ex- All@intransitivePRES-TENSverbsE in LFG carry a semantic form that indicates the relation denoted 32 (11) yawns by the( PverbREDand)=‘yawnalso theSUpressedfactBJ ’thatthroughthe verba simplemust appearset of templatein f-structuresdefinitions.containingThe usethe of parameterized templates These template definitionssingle@PgovernablecanRESbe3SarrangedG grammaticalinallowsa simplefunctionforhierarchyfurtherSUgeneralizationsBthatJ. Theindicatespredicate,theirto bein-ofcapturedcourse, difbyfersfactoringfrom out information provided terdependencies: verb to verb, but the SUBasJ subcategorizationan argument to theframetemplate.is commonThesetoarealldiscussedintransitives.next.We Thus we canseedefinethat aINnumberTRANSIofTIVhierarchicallyE as a parameterizedarrangedtemplategeneralizationsthat expressescanthebecommonex- sub- (6) PRES-TENSE FINITE pressed throughcategorization.a simple set ofThetemplatepredicate3 definitions.PaitselframecanteriThebezedprovidedusetemplofaparameterizedtases an argumenttemplatesthat is specified allows forPRfurtherESdifENferentlyT generalizationsin differenttolexicalbe capturedentries.byThisfactoringtemplateoutcaninformationbe used withprovidedall intransitive as an argumentverbs:to the template. TheseAllareintransitivediscussedverbsnext.in LFG carry a semantic form that indicates the relation denoted This diagram records the fact that the PRES-TbyENStheE andverbFINandITE templatesalso the factare boththat referthe verb- must appear in f-structures containing the enced in (or inherited(12)by) ItheNTRdefinitionANSITIVofE(PP)RES=ENT( . SimilarlyPRED)=‘,PweSUcanBJ ’also subdivide single governable grammatical function SUBJ. The predicate, of course, differs from the 3S3G templateParameastefollows:rized templates Whatever argument is providedverb toinverb,an invocationbut the SUofBJthissubcategorizationtemplate will be framesubstitutedis commonfor to all intransitives. We (7) All3PEintransitiveRSONSUBtheJ verbsparameter= (in SLFGUtoBJ createPcarryERS)=3athecansemanticdescriptiondefine IformNTthatRAthatNreplacesSIindicatesTIVE asthea theparameterizedtemplaterelationreference.denotedtemplateThusthattheexpresses the common subcategorization. The predicate itself can be provided as an argument that is specified bySINtheGSverbUBJ anddescription= (alsoSUtheBJinNfacttheUMoriginal)=thatSGtheentryverbformusttheappearverb yawinnsf-structurescan be equivalentlycontainingspecifiedthe as fol- single governablelows: grammatical functiondifferentlySUBJ. inThedifferentpredicate,lexicalof course,entries. difThisferstemplatefrom can be used with all intransitive verbs: verb3SG to verb,= but@3PtheERSSUONBSJ UsubcategorizationBJ frame is common to all intransitives. We (13) yawns @INTRANSITIVE(yawn) can define INT@RASINNSGISTIUVBEJ as a parameterized template that expresses the common sub- (12) INTRANSITIVE(P) = ( PRED)=‘P SUBJ ’ categorization. The predicate@PitselfRES3canSG be provided as an argument that is specified This information can also be represented as a template hierarchy: differently in different lexical entries.WhateverThis templateargumentcanisbeprovidedused within anallinvocationintransitiveof this template will be substituted for verbs: 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 fol- (12) INTRANSITIVE(P) = ( PRlows:ED)=‘P SUBJ ’

Whatever argument is provided in an(13)invocationyawnsof this@ItemplateNTRANSIwillTIVEbe(yawn)substituted for the parameter to create the description that replaces@thePRtemplateES3SG reference. Thus the description in the original entry for the verb yawns can be equivalently speciﬁed as fol- 202 203 lows:

(13) yawns @INTRANSITIVE(yawn) @PRES3SG

203

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 includes33 (“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 inheritance is interpreted. are disjunctively specified as different subtypes of the type HEAD. The type GERUND 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.34 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 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:

(14) VERB-PRT(P PRT) = ( PRED)=‘P SUBJ, OBJ ’ ( PRT-FORM)=c PRT

The few templates we have deﬁned serve to demonstrate the point that templates interpreted only by simple substitution allow commonalities between lexical entries to be represented succinctly and for linguistic generalizations to be expressed in a theoretically motivated manner. The parameterized template INTRANSITIVE(P) is shared by verbs 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 PRES3SG template, is also used by verbs like bake, are, and many others.

4 Templates and Boolean operators

In LFG, complex descriptions can be conjoined, disjoined, or negated. Since templates are just names forSubsequentdescriptions,workwe canwithinalso useHPSGthese operatorshas builtwithontemplates.this viewFor. Linguistic generalizations in instance, we could define a template PRESNOT3SG by negating the 3SG template, as follows: 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 sim- (15) PRESilarNOThierarchy3SG = @, thePRESconstructionalENT hierarchy. On the HPSG view, lexical generalizations @3SG are statable as relations between elements in the type lattice, where different subtypes The substitutionsrepresentspecifiedalternatives,by these invocationsand a typeproducecanthebelongfollowingtodescription:multiple supertypes. For example, Mal- Hierarchies: Templates vs. Types (16) ( VoufFORM(1998))=FINITEprovides the following depiction of a partial type hierarchy of HEAD values: ( TENSE)=PRES ( S(1)UBJ PERS)=3 HEAD ( SUBJ NUM)=SG NOUN RELATIONAL HPSG The first two lines are the result of expanding the PRESENT template, and the third and fourth lines are the negation of the expansion of the 3SG template. This template can be C-NOUN GERUND VERB used in the lexical entry of verbs which are present tense but whose subject is not third person singularThis(ydiagramawn, bake,representsappear, etc.).an AND/OR lattice: the alternative types NOUN and RELATIONAL With this addition we have the following template hierarchy: are disjunctively specified as different subtypes of the type HEAD. The type GERUND (17) PRinheritsES-TENSEfromFINtwoITE supertypes,3PERSONSUBJNOSUINNGSandUBJ RELATIONAL, and the information inherited LFG fromPRallESENsupertypesT is conjoined.3SG Work within LFG, on the other hand, has not appealed to typed feature structures PRESNOT3SG PRES3SG to encode linguistic generalizations. Instead, LFG encodes lexical generalizations not This indicatesin termsthat PREofSNformalOT3SG includesinheritance(“inherits”)relationsdescriptionsbetweenfrom bothtypes,of its an-but in terms of inclusion rela- cestors. However, unlike an HPSG type hierarchy, this does not entail that the inherited tions between descriptions of structures. An LFG functional description – a collection

of equations – can be given a name, and this35name 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 definitions204can 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).

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 Parameterized 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 36 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 informationTRANSisITconjoined.IVE templateFor toexample,be usedin for(15)verbsPRESNlikeOT3deSGvoinvokesur: 3SG via negation. Template sharing is distinct from the mode of combination, which is determined information is conjoined. For example, in (15) PRESNOT3SG invokes 3SG via nega- by the(18)contextTRofANtheSITinvocation.IVE(P) = ( PRED)=‘P SUBJ, OBJ ’ For anothertion. Tillustrationemplate sharingof this point,is distinctsupposefromthatthewemodehave definedof combination,a parameterizedwhich is determined TRANParameterizedSITIbyVE thetemplatecontextto beof usedtheTemplatesinvocation.for verbs like devour: This canForbe anothercombinedillustrationdisjunctivelyof thiswithpoint,thesupposeINTRAthatNSweITIVhaveE templatedefined atoparameterizeddefine a sub- (18)categorizationTRATNRSAITNISVIET(IPVtemplate)E template= ( PforRtoEDverbsbe)=‘usedP SthatUBforJ,canOverbsBJappear’ like deeithervour:with or without an object (eat, cook, bake, etc.): This can be(18)combinedTRANdisjunctivelySITIVE(P) with= (thePIRNETDR)=‘ANSPITSIUVBEJtemplate, OBJ ’ to define a subcategorization(19) TRtemplateANS-ORfor-INverbsTRANthatS(Pcan) appear= @eitherTRANwithSITorIVwithoutE(P) @an IobjectNTRA(NeaSt,ITIVE(P) cook, bakeThis, etc.):can be combined disjunctively with the INTRANSITIVE template to define a sub- Noticecategorizationthat the parametertemplateforforTRverbsANSthat-OR-canINTappearRANS eitherappearswithasoranwithoutargumentan objectin the invo-(eat, (19) TRANS-OR-INTRANS(P) = @TRANSITIVE(P) @INTRANSITIVE(P) cationscooofk,bothbake,INetc.):TRANSITIVE and TRANSITIVE. The reference @TRANS-OR-INTRANS(eat) Noticethusthatexpandsthe parameterultimatelyfor TRAtoNSthe-ORdisjunction-INTRANS appears as an argument in the invocations of both(19)INTTRRAANNSS-ITOIRV-EINandTRTARNASN(SPI)TIV=E. The@TreferenceRANSITI@VET(RPA)NS-@ORIN-ITNRTARANNSIST(eIVatE)(P) thus expands(20) ( ultimatelyPRED)=‘toeathet SdisjunctionUBJ, OBJ ’ ( PRED)=‘eat SUBJ ’ Notice that the parameter for TRANS-OR-INTRANS appears as an argument in the invo- (20) ( FinallyPcationsRED)=‘, weofeatbothcanSUBIextendJN, TORBAJ N’theSIT( IhierarchicalVPERandED)=‘TReAatNtemplateSSUITBIJV’E. Theinclusionreferencediagram@TRAsoNSthat-OR-itINbottomsTRANS(eat) thus expands ultimately to the disjunction Finallyout in, particularwe can extendlexicalthe hierarchicalitems, thustemplateshowinginclusionhowdiagramgeneralizationsso that it bottomsare captured not only out inamongparticular(20)thelexical(templatesPREitems,D)=‘butethusat alsoSUshowingBJacross, OBJhow’thegeneralizations(lexicon:PRED)=‘eaaret SUcapturedBJ ’ not only among the templates but also across the lexicon: (21) Finally, we can3PextendERSONtheSUhierarchicalBJ templateSINinclusionGSUBJ diagram37 so that it bottoms (21) out in particular3PERSOlexicalNSUBJitems, thus showingSINGSUhowBJ generalizations are captured not only PRESENT 3SG INTRANSITIVE TRANSITIVE PRamongESENT the templates but also3SacrossG INtheTRAlexicon:NSITIVE TRANSITIVE

(21) PRES3SPG3RPEESR3SSOGNSUBJ TRANS-OSR-INITNGRTSRAUANBNSJS-OR-INTRANS

PfaREllSsENfaT lls bakes bake3SsG INTRANScoIToIkeVdE TcoRAoNkeSIdTIVE

PRES3SG TRANS-OR-INTRANS 5 E5xprEesxprsingesdseifnaulg tdsefaults falls bakes cooked Default values can be expressed in LFG by means of existential constraints and disjunction.DefaultAn existevaluesntial cocannstrabeintexpressedasserts thatina featureLFG bymustmeansbe presentof existentialin an f-structureconstraintsbut and disjunc- it doestion.not5AndefineEexprxistheteesnvaluestiiangl codthatenfasulttheratsinfeaturet assertsmustthathave.a featureThus themustexistentialbe presentconstraintin an f-structure but in (22)it doesis satisfiednot defineonly ifthethevaluef-structurethatdenotedthe featureby musthas somehave.valueThusfor the featureexistential constraint CASEin: (22)Defaultis satisfiedvalues canonlybeifexpressedthe f-structurein LFGdenotedby meansbyof existentialhas someconstraintsvalue forandthedisjunc-feature CASEtion.: An existential constraint asserts that a feature must be present in an f-structure but (22) ( CASE) it does not define the value that the feature must have. Thus the existential constraint This asserts(22)in(that(22)CsomeAisSEsatisfied)(unspecified)only ifvaluethe f-structuremust be provideddenotedby abydefininghas equationsome valuefor for the feature the f-structureCASE:. Otherwise, the existential constraint is not satisfied. WThise canassertsdisjunctivelythat somecombine(unspecified)this specificationvaluewithmusta definingbe providedequationbystatinga definingthat equation for the f-structurethe f-structure(22) (hasCtheA.SEfeatureOtherwise,) CASE thewithexistentialvalue NOM:constraint is not satisfied. We can disjunctively combine this specification with a defining equation stating that (23) ( CThisASE)asserts( CthatASEsome)=NOM(unspecified) value must be provided by a defining equation for the f-structure has the feature CASE with value NOM: the f-structure . Otherwise, the existential constraint is not satisfied. We can disjunctively combine this specification with a defining equation stating that (23) ( CASE) ( CASE)=NOM the f-structure has the feature CASE with value NOM:

(23) ( CASE) ( CASE)=NOM

205

205 205 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) Temple( PRED)=‘ eHierarchyat SUBJ, OBJ ’ with( PR ELexicalD)=‘eat SU LeavesBJ ’ 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

yawnsfalls baeatskes 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 38 CASE:

(22) ( CASE)

This asserts that some (unspecified) value must be provided by a defining equation for the f-structure . Otherwise, the existential constraint is not satisfied. We can disjunctively combine this specification with a defining equation stating that the f-structure has the feature CASE with value NOM:

(23) ( CASE) ( CASE)=NOM

205 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)

(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

(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 equation must 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 Paramerized template for defaults. lated in a parameterized template: and we can use this to make more obviousAlsothe illustratesfact that thatNOM parameterizedis the default value of CASE: (24) DEFAULT(D V)templates= D canD =haveV multiple

(25) @DEFAULT(( CASE) NOM) arguments 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.39 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 The first part of the disjunction is satisfied if has some value for CASE provided by a defining equation elsewhere in the functional description (the existential constraint in the left disjunct is satisfied). The second part of the disjunction is satisfied if has the value NOM for CASE (the defining equation in the right disjunct is satisfied). The effect is that NOM is the default value for CASE: if no other value is defined for that feature, the value NOM will be installed. This technique for specifying a default value V for a designator D can be encapsu- lated in a parameterized template:

(24) DEFAULT(D V) = D D=V

and we can use this to make Themorefirst partobviousof the disjunctiontheis satisfiedfactif thathas someNOvalueMforisCAtheSE provideddefaultby value of CASE: a defining equation elsewhere in the functional description (the existential constraint in the left disjunct is satisfied). The second part of the disjunction is satisfied if has the value NOM for CASE (the defining equation in the right disjunct is satisfied). The effect (25) @DEFAULT(( CASEis)thatNNOOMMis the) default value for CASE: if no other value is defined for that feature, the value NOM will be installed. This technique for specifying a default value V for a designator D can be encapsu- The first part of the disjunction is satisfied if has somelatedvaluein aforparameterizedCASE providedtemplate:by a definingAnequationinvocationelsewhere in theoffunctionalthis defaultdescription (theCAexistentialSE assignmentconstraint in template could then be a part of the lex- the left disjunct is satisfied). The second part of the disjunction(24) DEisFAsatisfiedULT(D V)if = hasD theD=V value NicalOM fordescriptionCASE (the defining equationfor ain nounthe right disjunctin aislanguagesatisfied). The effectwith case clitics. If there is no case clitic to and we can use this to make more obvious the fact that NOM is the default value of CASE: is thatspecifyNOM is the defaulta particularvalue for CASE: caseif no otherforvaluetheis definednoun,for thatthefeature,default NOM case will appear. the value NOM will be installed. (25) @DEFAULT(( CASE) NOM) This technique for specifying a default value V for a designator D can be encapsu- lated in a parameterized template: An invocation of this default CASE assignment template could then be a part of the lexical description for a noun in a language with case clitics. If there is no case clitic to (24) 6DEFAUTLTe(DmplV) =atDesD=aVnd PhrasespecifyStraucparticularturcasee Anfor thennoun,ottheatdefaultionNsOM case will appear. and we can use this to make more obvious the fact that NO6M isTethempldefaultates anvalued PhraofseCSAtrSucE:ture Annotations

(25) Since@DEFAULTtemplates(( CASE) NOM) simply standSince templatesfor piecessimply standoffor piecesfunctionalof functional descriptions,descriptions,it is also possible it is also possible to use templates in annotations on phrase structure rules, to capture recurring gener- An invocationto useof thistemplatesdefault CASE assignmentin annotationstemplate alizationscould theninonbetheaspecificationpartphraseof the lex-of thestructurerelation betweenrules,c-structure configurationsto captureand f- recurring gener- ical description for a noun in a language with case clitics.structures.If thereThereis nois nocasedifferenceclitic toin the way templates are defined or invoked when they alizations in the specificationare usedofin phrasethe structurerelationrules; functionalbetweenannotationsc-structurein phrase structure rulesconfigurationscan and f- specify a particular case for the noun, the default NOM casesimplywillbeappearreplaced. with a template reference. structures. There is no differenceTo take aninexample,the supposewaythattemplatesevery adjunct in thearegrammardefinedmust be annotatedor invoked when they with both its grammatical function and an ADJUNCT-TYPE feature, e.g., (26). 6 Tearemplateuseds and Phinrase phraseStructure Anstructurenotations rules; functional annotations in phrase structure rules can Since templates simply stand for pieces of functional descriptions,(26) VP it is alsoV possible ADVP* = ( ADJUNCT) to use templates in annotations on phrase structure rules, to capture recurring gener- simply be replaced with a template reference.( ADJUNCT-TYPE)=VP-ADJ alizations in the specification of the relation between c-structure configurations and f- structures. ThereToistakeno differencean inexample,the way templatessupposeareThisdefinedcan beorrewrittenthatinvokedusingeverywhena theyparameterizedadjuncttemplate:in the grammar must be annotated are used in phrase structure rules; functional annotations in phrase structure rules can (27) VP V ADVP* simplywithbe replacedbothwith aitstemplategrammaticalreference. function and an ADJUNCT-TYPE feature, e.g., (26). = @ADJUNCT(VP-ADJ) ToC-structuretake an example, suppose Annotationthat every adjunct in the ofgrammar Templatesmust be annotated with both(26)its grammaticalVPfunction and an VADJUNCT-TYwherePE feature,the ADe.g.,JUNC(26).ADVP*T template expands to: (26) VP V ADVP* (28) a. ADJUNCT(P) = ( ADJUNCT) @ADJUNCT-TYPE(P) = ( ADJU=NCT) ( ADJUNCT) ( ADJUNCT-TYPE)=VP-ADJ ( ADb.JAUDJUNNCCT-TTY-PTE(PY) P=E()=ADVJUNPC-T-ATYDPE)=JP

This can be rewritten using a parameterized template: (27) ThisVP canV be rewrittenADVP* using⇧a parameterized template: = @ADJUNCT(VP-ADJ) where the ADJUNCT template expands to: (27) VP V ADVP* (28) a. ADJUNCT(P) = ( ADJUNCT) @ADJUNCT-T=YPE(P) @ADJUNCT(VP-ADJ206)

b. ADJUNCT-TYPE(P) = ( ADJUNCT-TYPE)=P where the ADJUNCT template expands to:

(28) a. ADJUNCT(P) = ( ADJUNCT) @ADJUNCT-TYPE(P) 40

b. ADJUNC206T-TYPE(P) = ( ADJUNCT-TYPE)=P

206 Features in the Minimalist Program

41 Features and Explanation

• The sorts of features that are associated with functional heads in the Minimalist Program are well-motivated morphosyntactically, although other theories may not draw the conclusion that this merits phrase structural representation (cf. Blevins 2008). • Care must be taken to avoid circular reasoning in feature theory: • The ‘strong’ meta-feature: “This thing has whatever property makes things displace, as evidenced by its displacement.” • The ‘weak’ meta-feature: “This thing lacks whatever property makes things displace, as evidenced by its lack of displacement.” • The EPP feature: “This thing has whatever property makes things move to subject position, as evidenced by its occupying subject position.”

42 Features and Simplicity

• Adger (2003, 2008) considers three kinds of basic features: • Privative, e.g. [singular] • Binary, e.g. [singular +] • Valued, e.g. [number singular] • Adger considers the privative kind the simplest in its own right. • This may be true, but only if it does not introduce complexity elsewhere in the system (Culicover & Jackendoff 2005: ‘honest accounting’). • Notice that only the ﬁnal type of feature treats number features as any kind of natural class within the theory (as opposed to meta- theoretically).

43 Kinds of Feature-Value Combinations

• Adger (2003):

• Privative

• [singular], [V], ...

• Binary

• [singular: +] (?)

• Attribute-value

• [Tense: past]

44 Interpreted vs. Uninterpreted Features

• Interpreted features:

• [F]

• Uninterpreted features:

• [uF]

• All uninterpreted features must be eliminated (‘checked’).

• Interpreted features are interpreted by the semantics.

• Presupposes an interpretive (non-combinatorial) semantics.

[Notation from Adger 2003]

45 Feature Strength

• Strong features must be checked locally: Trigger Move/Internal Merge/Remerge

• [F*]

• Weak features do not have to be checked locally: Do not trigger Move

• [F]

[Notation from Adger 2003]

46 An Example: Auxiliaries

• Adger (2003:181)

“When [uInﬂ: ] on Aux is valued by T, the value is strong; when [uInﬂ: ] on v is valued by T, the value is weak.”

Subject T

T[past] NegP

Neg vP

Subject v ! " Verb + v[uInﬂ]. . .

47 Locality of Feature Matching

• Adger (2003:218)

Locality of Matching Agree holds between a feature F on X and a matching feature F on Y if and only if there is no intervening Z[F].

Intervention In a structure [X ... Z ... Y], Z intervenes between X and Y iff X c- commands Z and Z c-commands Y.

48 Feature-Value Unrestrictiveness & Free Valuation

• Asudeh & Toivonen (2006) argue that the Minimalist feature system of Adger (2003) has two undesirable properties.

Feature-value unrestrictiveness Feature valuation is unrestricted with respect to what values a valued feature may receive.

Free valuation Feature valuation appears freely, subject to locality conditions.

• This results in a very unconstrained theory of features.

• This may sound good, because it’s less stipulative and hence more Minimal, but from a theory perspective it is bad: unconstrained theories are less predictive.

49 Example: English Subject Agreement

(1) Gilgamesh missed Enkidu (2) Gilgamesh misses Enkidu

TP TP

T[past] vP T[singular] vP

Gilgamesh v Gilgamesh v

v VP v VP

miss v[uInﬂ:past] miss NP miss v[uInﬂ:singular] miss NP ! " ! " Enkidu Enkidu

• Contrast with HPSG: MP has no typing of values (feature value unrestrictiveness)

• Contrast with LFG: MP has valuation without speciﬁcation (free valuation)

50 Two Contrasting Feature Theories

• HPSG (Pollard & Sag 1994): features are not just valued, the values are also typed

• If two values can unify, they must be in a typing relation (one must be a subtype of the other).

• Feature values in HPSG are thus tightly restricted by types.

• LFG (Kaplan & Bresnan 1982, Bresnan 2001): features are not restricted, but there is no free valuation

• A feature cannot end up with a given value unless there is an explicit equation in the system.

51 Feature Simplicity and Constraint Types

• LFG offers the opportunity to consider Adger’s three feature types in light of a single feature type, with varying constraint types.

• LFG features are valued (f is an LFG f(unctional)-structure):

f NUMBER singular

• Types of LFG feature! constraints. " • Deﬁning equation: (f NUMBER) = singular • Existential constraint: (f NUMBER) • Negative existential constraint: (f NUMBER) ¬ • Constraining equation: (f NUMBER) =c singular • Negative constraining equation: (f NUMBER) = singular !

52 Feature Simplicity and Constraint Types

• All features treated as valued features: no restriction on constraint types

• All features treated as binary features: only positive and negative constraining equations allowed

• All features treated as privative: only negative and existential constraints allowed

• This understanding of privative features actually does treat number as a natural class.

• This treats the notion of feature simplicity as a kind of meta- theoretical statement in an explicit, non-ad-hoc feature theory.

53 Control and Raising

54 Lexical Entries tried V ( PRED) = ‘try SUBJ,XCOMP ’ ↑ " # ( SUBJ) = ( XCOMP SUBJ) ↑ ↑ seemed V ( PRED) = ‘seem CF SUBJ’ ↑ " # ( SUBJ) = ( XCOMP SUBJ) { ↑ ↑ | ( SUBJ PRONTYPE) = EXPLETIVE ↑ ( SUBJ FORM) = IT ↑ ( COMP) ↑ }

55 Raising to Subject/Subject Control C-structure

( SUBJ) = = ↑ ↓ ↑ ↓ NP I!

= Gonzo ↑ ↓ VP

= = ↑ ↓ ↑ ↓ V0 VP

seemed/tried = = ↑ ↓ ↑ ↓ V0 VP

to = ↑ 0↓ V

leave

56 F-structures A S H A S U D E H (7)

(8)

In summary, the only syntactic diﬀerence between a control57 verb and a raising verb on this theory is that the former takes a thematic subject (i.e. non-expletive subject), while the latter takes a non-thematic subject (i.e. raised or expletive subject). Dalrymple (2001) has recently proposed that obligatory control in English should be modelled with anaphoric control rather than with functional control. I will assume the standard functional- control treatment of obligatory control and return to a discussion of Dalrymple (2001) in section 9.

3. G L U E S E M A N T I C S 3.1 Glue and the parallel projection architecture of LFG Although Glue does not necessarily have to be coupled with LFG, most work in Glue Semantics has been done with an LFG syntax (Dalrymple et al. 1993; Dalrymple 1999, 2001; Asudeh 2004). The more important architectural point is that Glue is coupled to an independent level of syntax, unlike Categorial Grammar, which makes no distinction between syntax proper and the syntax of semantic composition. Glue Semantics is thus a general theory of the syntax–semantics interface and semantic composition that assumes a separate level of syntax in which lexically contributed Glue premises are instantiated. LFG has a parallel-projection architecture. This means that there are various levels of linguistic representation, called PROJECTIONS, which are present in PARALLEL, and these projections are related by functional correspondences (also known as projection functions) which map elements of one projection onto elements of another (Kaplan 1987, 1989; Halvorsen & Kaplan 1988). This is a generalisation of the original notion of functional correspondence in which the w-function maps c(onstituent)-structures onto

474 Copy Raising

58 Data

(1)Thora seems like she enjoys hot chocolate.

(2)Thora seems like Isak pinched her again.

(3)Thora seems like Isak ruined her book.

(4)* Thora seems like Isak enjoys hot chocolate.

(5)* Thora seems like Isak pinched Justin again.

(6)* Thora seems like Isak ruined Justin’s book.

59 Data

(7)It seems like there is a problem here.

(8)It seems like Thora is upset.

(9)It seems like it rained last night.

(10) There seems like there’s a problem here.

(11) * There seems like it rained last night.

60 Lexical Entries like P0 ( PRED) = ‘like SUBJ,COMP ’ 1 ↑ " #

like P0 ( PRED) = ‘like CF SUBJ’ 2 ↑ " # ( SUBJ) = ( XCOMP SUBJ) { ↑ ↑ | ( SUBJ PRONTYPE) = EXPLETIVE ↑ ( SUBJ FORM) = IT ↑ ( COMP) ↑ }

61 376 CHAPTER 9. COPY RAISING IN ENGLISH

r3e7s6emblance verbs also have an alternant thCaHt AisPTnEoRt a9. raCiOsiPnYg RvAerISbINanGdINthEaNt GcaLnIStHake a thematic subject. Recall the CRV and PRV examples (9.5a) and (9.6a); as we observed for raising verbs and PRVs with AP complements, (9.5a) and (9.6a) have identical c-structures and f-structures, modulo resemblance verbs also have an alternant that is not a raising verb and that can take a thematic relevant lexical substitutions: subject. Recall the CRV and PRV examples (9.5a) and (9.6a); as we observed for raising verbs and PRVs with AP complements, (9.5a) and (9.6a) have identical c-structures and f-structures, modulo C-structure(9.54) a. IP relevant lexical substitutions:

(↑ SUBJ) = ↓ ↑ = ↓ (9.54) a. IP DP I! (↑ SUBJ) = ↓ ↑ = ↓ DP I! Richard ↑ = ↓ VP Richard ↑ = ↓ VP

↑ = ↓ (↑ XCOMP) = ↓ ↑ = ↓ V0 (↑ XCOMP) = ↓PP V0 PP

↑ = ↓ ↑ = ↓ seemsese/msmse/llsmells ! P! P

↑ = ↓↑ = ↓ (↑ COMP)(↑= ↓COMP) = ↓ 0 P P0 IP IP

(↑ SUBJ) = ↓ ↑ = ↓ like (↑ SUBJ) = ↓ ! ↑ = ↓ like DP I DP I! ↑ = ↓ he VP ↑ = ↓ he VP smokes smokes 62 9.3. SIMILARITIES BETWEEN CRVS AND PRVS ARE SYNTACTIC 377

b. PRED ‘seem/smell’

SUBJ   9.3. SIMILARITIES BETWEEN CRVS AND PRVS ARE SYNTACTIC 377  PRED ‘like’   9.3. SIMILARITIES BETWEEN CRVS AND PRVS ARE SYNTACTIC 377  F-structure      SUBJ PRED ‘Richard’       $ %    b. b. PRPPRERDEDD ‘‘sssmeeeeommk/se/ms’melle’ll’       SUBJ    XCOMP  SUBJ PRED    ‘pro’      PRED ‘like’         COMP  PPERRESD 3‘like’            SUBJ SUBJ PRED ‘Richard’              NSUUMBJ $ sgPRED‘Rich%ard’             PRED ‘smoke’      GEND m$ asc %    XCOMP           PREDPRE‘sDmo‘kpero’’                  XCOMP COMP  PERS 3   The f-structure in (9.54) is essentiallythe same as the f-SsUtrBuJcture inPR(9E.D23) f‘oprrot’he adjectival com-           NUM sg   plement. The only added complication is that theCOprMepPosition liketaPkEeRsSa clausalargument as well      3     SUBJGEND masc  as a SUBJ. It is the like-complementthat licenses the subject; the functionalcontrol equation in the     NUM sg         The f-structure in (9.54) isessentially the same asthe f-structure in (9.23) for the adjectival com- lexical entry for the CRV / PRV raises the subject to be the matrixsubject, too. Importantly,63since    GEND masc plement. Theonly added complicationis that the preposition like takesaclausal argument as well the PP lacks a c-structural positionto host a subject, the shared subject is realizedin the matrix as a SUBJ. It is the like-complement that licenses the subject; the functional control equation in the subject position andTnhoet ifn-stthruecPtuPre(siene (p9a.g5e4)3i7s9ebseselonwtia).lly the same as the f-structure in (9.23) for the adjectival com- lexical entry for the CRV / PRV raises the subject to be the matrix subject, too. Importantly, since I have thus far acpcleomuntehtneetd.PPTfolharectkhosenalfyco-lsaltdorudwcetiudnrgaclospmiomspiitlilioacnraittoioehsnobsitseattwhsauetbejntehcect,optphreyepsrhoaasirsietidinogsnuvbljeiekrcbet sitsaarkneeadslipzaeedrcclianeuptsh-aelmaartgriuxment as well tual resemblance vearbssa: Ss1uU)bBjePJc.Rt IpVtosissitaitonhndealnridakienso-inct oignmtvhpeelrePbmPs (etsnaeekt epthapgaetre3ldi7ci9ecbnaetslieovswe)t.hceomsupblejemcte;ntthse; f2u)nCctRioVnaslacnodntrol equation in the PRVs take like-complelxemicaelntesIn.htarNyvefxtohtruIstthfuaerrnaCctRcooVuann/tePadcRfcoVor uthrnaetifsoelfslotwthhieenigrssubimbehjielaacvrtiitoiteousrbbewetwitthehenemxcopapltyeritrxiavisesiusnb.gjevecrtb,stoanod. pIemrcpepo-rtantly, since the PtPuallarceskesmablacn-csetrvuecrtbus:ra1l)pPoRsVitsioanndtoraihsiongstvaerbssubtajkeectp,retdhiecastihvearceodmspulebmjenctts;is2)reCaRlVizseadndin the matrix PRVs take like-complements. Next I turn to an account of their behaviour with expletives. 9.3.3 Expletivessubject position and not in the PP (see page 379 below). I have thus far accounted for the following similarities between copy raising verbs and percep- Copy raising verbs and p9e.3r.c3eptEuxapl lreetisveems blance verbs have interesting behaviour with respect to tual resemblance verbs: 1) PRVs and raising verbs take predicative complements; 2) CRVs and expletives: Copy raising verbs and perceptual resemblance verbs have interesting behaviour with respect to PRVsextpalkeetivleisk:e-complements. Next I turn to an account of their behaviour with expletives. (9.55) a. It seemed / looked / smelled like Richard was drunk. (9.55) a. It seemed / looked / smelled like Richard was drunk. 9.3.3 Expletives b. It seemed / lookedb./ smItesleleemdeldik/eloiotkreadi/nsemde.lled like it rained. c. It seeCmopeyd /raloisoinkegdcv./esrbmIsteslaelneemdelpdike/relcoteohkpeetdruea/lwsmraeeslsleeadmplbrikoleabntlhecemere.vwearsbasphroabvlemi.nteresting behaviour with respect to d. %Thereexspeletmiveeds:/ lodo.ke%dT/hesrme seelelmededli/kleootkheedr/eswmealslead lpikreobthleerme w. as a problem. e. *There seemed / looked / smelled like it rained. e. *Ther(e9.s5e5e)med a/ .lookIetdse/esmmeedlle/dloloikkeedit/rsamineeldle. d like Richard was drunk. There are two noteworthy aspects here. First, as shown in examples (9.55a–9.55c), CRVs and There are two noteworthPyRVasspcbea.ncttsakIheteesrxeepe.lmetFieviderss/tu,lbojaeoscktsesdhano/dwstmnheeielnlxepedlextlaiivkmeepisilteitrs,aai(ns9e.w5de5. aw–o9ul.d55ecxp),ecCt. RSVecsonadn, dand more PRVs can take expletive subjecc.ts anItdsteheemeexdp/lelotiovkeeids /its,maesllwede lwikoeutlhdereexpweacst.a Spreocbolnedm,.and more

d. %There seemed / looked / smelled like there was a problem. e. *There seemed / looked / smelled like it rained.

There are two noteworthy aspects here. First, as shown in examples (9.55a–9.55c), CRVs and PRVs can take expletive subjects and the expletive is it, as we would expect. Second, and more 380 CHAPTER 9. COPY RAISING IN ENGLISH

2001). The key point is that the criterial difference between a COMP and an XCOMP is that the latter lacks a c-structural position to host a subject, while the former does not. However, the complement of like / as is always an IP or CP, even when it is an XCOMP. The

alternative would be for it to be a COMP and for the functional control equation in like2 to read (↑ SUBJ) = (↑ COMP SUBJ). But, this effectively removes the distinction between open and closed complement functions at f-structure, despite the fact that grammatical functions in general are f- structural entities. Arguably, it is better to remove the c-structural requirement that an XCOMP always corresponds to a lexical projection. Under the modiﬁcation to LFG theory proposed here, C-structurethe deﬁning property of XCOMP is not its c-structural category, but rather whether it contains a grammatical function that is the target of a functional control equation. The following c-structure and f-structure for (9.55d) illustrate the proposal:

(9.59) a. IP

(↑ SUBJ) = ↓ ↑ = ↓ DP I!

↑ = ↓ There VP

↑ = ↓ (↑ XCOMP) = ↓ V0 PP

↑ = ↓ (↑ XCOMP) = ↓ seemed P0 IP

(↑ SUBJ) = ↓ ↑ = ↓ like DP I!

there was a problem

64 9.3. SIMILARITIES BETWEEN CRVS AND PRVS ARE SYNTACTIC 381 F-structure

(9.60) PRED ‘seem’

SUBJ     PRED ‘like’          SUBJ         PRED ‘be’     XCOMP      SUBJ EXPL there      XCOMP      $ %     PRED ‘problem’        OBJ      SPEC PRED ‘a’               $ %    The verb was subcategorizes for a there expletive subject. This subject is raised to be the subject of 65 the like-complement via the functional control equation in the entry for like2. The matrix raising verb or PRV raises the same expletive again to matrix subject position. Each raising step is entirely local, from complement’s subject to own subject, resulting in the same expletive ﬁlling three SUBJ values. Given that there are three f-structural subject positions, why do only two expletives occur in the c-structure? That is, what prevents the occurrence of sentences such as:

(9.61) *There seemed there like there was a problem

Sentences like this are blocked because the like-complement, being a PP headed by the lexical category P0, cannot host a subject in its speciﬁer. I have thus far accounted for example (9.55d), the puzzling case of long distance there-raising. We have seen that we can maintain the locality of raising if we assume that like / as have raising alternants. Yet we noted that not all dialects have the possibility of there-raising with like- complements. Horn (1981) argues that these dialects nevertheless have expletive raising with it expletives, as in sentence (9.55c) above. Horn notes that the Richard sentence (9.62) below is non- contradictory, even though the closely related extraposition sentence (9.63) is contradictory.

(9.62) It seems like it’s raining harder than it is.

(9.63) #It seems that it’s raining harder than it is.

Since (9.62) patterns like raising sentences, Horn argues that there is it-raising through like-complements, even in dialects without there-raising. However, in the present analysis there would still be raising from the subject of like in (9.62) to the matrix subject, which may in fact be the crucial Unbounded Dependencies

66 Filler-Gap Dependencies

67 Functional Uncertainty

• The syntactic relationship between the top and bottom of an unbounded dependency is represented with a functional uncertainty:

• Top = MiddlePath-Func-Uncertainty Bottom-Func-Uncertainty

(1) [What] [did Kim claim that Sandy suspected that Robin knew] [ ] top middle bottom

( FOCUS) = ( COMP∗ OBJ OBJ ) ↑ ↑ { | θ}

top middle bottom (2) [What] [did Kim claim that Sandy suspected that Robin gave Bo] [ ]

68 406 14. Long-Distance Dependencies

Wh-Questions: Example (42) Who does David like?

CP PRED ‘PRO’ NP C FOCUS PRONTYPE WH N C IP Q

Who does NP I PRED ‘LIKE SUBJ,OBJ ’

N VP SUBJ PRED ‘DAVID’

David V OBJ like To analyze constructions like (42), the following simpliﬁed rule was proposed in Chapter 6, Section 1.1:

(43) CP XP C 69 ( FOCUS) = = ( FOCUS) = ( COMP GF)

This rule ensures that the phrase in the specifier position of CP bears the FOCUS function and also fills a grammatical function within the utterance. We now re- fine this rule to take into account constraints on the phrase structure category of the fronted phrase and to give a more complete characterization of the path to its within-clause function. We also introduce the Q attribute, whose value is the f-structure of the possibly embedded interrogative pronoun within the fronted FOCUS phrase; see Kaplan and Bresnan (1982) for more discussion of this attribute. We use the constituent structure metacategory QuesP and the functional abbre- viations QFOCUSPATH and WHPATH in the following reformulation of rule (43):

(44) CP QuesP C ( FOCUS) = = ( FOCUS) = ( QFOCUSPATH) ( Q) = ( FOCUS WHPATH) ( Q PRONTYPE) WH The first issue is the correct definition of QuesP: which phrasal categories can appear as the FOCUS constituent in the specifier of CP? All of the examples in (45) are wellformed:

(45) a. NP: Who do you like? b. PP: To whom did you give a book? c. AdvP: When did you yawn? 406 14. Long-Distance Dependencies

(42) Who does David like?

CP PRED ‘PRO’ NP C FOCUS PRONTYPE WH N C IP Q

Who does NP I PRED ‘LIKE SUBJ,OBJ ’

N VP SUBJ PRED ‘DAVID’

David V OBJ like To analyze constructions like (42), the following simpliﬁed rule was proposed in Chapter 6, Section 1.1:

(43) CP XP C ( FOCUS) = = ( FOCUS) = ( COMP GF)

This rule ensures that the phrase in the specifier position of CP bears the FOCUS function and also fills a grammatical function within the utterance. We now re- fine this rule to take into account constraints on the phrase structure category of the fronted phrase and to give a more complete characterization of the path to its within-clause function. We also introduce the Q attribute, whose value is the f-structure of the possibly embedded interrogative pronoun within the fronted FOCUS phrase; see Kaplan and Bresnan (1982) for more discussion of this at- tribuWhte. -Questions: Annotated PS Rule We use the constituent structure metacategory QuesP and the functional abbre- viations QFOCUSPATH and WHPATH in the following reformulation of rule (43):

(45) a. NP: Who do you like? b. PP: To whom did you give a book? c. AdvP: When did you yawn? 70 Syntax of Long-Distance Dependencies 407

d. AP: How tall is Chris?

ThusWh, we-Questions:deﬁne QuesPQues MetacategoryP in (44) above as the following disjunction of categories: (46) QuesP NP PP AdvP AP

(1)NP: Who do you like?

Th(2)ePP:a Ton whomnot didat youio ngives a obook?n the QuesP node in rule (44) are similar to those on the relative(3)cAdvP:lau Whense didr uyoule yawn?in (29) of this chapter. The first two annotations require the (4)AP: How tall is Chris? f-structure corresponding to the QuesP node to fill the FOCUS role and also to bear some grammatical function defined by the long-distance path QFOCUSPATH; the correct definition of QFOCUSPATH will be our first topic of discussion in the following. The third annotation requires t71he value of the Q attribute to appear at the end of the long-distance path WHPATH within the FOCUS f-structure; we discuss constraints on WHPATH below. The fourth annotation requires the PRONTYPE attribute of the Q f-structure to bear the value WH, ensuring that an interrogative pronoun plays the Q role. Our first task is to define QFOCUSPATH, the long-distance path involved in question formation. Constraints on QFOCUSPATH appear to be largely similar to those defined for TOPICPATH in (16) of this chapter (though see Postal 1998 for a discussion of differences between the two types of paths): (47) a. Chris, we like. b. Who do you like? (48) a. Chris, we think that David saw. b. Who do you think that David saw? (49) a. *Chris, we whispered that David saw. b. *Who did you whisper that David saw? (50) a. *Chris, [that David saw ] surprised me. b. *Who did [that David saw ] surprise you? (51) a. This hammer, we smashed the vase with. b. What did you smash the vase with? (52) a. *Chris, we think that David laughed when we selected. b. *Who did you think that David laughed when we selected?

Therefore, we provisionally provide the same deﬁnition for QFOCUSPATH as we gave for TOPICPATH in (16) of this chapter. Future research may reveal various additional reﬁnements:

(53) English QFOCUSPATH:

XCOMP COMP OBJ ADJ GF GF ( LDD) ( TENSE) ( TENSE) Syntax of Long-Distance Dependencies 407

d. AP: How tall is Chris?

Thus, we define QuesP in (44) above as the following disjunction of categories: (46) QuesP NP PP AdvP AP The annotations on the QuesP node in rule (44) are similar to those on the relative clause rule in (29) of this chapter. The first two annotations require the f-structure corresponding to the QuesP node to fill the FOCUS role and also to bear some grammatical function defined by the long-distance path QFOCUSPATH; the correct definition of QFOCUSPATH will be our first topic of discussion in the following. The third annotation requires the value of the Q attribute to appear at the end of the long-distance path WHPATH within the FOCUS f-structure; we discuss constraints on WHPATH below. The fourth annotation requires the PRONTYPE attribute of the Q f-structure to bear the value WH, ensuring that an interrogative pronoun plays the Q role. Our first task is to define QFOCUSPATH, the long-distance path involved in question formation. Constraints on QFOCUSPATH appear to be largely similar to those defined for TOPICPATH in (16) of this chapter (though see Postal 1998 for a discussion of differences between the two types of paths): (47) a. Chris, we like. b. Who do you like? (48) a. Chris, we think that David saw. b. Who do you think that David saw? (49) a. *Chris, we whispered that David saw. b. *Who did you whisper that David saw? (50) a. *Chris, [that David saw ] surprised me. b. *Who did [that David saw ] surprise you? (51) a. This hammer, we smashed the vase with. b. What did you smash the vase with? (52) a. *Chris, we think that David laughed when we selected. Whb. *-Questions:Who did you think Unboundedthat David laug hDependencyed when we selec tEquationed?

Therefore, we provisionally provide the same deﬁnition for QFOCUSPATH as we gave for TOPICPATH in (16) of this chapter. Future research may reveal various additional reﬁnements:

(53) English QFOCUSPATH:

XCOMP COMP OBJ ADJ GF GF ( LDD) ( TENSE) ( TENSE)

72 408 14. Long-Distance Dependencies

In (41), we provided a constraint on RELPATH, the path to the relative pronoun within the fronted TOPIC phrase in a relative clause. Similarly, we must deﬁne WHPATH, the path to the interrogative pronoun in the fronted FOCUS phrase in a wh-question. Like the relative pronoun, the interrogative pronoun may be embedded inside the fronted phrase, appearing as a possessor or the possessor of a possessor and bearing the SPEC role, or as the OBJ of the fronted argument: (54) a. [Whose book] did you read? b. [Whose brother’s book] did you read? c. [In which room] do you teach?

However, WHPATH is more constrained than RELPATH, as the examples in (55–57) show: (55) a. *[The cover of which report] did you design? b. (cf. Which report did you design the cover of?) c. the report [the cover of which] I designed (56) a. *[The height of the lettering on the cover of which report] does the government prescribe? b. the report [the height of the lettering on the cover of which] the government prescribes (57) a. *[Faster than whom] can you run? b. the man [faster than whom] I can run (58) a. *[Proud of whom] are you? b. the kind of person [proud of whom] I could never be Wh-Questions: Pied Piping Therefore, we propose the following deﬁnition of WHPATH in English:

(59) English WHPATH:

SPEC OBJ Webelhuth (1992) provides more discussion of constraints on pied piping in Ger- (1)[Whose book]man didic youla nread?guages, showing that pied piping constraints in English wh-questions (2)[Whose brother’sare th ebook]sa mdide youas read?in other Germanic languages. (3)[In which room] do you teach?

2. MORPHOLOGICAL SIGNALING73

Some languages signal long-distance dependency constructions by means of special morphological or phonological forms, as noted by Clements and Ford Relative SyClauses:ntax of Long-Distance De Examplependencies 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 saw

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 subconstituent of the initial phrase. Here the relative pronoun whose is a subconstituent 74 of the fronted phrase whose book: SyntRelativeax of Long -DiClauses:stance Dep eAnnotatedndencies PS Rule 403

(29) CP RelP C ( TOPIC) = = ( TOPIC) = ( RTOPICPATH) ( RELPRO) = ( TOPIC RELPATH) ( RELPRO PRONTYPE) REL The constituent structure metacategory RelP in (29) represents the phrase structure categories that can appear in initial position in a CP relative clause. The phrases in (30) exemplify the possible instantiations of RelP in English:3

(30) a. NP: a man who I selected b. PP: a man to whom I gave a book c. AP: the kind of person proud of whom I could never be d. AdvP: the city where I live 75

Therefore, we deﬁne RelP for English in the rule in (29) as the following disjunction of categories: (31) RelP NP PP AP AdvP

The first two annotations on the RelP daughter in rule (29) are similar to the annotations on the TOPIC rule in (14) of this chapter. The constraint ( TOPIC) = requires the f-structure corresponding to the RelP node to fill the TOPIC role in the f-structure. The constraint ( TOPIC) = ( RTOPICPATH) ensures that the TOPIC f- structure also fills a grammatical function within the clause, constrained by the long-distance path RTOPICPATH; we define RTOPICPATH below. The third and fourth annotations require the f-structure for the relative pronoun to appear as the value of the RELPRO attribute in the relative clause f-structure. The constraint in the third line, ( RELPRO) = ( TOPIC RELPATH), requires the value of the RELPRO attribute to appear at the end of the path RELPATH within the TOPIC f- structure. Below, we provide a definition of RELPATH that properly constrains the role of the relative pronoun within the fronted TOPIC phrase. Finally, the constraint ( RELPRO PRONTYPE) REL is a constraining equation (Chapter 5, Section 2.8) requiring the value of the RELPRO attribute to have a PRONTYPE feature with value REL: the value of the RELPRO attribute must be a relative pronoun. We first discuss the definition of RTOPICPATH, the path relating the fronted constituent in a relative clause to its within-clause grammatical function. Constraints on RTOPICPATH are very similar to constraints on TOPICPATH, defined in (16) of this chapter: (32) a. Chris, we like. b. a man who we like 3Example (30c) is due to Webelhuth (1992). Syntax of Long-Distance Dependencies 403

(30) a. NP: a man who I selected b. PP: a man to whom I gave a book c. AP: the kind of person proud of whom I could never be d. AdvP: the city where I live

Therefore, we deﬁne RelP for English in the rule in (29) as the following disjunction oRelativef cat eClauses:gorie sRelP: Metacategory (31) RelP NP PP AP AdvP

(1)NP: a man who I selected

Th(2)ePP:fi a manrst to twhomwo I gavean a nbooko tations on the RelP daughter in rule (29) are similar to the anno(3)taAP:ti theo nkinds ofo personn th proude T ofO whomPI CI couldru neverle iben (14) of this chapter. The constraint ( TOPIC) = requi(4)rAdvP:es ttheh citye fwhere-st Ir liveu cture corresponding to the RelP node to fill the TOPIC role in the f-structure. The constraint ( TOPIC) = ( RTOPICPATH) ensures that the TOPIC f- structure also fills a grammatical function within the clause, constrained by the

76 long-distance path RTOPICPATH; we define RTOPICPATH below. The third and fourth annotations require the f-structure for the relative pronoun to appear as the value of the RELPRO attribute in the relative clause f-structure. The constraint in the third line, ( RELPRO) = ( TOPIC RELPATH), requires the value of the RELPRO attribute to appear at the end of the path RELPATH within the TOPIC f- structure. Below, we provide a definition of RELPATH that properly constrains the role of the relative pronoun within the fronted TOPIC phrase. Finally, the constraint ( RELPRO PRONTYPE) REL is a constraining equation (Chapter 5, Section 2.8) requiring the value of the RELPRO attribute to have a PRONTYPE feature with value REL: the value of the RELPRO attribute must be a relative pronoun. We first discuss the definition of RTOPICPATH, the path relating the fronted constituent in a relative clause to its within-clause grammatical function. Constraints on RTOPICPATH are very similar to constraints on TOPICPATH, defined in (16) of this chapter: (32) a. Chris, we like. b. a man who we like 3Example (30c) is due to Webelhuth (1992). 404 14. Long-Distance Dependencies

(33) a. Chris, we think that David saw. b. a man who you think that David saw (34) a. *Chris, we whispered that David saw. b. *a man who you whispered that David saw (35) a. *Chris, [that David saw ] surprised me. b. *a man who [that David saw ] surprised me (36) a. This hammer, we smashed the vase with. b. the hammer which you smashed the vase with (37) a. *Chris, we think that David laughed when we selected. Relativeb. *a man wClauses:ho we think t hUnboundedat David laugh eDependencyd when we select eEquationd

We therefore propose the same constraints on the English RTOPICPATH as in (16) of this chapter, which constrains the long-distance path in topicalization constructions. The expressions in (16) and (38) are exactly the same:

(38) English RTOPICPATH:

XCOMP COMP OBJ ADJ GF GF ( LDD) ( TENSE) ( TENSE)

Examination of other languages reveals different constraints on RTOPICPATH. As noted earlier, Kroeger (1993, Chapter 7) shows that RTOPICPATH in Tagalog is SUBJ , paths consisting only of SUBJ. Saiki (1985) discusses the deﬁnition of RTOPICPATH in Japanese, exploring constraints on RTOPICPATH in the causative and passive constructions. Finally, we must deﬁne RELPATH so as to appropriately constrain the grammatical function of the relative pronoun within the fronted TOPIC f-structure. As originally noted by Ross (1967) and explored in detail by Bresnan (1976), Webelhuth (1992), Falk (2001), and many others, the relative pronoun may be embedded inside the fronted phrase. Ross (1967) provides this example of a deeply embedded 77 relative pronoun: (39) [Reports [[the height of the lettering on the cover of which] the government prescribes ]] should be abolished. Ross (1967) originally used the term pied piping in the transformational analysis of these constructions: in moving to the front of the sentence, the relative pronoun lures some additional material along with it, like the Pied Piper of Hamelin lured rats and children along with him as he left Hamelin. Research on pied piping has revealed a range of constraints on the long-distance path RELPATH to the relative pronoun in the fronted TOPIC phrase: Syntax of Long-Distance Dependencies 405

(40) a. the man [who] I met b. the man [whose book] I read c. the man [whose brother’s book] I read d. the report [the cover of which] I designed e. the man [faster than whom] I can run f. the kind of person [proud of whom] I could never be g. the report [the height of the lettering on the cover of which] the government prescribes h. *the man [a friend of whose brother] I met i. the room [in which] I teach j. *the man [the woman next to whom] I met In all of these examples, the phrase structure category of the fronted phrase is one of the categories defined by RelP, and no constraints on RTOPICPATH are vio- lated. Example (40a) shows that the relative pronoun can itself appear in fronted position; in such a case, RELPATH is the empty path. Examples (40b–c) indicate that the relative pronoun can appear as a possessor phrase, filling the SPEC role in the TOPIC f-structure, or as the possessor of a possessor. It can also appear as the object of an oblique argument, as in (40d–f), or embedded inside an oblique argument, as in (40g), though it may not fill the SPEC role inside an oblique phrase (40h). It can appear as the object of a fronted adjunct phrase (40i), though it may not appear as an adjunct inside the fronted phrase (40f). GivRelativeen thes eClauses:facts, we Piedpr oPipingpose the following definition of RELPATH in English:

(41) English RELPATH: (1)the man [who] I met (2)the man [whose book] I read (3)the man [whose brother’s book] I SPEC OBL OBJ read (4)the report [the cover of which] I In other languages the deﬁnitiondesignedof R ELPATH differs. Webelhuth (1992) provides (5)the man [faster than whom] I can a thorough discussion of pied prunip ing in Germanic, showing that constraints on (6)the kind of person [proud of pied piping in English relative cwhom]laus I ecoulds a neverre dbei fferent from the constraints that hold (7)the report [the height of the in German, Dutch, Swedish, andletteringoth one rtheGe coverr mof which]ani c languages. the government prescribes

1.3. Wh-Questions 78 In Chapter 4, Section 2.2.2, we noted that the question word in an English wh- question appears in initial position in the sentence, in the speciﬁer position of CP: Relative Clauses:402 Pied Piping14. Long -DiExamplestance 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 pronoun whose. We examine syntactic constraints on both of these dependencies 79 in the following. We propose the phrase structure rules in (28–29) for the analysis of these examples:

(28) N N CP = ( ADJ) Constraints on Extraction

80 Empty Category Principle/That-Trace

(1)Who do you think [__ left]?

(2)* Who do you think [that __ left]?

(3)* What do you wonder [if __ smells bad]?

(4)Who do you think [__ should be trusted]?

(5)* Who do you think [that __ should be trusted]?

(6)Who do you think [that, under no circumstances, __ should be trusted]?

(7)Who do you wonder [if, under certain circumstances, __ could be trusted]?

81 That-Trace in LFG

• LFG has a relation called f-precedence that uses the native precedence of c-structure to talk about precedence between bits of f-structure.

• F-precedence relies on LFG’s projection architecture and the inverse of the c-structure–f-structure mapping function ϕ.

• The inverse is written ϕ-1 and returns the set of c-structure nodes that map to its argument f-structure node.

F-precedence An f-structure f f-precedes an f-structure g (f ＜f g) if and only if -1 -1 for all n1 ∈ ϕ ( f ) and for all n2 ∈ ϕ ( g ), n1 c-precedes n2.

82 That-Trace in LFG

• We can leverage LFG’s projection architecture to capture the fact that That-Trace is a ‘surfacy’ phenomenon (cf. ECP as a PF constraint in recent Minimalism).

Form φ π ...... str•ing c-stru•cture f-stru•cture

83 That-Trace in LFG

• Assume a native precedence relation on strings, yielding a notion of element that is string-adjacent to the right (‘next string -1 element’), which we deﬁne as Rightstring(π (*)), where * designates the current c-structure node in a phrase structure rule element or lexical entry.

• Let’s abbreviate the right string-adjacent element to * as ≻.

• The semantics of ≻ is ‘the string element that is right string- adjacent to me’.

• Note that π-1 returns string elements, not sets of string elements, because π is bijective, since c-structures are trees.

84 That-Trace in LFG

• We can use f-precedence and ≻ to capture the surfacy nature of That-Trace.

• Basically, English has a (somewhat arbitrary) constraint that the right-adjacent string element to the complementizer must be locally realized.

• This can be stated by requiring that any unbounded dependency function in the f-structure corresponding to the element that occurs in the string immediately after the complementizer should not f-precede the complementizer’s f-structure.

85 Left Branch Constraint

(1)Whose car did you drive __?

(2)* Whose did you drive [__ car]?

86 Syntax of Long-Distance Dependencies 407

d. AP: How tall is Chris?

Thus, we define QuesP in (44) above as the following disjunction of categories: (46) QuesP NP PP AdvP AP The annotations on the QuesP node in rule (44) are similar to those on the relative clause rule in (29) of this chapter. The first two annotations require the f-structure corresponding to the QuesP node to fill the FOCUS role and also to bear some grammatical function defined by the long-distance path QFOCUSPATH; the correct definition of QFOCUSPATH will be our first topic of discussion in the following. The third annotation requires the value of the Q attribute to appear at the end of the long-distance path WHPATH within the FOCUS f-structure; we discuss constraints on WHPATH below. The fourth annotation requires the PRONTYPE attribute of the Q f-structure to bear the value WH, ensuring that an interrogative pronoun plays the Q role. Our first task is to define QFOCUSPATH, the long-distance path involved in question formation. Constraints on QFOCUSPATH appear to be largely similar to those defined for TOPICPATH in (16) of this chapter (though see Postal 1998 for a discussion of differences between the two types of paths): (47) a. Chris, we like. b. Who do you like? (48) a. Chris, we think that David saw. b. Who do you think that David saw? (49) a. *Chris, we whispered that David saw. b. *Who did you whisper that David saw? (50) a. *Chris, [that David saw ] surprised me. b. *Who did [that David saw ] surprise you? (51) Lefta. T hBranchis hammer, wConstrainte smashed the va sine w iLFGth. b. What did you smash the vase with? (52) • a.Do*C nothris include, we thin kSPEC/POSSthat David lau ingh GFsed w hofen possiblewe select eextractiond. sites. b. *Who did you think that David laughed when we selected? • Note that the equation we looked at previously already disallows Thereforthee, we extractionprovision afromlly p rpassingovide the throughsame defi an iSPECtion fo rinQ theFOC firstUSPA part.TH as we gave for TOPICPATH in (16) of this chapter. Future research may reveal various additi•onWeal re modifyfinemen tthes: equation as follows

(53) English QFOCUSPATH:

XCOMP COMP OBJ ADJ GF GF SPEC ( LDD) ( TENSE) ( TENSE) − }

87 Syntax of Long-Distance Dependencies 407

d. AP: How tall is Chris?

Thus, we define QuesP in (44) above as the following disjunction of categories: (46) QuesP NP PP AdvP AP Syntax of Long-Distance Dependencies 407 The annotations on the QuesP node in rule (44) are similar to those on the relative clause rule in (29) of this chapter. The first two annotations require the f-strucdtu. reAPco:rrHoespwontadlilnigstCohthries?QuesP node to fill the FOCUS role and also to bear Tshoums,ewegradmemfinaetiQucalefsuPnicnti(o4n4)daebfionveedabsyththeefolollnogwi-dnigstadniscjeunpcattihonQoFfOcCaUteSgPoArTiHes;:the correct definition of QFOCUSPATH will be our first topic of discussion in the fol- (4lo6wi) nQug. eTshPe thiNPrd anPnPotaAdtiovnPreAPquires the value of the Q attribute to appear at the enTdhoefatnhneotlaotniogn-dsisotnanthce pQuatehsPWnHoPdAeTiHn wirultehi(n44th)earFeOsCiUmSilfa-rsttroucthtuorsee; owen thdeisrceuls-s actiovnestcrlaaiunstse ornuleWiHnP(A2T9H)boeflotwhi.s Tchheapftoeur.rthTahnenfiortastiotwnoreaqnuniroetsattihoensPRreOqNuTiYrePEthaet- tribute of the Q f-structure to bear the value WH, ensuring that an interrogative f-structure corresponding to the QuesP node to fill the FOCUS role and also to bear pronoun plays the Q role. some grammatical function defined by the long-distance path QFOCUSPATH; the Our first task is to define QFOCUSPATH, the long-distance path involved in ques- correct definition of QFOCUSPATH will be our first topic of discussion in the fol- tion formation. Constraints on QFOCUSPATH appear to be largely similar to those lowing. The third annotation requires the value of the Q attribute to appear at the defined for TOPICPATH in (16) of this chapter (though see Postal 1998 for a dis- end of the long-distance path WHPATH within the FOCUS f-structure; we discuss cussion of differences between the two types of paths): constraints on WHPATH below. The fourth annotation requires the PRONTYPE at- tr(i4b7u)te oaf. thCe hQrifs-,swtreuclitkuer.e to bear the value WH, ensuring that an interrogative pronoun plays the Q role. b. Who do you like? Our first task is to define QFOCUSPATH, the long-distance path involved in ques- ti(o4n8)forma.atioCnh.rCiso, nwsetrtahiinntks othnaQt DaFOvCiUdSsPaAwT.H appear to be largely similar to those defined bfo. r TWOhPoICdPoATyHouinth(i1n6k)thoaftthDaisvcihdaspatwer?(though see Postal 1998 for a discussion of differences between the two types of paths): (49) a. *Chris, we whispered that David saw. (47) a. Chris, we like. b. *Who did you whisper that David saw? b. Who do you like? (50) a. *Chris, [that David saw ] surprised me. (48) a. Chris, we think that David saw. b. *Who did [that David saw ] surprise you? b. Who do you think that David saw? (51) a. This hammer, we smashed the vase with. (49) a. *Chris, we whispered that David saw. b. What did you smash the vase with? Whb. *W-Islandsho did you w hinis pLFG:er that Da Off-Pathvid saw? Constraints (52) a. *Chris, we think that David laughed when we selected. (50) a. *Chris, [that David saw ] surprised me. b. *Who did you think that David laughed when we selected? •b.The*Wh off-patho did [tha metavariablet David saw ←] srefersurpris etoyo theu? f-structure that contains Thereforthee, we attributeprovisio thatnally thepro vconstraintide the sam ise dattachedefinition f to.or QFOCUSPATH as we (5g1av)e fao.r TTOhPiIsChPAaTmmeH inr,(w16e)somaf tshhiesdcthhaepvtears.eFwuittuhr.e research may reveal various additi•obn.Theal Wreh fioff-pathantedmidenytos: umetavariablesmash the vas e→w irefersth? to the f-structure that is the value of the attribute that the constraint is attached to. (5(523)) aE.n*glCishhriQs,FwOeCUthSiPnAkTtHh:at David laughed when we selected.

b.X*COWMhPo didCyOoMu Pthink thatODaBJ vid laughedADwJhen we selected?GF GF SPEC ( LDD) ( TENSE) ( TENSE) − } Therefore, we provisionally provide the same deﬁnition for QFOCUSPATH as we gave f•or UseTOPI C←PA toTH statein (16 the) of bottomthis chap cannotter. Fut ubere rines eanar cf-structureh may revea thatl var ihasous an additionaunboundedl reﬁnements :dependency function UDF, where UDF = {TOPIC | FOCUS}. (53) English QFOCUSPATH:

XCOMP COMP OBJ ADJ GF GF SPEC ( LDD) ( TENSE) ( TENSE) ( − UDF) } ¬ ←

88 Successive Cyclic Effects

89 Successive Cyclicity

• Data from languages such as Irish and Chamorro, which show successive marking along the extraction path, have motivated the claim that extraction/movement is ‘cyclic’ (not all at once). Cf. Phases in Minimalism.

• Of course, this data does not argue for movement per se, as some have wrongly assumed, but rather that unbounded dependencies should

1. Be made up of a series of local relations; or

2. Have a way to refer to their environments as the dependency is constructed.

• HPSG has adopted the ﬁrst approach, LFG the second.

90 26 GOSSE BOUMA ET AL.

(34) LOC NP sgap-ss ⇒ SLASH S ! { }"

So, the additional ﬂexibility introduced by the constraints on gaps allows us to account for examples of limited connectivity between ﬁllers and gaps that provide a serious challenge to standard movement-based treatments of extraction.13

3.2. Cross-linguistic Support As a further illustration of our approach, consider how it might account for one of the phenomena mentioned in the introduction. As McCloskey (1979, 1989) notes, Irish has two different complementizer particles, goN and aL. The only difference between the two is that the former cannot appear in a clause out of which something has been extracted, whereas the latter can only appear in a clause out of which something has been Data: Irish extracted. The pattern is illustrated in (35): (35) a. Shíl mé goN mbeadh sé ann thought I PRT would-be he there • Note: Date from McCloskey I thought that he would be there. via Bouma et al. (2001). b. Dúirt mé gurL shíl mé goN mbeadh sé ann said I goN+PAST thought I PRT would-be he there I said that I thought that he would be there.

c. an fear aL shíl mé aL bheadh ann [the man] j PRT thought I PRT would-be j there the man that I thought would be there

d. an fear aL dúirt mé aL shíl mé aL bheadh ann [the man] j PRT said I PRT thought I PRT would-be j there The man that I said I thought would be there

e. an fear aL shíl goN mbeadh sé ann [the man] j PRT thought j PRT would-be he there the man that thought he would be there

13 See Bresnan (2000) for more discussion of mismatches between elements that are related via grammatical dependency.

91 Irish Successive Cyclicity in LFG

aL Cˆ ( UDF) = ( CF∗ GF) ↑ ↑ ( UDF) = ( UDF) → ↑ Note: UDF = {TOPIC | FOCUS}, CF = {XCOMP | COMP} goN Cˆ ( TENSE) ↑ ( UDF) ¬ ↑

92 Glue Semantics

93 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, in prep.), Lev 2007, Kokkonidis (in press)

94 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 ptrhoenocunassaetuorafticngoapsyemraanistiicnagrg,uimteinst ptohseitisonpethcaitfication of a manager resource thamtuslticbee nlesfteosptehneincoordpeyr torapirsoipnerglyscuombjpeocset tahendsubtjhecet c(foorpcyopryariasiisningg)roerltahteiotonp.ofAthnearpeshumorpiticveblionndg-ing of the copy pronoun by the sudbisjteacnctesdyepnetnadcetniccieasl(lfyorirdeseunmtpitfiiveesprtohneoupnsrionnuonbuonuntdhedatdeipsencdaeuncsieins)g. Tthheeremsaotvualroaftithoenprpornooubnlfermom for semantic composition and semantic composition is carried out by a lexically specified manager resource. Thus, both types of resumption thearemlicaennasegdethrroreugsholuexricceal espfefceificctastiiotns. Irnetmheocavsaelofdcuorpiynrgaiscinogm, itpisotshietsipoenci.ficTahtioenkofeaymdainfafgeerrerensocuercbeetween copy raising verbs and petrhcatelpicteunsaelsrtheesceompybrlaaisnincgesuvbejercbt sanidsththe econpyreradisuincgerdelattoiona. sAinmapphloericlebxinidcinaglodfitfhfeecroepnycpreo:nocuonpbyy trhaeising verbs contribute manager subject syntactically identifies the pronoun that is causing the saturation problem for semantic composition and resthoeumracneasge,rpreesrocuercpeteuffaelctrseitsseremmbovlalndcureinvgecrobmspodsiotionno. Tt.he key difference between copy raising verbs and perTcehpetutael rremsemmblaanncaegveerrbsriessthoeunrrecdeucietdsetolfa ssitmepmleslefxricoaml difGfelreuneceS: ceompyarnaitsiincgsv(eDrbas clroyntmribputleem1a9na9g9er, 2001), a theory of the syntax– sermesaounrtciecs,speirncteeptrufaalcreeseamnbdlansce mverabns tdiocnocto. 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 rGcleue lSoegmiacn,ticas,sthdeilsocguicsosfesdemianntimc coormepodsietitoanilisblieneloarw. Each lexically contributed meloagnicin(Ggiracrodn1s98is7t)s, wohficah itsearmresofurrocme loagicm, aesadnisicnugsseldaningmuoargeedeatasisl obeclioawt.edEacwhiltehxicaaltlyercmontroibfutleidnear 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 siysnttahxetolsienmeaanrticlsoagnidcspteecrifimes (htohwesecmoalnotinc teirsmas nareuninterpreted pairing symbol). • Proof-theoreticThtoebleincoemaprosleodg. iTchesmerevaneinsgacsonastr‘ugctloures alrae nusgeud asgpere’mthiseastinreal(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(f Semanticsollowing 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 and95 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, rinptehrpisremtatibonetiws 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 lcinaesareloignicthteirms spianpGelur.e STemhaunsti,csaaltnhdough semantic composition is categories in Categorial Grammar (Ajdukiewicz 1935, Bar-Hillel 1953, Lambek 1958, Ades and Steedman 1982, drSivteeendmpanro19o9f6-,t2h0e0o0,rBeutsizckaolwlysk,i ient atle.r1p98r8e,tOateihorlne eitsal.m19o8d8,eMl-otrhriello1r9e94ti,cC.arpTenhteirs1h99a7s, Mthooertgaadt 1v9a9n7)t,age that meaning construction is assednissciutsisvede inondeltyailtboy Dthaelrymlipnleeaetrall.o(1g9i9c9at)y. pAensothoefr ptehrsepemctiveeaonninthgis creolantisotnrsuhicptiosrtshaat lnindearnlootgicto the actual meanings in M. is essentially equivalent to the commutative Lambek Calculus (Moortgat 1997, Asudeh 2004, Ja¨ger 2005). In Cohmis dpisocsuistsioonnoafldietysiraibsletphreoprerftioesreofg“Luaamrbaenkt-seteylde,CastiengcoreialnGoramasmsaur”m, Jpa¨gteior (n2s00a5:reix)mnoatedsethaatb“o[Tu]htethe content of meaning terms inCausrrsye-Hmowbalirdngcormresepaonndienngces. .(.Dsuapplrliyesmthpelteypeetloagli.ca1l 9sy9n9taax:w2ith62an–e2x6tre3m).elyTelhegeanltiannedainrdelopegnidcenptlyroof thus serves as the syntax ofmsoetimvataend tinictercfaocemtopmoosdietil-othne,orwetihc iscemhanrteicvse.”aTlhsisacocmlmeaenrt erqeulaaltlyioanppslhieisptobGelutewSeeemnantliicns.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-gHciolnlsetrlu1ct9or5s 3m,neLmaomnicbneakm1es9, 58, Ades and Steedman 1982,

Stee18dThme taypning1in9t9he6li,ne2ar0lo0g0ic,siBde uGsizs ikndoepwensdekntioef,tbuat lr.ela1te9d 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 ascodrriespconudss stoethde 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 assumpti96on 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 constructed 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

97 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

98 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

99 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

100 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

101 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)

102 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 ⇒

103 Further Points of Interest

• Glue Semantics can be understood as a representationalist theory, picking up on a theme from Wednesday’s semantics workshop.

• 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

104