LexicalFunctional A

Formal System for Grammatical

Representation

Ronald M Kaplan and Joan Bresnan

In learning their native language children develop a remarkable set of

capabilities They acquire knowledge and skills that enable them to pro

duce and comprehend an indenite number of novel utterances and to

make quite subtle judgments ab out certain of their prop erties The ma

jor goal of psycholinguistic research is to devise an explanatory account

of the mental op erations that underlie these linguistic abilities

In pursuing this goal wehave adopted what wecallthe Competence

Hypothesis as a metho dological principle Weassumethatanexplana

tory mo del of human language p erformance will incorp orate a theoreti

cally justied representation of the nativespeakers linguistic knowledge

a grammar as a comp onent separate b oth from the computational mech

anisms that op erate on it a processor and from other nongrammatical

pro cessing parameters that might inuence the pro cessors b ehavior To

a certain extentthevarious comp onents that we p ostulate can b e studied

indep endently guided where appropriate bythewellestablished metho ds

and evaluation standards of computer science and exp erimen

tal psychologyHowever the requirement that the various comp onents

ultimately must t together in a consistent and coherent mo del imp oses

even stronger constraints on their structure and op eration

This pap er originally app eared in The Mental Representation of Grammatical Rela

tions ed Joan Bresnan Cambridge MA The MIT Press

Kaplan ab gives an early version of the Comp etence Hyp othesis and discusses

some ways in which the grammatical and pro cessing comp onents mightinteract Also

see Ford Bresnan and Kaplan

Formal Issues in LexicalFunctional Grammar

edited by

Mary Dalrymple

Ronald M Kaplan

John T Maxwell I I I

Annie Zaenen

c

Copyright Stanford University

Ronald M Kaplan and Joan Bresnan

This pap er presents a formalism for representing the native sp eakers

syntactic knowledge In keeping with the Comp etence Hyp othesis this

formalism called lexicalfunctional grammar LFG has b een designed

to serve as a medium for expressing and explaining imp ortant general

izations ab out the of human languages and thus to serveasa

vehicle for indep endent linguistic research Of equal signicance it is a

restricted mathematically tractable notation for which simple psycholog

ically plausible pro cessing mechanisms can b e dened Lexicalfunctional

grammar has evolved b oth from previous research within the transforma

tional framework eg Bresnan and from earlier computational and

psycholinguistic investigations Wo o ds Kaplan a

Wanner and Maratsos

The fundamental problem for a theory of syntax is to characterize the

mapping b etween semantic predicate relationships and the sur

face word and phrase congurations bywhich they are expressed This

mapping is suciently complex that it cannot b e characterized in a simple

unadorned phrase structure formalism a single set of predicateargument

relations can b e realized in many dierent phrase structures eg ac

tive and passive constructions and a single phrase structure can express

several dierent semantic relations as in cases of ambiguity In lexical

functional grammar this corresp ondence is dened in two stages Lexical

entries sp ecify a direct mapping b etween semantic arguments and con

gurations of surface grammatical functions Syntactic rules then iden

tify these surface functions with particular morphological and constituent

structure congurations Alternative realizations may result from alter

native sp ecications at either stage of the corresp ondence Moreover

grammatical sp ecications imp ose wellformedness conditions on b oth the

functional and constituent structures of sentences

The present pap er is concerned with the grammatical formalism it

self its linguistic computational and psychological motivation are dealt

with in separate pap ers In the next several sections weintro duce the

formal ob jects of our theory discuss the relationships among them and

dene the notation and op erations for describing and manipulating them

Illustrations in these and later sections show p ossible LFG solutions to

various problems of linguistic description Section considers the func

tional requirements that strings with valid constituent structures must

satisfy Section summarizes arguments for the indep endence of the con

stituent functional and semantic levels of representation In Section

weintro duce and discuss the formal apparatus for characterizing long

distance grammatical dep endencies Weleave to the end the question of

our systems generativepower Weprove in Section that despite their

AFormal System for Grammatical Representation

linguistic expressiveness lexicalfunctional are not as p owerful

as unrestricted rewriting systems

Constituent structures and functional structures

A lexicalfunctional grammar assigns two levels of syntactic description

to every sentence of a language Phrase structure congurations are

represented in a constituent structure A constituent structure or c

structure is a conventional phrase structure tree a wellformed lab eled

bracketing that indicates the sup ercial arrangementofwords and phrases

in the sentence This is the representation on which phonological interpre

tation op erates to pro duce phonetic strings Surface grammatical func

tions are represented explicitly at the other level of description called

functional structure The functional structure fstructure provides a

precise characterization of such traditional syntactic notions as sub ject

understo o d sub ject ob ject complement and adjunct The fstructure

is the sole input to the semantic comp onent whichmay either translate

the fstructure into the appropriate formulas in some logical language or

provide an immediate mo deltheoretic interpretation for it

Constituent structures are formally quite dierent from functional

structures Cstructures are dened in terms of syntactic categories ter

minal strings and their dominance and precedence relationships whereas

fstructures are comp osed of grammatical function names semantic forms

and feature symbols Fstructures and cstructures are also distinct

from semantic translations and interpretations in which for example

quantierscop e ambiguities are resolved By formally distinguishing

these levels of representation our theory attempts to separate those gram

matical phenomena that are purely syntactic involving only cstructures

and fstructures from those that are purely lexical involving lexical en

tries b efore they are inserted into cstructures and fstructures or se

mantic for example involving logical inference Our framework thus

facilitates an empirically motivated division of lab or b etween the lexical

syntactic semantic and phonological comp onents of a grammar

A cstructure is determined by a grammar that characterizes all p os

sible surface structures for a language This grammar is expressed in a

slightly mo died contextfree formalism or a formally equivalent sp eci

cation such as a recursive transition network Wo o ds Kaplan

For example the ordinary rewriting pro cedure for contextfree grammars

would assign the cstructure to the sentence given the rules in

a S NP VP

b NP Det N

c VP VNPNP

Ronald M Kaplan and Joan Bresnan

A girl handed the babya toy

S

NP VP

Det N V NP NP

Det N Det N

A girl handed the baby a toy

We emphasize that cstructure no des can b e derived only by phrase struc

ture rules such as abc There are no deletion or movement op erations

which could for example form the doubleNP sequence from a phrase

structure with a to prep ositional phrase Suchmechanisms are unneces

sary in LFG b ecause we do not map b etween semantically and phonolog

ically interpretable levels of phrase structure Semantic interpretation is

dened on functional structure not on the phrase structure representation

that is the domain of phonological interpretation

The functional structure for a sentence enco des its meaningful gram

matical relations and provides sucient information for the semantic com

p onent to determine the appropriate predicateargumentformulas The

fstructure for would indicate that the girl noun phrase is the gram

matical sub ject handed conveys the semantic predicate the baby NP is

the grammatical ob ject and toy serves as the second grammatical ob ject

The fstructure represents this information as a set of ordered pairs eachof

which consists of an attribute and a sp ecication of that attributes value

for this sentence An attribute is the name of a grammatical function or

feature subj pred obj num case etc There are three primitive

typ es of values

a Simple symbols

b Semantic forms that govern the pro cess of semantic interpre

tation

c Subsidiary fstructures sets of ordered pairs representing com

plexes of internal functions

A fourth typ e of value sets of symb ols semantic forms or fstructures

is also p ermitted We will discuss this typ e when we consider the gram

matical treatment of adjuncts

AFormal System for Grammatical Representation

Given p ossibility c an fstructure is in eect a hierarchyofat

tributevalue pairs We write an fstructure by arranging its pairs verti

cally inside square brackets with the attribute and value of a single pair

placed on a horizontal line The following is a plausible fstructure for

sentence

spec a

num sg

subj

pred girl

tense past

pred hand h subj obj obji

spec the

num sg

obj

pred baby

spec a

num sg

obj

pred toy

In this structure the tense attribute has the simple symbol value past

pairs with this kind of value representsyntactic features Grammatical

functions have subsidiary fstructure values as illustrated by the sub ject

function in this example

spec a

num sg

pred girl

The attributes spec sp ecier and num mark emb edded features with

the symbol values a and sg resp ectively

The quoted values of the pred attributes are semantic forms Se

mantic forms usually arise in the lexicon and are carried along bythe

syntactic comp onent as unanalyzable atomic elements just like simple

symb ols When the fstructure is semantically interpreted these forms

are treated as patterns for comp osing the logical formulas enco ding the

meaning of the sentence Thus the semantic interpretation for this sen

tence is obtained from the value of its pred attribute the semantic form

in

hand h subj obj obji

This is a predicateargument expression containing the semantic predicate

name hand followed by an argumentlist sp ecication enclosed in angle



Semantic forms with a lexical source are often called lexical forms Less commonly

semantic forms are pro duced bysyntactic rules for example to represent unexpressed

pronouns this will b e illustrated in Section in the discussion of English imp erative sub jects

Ronald M Kaplan and Joan Bresnan

brackets The argumentlist sp ecication denes a mapping b etween the

logical or thematic arguments of the threeplace predicate hand eg

agent theme and goal and the grammatical functions of the fstructure

The parenthetic expressions signify that the rst argument p osition of that

predicate is lled by the formula that results from interpreting the subj

function of the sentence the formula from the obj is substituted in the

second argument p osition and so on The formula for the emb edded subj

fstructure is determined by its pred value the semantic form girl Girl

do es not have an argumentlist b ecause it do es not apply to arguments

sp ecied by other grammatical functions It is a predicate on individuals

in the logical universe of discourse quantied by information derived from

the spec feature

There are very strong compatibility requirements b etween a seman

tic form and the fstructure in which it app ears Lo osely sp eaking all

the functions mentioned in the semantic form must b e included in the

fstructure and all functions with subsidiary fstructure values must b e

mentioned in the semantic form A given semantic form is in eect com

patible with only one set of grammatical functions although these may

b e asso ciated with several dierent cstructures Thus the semantic form

in is not compatible with the grammatical functions in b ecause

it do es not mention the obj function but do es sp ecify to obj the

ob ject of the prep osition to

hand h subj obj to obji

This semantic form is compatible instead with the functions in the f

structure



The anglebrackets corresp ond to the parentheses in the logical language that would

ordinarily b e used to denote the application of a predicate to its arguments Weuse

anglebrackets in order to distinguish the semantic parentheses from the parentheses

of our syntactic formalism



This pap er is not concerned with the details of the semantic translation pro cedure for

NPs and the sp ecications for the spec and common noun pred features are simplied

accordingly With more elab orate expressions for these features NPs can also b e

translated into a higherorder intensional logic by a general substitution pro cedure

For instance supp ose that the symbol a is taken as an abbreviation for the semantic

form

QP xhQx P xi

which represents the meaning of an existential quantier and supp ose that girl is

replaced by the expression spechgirl i Then the translation for the subj f

structure would b e a formula in which the quantier is applied to the common noun

meaning See Halvorsen for an extensive discussion of fstructure translation

and interpretation

AFormal System for Grammatical Representation

spec a

num sg

subj

pred girl

tense past

pred hand h subj obj to obji

spec a

num sg

obj

pred toy

pcase to

spec the

to

num sg

obj

pred baby

WeshowinSection how this fstructure is assigned to the NPto NP

sentence

A girl handed a toy to the baby

This fstructure with as its pred value denes girl baby andtoy

as the agent goal and theme arguments of hand just as in The

nativespeakers paraphrase intuitions concerning and are thus

accurately expressed This account of the English dative alternation is

p ossible b ecause our grammatical functions subj obj to obj etc de

note surface grammatical relationships not the underlying logical rela

tionships commonly represented in transformational deep structures

The semantic forms and are found in alternativeentries of the

lexical item handed reecting the fact that the predicate hand p ermits

the alternative surface realizations and among others Of course

many other verbs in the lexicon are similar to handed in having separate

entries along the lines of and Our theory captures the systematic

connection b etween NPNP and NPto NP constructions by means of a

lexical redundancy rule of the sort suggested by Bresnan c

The semantic form results from applying the dativizing lexical rule

shown in to the semantic form in

obj obj

to obj obj

According to this rule a word with a lexical entry containing the sp ecica

tions objand to objmayhave another entry in which obj

app ears in place of objand obj app ears in place of to obj

It is imp ortant to note that these relationchanging rules are not ap

plied in the syntactic derivation of individual sentences They merely

express patterns of redundancy that obtain among large but nite classes

of lexical entries and presumably simplify the childs languageacquisition

Ronald M Kaplan and Joan Bresnan

task see Pinker for discussion Indeed just as our formalism ad

mits no rules for transforming cstructures it emb o dies a similar prohi

bition against syntactic manipulations of function assignments and func

tionargument mappings

Direct Syntactic Encoding

No rule of syntax may replace one function name by another

This principle is an immediate consequence of the Uniqueness Condition

which is stated in the next section The principle of direct syntactic en

co ding sharp ens the distinction b etween two classes of rules rules that

change relations are lexical and range over nite sets while syntactic

rules that pro ject onto an innite set of sentences preserve grammatical

relations Our restrictions on the expressivepower of syntactic rules

guarantee that a sentences grammatical functions are visible directly

in the surface structure and thus aord certain computational and psy

chological advantages

Functional descriptions

A strings constituent structure is generated by a contextfree cstructure

grammar That grammar is augmented so that it also pro duces a nite

collection of statements sp ecifying various prop erties of the strings f

structure The set of such statements called the functional description

fdescription of the string serves as an intermediary b etween the c

structure and the fstructure

The statements of an fdescription can b e used in twoways They

can b e applied to a particular fstructure to decide whether or not it

has all the prop erties required by the grammar If so the candidate f

structure maybetaken as the fstructure that the grammar assigns to the

string The fdescription may also b e used in a constructive mo de the

statements supp ort a set of inferences bywhich an fstructure satisfying

the grammars requirements maybesynthesized The fdescription is thus

analogous to a set of simultaneous equations in elementary algebra that

express prop erties of certain unknown numb ers Such equations maybe

used to validate a prop osed solution or they maybesolved bymeans

of arithmetic inference rules canceling substitution of equals for equals

etc to discover the particular numb ers for which the equations are true

In line with this analogy this section presents an algebraic formalism for

representing an fdescription



This correlation of rule prop erties is a signicant dierence b etween lexicalfunctional

grammar and Relational Grammar see for example the pap ers in Perlmutter

The two approaches are similar however in the emphasis they place on grammatical

relations Bell oers a more extensive comparison of the two theories

AFormal System for Grammatical Representation

The statements in an fdescription and the inferences that maybe

drawn from them dep end crucially on the following axiom

Uniqueness

In a given fstructure a particular attribute mayhaveatmostone

value

This condition makes it p ossible to describ e an fstructure by sp ecifying

the unique values of the grammatical functions of which it is comp osed

Thus if we let the variables f and f stand for unknown fstructures

the following statements have a clear interpretation

a the subj of f f

b the spec of f a

c the num of f sg

d the pred of f girl

In fact these statements are true if f and f are the fstructures

and and the statements in maythus b e considered a part of the

fdescription of sentence

Wehave dened a functional structure as a set of ordered pairs satisfy

ing the Uniqueness Condition Wenow observe that this is precisely

the standard denition of a mathematical function There is a systematic

ambiguityinouruseoftheword function an fstructure is a mathe

matical function that represents the grammatical functions of a sentence

This coincidence provides a more conventional terminology for formulat

ing the statements of an fdescription For example statement c can

b e paraphrased as a and this can b e stated more formally using the

familiar parenthesis notation to indicate the application of a function to

an argument as in b

a The function f is such that applying it to the argument num

yields the value sg

b f num sg

Thus the statements of an fdescription are simply equations that de

scrib e the values obtained byvarious function applications Unlikethe

typical functions of elementary algebra an fstructure is a function with

a nite domain and range and thus can b e dened by a nite table of ar

guments and values as represented in our squarebracket notation Also

wedonotdraw a clear distinction b etween functions and their values

Algebraic equations commonly involve a known function that takeona

given value when applied to some unknown argument the problem is to

determine that argument In b however the argument and the corre

Ronald M Kaplan and Joan Bresnan

sp onding value are both known and the problem is to nd the function

Moreover applying an fstructure to an argumentmay pro duce a function

that may b e applied in turn to another argument If a is true then

the stipulations in b and b are equivalent

spec a

num sg

f a f subj



pred girl

b f subj num sg

The form of function comp osition illustrated in equation b o ccurs

quite often in fdescriptions Wehave found that a slight adaptation of

the traditional notation improves the readabilityofsuch sp ecications

Thus we denote a function application by writing the function name

inside the parentheses next to the argument instead of putting it in front

In our mo died notation the stipulation b is written as a and the

comp osition b app ears as b

a f num sg

b f subj num sg

Wemake one further simplication since all fstructures are functions of

one argument parenthetic expressions with more than two elements a

function and its argument do not normally o ccur Thus weintro duce

no ambiguityby dening our parenthetic notation to b e leftasso ciative

by means of the identity

f f

This allows any leftmost pair of parentheses to b e removed or inserted

when convenient so that b may b e simplied to

f subj num sg

With this notation there is a simple way of determining the value of a

given functionapplication expression we lo cate the fstructure denoted

by the leftmost element in the expression and match the remaining el

ements from left to right against successive attributes in the fstructure



There is an equivalentformulation in which the symbols subj

obj etc are taken to b e the names of functions that apply to fstructure arguments

Wewould then write subj f instead of f subj and the left and righthand elements

of all our expressions would b e systematically interchangedEven with this alterna

tive however there are still cases where the function is an unknown see for example

the discussion b elow of oblique ob jects The conceptual consideration underlying our

decision to treat fstructures as the formal functions is that only total nite functions

are then involved in the characterization of particular sentences Otherwise our con

ceptual framework would b e p opulated with functions on innite domains when only

their restriction to the sentence at hand would ever b e grammatically relevant Only

this intuition would b e aected if the alternativeformulation were adopted

AFormal System for Grammatical Representation

hierarchy Also the English genitive construction provides a natural gloss

for these expressions maybereadasf s subjs num is sg

From cstructures to fdescriptions

Having said what an fdescription is wenow consider how the fdescription

for a string is pro duced from a grammar and lexicon This is followed by

a discussion of the inferences that lead from an fdescription to the f

structure that it describ es

The statements in an fdescription come from functional sp ecications

that are asso ciated with particular elements on the righthand sides of

cstructure rules and with particular categories in lexical entries These

sp ecications consist of templates from which the fdescription statements

are derived A template or statement schema has the form of the state

menttobederived from it except that in place of fstructure variables

it contains sp ecial metavariables If a rule is applied to generate a c

structure no de or a lexical item is inserted under a preterminal category

the asso ciated schemata are instantiated by replacing the metavariables

with actual variables f f Which actual variables are used de

p ends on whichmetavariables are in the schemata and what the no des

relationship is to other no des in the tree The metavariables and gram

matically signicant tree relations are of just twotyp es

Immediate dominationwithmetavariables and

Bounded domination with metavariables and

Statements based on nonimmediate but b ounded tree relations are needed

to characterize the longdistance dep endencies found in relative clauses

questions and other constructions We p ostp one our discussion of b ounded

domination to Section since it is more complex than immediate domi

nation

Schemata involving immediate domination metavariables and relations

yield fdescription statements dening the lo cal predicateargument con

gurations of simple sentence patterns such as the dative To illustrate

the cstructure rules abc are versions of abc with schemata writ

ten b eneath the rule elements that they are asso ciated with

Ronald M Kaplan and Joan Bresnan

a S NP VP

subj

b NP Det N

c VP V NP NP

obj obj

According to the instantiation pro cedure describ ed b elow the subj and

obj schemata in this grammar indicate that the sub ject and ob ject f

structures come from NPs immediately dominated by S and VP While

sup ercially similar to the standard transformational denitions of sub

ject and ob ject Chomsky our sp ecications apply only to surface

constituents and establish only a lo ose coupling b etween functions and

phrase structure congurations Given the obj schema for example

an NP directly dominated by VP can also function as a second ob ject

These schemata corresp ond more closely to the setr op eration of the aug

mented transition network notation ATN Wo o ds subj

has roughly the same eect as the ATN action setr subj The direct

equality on the VP category in a has no ATN or transformational

equivalent however It is an identication schema indicating that a sin

gle fstructure is based on more than one constituent and thus that the

fstructure is somewhat atter than the cstructure

The syntactic features and semantic content of lexical items are de

termined byschemata in lexical entries The entries for the vo cabulary

of sentence are listed in

a Det speca

num sg

girl N num sg

pred girl

handed V tensepast

pred hand h subj obj obji

the Det specthe



This illustration ignores the morphological comp osition of lexical items which makes

a systematic contribution to the set of inectional features represented in the schemata

AFormal System for Grammatical Representation

baby N num sg

pred baby

toy N num sg

pred toy

A lexical entry in LFG includes a categorial sp ecication indicating the

preterminal category under which the lexical item may b e inserted and a

set of schemata to b e instantiated As shown in schemata originating

in the lexicon are not formally distinct from those coming from cstructure

rules and they are treated uniformly by the instantiation pro cedure

Instantiation is carried out in three phases The schemata are rst

attached to appropriate no des in the cstructure tree actual variables are

then intro duced at certain no des and nally those actual variables are

substituted for metavariables to form valid fdescription statements In

the rst phase schemata asso ciated with a cstructure rule elementare

attached to the no des generated by that element Lexical schemata are

considered to b e asso ciated with a lexical entrys categorial sp ecication

and are thus attached to the no des of that category that dominate the

lexical item Attaching the grammatical and lexical schemata in

and to the cstructure for sentence pro duces the result in

In this example wehave written the schemata ab ove the no des they are

attached to

In the second phase of the instantiation pro cedure a new actual vari

able is intro duced for the ro ot no de of the tree and for each no de where

aschema contains the metavariable Intuitively the existence of at a

no de means that one comp onent of the sentences fstructure corresp onds

to that sub constituent The new variable called the variable of the

no de is a device for describing the internal prop erties of that fstructure

called the no des fstructure and its role in larger structures In

wehave asso ciated variables with the no des as required by the schemata

in

With the schemata and variables laid out on the tree in this way

the substitution phase of instantiation is quite simple Fully instantiated

statements are formed by substituting a no des variable rst for all

the s at that no de and then for all the s attached to the no des it

immediately dominates Thus arrows p ointing toward each other across



Another convention for lexical insertion is to attach the schemata directly to the

terminal no des While the same functional relationships can b e stated with either

convention this alternative requires additional identication schemata in the common

case where the preterminal category do es not corresp ond to a distinct functional unit

It is thus more cumb ersome to work with

Ronald M Kaplan and Joan Bresnan y sg to y N to num pred NP obj a sg a Det spec num y sg y bab VP N bab num pred NP obj the Det i the spec h S ast p V hand handed tense pred sg girl N girl num pred NP subj a sg A Det spec num

AFormal System for Grammatical Representation y sg to y N to num pred NP obj a sg f a Det spec num y sg y bab N VP bab f num pred NP obj the f Det i the spec h S ast p f V hand handed tense pred sg girl N girl num pred NP subj a sg f A Det spec num

Ronald M Kaplan and Joan Bresnan

one line in the tree are instantiated with the same variable The is

called the mother metavariable since it is replaced bythe variable of

its mother no de From the p oint of view of the Sdominated NP no de

the schema subj may b e read as My mothers fstructures subj

is my fstructure In this case the mothers variable is the ro ot no des

variable and so represents the fstructure of the sentence as a whole

When we p erform the substitutions for the schemata and variables in

the schemata attached to the Sdominated NP and VP no des yield

the equations in and the daughters of the VP cause the equations

in to b e included in the sentences fdescription

a f subj f

b f f

a f objf

b f objf

The equations in taken together constitute the syntactically de

termined statements of the sentences functional description The other

equations in the fdescription are derived from the schemata on the preter

minal no des



If a schema containing is attached to a no de whose mother has no variable

the cannot b e prop erly instantiated and the string is marked ungrammatical This

situation is not likely to o ccur with immediate domination metavariables but provides

an imp ortantwellformedness condition for b ounded domination This is discussed in

Section

In eect the instantiation pro cedure adds to the schemata information ab out the

tree congurations in which they app ear As shown in Section the fstructure for

the sentence can then b e inferred without further reference to the cstructure An

equivalent inference pro cedure can b e dened that do es not require the intro duction

of variables and instead takes into account the relative p osition of schemata in the

tree This alternative pro cedure searches the cstructure to obtain the information

that we are enco ding byvariables in instantiatedschemata It essentially intermixes

our instantiation op erations among its other inferences and is thus more dicult to

describ e

For simplicityinthispaperwe do not instantiate the metavariablewhenitap

p ears within semantic forms This is p ermissible b ecause the internal structure of

semantic forms is not accessible to syntactic rules However the semantic translation

or interpretation pro cedure may dep end on a full instantiation

AFormal System for Grammatical Representation

a f speca from a

b f num sg

c f num sg from girl

d f pred girl

e f tensepast from handed

f f pred hand h subj obj obji

g f specthe from the

h f num sg from baby

i f pred baby

j f speca from a

k f num sg

l f num sg from toy

m f pred toy

Adding these to the equations in gives the complete fdescription

for sentence

From fdescriptions to fstructures

Once an fdescription has b een pro duced for a given string algebraic ma

nipulations can b e p erformed on its statements to make manifest certain

implicit relationships that hold among the prop erties of that strings f

structure These manipulations are justied by the leftasso ciativityof

the functionapplication notation and by the substitution axiom for

equalityTo take an example the value of the numb er feature of sentence

s fstructure that is the value of f obj num can b e inferred in

the following steps

f obj num f obj num Substitution using b

f obj num Leftasso ciativity

f num Substitution using a

sg Substitution using h

An fdescription also supp orts a more imp ortant set of inferences the

equations can b e solved by means of a construction algorithm that

actually builds the fstructure they describ e

An fstructure solution may not exist for every fdescription however

If the fdescription stipulates two distinct values for a particular attribute

or if it implies that an attributename is an fstructure or semantic form

instead of a symb ol then its statements are inconsistent with the basic

Ronald M Kaplan and Joan Bresnan

axioms of our theory In this case we classify the string as syntacti

cally illformed even though it has a valid cstructure The functional

wellformedness conditions of our theory thus account for manytyp es of

ungrammaticality It is therefore essential that there b e an algorithm for

deciding whether or not an fdescription is consistent and for pro ducing

a consistent fdescriptions fstructure solution Otherwise our grammars

would generate all but not only the sentences of a language

Fortunately fdescriptions are wellundersto o d mathematical ob jects

The problem of determining whether or not a given fdescription is sat

isable is equivalent to the decision problem of the quantierfree theory

of equalityAckermann proved that this problem is solvable and

several ecient solution algorithms have b een discovered for example

the congruence closure algorithm of Nelson and Opp en In this sec

tion we outline a decision and construction algorithm whose op erations

are sp ecially adapted to the linguistic representations of our theory

We b egin by giving a more precise interpretation for the formal ex

pressions that app ear in fdescription statements We imagine that there

is a collection of entities symb ols semantic forms and fstructures that

an fdescription characterizes and that each of these entities has a variety

of names or designators bywhich the fdescription may refer to it The

character strings that wehave used to represent symb ols and semantic

forms the algebraic variables weintro duce and the functionapplication

expressions are all designators The entity denoted by a designator is

called its value Thevalue of a symb ol or semantic form character string

is obviously the identied symbol or semantic form The value of a vari

able designator is of course not obvious from the variables sp elling it is

dened by an assignment list of variableentity pairs A basic function

application expression is a parenthesized pair of designators and its value

is the entityifany obtained by applying the fstructure value of the left

designator to the symbol value of the right designator This rule applies

recursively if either expression is itself a functionapplication to obtain

the value of f obj num wemust rst obtain the value of f objby

applying the value of f to the symbol obj

Note that several dierent designators may refer to the same en

tity The deduction in for example indicates that the designa

tors f obj num andf num b oth have the same value the symbol

sg Indeed weinterpret the equality relation b etween two designators as

an explicit stipulation that those designators name the same entityIn



An attribute in an fstructure is thus a sp ecial kind of designator and the notion

of a designators value generalizes our use of the term value which previously referred

only to the entity paired with an attribute in an fstructure

AFormal System for Grammatical Representation

pro cessing an fdescription our algorithm attempts to nd a wayofas

so ciating with designators values that are consistent with the synonymy

relation implied by the equality statements and with the pro cedure just

outlined for obtaining the values of dierenttyp es of designators

The algorithm works by successiveapproximation It go es through

a sequence of steps one for each equation in the fdescription Atthe

b eginning of each step it has a collection of symb ols semantic forms and

fstructures that satisfy all the equations considered at preceding steps

together with an assignmentoftentativevalues for the variables o ccurring

in those equations The algorithm revises the collection of entities and

value assignments to satisfy in addition the requirements of one more

equation from the fdescription The entities after the last equation is

pro cessed thus satisfy the fdescription as a whole and provide a nal

value for the variable of the cstructure trees ro ot no de This is the

fstructure that the grammar assigns to the string

The pro cessing of a single equation is carried out by means of two

op erators One op erator called Locate obtains the value for a given des

ignator The entities in the collection might b e augmented by the Lo cate

op erator to ensure that a value exists for that designator When the values

for the equations lefthand and righthand designators have b een lo cated

the second op erator checks to see whether those values are the

same and hence already satisfy the equality relation If not it constructs

a new entitybycombining the prop erties of the distinct values provided

those prop erties are compatible The collection is revised so that this

entity b ecomes the common value of the two designators and also of all

previously encountered synonyms of these designators Stated in more

formal terms if d and d are the designators in an equation d d and

if brackets represent the application of an op erator to its arguments then

that equation is pro cessed by p erforming MergeLo cated Lo cated

Atechnical denition of these op erators is given in the App endix

In this section we presentanintuitive description of the solution pro cess

using as an example the fdescription in The nal result do es not

dep end on the order in which equations are considered so we will simply

take them as they app ear ab ove We start with an empty collection of

entities and consider equation a f subjf To lo cate the value



This algorithm is designed to demonstrate that the various conditions imp osed by

our theory are formally decidable It is unlikely that this particular algorithm will b e

incorp oratedintact into a psychologically plausible mo del of language p erformanceor

even into a computationally ecient parser or generator For these other purp oses

functional op erations will presumably b e interleaved with cstructure computations

and functional data representations will b e chosen so as to minimize the combinatoric

interactions with the nondeterministic uncertainty of the cstructure rules

Ronald M Kaplan and Joan Bresnan

of f subj wemust rst obtain the value of f There is as yet no

assignment for that variable so the Lo cate op erator creates a value out

of whole cloth it adds a sp ecial placeholder entity to our collection

and assigns it as the value of f A representation for the new entity and

variable assignmentisshown in

f

A placeholder is represented by a blank line indicating that it is an

entity none of whose prop erties are known The variable prex signies

that whatever that entity is it has b een assigned as the tentativevalue of

f A placeholder is just a b o okkeeping device for recording the relations

between entities b efore wehave discovered anything else ab out them

With the value of f in hand we return to the larger designator

f subj This provides more sp ecic information ab out the entity that

the placeholder stands for the value of f must b e an fstructure that

has subj as one of its attributes We revise our collection again to take

account of this new information

subj

f

Knowing nothing ab out the value of subj in the f fstructure wehave

represented it by another placeholder This placeholder is the entity

lo cated for the designator f subj Wenowturnto f the second

designator in the equation This is a variable with no previous assignment

so our lo cation pro cedure simply assigns it to another newly created place

holder

f

This completes the lo cation phase of the algorithms rst step the equa

tions designators now denote the placeholders in and

The Merge op erator changes the collection once more so that the two

designators denote the same entityThetwo placeholders are distinct

but neither has any prop erties Thus a common value also a placeholder

with no prop erties can b e constructed This placeholder app ears as the

value of subj in the f fstructure but it is also assigned as the value of

f as shown in

subj f

f



The structure is now the only member of our entity collection Notice

that with this assignmentofvariables the designators f subjandf

have the same value so the equation f subj f is satised

Wemove on to equation b the identication f f This means

that the variables f and f are two dierent designators for a single entity

That entity will have all the prop erties ascrib ed via the designator f and

AFormal System for Grammatical Representation

also all the prop erties ascrib ed to the synonymous f The fstructure

is lo cated as the value of f and a new placeholder is assigned

to f Since the placeholder has no prop erties the result of combining

it with the fstructure is simply that fstructure again with its variable

prexes mo died to reect the new equalityThus the result of the merge

for the second equation is

subj f

f f





The variable assignments in now satisfy the rst two equations of the

fdescription

The equation at the next step is a f objf f already

has an fstructure value in but it do es not include obj as one of its

attributes This is remedied by adding an appropriate placeholder

subj f



f f



obj

This placeholder is merged with one created for the variable f yield

ing

subj f



f f



obj f



Equation b is handled in a similar fashion and results in

subj f



obj f

f f





obj f



After wehave pro cessed these equations our collection of entities and

variable assignments satises all the syntactically determined equations

of the fdescription

The lexically derived equations are nowtaken into account These

have the eect of adding new features to the outer fstructure and lling

in the internal prop erties of the placeholders Lo cating the value of the

lefthand designator in equation a f speca converts the subj

placeholder to an fstructure with a spec feature whose value is a new

placeholder

spec

subj f



obj f

f f





obj f



The value of the righthand designator is just the symbol a Merging this

with the new spec placeholder yields

Ronald M Kaplan and Joan Bresnan

spec a

subj f



obj f

f f





obj f



Note that this mo dication do es not falsify any equations pro cessed in

previous steps

Equation b has the same form as a and its eect is simply to

add a num sg feature to the subj fstructure alongside the spec

h i

spec a

subj f



num sg

f f



obj f



obj f



Though derived from dierent lexical items equation c is an exact

duplicate of b Pro cessing this equation therefore has no visible ef

fects

The remaining equations are quite straightforward Equation d

causes the pred function to b e added to the subj fstructure ef

yield the tense and pred functions in the f f structure and gm

complete the obj and obj placeholders Equation l is similar to

c in that it duplicates another equation in the fdescription and hence

do es not have an indep endent eect on the nal result After considering

all the equations in wearrive at the nal fstructure

spec a

num sg

subj f



pred girl

tense past

pred hand h subj obj obji

spec the

f f



num sg

obj f



pred baby

spec a

num sg

obj f



pred toy

Since f is the variable of the ro ot no de of the tree the outer f

structure is what our simple grammar assigns to the string This is just

the structure in if the variable prexes and the order of pairs are

ignored

This example is sp ecial in that the argument p ositions of all the

functionapplication designators are lled with symb ol designators Cer

tain grammatical situations give rise to less restricted designators where

AFormal System for Grammatical Representation

the argument p osition is lled with another functionapplication This

is p ossible b ecause symb ols have a dual status in our formalismthey

can serve in an fstructure b oth as attributes and as values These more

general designators p ermit the grammatical relation assigned to the f

structure at a given no de to b e determined byinternal features of that

fstructure rather than by the p osition of that no de in the cstructure

The arguments to a large numb er of English verbs for instance may ap

p ear as the ob jects of particular prep ositions instead of as subj objor

obj noun phrases In our theory the lexical entry for a casemarking

prep osition indicates that its ob ject noun phrase maybetreatedaswhat

has traditionally b een called a verbs oblique The semantic form

for the verb then sp ecies how to map that oblique ob ject into the ap

propriate argument of the predicate

The to alternative for the doubleNP realization of handed provides a

simple illustration The contrasting sentence to our previous example

is rep eated here for convenience

A girl handed a toy to the baby

The cstructure for this sentence with a set of variables for the function

ally relevant no des is shown in It includes a prep ositional phrase

following the ob ject NP as p ermitted by the new cstructure rules

f S

f NP f VP

Det N V f NP f PP

Det N P f NP

Det N

A girl handed a toy to the baby



We use the standard contextfree abbreviation for optionalityparentheses that en

close categories and schemata Thus a also derives intransitive and transitiveverb

phrases Optionality parentheses should not b e confused with the functionapplication

parentheses within schemata We also use braces in rules to indicate alternativec structure expansions

Ronald M Kaplan and Joan Bresnan

a VP

V PP

NP NP

pcase

obj obj

b PP P NP

obj

The PP element in a exhibits two new rule features The asterisk on

the PP category symb ol is the Kleenestar op erator it indicates that that

rule elementmay b e rep eated anynumb er of times including none The

schema on the PP sp ecies that the value of the pcase attribute in the

PPs fstructure determines the functional role assigned to that structure

Because the lexical schemata from to are attached to the Prep no de that

feature p ercolates up to the fstructure at the PP no de Supp ose that to

has the casemarking lexical entry shown in a and that handed has

the entry b as an alternative to the one given in Then the PP

fstructure serves the to function as shown in

a to P pcase to

b handed V tensepast

predhand h subj obj to obji



Our cstructure rules thus diverge from a strict contextfree formalism Weper

mit the righthand sides of these rules to b e regular expressions as in a recursive

transition network not just simplyordered category sequences The is therefore

not interpreted as an abbreviation for an innite numb er of

As our theory evolves we might incorp orate other mo dications to the cstructure

formalism For example in a formalism which although oriented towards systemic

grammar descriptions is closely related to ours Kay uses patterns of partially

ordered grammatical relations to map b etween a linear string and his equivalenttoan

fstructure Such partial orderings might b e particularly wellsuited for free wordorder

languages



The casemarking entry is distinct from the entry for to when it serves as a predicate

in its own right as in prep ositional complements or adjuncts

AFormal System for Grammatical Representation

spec a

num sg

subj

pred girl

tense past

pred hand h subj obj to obji

spec a

num sg

obj

pred toy

pcase to

spec the

to

num sg

obj

pred baby

The baby fstructure is accessible as the to obj and it is correctly

mapp ed onto the goal argument of hand by the semantic form for handed

in b and As mentioned earlier this is systematically related to

the semanticforminby a dative lexical redundancy rule so that the

generalization marking sentences and as paraphrases is not lost

Most of the statements in the fdescription for are either the same

as or very similar to the statements in The statements most

relevant to the issue at hand are instantiated inside the prep ositional

phrase and at the PP no de in the verb phrase

a f f pcase f from PP in a

b f pcaseto from to

The designator on the left side of a is of course the crucial one This

is pro cessed by rst lo cating the values of f and f pcase and then

applying the rst of these values to the second If b is pro cessed b efore

a then the value of f pcase willbethesymbol to and a

will thus receive the same treatment as the more restricted equations we

considered ab ove

We cannot insist that the fdescription b e pro cessed in this or any

other order however Since equality is an equivalence relation whether

or not an fstructure is a solution to a given fdescription is not a prop erty

of any ordering on the fdescription statements An order dep endency in

our algorithm would simply b e an artifact of its op eration Unless we

could prove that an acceptable order can b e determined for any set of

statements wewould run the risk of ordering paradoxes whereby our al

gorithm do es not pro duce a solution even though satisfactory fstructures

do exist A p otential order dep endency arises only when one equation

establishes relationships b etween entities that have not yet b een dened

Placeholders serve in our algorithm as temp orary surrogates for those

unknown entities Our examples ab ove illustrate their use in represent

Ronald M Kaplan and Joan Bresnan

ing simple relationships Changing the order in which equations are

pro cessed demonstrates that the prop er treatment of more complicated

co o ccurrence relationships do es not dep end on a particular sequence of

statements

Supp ose that a is pro cessed b efore b Then the value of

f pcase will b e a placeholder as shown in a and f will b e assigned

an fstructure with placeholders in b oth attribute and value p ositions as

in b

a pcase

f



b

f



The value of the larger designator f f pcase will thus b e the second

placeholder in b When this is merged with the fstructure assigned

to f the result is

pcase

f

f





It is not clear from that the two blank lines stand for the same place

holder One way of indicating this fact is to annotate blank lines with an

identifying index whenever they represent o ccurrences of the same place

holder in multiple contexts as shown in An alternative and p erhaps

more p erspicuous way of marking the imp ortant formal relationships is to

display the blank line in just one of the placeholders p ositions and then

draw connecting lines to its other o ccurrences as in

h i

pcase

f

f





pcase

f

f





This problem of representation arises b ecause our hierarchical fstructures

are in fact directed graphs not trees so all the connections cannot easily

b e displayed in textual form With the co o ccurrences explicitly repre

sented pro cessing equation b causes the symbol to to b e substituted

for the placeholder in b oth p ositions

pcase to

to f

f





The index or connecting line is no longer needed b ecause the common

sp elling of symb ols in two p ositions suces to indicate their formal iden

tity The structure is combined with the result of pro cessing the

remaining equations in the fdescription yielding the nal structure

The Kleenestar op erator on the PP in a allows for sentences hav ing more than one oblique ob ject

AFormal System for Grammatical Representation

The toywas given to the babyby the girl

The fstructure of this sentence will have b oth a to obj and a by obj

Because of the functional wellformedness conditions discussed in the next

section these grammatical relations are compatible only with a semantic

form that results from the passive lexical rule

hand h by obj subj to obji

Although the cstructure rule suggests that anynumb er of oblique ob jects

are p ossible they are in fact strictly limited by semantic form sp ecica

tions Moreover if two prep ositional phrases have the same prep osition

and hence the same pcase feature the Uniqueness Condition implies that

only one of them can serve as an argument If the sentence is to b e gram

matical the other must b e interpreted as some sort of adjunct In

either the policeman or the boy must b e a nonargument lo cative

The babywas found bytheboyby the p oliceman

Thus the PP element in rule a derives the PP no des for dative

to phrases agentive by phrases and other more idiosyncratic English

oblique ob jects Schemata similar to the one on the PP will b e much

more common in languages that make extensive use of lexically as opp osed

to structurally induced grammatical relations eg heavily casemarked

noncongurational languages

Wehave illustrated how our algorithm builds the fstructure for two

grammatical sentences However as indicated ab ove fdescriptions which

contradict the Uniqueness Condition are not solvable and our algorithm

must also inform us of this inconsistency Consistency checking is carried

out by b oth the Lo cate and the Merge op erators The Lo cate op erator

for example cannot succeed if a statement sp ecies that a symbol or

semantic form is to b e applied as a function or if a function is to b e

applied to an fstructure or semantic form argument The string is marked

ungrammatical if this happ ens Similarly a merger cannot b e completed

if the twoentities to b e merged are incompatible either b ecause they are

of dierenttyp es a symb ol and an fstructure for example or b ecause

they are otherwise in conict two distinct symb ols or semantic forms or

two fstructures that assign distinct values to the same argument Again

this means that the fdescription is inconsistent

Our algorithm thus pro duces one solution for an arbitrary consistent

fdescription but it is not the only solution If an fstructure F is a

solution for a given fdescription then any fstructure formed from F by

adding values for attributes not already present will also satisfy the f

description Since the fdescription do es not mention those attributes or

values they cannot conict with any of its statements For example we

Ronald M Kaplan and Joan Bresnan

could add the arbitrary pairs xy and zw to the subj fstructure of

to form

spec a

num sg

pred girl

f



x y

z w

Substituting this for the original subj value yields another solution for

This addition pro cedure which denes a partial ordering on

the set of fstructures can b e rep eated indenitely In general if an

fdescription has one solution it has an innite numb er of larger solu

tions

Of course there is something counterintuitive ab out these larger solu

tions The extra features they contain cannot conict with those sp eci

cally required by the fdescription In that sense they are grammatically

irrelevant and should not really count as fstructures that the grammar

assigns to sentences This intuition that weonlycountenance fstructures

with relevant attributes and values can b e formalized in a technical rene

ment to our previous denitions that makes the fstructure of a sentence

awelldened notion

Lo oking at the partial ordering from the opp osite direction an f

description may also have solutions smaller than a given one These

are formed by removing various combinations of its pairs for example

removing the xy zw pairs from pro duces the smaller original so

lution in Some smaller fstructures are to o small to b e solutions of

the fdescription in that they do not contain pairs that the fdescription

requires For example if the spec feature is removed from the

resulting structure will not satisfy equation a Wesaythatanf

structure F is a minimal solution for an fdescription if it meets all of the

fdescriptions requirements and if no smaller fstructure also meets those

requirements

A minimal solution exists for every consistent fdescription By de

nition each has at least one solution Either that one is minimalorthere

is a smaller solution If that one is also not minimal there is another still

smaller solution Since an fstructure has only a nite number of pairs

to b egin with there are only a nite numb er of smaller fstructures This

sequence will therefore stop at a minimal solution after a nite number

of steps

However the minimal solution of an fdescription is not necessarily

unique The fact that fstructures are partially but not totally ordered

means that there can b e two distinct solutions to an fdescription b oth

of which are minimal but neither of which is smaller than the other

AFormal System for Grammatical Representation

This would b e the case for an fdescription that contained the equation

asserting that the sub ject and ob ject have the same p erson if other

equations were not included to sp ecify that common features value

subj pers obj pers

Any fstructure that is a minimal solution for all other equations of the f

description and contains anyvalue at all for b oth the obj and subj person

features will also b e a minimal solution for the larger fdescription that

includes The values first secondorthird for instance would

all satisfy but an fstructure without some p erson value would not b e

a solution An fdescription that do es not have a unique minimal solution

is called indeterminate In eect such an fdescription do es not have

enough indep endent sp ecications for the numberofunknown entities

that it mentions

Wecannowformulate a precise condition on the wellformedness of a

string

Condition on

A string is grammaticalonlyifithasavalid cstructure with

an asso ciated fdescription that is b oth consistent and determi

nate The fstructure assigned to the string is the value in the

fdescriptions unique minimal solution of the variable of the

cstructures ro ot no de

This condition is necessary but not sucient for grammaticality we later

p ostulate additional requirements As presented ab ove our solution al

gorithm decides whether or not the fdescription is consistent and if it is

constructs one solution for it We observe that if no placeholders remain

in that solution it is the unique minimal solution if any attribute or value

is changed or removed the resulting structure is not a solution since it

no longer satises the equation the pro cessing of whichgave rise to that

attribute or value On the other hand if there are residual placeholders

in the fstructure pro duced by the algorithm the fdescription is indeter

minate Those placeholders can b e replaced byanynumber of values to

yield minimal solutions Our algorithm is thus a decision pro cedure for

all the functional conditions on grammaticality sp ecied in

Functional wellformedness

The functional wellformedness conditions of our theory cause strings with

otherwise valid cstructures to b e marked ungrammatical Our functional

comp onentthus acts as a lter on the output of the cstructure comp o

nent but in a sense that is very dierent from the way surface structure ltering has b een used in transformational theory eg Chomsky and

Ronald M Kaplan and Joan Bresnan

Lasnik We do not allow arbitrary predicates to b e applied to the

cstructure output Rather we exp ect that a substantive linguistic the

ory will makeavailable a universal set of grammatical functions and fea

tures and indicate how these may b e assigned to particular lexical items

and particular cstructure congurations The most imp ortantofour

wellformedness conditions the Uniqueness Condition merely ensures

that these assignments for a particular sentence are globally consistent

so that its fstructure exists Other general wellformedness conditions

the Completeness and Coherence Conditions guarantee that grammatical

functions and lexical predicates app ear in mutually compatible fstructure

congurations

Consider the string which is ungrammatical b ecause the numbers

of the nal determiner and noun disagree

A girl handed the babyatoys

The only fdescription dierence b etween this and our previous example

is that the lexical entry for toys pro duces the equation instead of

l

f num pl

A conict b etween the lexical sp ecications for a and toys arises b ecause

their schemata are attached to daughters of the same NP no de Some of

the prop erties of that no des fstructure are sp ecied by the determiners

lexical schemata and some by the nouns According to the Uniqueness

Condition all prop erties attributed to it must b e compatible if that f

structure is to exist In the solution pro cess for f will havethe

tentativevalue shown in when equation is encountered in place

of l The value of the lefthand designator is the symbol sgwhichis

incompatible with the pl value of the righthand designator These two

symb ols cannot b e merged

h i

spec a

f



num sg

The consistency requirement is a general mechanism for enforcing

grammatical compatibilities among lexical items widely separated in the



Our general Uniqueness Condition is also the most crucial of several dierences

between lexicalfunctional grammar and its augmented transition network precursor

ATN setr op erations can arbitrarily mo dify the fstructure values or register con

tents in ATN terminology as they are executed in a lefttoright scan of a rule or

network The register subj can haveonevalue at one p oint in a rule and a completely

dierentvalue at a subsequentpoint This revision of value assignments is not allowed

in LFG Equations at one p oint cannot override equations instantiated elsewhereall

equations must b e simultaneously satised bythevalues in a single fstructure As

wehave seen the prop erties of that fstructure thus do not dep end on the particular

sequence of steps bywhichschemata are instantiated or the fdescription is solved

AFormal System for Grammatical Representation

cstructure The items and features that will enter into an agreementare

determined by b oth lexical and grammatical schemata Number agree

ment for English sub jects and verbs illustrates a compatibility that op

erates over a somewhat wider scop e than agreement for determiners and

nouns It accounts for the unacceptability of

The girls hands the babya toy

The grammar fragment in needs no further elab oration in order to

reject this string The identication on the VP in a indicates that one

fstructure corresp onds to b oth the S and the VP no des This implies that

any constraints imp osed on a subj function by the verb will in fact apply

to the subj of the sentence as a whole the fstructure corresp onding to

the rst NPThus the following lexical entry for hands ensures that it

will not co o ccur with the plural sub ject girls

hands V tense pres

subj num sg

pred hand h subj obj obji

The middle schema whichiscontributed by the present tense morpheme

sp ecies the numb er of the verbs sub ject It is instantiated as a and

this is inconsistent with b whichwould b e derived from the lexical

entry for girls

a f subj num sg

b f num pl

The conict emerges b ecause f is the subj of f andf is equal to f

We rely on violations of the Uniqueness Condition to enforce many

co o ccurrence restrictions b esides those that are normally thoughtofas

agreements For example the restrictions among the elements in an En

glish auxiliary sequence can b e handled in this wayeven though the

matching of features do es not at rst seem to b e involved There is a

natural way of co ding the lexical features of auxiliaries participles and

tensed verbs so that the axhopping phenomena followasaconse

quence of the consistency requirement Auxiliaries can b e treated as main



verbs that takeemb edded VP complements We expand our grammar as

shown in in order to derive the appropriate cstructures



The optional to p ermitted by rule b while necessary for other typ es of VP

complements do es not app ear with most auxiliary heads This restriction could b e

imp osed by an additional schema

Ronald M Kaplan and Joan Bresnan

a VP



V PP

VP NP NP

pcase

vcomp obj obj



b VP to VP



Rule a allows an optional VP following the other VP constituents

Of course auxiliaries exclude all the VP p ossibilities except the vcomp

this is enforced by general completeness and coherence conventions as

describ ed b elow For the moment we fo cus on their ax co o ccurrence

restrictions which are represented byschemata in the lexical entries for

verbs Each nonnite verb will haveaschema indicating that it is an

innitive or a participle of a particular typ e and each auxiliary will have

an equation stipulating the inectional form of its vcomp The lexi

cal entries in are for handing considered as a present participle

as opp osed to a past tense or passive participle form and for is as a

progressive auxiliary

handing V participlepresent

pred hand h subj obj obji

is V a tensepres

b subj num sg

c pred progh vcomp i

d vcomp participle present

e vcomp subj subj

Schema d stipulates that the participle feature of the verb phrase

complementmust have the value present The vcomp is dened in



a as the fstructure of the VP no de and this is identied with the

fstructure of the VP no de bytheschema in b This means that

the participle stipulations for handing and is b oth hold of the same f

structure Hence sentence a is accepted but b is rejected b ecause

has demands of its vcomp anonpresent participle

a A girl is handing the babya toy



A small numb er of additional features are needed to account for the ner details

of auxiliary ordering and for other co o ccurrence restrictions as noted for example by

Akma jian Steele and Wasow



In a more detailed treatment of morphology the schemata for handing would b e

derived systematically by combining the schemata for hand namelythe pred schema

in with ing s schemata the participle sp ecication as the word is formed by suxation

AFormal System for Grammatical Representation

b A girl has handing the babyatoy

Schemata ce deserve sp ecial comment The semantic form for

is sp ecies that the logical formula derived byinterpreting the vcomp

function is the single argument of a predicate for progressiveness Even

though the fstructure for a will include a subj function at the level of

the prog predicate that function do es not serve as an argumentofprog

Instead it is asserted by e to b e equivalenttothe subj at the handing

level This would not otherwise exist b ecause there is no sub ject NP in



the VP expansion The eect is that girl is correctly interpreted as the

rst argument of hand e is an example of a schema for functional

control whichwe will discuss more fully b elow

These illustrations of the ltering eect of the Uniqueness Condition

have glossed over an imp ortant conceptual distinction A schema is of

ten included in a lexical entry or grammatical rule in order to dene the

value of some feature That is instantiations of that schema provide suf

cient grounds for inserting the featurevalue pair into the appropriate

fstructure assuming of course that there is no conict with the value de

ned by other equations However sometimes the purp ose of a schema is

only to constrain a feature whose value is exp ected to b e dened by a sep

arate sp ecication The feature remains valueless when the fdescription

lacks that sp ecication Intuitively the constraint is not satised in that

case and the string is to b e excluded Constraints of this sort thus imp ose

stronger wellformedness requirements than the denitional inconsistency

discussed ab ove

Let us reexamine the restriction that schema d imp oses on the

participle of the vcomp of is Wehave seen howthisschema conspires

with the lexical entries for handing and has to account for the facts

in Intuitively it seems that the same presentparticiple restriction

ought to account for the unacceptability of

A girl is hands the babya toy

This string will not b e rejected however if hands has the lexical entry

in and d is interpreted as a dening schema The participle

feature has no natural value for the nite verb hands and therefore

has no sp ecication at all for this feature This p ermits d to dene

the value present for that feature without risk of inconsistency and the

nal fstructure corresp onding to the hands VP will actually contain a

participlepresent pair Wehave concluded that hands is a present

participle just b ecause is would likeittobethatway If on the other

hand weinterpret d as a constraining schema weareprevented from

making this implausible inference and the string is appropriately rejected

The constraining interpretation is clearly preferable

Ronald M Kaplan and Joan Bresnan

Intro ducing a sp ecial interpretation for fdescription statements is not

strictly necessary to account for these facts We could allowonlythe

dening interpretation of equations and still obtain the right pattern of

results by means of additional feature sp ecications For example we

could insist that there b e a participle feature for every verbal form

even nite forms that are notionally not participles at all The value

for tensed forms mightbe none and this would b e distinct from and

thus conict with present and all other real values The lexical entry

for hands would b ecome and would b e ruled out even with a

dening interpretation for d

hands V participlenone

tense pres

subj num sg

pred hand h subj obj obji

There are two ob jections to the presence of such otherwise unmotivated

features they make the formal system more cumb ersome for linguists

to work with and less plausible as a characterization of the linguistic

generalizations that children acquire Lexical redundancy rules in the

form of marking conventions provide a partial answer to b oth ob jections

A redundancy rule for example could assign sp ecial novalue schemata

to every lexical entry that is not already marked for certain syntactic

features Then the none schema would not app ear in the entry for hands

but would still b e available for consistency checking

Although we utilize lexical redundancy rules to express a varietyof

other generalizations wehavechosen an explicit notational device to

highlight the conceptual distinction b etween denitions and constraints

The ordinary equalsign that has app eared in all previous examples in

dicates that a schema is denitional while an equalsign with the letter

c as a subscript indicates that a schema expresses a constraint With

this notation the lexical entry for is can b e formulated more prop erly as

is V tense pres

subj num sg

pred progh vcomp i

vcomp participle present

c

vcomp subj subj

The notational distinction is preserved when the schemata are instanti

ated so that the statements in an fdescription are also divided into two

classes Dening equations are interpreted by our solution algorithm in

the manner outlined ab oveandthus provide evidence for actually con

AFormal System for Grammatical Representation

structing satisfactory structures Constraining equations are simply not

given to the solution algorithm They are reserved until all dening equa

tions have b een pro cessed and all variables have b een assigned nal f

structure values At that p oint the constraining equations are evaluated

and the string is accepted only if they all turn out to b e true This

dierence in interpretation accurately reects the conceptual distinction

represented by the twotyp es of equations It also gives the right result

for string since the revised vcomp requirement in will b e false

for the fstructure constructed from its dening equations that string will

b e rejected without adding the sp ecial none value to hands

Whether or not a particular co o ccurrence restriction should b e en

forced by consistency among dening equations or the later evaluation of

constraining equations dep ends on the meaning that is most naturally as

signed to the absence of a feature sp ecication A constraining equation is

appropriate if as in the examples ab ove an unsp ecied value is intended

to b e in conict with all of a features real values On the other hand

avalue sp ecication may b e omitted for some features as an indication

of vagueness and the restriction is then naturally stated in terms of a

dening equation The case features of English nouns seem to fall into

this second category only pronouns have explicit nominativeaccusative

markings all other nouns are intuitively unmarked yet may app ear in

either sub ject or ob ject p ositions The new sub jectNP schema in

denes the sub jects case to b e nom Thenom value will thus b e included

in the fstructure for anysentence with a nominative pronoun or nonpro

noun sub ject Only strings with accusative pronouns in sub ject p osition

will have inconsistent fdescriptions and b e excluded

S NP VP

subj

casenom tense

Dening schemata always assert particular values for features and thus

always take the form of equations For constraints two nonequational

sp ecication formats also make sense The new tense schema in

for example is just a designator not emb edded in an equality An instan

tiation of such a constraint is satised just in case the expression has some

value in the nal fstructure these are called existential constraints The

tense schema thus expresses the requirement that Sclauses must have

tensed verbs and rules out strings like



A marking convention account of the deningconstraining distinction would have

to provide an alternative lexical entry for eachvalue that the vaguely sp ecied feature

could assume A vague sp ecication would thus b e treated as an ambiguity contrary

to intuition

Ronald M Kaplan and Joan Bresnan

A girl handing the babya toy

As with equational constraints it is p ossible to achieve the eect of an

existential schema byintro ducing ad ho c feature values eg one that dis

criminates tensed forms from all other verbals but this sp ecial constraint

format more directly represents the intuitivecontent of the requirement

Finally constraints may also b e formed by adding a negation op erator

to an equational or existential constraint The sentence is then acceptable

only if the constraint without the negation turns out to b e false Such

constraints fall quite naturally within our formal framework and may

simplify a variety of grammatical descriptions The negative existential

constraint in for example is one way of stipulating that the VP after



the particle to in a VP is untensed



VP VP

to

tense

According to these wellformedness conditions strings are rejected

when an fstructure cannot b e found that simultaneously satises all the

explicit dening and constraining statements in the fdescription LFG

also includes implicit conventions whose purp ose is to make sure that f

structures contain mutually compatible combinations of lexical predicates

and grammatical functions These conventions are dened in terms of a

prop er subset of all the features and functions that may b e represented

in an fstructure That subset consists of all functions whose values can

serve as arguments to semantic predicates such as sub ject and various

ob jects and complements We refer to these as the governable grammati

cal functions Agiven lexical entry mentions only a few of the governable

functions and wesay that that entry governs the ones it mentions Our

conditions of functional compatibility simply require that an fstructure

contain all of the governable functions that the lexical entry of its predi

cate actually governs and that it contain no other governable functions

This compatibility requirement gives a natural accountformanytyp es

of illformedness The English cstructure grammar for example must

p ermit verbs not followed by NP arguments so that ordinary intransitive

sentences can b e generated However the intransitiveVPrulecanthenbe

applied with a verb that normally requires ob jects to yield a cstructure

and fstructure for illformed strings suchas

The girl handed



In the more rened theory of lexical representation presented in Bresnan bc

the relevant functions are those that app ear in the functionassignment lists of lexical

predicates The twocharacterizations are essentially equivalent



For a fuller discussion of government in lexicalfunctional theory see Bresnan a

AFormal System for Grammatical Representation

The unacceptability of this string follows from the fact that the lexical

entry for handed governs the grammatical functions obj and obj or

to objwhich do not app ear in its fstructure On the other hand there

is nothing to stop the cstructure rule that generates ob jects from applying

in strings such as where the verb is intransitive

The girl fell the apple the dog

This string exhibits the opp osite kind of incompatibility the governable

functions obj and obj do app ear in its fstructure but are not governed

by the intransitiveverb fel l

Stated in more technical terms string is ungrammatical b ecause

its fstructure is not complete while fails b ecause its fstructure is not

coherent These prop erties of fstructures are precisely dened as follows

Denitions of Completeness and Coherence

a An fstructure is local ly complete if and only if it contains

all the governable grammatical functions that its predicate

governs An fstructure is complete if and only if it and all

its subsidiary fstructures are lo cally complete

b An fstructure is local ly coherent if and only if all the gov

ernable grammatical functions that it contains are governed

by a lo cal predicate An fstructure is coherent if and only

if it and all its subsidiary fstructures are lo cally coherent

Functional compatibilitythenenters into our notion of grammaticalityby

way of the following obvious condition

Grammaticality Condition

A string is grammatical only if it is assigned a complete and

coherent fstructure

Since coherence and completeness are dened in terms of lo cal cong

urations of functions there are straightforward ways of formally verifying

that these conditions are satised For example a set of constraints that

enco de these requirements can b e added to all fdescriptions by a simple

redundancy convention Weidentify a set of governable designators cor

resp onding to the governable grammatical functions and a set of governed

designators corresp onding to the functions governed by a particular lexi

cal entry The set of governable designators for a language is simply a list

of every designator that app ears as an argumentinasemantic form for at

least one entry in the lexicon Thus the set of governable designators for

English includes subj obj by obj vcomp etc The

set of governed designators for a particular lexical entry then contains

only those memb ers of the governable list that app ear in that entryIf

existential constraints for all the governed designators are instantiated

Ronald M Kaplan and Joan Bresnan

along with the other schemata in the lexical entry then the fstructure in

which the lexical predicate app ears will b e lo cally complete if and only if

it satises all those constraints The fstructure will b e lo cally coherent

if and only if negative existential constraints for all the governable but

ungoverned designators are also satised Under this interpretation ex

ample ab ove is incomplete b ecause its fstructure do es not satisfy the

constraining schema obj and is incoherentbecause objis

not satised

It is imp ortant to observe that a designator is considered to b e gov

erned byanentry if it app ears anywhere in the entry not solely in the

semantic form argumentlist though to b e governable it must app ear

as an argumentin some lexical entry In particular the designator may

app ear only in a functional control schema or only in a schema dening or

constraining some feature Thus the lexical entry for is in ab oveis

considered to govern the designator subj b ecause of its app earance in

b oth the numb erdening schema and the control schema for the vcomp s

subj subj however is not assigned to an argument in the semantic

form progh vcomp i

A grammatical function is also considered to b e governed byanentry

even when its value is constrained to b e a semantically emptysyntactic

formative Among these formatives are the expletives there and it plus

the comp onents of various idiomatic expressions eg the idiomatic sense

of tabs in the expression keep tabs on The lexicon marks such items

as b eing in ordinary syntactic categories pronoun or noun for example

but their schemata sp ecify a symbol value for a form attribute instead

of a semantic form value for a pred attribute

tabs N formtabs

num pl

A tabs NP may app ear in any cstructure NP p osition and will b e assigned

the asso ciated grammatical function The Coherence Condition ensures

that that function is governed by the lexical head of the fstructure

is ruled out for the same reason that is illformed

The girl fell tabs

If the fstructure is coherent then its lexical head makes some sp ecication

ab out the tabs function For the acceptable sentence the lexical entry

for the idiomatic kept has a constraining schema for the necessary form

value as illustrated in

The girl kept tabs on the baby

AFormal System for Grammatical Representation

kept V tense past

pred observe h subj on obji

obj form tabs

c

This constraining schema precludes the observe reading of kept with the

nonidiomatic obj in a and also rejects objs with the wrong formative

feature b

a The girl kept the dog on a baby

b The girl kept there on a baby

The illformedness of however is not predicted from the func

tional compatibility conditions wehave presented

The girl handed there tabs

In this example a governed function serving as an argument to the pred

icate hand has a semantically emptyvalue A separate condition of

semantic completeness could easily b e added to our grammaticality re

quirements but such a restriction would b e imp osed indep endently bya

semantic translation pro cedure A separate syntactic stipulation is there

fore unnecessary

In this section wehave describ ed several mechanisms for rejecting as

functionally deviant strings that have otherwise valid cstructure deriva

tions The Uniqueness Condition is the most basic wellformedness re

quirement since an fstructure do es not even exist if it is not satised If

an fstructure do es exist it must satisfy any constraining schemata and

the Completeness and Coherence Conditions must hold The combined

eect of these conventions is to imp ose very strong restrictions among the

comp onents of a sentences fstructure and cstructure so that seman

tic forms and grammatical formatives can app ear only in the appropri

ate functional and constituentenvironments Because of these functional

wellformedness conditions there is no need for a separate notion of c

structure sub categorization to guarantee that lexical co o ccurrence restric

tions are satised Indeed Grimshaw and Maling suggest

that an account of lexical co o ccurrences based on functional compatibility

is sup erior to one based on sub categorization

These mechanisms ensure that syntactic compatibility holds b etween

a predicate and its arguments A sentence mayhave other elements how

ever that are syntactically related to the predicate but are not syntacti

cally restricted by it These are the adverbial and prep ositional mo diers

that serveasadjuncts of a predicate Although adjuncts and predicates

must b e asso ciated in an fstructure so that the correct semantic relation

ship can b e determined adjuncts are not within range of a predicates

syntactic schemata A predicate imp oses neither category nor feature

Ronald M Kaplan and Joan Bresnan

restrictions on its adjuncts semantic appropriateness b eing the only re

quirement that must b e satised As the temp oral adjuncts in sentence

illustrate adjuncts do not even ob ey the Uniqueness Condition

The girl handed the babyatoyonTuesday in the morning

Since adjuncts do not serve as arguments to lexical predicates they are

not governable functions and are thus also immune to the Completeness

and Coherence Conditions

Given the formal devices wehave so far presented there is no f

structure representation of adjuncts that naturally accounts for these

prop erties If an individual adjunct is assigned as the value of an at

tribute eg temp loc or simply adjunct the Uniqueness Condition

is immediately applicable and syntactic co o ccurrence restrictions can in

principle b e stated However the shared prop erties of adjuncts do follow

quite naturally from a simple extension to the notion of what a p ossible

value is Besides the individual fstructure values for the basic grammati

cal relations we allow the value of an attribute to b e a set of fstructures

Values of this typ e are sp ecied by a new kind of schema in whichthe

memb ership symbol app ears instead of a dening or constraining equal

sign

The memb ership schema adjuncts in the VP rule for

example indicates that the value of adjuncts is a set containing the

PPs fstructure as one of its elements

VP V NP NP PP

obj obj adjuncts

The p ermits anynumb er of adjuncts to b e generated and the

metavariable will b e instantiated dierently for each one The fdescription

for sentence will thus havetwomemb ership statements one for the

on Tuesday PP and one for in the morning These statements will b e

true only of an fstructure in which adjuncts has a set value containing

one element that satises all other statements asso ciated with on Tuesday

and another element satisfying the other statements of in the morning

The outline of such an fstructure is shown in

AFormal System for Grammatical Representation

spec a

num sg

subj

pred girl

tense past

pred hand h subj obj obji

spec the

num sg

obj

pred baby

spec a

num sg

obj

pred toy

adjuncts f on Tuesday in the morning g

The braces in this representation surround the elements of the set value

they are distinct from the braces in cstructure rules that indicate alter

native expansions Wehave elided the adjuncts internal functions since

they are not immediately relevant to the issue at hand and are the topic

of currentsyntactic and semantic research eg Neidle Halvorsen

The p eculiar prop erties of adjuncts nowfollow from the fact that they

are treated syntactically as elements of sets Memb ership statements

dene adjuncts to b e elements of a predicates adjunct p o ol but there

is no requirementofmutual syntactic compatibility among the various

elements Hence the Uniqueness Condition do es not apply Further

since there is no notation for subsequently referring to particular memb ers

of that set there is no way that adjuncts can b e restricted by lexical

schemata asso ciated with the predicate Adjuncts are susceptible only

to conditions that can b e stated on the rule elements that generate them

Their category can b e sp ecied and feature requirements can b e imp osed

byschemata involving the metavariable Since reference to the adjunct

via is not p ossible from other places in the string our formal system

makes adjuncts naturally contextfree

Although the PP in app ears in the same p osition as the oblique

ob ject PP category in our previous VP rule the schemata on the twoPP

rule elements are quite dierent and apply to alternative lexical entries

of the prep osition The oblique ob ject requires the casemarking lexical



Unless of course the element is also the nonset value of another attribute The

point is that the element is inaccessible in its role as adjunct An interesting conse

quence of this representation is that no co o ccurrence restrictions b etween temp oral

adverbs and tense can b e stated in the syntax a conclusion justied indep endently by

Smith



Conjoined elements are similar to adjuncts in some of these resp ects and mightalso

b e represented in an fstructure as sets

Ronald M Kaplan and Joan Bresnan

entry with the pcase feature dened while semantic translation of the

adjunct requires the predicate alternative of the prep osition Adjuncts

and oblique ob jects can b oth app ear in the same sentence and in any

order as illustrated by ab and sometimes a PP maybeinterpreted

ambiguously as either an adjunct or an oblique ob ject as in c

a The babywas handed the toyatve oclo ckby the girl

b The babywas handed the toyby the girl at ve oclo ck

c The babywas handed the toyby the girl by the p oliceman

To account for these facts the adjunct p ossibilitymustbeaddedasan

alternative to the oblique ob ject PP in our previous VP rule a The

star op erator outside the braces in means that the choice b etween

the two PPs may b e rep eated arbitrarily

VP



PP

pcase



V

NP NP VP

PP

obj obj vcomp

adjuncts

An equivalent but more compact formulation of this rule is given in

Wehave factored the common elements of the two PP alternatives moving

the braces so that they enclose just the alternativeschemata

VP



V PP

NP NP VP

pcase

obj obj vcomp

adjuncts

A simple extension to our solution algorithm p ermits the correct in

terpretation of memb ership statements We use a new op erator Include

for memb ership statementsjustaswe use Merge for equalities If d

and d are designators a statement of the form d d is pro cessed

by p erforming IncludeLo cated Lo cated As formally dened in the

App endix the Include op erator makes the value lo cated for the rst desig

nator b e an element of the set value lo cated for the second designator the

fdescription is marked inconsistent if that second value is known not to

b e a set With this extension our algorithm b ecomes a decision pro cedure

for fdescriptions that contain b oth memb ership and equality statements



There is sometimes a preferred ordering of adjuncts and oblique ob jects Grammat

ical descriptions might not b e the prop er account of these biases they mightresult

from indep endent factors op erating in the psychological p erception and pro duction

pro cesses See Ford Bresnan and Kaplan for further discussion

AFormal System for Grammatical Representation

Levels of representation

Wehavenowcovered almost all the ma jor structures and mechanisms

of lexicalfunctional grammar except for the b ounded tree relations that

govern longdistance grammatical dep endencies We p ostp one that dis

cussion for still a few more pages in order to rst review and reinforce

some earlier claims

We said at the outset that constituent structures and functional struc

tures are formally quite dierent and the descriptions of the preceding

pages have amplied that p oint considerablyHowever the mechanisms

of our formal systemthe immediate domination metavariables and the

various grammatical and lexical schematapresupp ose and also help to

establish a very close systematic connection b etween the two levels of

representation Our claim of formal distinctness would of course b e mean

ingless if this close connection turned out to b e an isomorphismsoitis

worth describing and motivating some ways in which cstructures and f

structures for English diverge Weshow that individual cstructure no des

are not isomorphic to subsidiary fstructures for particular sentences and

more generally that there is no simple relationship b etween no de cong

urations and grammatical functions

We observe rst that our instantiation pro cedure denes only a par

tial corresp ondence b etween cstructure no des and subsidiary fstructures

There are b oth cstructure no des with no corresp onding fstructures and

also fstructures that do not corresp ond to cstructure no des The former

situation is illustrated in our previous examples byevery cstructure no de

which is not assigned a variable and therefore has no fstructure The

English imp erative construction gives a simple illustration of the latter

case the subsidiary fstructure representing you as the understo o d

sub ject is not asso ciated with a cstructure no de Plausible c and f

structures for the imp erativesentence a would b e generated bythe

alternative expansion for S in b assuming that the lexical entry for

hand has a valued infinitive feature

a Hand the babya toy

b S VP

inf

c

subj pred you

With this rule the cstructure contains no NP dominated bySyet the



A more realistic example would sp ecify an imp erative mood marker and p erhaps other features

Ronald M Kaplan and Joan Bresnan

fstructure of the S no de has as its subj another fulledged fstructure

dened completely by grammatical schemata

pred you

subj

inf

pred hand h subj obj obji

spec the

num sg

obj

pred baby

spec a

num sg

obj

pred toy

A standard provides a dummyNPasadeep

structure sub ject so that the correct semantic interpretation can b e con

structed and the necessary co o ccurrence restrictions enforced Our func

tional sub ject is sucient for these purp oses the dummyNPiswithout

surface justication and therefore do es not app ear in the cstructure

Second when no des and subsidiary fstructures do corresp ond the

corresp ondence is not necessarily onetoone An identication schema

for example usually indicates that two distinct no des are mapp ed onto

a single fstructure In a single fstructure is assigned to the

variables for b oth the S and VP no des in the cstructure given in

in accordance with the identication equation b The two distinct

no des exist in to capture certain generalizations ab out phrase struc

ture co o ccurrence s and phonological patterns The identication has the

eect of promoting the functional information asso ciated with the VP

so that it is at the same hierarchical level as the subj This brings the

subj within range of the pred semantic form simplifying the statement

of the Completeness and Coherence Conditions and allowing a uniform

treatment of sub jects and ob jects As noted ab ove this kind of promotion

also p ermits lexical sp ecication of certain contextual restrictions such

as sub jectverb numb er agreements

Let us now consider the relationship b etween congurations of c

structure no des and grammatical functions The imp erative example

shows that a single functional role can b e lled from distinct no de con

gurations While it is true for English that an Sdominated NP always

yields a subj function a subj can come from other sources as well The

grammatical schema on the VP for the imp erative actually denes the

subjs semantic form For a large class of other examples the understo o d

sub ject that is not from an SNP conguration is supplied through a

schema of functional control Control schemata which identify grammat

AFormal System for Grammatical Representation

ical relations at two dierentlevels in the fstructure hierarchyoera

natural account for socalled equi and raising phenomena

Sentence contains the equityp e verb persuaded Theintuitive in

terpretation of the baby NP in this sentence is as an argument of b oth per

suade and go This interpretation will b e assigned if persuaded has the

lexical entry given our previous VP rule and the new schemata



in for the VP s optional to

The girl p ersuaded the babytogo

persuaded V tense past

vcomp to

c

vcomp subj obj

pred p ersuade h subj obj vcomp i



VP VP

to

A

to

inf

c

Our rules generate a cstructure in which persuaded is followed byanNP

 

and a VP where the VP is expanded as a tocomplement This is shown

in

S

NP VP



Det N V NP VP

Det N V

The girl p ersuaded the baby to go

The fstructure for the baby NP b ecomes the obj of persuaded and the



VP provides the vcomp The control schema the second to last one in

identies the obj fstructure as also b eing the subj of the vcomp

That fstructure thus app ears in two places in the functional hierarchy



The term grammatical control is sometimes used as a synonym for functional control

This kind of identication is distinct from anaphoric control which links pronouns to

their antecedents and constituent control which represents longdistance dep enden

cies Constituentcontrol is discussed in Section For discussions of functional and

anaphoric control see Andrews b Bresnan a Neidle

Ronald M Kaplan and Joan Bresnan

spec a

num sg

subj

pred girl

tense past

pred p ersuade h subj obj vcompi

spec the

num sg

obj

pred baby

spec the

num sg

subj

pred baby

vcomp

inf

to

pred go h subji

The complement in this fstructure has essentially the same grammatical

relations that would b e assigned to the that complementsentence

even though the cstructure for the that complement is quite dierent

The girl p ersuaded the baby that the baby should go

The contrast b etween oblique ob jects and adjuncts shows that similar

cstructure congurationsa VP dominating a PPcan b e mapp ed into

distinct grammatical functions A comparison of the equi verbs persuaded

and promised provides another illustration of the same p oint Sentence

is the result of substituting promised for persuaded in sentence

The girl promised the babytogo

This substitution do es not change the cstructure congurations but for

the girl not the baby is understo o d as an argument of b oth the

matrix and complement predicates This fact is easily accounted for if the

control schema in the lexical entry for promised identies the complement

subj with the matrix subj instead of the matrix obj

promised V tense past

pred promise h subj obj vcomp i

vcomp to

c

vcomp subj subj

With this lexical entry the fstructure for correctly denes girl as

the argumentofgo

AFormal System for Grammatical Representation

spec a

num sg

subj

pred girl

tense past

pred promise h subj obj vcompi

spec the

num sg

obj

pred baby

spec a

num sg

subj

pred girl

vcomp

inf

to

pred go h subji

The fstructure dierence for the twotyp es of equi verbs thus follows from

the diering functional control schemata in their lexical entries not from

any cstructure dierence

From a formal p oint of view there is no restriction on which grammat

ical relations in the matrix and complementmay b e identied byaschema

for functional control Very strong limitations however are imp osed by

the substantive linguistic theory that is based on our lexicalfunctional for

malism As discussed by Bresnan a the functional control schemata

of human languages universally identify the subj of a complementwith

the subj objorobj of the matrix Control schemata for verb phrase

complements dierent from those ab ove for promised and persuaded may

not app ear in the grammar or lexicon of anyhuman language This

universal stipulation explains the familiar contrast in the passivization

b ehavior of persuade and promise

a The babywas p ersuaded to go by the girl

b The babywas promised to go by the girl

Bresnan c argues that the systematic relationship b etween actives

and their corresp onding passives can b e expressed by a universal lexical

rule In simple terms this rule asserts that for any language if an active

lexical entry for a stem mentions the subj and obj functions then there

is a passive lexical entry based on the same stem in which subj is replaced

by an obliqueob ject function and obj is replaced by subjFor English



The topic function in English relative clauses and in tough movement constructions

may also b e functionally controlled as describ ed in Section

Ronald M Kaplan and Joan Bresnan

the passive oblique ob ject is marked by the prep osition by so the English

instance of this universal rule is as follows

subj by obj

obj subj

participlepassive

This rule indicates the replacements to b e p erformed and also sp ec

ies that a participle schema app ears in passiveentries in addition to

other schemata derived from the stem Accordingly the passive lexical

entries based on the stems underlying the past tense forms persuaded and

promised are as follows

a persuaded V participlepassive

vcomp to

c

vcomp subj subj

pred p ersuade h by obj subj vcomp i

b promised V participle passive

vcomp to

c

vcomp subj by obj

pred promise h by obj subj vcomp i

Notice that subjand obj the lefthand designators in the lexical

rule are replaced inside semantic forms as well as in schemata The con

trol schema in a conforms to the universal restriction on functional

control but the one in b do es not Since b is not a p ossible

lexical entry promise may not b e passivized when it takes a verb phrase

complement

Wehave argued that the to complementand that complementof per

suaded have essentially the same internal functions The sentences

and in which those complements are emb edded are not exact para

phrases however The that complementsentence allows a reading in

whichtwo separate babies are b eing discussed while for sentence

there is only one baby who is an argumentofboth persuade and go This

dierence in interpretation is more obvious when quantiers are involved

a and b are roughly synonymous and neither is equivalentto

c

a The girl p ersuaded every babytogo

b The girl p ersuaded every baby that he should go

c The girl p ersuaded every babythatevery other baby should

go



See Bresnan c for a discussion of the morphologicalchanges that go along

with these functional replacements

AFormal System for Grammatical Representation

Since semantic translation is dened on functional structure fstructures

must mark the dierence b etween o ccurrences of similar subsidiary f

structures where semantic coreferentiality isimpliedasinthe to

complement and o ccurrences where the similarity is only accidental

The necessary fstructure distinction follows from a simple formal

prop erty of semantic forms that wenowintro duce The semantic form

representations that app ear in schemata are treated as meta seman

tic forms templates for an innite numb er of distinct actual semantic

forms Just as an actual variable is substituted for a metavariable bythe

instantiation pro cedure so a metaform is replaced by a unique actual

form identied by attaching an index to the predicateargument sp eci

cation A given schema say a might b e instantiated as b at

one no de in the tree and c at another

a predbaby

b f pred baby

c f pred baby

Fdescription statements and fstructures thus contain recognizably dis

tinct instances of the semantic forms in the grammar and lexicon Each

indexed actual form enters into predicateargument relations as indicated

by the metaform but the dierent instances are not considered identical

for the purp oses of semantic translation or functional uniqueness

Returning to the two complements of persuaded weobserve that only

one schema with baby is involved in the derivation of the to complement

while twosuchschemata are instantiated for the that complement The

indices of the two o ccurrences of baby are therefore the same in the

indexed version of the tocomplements fstructure but dierentin

the fstructure for the that complement



Fstructure ignores such details as the tense and mo o d of the that complement

Ronald M Kaplan and Joan Bresnan

spec a

num sg

subj

pred girl

tense past

pred p ersuade h subj obj vcompi



spec the

num sg

obj

pred baby



spec the

num sg

subj

pred baby



vcomp

inf

to

pred go h subji



spec a

num sg

subj

pred girl

tense past

pred p ersuade h subj obj vcompi



spec the

num sg

obj

pred baby



spec the

num sg

subj

pred baby



scomp

inf

to

pred go h subji



The semantic contrast b etween the two complementtyp es is marked in

these fstructures by the diering patterns of semantic form indexing

It is technically correct to include indices with all semantic forms in

fdescriptions and fstructures but the nonidentityoftwo forms with dis

similar predicateargument sp ecications is clear even without explicit

indexing We adopt the following convention to simplify our representa

tions twosemantic form o ccurrences are assumed to b e distinct unless

they have the same predicateargument sp ecication and the same index

With this convention only the indices on the baby semantic forms are

necessary in and none of the indices are needed in Control

equations imply that entire substructures to which coindexed semantic

forms b elong will app ear redundantly in several p ositions in an enclosing

AFormal System for Grammatical Representation

fstructure This suggests a stronger abbreviatory convention which also

highlights the cases of fstructure identityTheinternal prop erties of a

multiplyapp earing subsidiary fstructure are displayed at only one place

in an enclosing fstructure The fact that it is also the value of other

attributes is then indicated by drawing lines from the lo cation of those

other attributes to the fully expanded value

spec a

num sg

subj

pred girl

tense past

pred p ersuade h subj obj vcompi

spec the

num sg

obj

pred baby

subj

inf

vcomp

to

pred go h subji

This graphical connection makes it clear even without explicit indices on

baby that the ob ject fstructure serves in several functional roles

While a semantic form instance o ccurring in several p ositions indicates

semantic coreferentiality dierent instances are seen as b oth semantically

and functionally distinct This means that any attempt to equate dierent

instances will violate the Uniqueness Condition even if they havethe

same predicateargument sp ecication This is an imp ortant consequence

of the semantic form instantiation pro cedure For example it rules out

an analysis of string in which b oth prep ositional phrases are merged

together as the by objeven though the PP fstructures agree in all other

features

The babywas given a toyby the girl by the girl

As another example the distinctness of semantic form instances p ermits

a natural description of English sub jectauxiliary inversion As shown in

the auxiliary can o ccur either b efore or after the sub ject but it

must app ear in one and not b oth of those p ositions

a A girl is handing the babya toy

b Is a girl handing the babya toy

c A girl the babyatoy

d Is a girl is handing the babyatoy

In transformational theories facts of this sort are typically accounted for

Ronald M Kaplan and Joan Bresnan

by a rule that moves a single basegenerated item from one p osition to

another Since no transformational apparatus is included in LFG we

must allow the cstructure grammar to optionally generate the auxiliary

in b oth p ositions for example by means of the following mo died S and

VP rules

a S NP VP

V

subj

aux

c

casenom tense

b VP



PP

V NP NP VP

pcase

vcomp obj obj

adjuncts

These rules provide cstructure derivations for all the strings in

However c is incoherent b ecause there are no pred s for the NP ar

guments and it also fails to satisfy the tense existential constraint The

fdescription for d is inconsistent b ecause the separately instantiated

semantic forms for is are b oth assigned as its pred The aux constraint

in a p ermits only verbs marked with the aux feature to b e fronted

In Section we treated the auxiliary is as a main verb taking an

emb edded VP complement with a control schema identifying the matrix

and emb edded sub jects see Is is unlike persuaded and promised in

that the fstructure serving two functional roles is not an argumentoftwo

predicates subj do es not app ear in the semantic form progh vcompi

The wider class of raising verbs diers from equi verbs in just this resp ect

Thus the lexical entry for persuade maps the baby fstructure in into

argument p ositions of b oth persuade and goTheobj of the raising verb

expected however is an argument only of the complements predicate as

stipulated in the lexical entry

expected V tense past

pred exp ect h subj vcomp i

vcomp to

c

vcomp subj obj

Except for the semantic form change the fstructure for sentence a

is identical to This minor change is sucient to account for the

wellknown dierences in the b ehavior of these two classes of verbs as

illustrated by b and c see Bresnan c for a fuller discussion

a The girl exp ected the babytogo

b The girl exp ected there to b e an earthquake

c The girl p ersuaded there to b e an earthquake

AFormal System for Grammatical Representation

The dierence b etween the raising and equi semantic forms shows that

the set of grammatical relations in an fstructure cannot b e identied with

argument p ositions in a semantic translation This is evidence for our

early claim that the functional level is also distinct from the semantic level

of representation A stronger justication for this distinction comes from

considerations of quantier scop e ambiguities The sentence a has a

single fstructure yet it has two semantic translations or interpretations

corresp onding to the readings b and c

a Every man voted in an election

b There was an election suchthatevery man voted in it

c For every man there was an election suchthathevoted in it

The election quantier has narrow scop e in b and wide scop e in

c This ambiguity is not represented at the level of syntactic func

tions since no syntactic generalizations dep end on it Instead the alter

native readings are generated by the pro cedure that pro duces semantic

translations or interpretations for fstructures

The distinctions b etween cstructure fstructure and semantic struc

ture are supp orted by another scop erelated phenomenon Sentence

a also has two readings as indicated in b and c

a Everyb o dy has wisely selected their successors

b Wiselyeveryb o dy has selected their successors ie it is wise

of everyb o dy to have selected their successors

c Everyb o dy selected their successors in a wise manner

The adverb has sentence scop e in b and socalled VP scop e in c

The single fstructure for this sentence not only fails to representthe

ambiguity but also fails even to preserve a VP unit to which the narrow

scop e might b e attached The fstructure is attened to facilitate the

statement of certain syntactic co o ccurrence restrictions to simplify the

Completeness and Coherence Conditions as mentioned ab ove and also to

p ermit simple sp ecications of control relations Indep endentmotivation

for our prop osal that the scop e of semantic op erators is not tied to a VP c

structure no de or an fstructure corresp onding to it comes from Mo dern

Irish a VSO language that nonetheless exhibits this kind of ambiguity

McCloskey

Wehaveshown that functional structure in LFG is an autonomous

level of linguistic description Functional structure contains a mixture of

syntactically and semantically motivated information but it is distinct



This line of argumentation was suggested byPKHalvorsen p ersonal communica

tion Halvorsen gives a detailed description of a translation pro cedure

with multiple outputs

Ronald M Kaplan and Joan Bresnan

from b oth constituent structure and semantic representation Of course

wehave not demonstrated the necessityofsuchanintermediate level

for mapping b etween surface sequences and predicateargument relations

Indeed Gazdar argues that a much more direct mapping is p ossi

ble In Gazdars approach the semantic connection b etween a functional

controller and controllee for example is established bysemantic trans

lation rules dened directly on cstructure congurations The semantic

representation for the emb edded complement includes a logical variable

that is b ound to the controller in the semantic representation of the ma

trix It seems however that there are languageparticular and universal

generalizations that have no natural expression without an fstructure

likeintermediate level For example in addition to semantic connections

functional control linkages seem to transmit purely syntactic elements

expletives like it and there syntactic casemarking features Andrews

ab and semantically emptyidiomchunks Without an fstructure

level either a separate feature propagation mechanism must b e intro duced

to handle this kind of dep endency in the cstructure or otherwise unmo

tivated semantic entities or typ es must b e intro duced so that semantic

ltering mechanisms can b e applied to the syntactic elements As an

other example Levin has argued that a natural account of sluicing

constructions requires the mixture of information found in fstructures

And nally Bresnan ac and Mohanan ab observe that uni

versal characterizations of lexical rules and rules of anaphora are stated

more naturally in terms of grammatical functions than in terms of phrase

structure congurations or prop erties of semantic representations Fur

ther investigation should provide even stronger justication for functional

structure as an essential and indep endentlevel of linguistic description

Longdistance dep endencies

Wenow turn to the formal mechanisms for characterizing the long

distance grammatical dep endencies such as those that arise in English

questions and relatives As is well known in these constructions an ele

ment at the front of a clause is understo o d as lling a particular grammat

ical role within the clause Exactly which grammatical function it serves

is determined primarily by the arrangement of cstructure no des inside

the clause The who b efore the indirect question clause is understo o d as

the sub ject of the question in a but as the ob ject in b

a The girl wondered who saw the baby

b The girl wondered who the babysaw

saw c The girl wondered who

d The girl wondered who the babysaw the toy

AFormal System for Grammatical Representation

In b oth cases who is assigned the clauseinternal function appropriate

to the cstructure p osition marked by the blank a p osition where an

exp ected element is missing Examples cd indicate that there must

b e one and only one missing element Sentence in whichthewho is

understo o d as the ob ject of a clause emb edded inside the question shows

the longdistance nature of this kind of dep endency

The girl wondered who John b elieved that Mary claimed that the

babysaw

Sentence however demonstrates the wellknown fact that the re

gions of the cstructure that such dep endencies maycover are limited in

some way although not simply by distance

The girl wondered who John b elieved that Mary asked who

saw

The dep endencies illustrated in these sentences are examples of what

we call constituent control As with functional control constituentcontrol

establishes a syntactic identitybetween elements that would otherwise b e

distinct In the case of functional control the linkage is b etween the

entities lling particular functional roles and as describ ed in Section

is determined by lexical schemata that are very restricted substantively

Functional control schemata identify particular functions suchassubj

or obj at one fstructure level with the subj of a particular complement

Linkages over apparently longer distances as in are decomp osed

into several strictly lo cal identications eachofwhich links a higher func

tion to the subj one level down

John p ersuaded the girl to b e convinced to go

The fdescription for this example contains statements that equate the

obj of persuaded with the subj of be thesubj of be with the subj of

convinced and nally the subj of convinced with the subj of go The fact

that girl is understo o d as the sub ject of go then follows from the transi

tivity of the equality relation However it is characteristic of functional

control that girl also b ears grammatical relations to all the intermedi

ate verbs and that the intermediate verbs necessarily carry the required

control schemata A longdistance functional linkage can b e made unac

ceptable byanintermediate lexical change that has no cstructure conse

quences

a There was exp ected to b e an earthquake

b There was p ersuaded to b e an earthquake



The term syntactic binding is sometimes used as a synonym for constituentcontrol

Ronald M Kaplan and Joan Bresnan

The fstructure b ecomes semantically incomplete when the equi verb per

suaded is substituted for the intervening raising verb

Constituentcontrol diers from functional control in that constituent

structure congurations not functional relations are the primary con

ditioning factors As illustrated in at one end of the linkage

called the constituent control lee the clauseinternal function maybede

termined by the p osition of a cstructure gap The relative clause in

demonstrates that the cstructure environment alone can also dene the

other end of the linkage called the constituent control ler

The toy the girl handed to the babywas big

This sentence has no sp ecial words to signal that toy must enter into a

control relationship Finally the linked entity b ears no grammatical rela

tiontoany of the predicates that the constituent dep endency covers eg

believed and claimed in and there are no functional requirements on

the material that mayintervene b etween the controller and the controllee

Instead the restrictions on p ossible linkages involve the conguration of

no des on the controllercontrollee cstructure path for example the in

terrogative complementof asked on the controllercontrollee path in

is the source of that strings ungrammaticality

Decomp osing these longdistance constituent dep endencies into chains

of functional identications would require intro ducing otherwise unmoti

vated functions at intermediate fstructure levels Such a decomp osition

therefore cannot b e justied A strategy for avoiding spurious functions

is to sp ecify these linkages by sets of alternative direct functional identi

cations One alternativewould link the who to the subj of the clause

for a and a second alternativewould link to the obj for b

Question clauses with one emb edded sentential complementwould require

alternatives for the scomp subj and scomp objthetwoemb eddings in

would require scomp scomp obj and so on This strategy has an

obvious diculty without a b ound on the functional distance over which

this kind of dep endency can op erate the necessary alternative identi

cations cannot b e nitely sp ecied The functional apparatus of our

theory thus do es not p ermit an adequate account of these phenomena



In anyevent the schemata in these alternatives violate the substantive restriction

on functional control mentioned ab ove They also run counter to a second substantive

restriction the principle of functional locality This principle states that for human

languages designators in lexical and grammaticalschemata may sp ecify no more than

two functionapplications This limits the context over which functional prop erties

may b e explicitly stipulated The recursivemechanisms of the cstructure grammar are

required to propagate information across wider functional scop es The lo cality principle

is a functional analogue of the contextfree nature of our cstructure grammars

AFormal System for Grammatical Representation

If a single constituentcontains no more than one controllee it is p os

sible to enco de enough information in the cstructure categories to ensure

a corresp ondence b etween controllers and controllees as suggested by

Gazdar This enco ding obviously captures the fact that these de

p endencies are sensitive to constituent congurations Gazdar also shows

that appropriate semantic representations can b e dened by translations

asso ciated with the phrase structure rules Maling and Zaenen

p oint out that this approach b ecomes considerably less attractive if a sin

gle constituent can contain more than one controllee as in the familiar

interaction of tough movement and questions in English

Iwonder which violin the sonatas are easy to play on

Furthermore no enco ding into a nite numb er of categories is p ossible for

languages suchasSwedish and Norwegian for which according to Maling

and Zaenen and Engdahl ab no natural limit can b e set on

the number of controllees in a single constituent

Our problem then is to provide a formal mechanism for representing

longdistance constituent dep endencies that do es not require unmotivated

grammatical functions or features allows for an unb ounded number of

controllees in a single constituent and p ermits a succinct statementof

the generalizations that govern grammatical phenomena of this sort The

necessary descriptive apparatus is found in the formal interpretation of

bounded domination metavariables

The b ounded domination metavariables and are similar to the

immediate domination variables and in that they app ear in gram

matical and lexical schemata but are instantiated with actual variables

when the fdescription is formed The instantiation pro cedure for b oth

kinds of variables has the eect of substituting the same actual variable for

matched metavariables attached to dierent no des in the cstructure The

dierence is that for a matched pair the schemata must b e attached

to no des in a relationship of immediate domination while matching

and may b e attached to no des separated in the tree by a longer path

These are called b ounded domination metavariables b ecause that path

is limited by the o ccurrence of certain b ounding no des The metavari

able is attached to a no de at the upp er end of the path and represents

the controller of a constituentcontrol relationship The matching is

lower in the tree and represents the controllee of the relationship The

instantiation pro cedure for these variables establishes the longdistance



Technically the terms control ler and control lee refer to the b ounded domination

metavariables and not to the no des that they are attached to In this resp ect we

depart from the way these terms have b een used in other theoretical frameworks

Ronald M Kaplan and Joan Bresnan

identication of the controller and controllee directly without reliance on

transitivechains of intervening equations

We illustrate the general prop erties of our mechanism with a simple

example suppressing for the momenta numb er of formal and linguistic

details Consider the indirect question sentence b rep eated here for

convenience

b The girl wondered who the babysaw

We assume that the predicate for wondered takes an interrogative com

plement argument as indicated in the lexical entry

wondered V tensepast

predwonder h subj scompi

According to the rules in scomps are based on constituents in

 

the category S andS expands as an NP followed byanS



a VP V S

scomp



b S NP S

qfocus

The schemata in b mark the initial NP as the questions fo cus

qfocus and also identify it with the controller of a gap in the fol

lowing S The initial NP for our example is realized as the interrogative

pronoun who which has the following lexical entry

who N pred who

The nal rule for this example asso ciates the controllee metavariable

with a gap p osition inside the clause As shown in we allowc

structure rules to expand a nonterminal category as the empty string

symb olized by e This gives a formal representation for the intuition that

an element of that category is missing

NP e



Grimshaw has argued that the sentential complement is restricted to b e

interrogativeby the semantic typ e of the predicate wonder A separate functional

sp ecication of this restriction is therefore unnecessary

AFormal System for Grammatical Representation

The schema on the empty expansion intro duces the controllee meta

variable This NP alternativemust b e utilized for the ob ject of saw

so that b is assigned the cstructure

S

NP VP



Det N V S

NP S

N NP VP

Det N V NP

The girl wondered who the baby saw e

The instantiation pro cedure for metavariables still has an attachment

phase a variable intro duction phase and a substitution phase just as

it was presented in Section Schemata are attached to appropriate c

structure no des in the rst phase without regard to the kinds of metavari



ables they contain The attachments for no des in the emb edded S subtree

are shown in



Our controlled e is a basegenerated analogue of the traces left by Chomskys

rule of wh movement However controlled e s are involved only in the description of

constituentcontrol whereas Chomskys traces are also used to account for functional

control phenomena

Our controller and controllee metavariables also resemble the hold action and the

virtualretrieve arcs of the ATN formalism Plausible pro cessing mo dels for b oth sys

tems require similar computational resources to lo cate and identify the twoendsof

the control relationshipThus the exp erimental results showing that ATN resource

demands predict human cognitiveloadWanner and Maratsos Kaplan b

are also compatible with lexicalfunctional grammar However we discuss b elowcer

tain asp ects of our theory for which standard ATN notation has no equivalents the

app earance of controllees in the lexical entries of fully realized items the ro otno de

sp ecications and the b ounding no de conventions Moreover our theory do es not have

the characteristic leftright asymmetry of the ATN notation and thus applies equally

well to languages like Basque where constituent ordering is reversed

Ronald M Kaplan and Joan Bresnan

scomp



S

qfocus

S

NP

pred who subj

N NP VP

num sg

specthe

predbaby

Det

N

obj

NP

tensepast

predseehi

V

who the baby saw

e

In the second phase distinct actual variables are intro duced for the ro ot

no de and for every no de where a schema contains a metavariable This

provides the variables for the no des as b efore However an additional

variable is intro duced for each no de with a schema containing the con

troller metavariable providing a variable for that no de For this

simple example only the who NP no de has a controller and receives the

extra variable assignment The annotations f and f on that no de in

record the asso ciation b etween metavariables and actual variables

AFormal System for Grammatical Representation

scomp



f S

qfocus

f f S

NP

f

pred who subj

N f NP f VP

num sg

specthe

predbaby

Det

N

obj

f NP

tensepast

predseehi

V

who the baby saw

e

For immediate domination metavariables the instantiation is completed

by substituting a no des variable for all the s at that no de and for all

corresp onding s those in schemata attached to its daughter no des The

treatment of b ounded domination metavariables is similar in that the

variable of a no de replaces all the s at that no de and all corresp onding

s The essential dierence is that the no des to which corresp onding s

are attached may b e further away in the cstructure

The corresp onding to the on the who NP in is attached to

the emptyobjectofsaw The substitution phase of instantiation thus

adds the following statements to the fdescription

a f qfocusf

b f f

c f pred who

d f obj f

e f f

Ronald M Kaplan and Joan Bresnan

Equation b comes from the who NP no de and e comes from

the empty NP expansion Both equations contain the variable f and

thereby establish the crucial linkage the semantic form who serves as

the pred in the ob ject fstructure for saw and accounts for the fact that

who is understo o d as the second argument of see This is apparentin

fstructure the solution to sentence bs fdescription

spec the

num sg

subj

pred girl

tense past

pred wonder h subj scompi

qfocus pred who

spec the

num sg

subj

pred baby

scomp

pred see h subj obji

tense past

obj

Thus constituentcontrol dep endencies are handled in LFGbyex

tending the instantiation pro cedure for mapping schemata on cstructure

no des into fdescription statements Because we do not rely on inter

mediate functional identications the statements in are sucient

to establish the same connection over longer cstructure distances for

example over the intervening to complementin

The girl wondered who the baby p ersuaded the b oy to see

Except for p ossibly a dierentchoice of actual variables the instantiation

pro cedure would again pro duce the statements correctly represent

ing the constituentcontrol relation The fstructure for this sentence has

b oth a functional control linkage and a constituentcontrol linkage

AFormal System for Grammatical Representation

spec the

num sg

subj

pred girl

tense past

pred wonder h subj scompi

qfocus pred who

spec the

num sg

subj

pred baby

tense past

pred p ersuade h subj obj vcompi

spec the

num sg

scomp

obj

pred b oy

subj

pred see h subj obji

vcomp

inf

to

obj

Note that there are no extraneous attributes or values to carry the con

stituentcontrol linkage through the persuade fstructure

The instantiation pro cedure as describ ed substitutes the same actual

variable for a and any corresp onding s Beneath this vague notion

of corresp ondence lies some additional notation and a rich set of deni

tions and restrictions that wenowmake precise We observerstthat

corresp onding s and s must meet certain category requirements As

examples ab indicate the verb grow meaning b ecome may b e fol

lowed by an adjective phrase but not an NP while the verb reach meaning

extend to has just the opp osite distribution Example c shows that

acontroller may b e asso ciated with an AP at the b eginning of an indirect

question but its corresp onding controllee must then b e in an adjecti

val p osition Example d demonstrates that metavariables asso ciated

with NPs must also b e compatible

a Shell grow that tallheight

b Shell reach that tallheight

c The girl wondered how tall she would growreach

d The girl wondered what height she would growreach

Ronald M Kaplan and Joan Bresnan

We therefore allow b ounded domination metavariables to carry sp ecica

tions of cstructure categorial features These sp ecications are written

as subscripts on the metavariables and we require that corresp onding

controllers and controllees have compatible subscripts Thus a may

NP

corresp ond to a but not to a The contrast in d then follows

NP AP

from adding the subscript NP to the metavariables in our previous rules

 

a S NP S

qfocus

NP

b NP e

NP

The rules for handling adjectival and prep ositional dep endencies have

analogous categorial markings and crosscategorial corresp ondences are

thereby excluded

For these examples the categorial subscripts are redundant with the

categories of the no des that the metavariables are asso ciated with but

this is not always the case In a the metavariable asso ciated with



the topicalized S is matched with a controllee on an e in a cstructure

NP p osition a prep ositional ob ject b rules out the p ossibility that



the S is dominated byanNPThecontrast b etween c and d

 

shows that a topicalized S cannot control an S cstructure p osition

a That he might b e wrong he didnt think of

b He didnt think of that he might b e wrong

c He didnt think that he might b e wrong

d That he might b e wrong he didnt think

This pattern follows directly from asso ciating a metavariable with

NP



the fronted S no de

Another obvious prop erty of acceptable corresp ondences is that cer

tain tree relations must hold b etween the no des to which corresp onding

controller and controllee metavariables are attached The e corresp ond

ing to the who controller in must b e dominated by the adjacentS

no de It cannot b e lo cated earlier or later in the main clause nor inside

a more complicated NP in the who p osition To put it in more technical

terms wesay that the S no de in is the ro ot of a control domain for

the who For a controller attached to a given no de in the cstructure

NP

acontrol domain consists of the no des in a subtree that a corresp onding

controllee maybeattached to Our notion of corresp onding metavariables

thus turns on a rigorous characterization of what no des can b e ro ots of

control domains and what no des dominated by the ro ot are contained in the domain

AFormal System for Grammatical Representation

Acontroller metavariable carries still another sp ecication that de

termines what no de may b e its domain ro ot A closer examination of

the indirect question construction shows why this is needed Rule a

suggests that any noun phrase may app ear at the front of an indirect

question but this is of course not the case The fronted phrase is re

stricted to contain an interrogativeword of some sort That word need

notbeatthetoplevel of the NP as in b but may rather b e deeply

emb edded within it

The girl wondered whose playmates nurse the babysaw

This sentence would b e generated by the alternative NP rule which

allows for p ossessors with genitive case in prenominal p osition

NP NP N

case gen

c

poss

Avery natural way of guaranteeing the presence of a question word in the

appropriate contexts is to sp ecify a constituentcontrol relation b etween

the fronted NP of an indirect question and the interrogativeemb edded

underneath it This is p ossible b ecause constituentcontrol in our theory

may aect not only null elements but also a designated set of lexical items

which includes interrogative pronouns determiners and adverbs

Even though interrogative elements dier in their ma jor categorial

features we assume that they are distinguished from other lexical items

by the app earance of a morphosyntactic feature wh in their categorial

feature matrices and we use this feature as the metavariable subscript

for the interrogative constituentcontrol dep endencyHoweveritisnot



sucient to revise our previous S rule simply by adding a wh controller

metavariable to the fronted NP



S NP S

q

wh

focus

NP

When the schemata from this rule are attached to the no des in sentence

s cstructure two dierentcontrollers and are asso ci

NP wh

ated with the fronted NP no de While we still intendtheStobethe

domain ro ot for the weintend the ro ot for to b e the fronted

NP wh

NP itself In order to represent this distinction wemust explicitly mark

the individual controllers with category symb ols that determine their re

S

sp ective domain ro ots The sup erscript S in the controller indicates

NP



We assume that morphological rules correlate the genitive case marking with the s

sux and that whose is morphologically comp osed of who s

Ronald M Kaplan and Joan Bresnan

that the corresp onding must b e found in an Sro oted control domain

NP

NP

while the wh controllee for must b e found b eneath an NP no de

wh

Moreover the domain ro ots must b e either the no des to which the con

trollers are attached or sisters of those no des as indicated in the following

denition

Root nodeofaconstituent control domain

r

Supp ose is a controller metavariable attached to a no de N

c

r

Then a no de R is the ro ot no de of a control domain for if and

c

only if

a R is a daughter of N s mother and

b R is lab eled with category r



Intro ducing ro otcategory sup erscripts into the S rule wehave



S NP S

NP

q

wh

focus

S

NP

The wh controllee for the interrogative linkage is asso ciated with a

lexically realized N no de not with an empty string expansion and the

schema containing the controllee metavariable do es not come from the

grammar but rather from the lexical entry for who

who N pred who

wh

This lexical entry and our revised question rule yield the following f

structure for sentence



Note as an aside that wehavechanged the qfocus identication schema from

a to b ecause the questioned element is no longer the fstructure of the

fronted NP The new schema places the interrogative semantic form in a canonical

fstructure lo cation that is indep endent of its degree of emb edding The complete

fronted NP is also recorded in a canonical fstructure lo cation as the value of the

function focus That NP is accessible as the focus of the question as well as through

its clauseinternal function obj as indicated by the connecting line in These

separate access paths dene the scop e of dierent rules for interpreting anaphors The

focus path in the fstructure for sentence i p ermits the ordinary pronoun she to b e

coreferential with Sal ly even though this is not p ermitted by its clauseinternal ob ject

function as shown byii

i Which of the men that Sally dated did she hate

ii She hated one of the men that Sally dated

iii Iwonder how proud of herself Bill thinks Sally is

The clauseinternal function governs the interpretation of reexive pronouns iii

would otherwise b e unacceptable b ecause the reexive is not a clausemate of the

antecedent Sal ly The problem p osed by the contrast b etween examples i and ii

AFormal System for Grammatical Representation

spec the

num sg

subj

pred girl

tense past

pred wonder h subj scompi

i h

case gen

q

pred who

num sg

pred nurse

num sg

case gen

focus

poss

pred playmate

poss

scomp

spec the

num sg

subj

pred baby

pred see h subj obji

tense past

obj

The ro otno de category sp ecication provides one part of the charac

terization of what a control domain can b e To complete this character

ization wemust dene which no des dominated by the domain ro ot are

contained in the domain The wh island in example demonstrates

that at least some no des in the domain ro ots subtree do not b elong to

the domain

The girl wondered what the nurse asked who saw

Without some limitation on the extent of a domain s at the gaps

NP

would b e interpretable as the controllees for who and what resp ectively

Limitations on what no des may b elong to a given control domain come

from the fact that no des in certain cstructure congurations are classied

as bounding nodes The path from a no de in a domain to the domain ro ot

is then restricted as follows

Bounding Convention

AnodeM b elongs to a control domain with ro ot no de R if and

only if R dominates M and there are no b ounding no des on the

path from M up to but not including R

was observed originally byPostal The solution sketched here is develop ed in

greater detail by Zaenen

Ronald M Kaplan and Joan Bresnan

The domain ro ot thus carries a substantial theoretical burden as a c

structure intermediary b etween the no des to which a controller metavari

able and its corresp onding controllees are attached The categorial su

p erscript on the controller metavariable is a direct and denite selector

of its domain ro ots However the path from a ro ot to a corresp onding

controllees no de while restricted by the Bounding Convention is not

uniquely determined by the grammar

It remains to extend our notion of grammaticalitytotake b ounded

domination metavariables explicitly into account Intuitivelywe require

all controllers to have corresp onding controllees and all controllees to have

corresp onding controllers so that there are no uninstantiated metavari

ables in the fdescription We add the following to our previous list of

grammaticality conditions

Grammaticality Condition

A string is grammatical only if its fdescription is properly instan

tiated

The controllercontrollee corresp ondence is one consequence of the formal

denition of prop er instantiation

Denition of Proper Instantiation

The fdescription from a cstructure with attached schemata is

prop erly instantiated if and only if

a no no de is a domain ro ot for more than one controller

b every controller metavariable has at least one control do

main

c every controller metavariable corresp onds to one and only

one controllee in each of its control domains

d every controllee metavariable corresp onds to one and only

one controller

e all metavariable corresp ondences are nearly nested and

f every domain ro ot has a lexical signature

For a prop erly instantiated fdescription there is a onetoone mapping

between controllees and domain ro ots and each domain ro ot is asso ci

ated with one and only one controller This establishes the necessary

corresp ondence b etween metavariables The denition of nearly nested

correspondences and the consequences of the restriction e are pre

sented at the end of this section where we discuss the p ossibilityofa

single constituentcontaining several controllees

The lexical signature clause is motivated primarily by formal consid

erations It establishes a connection b etween controlled e s and actual

lexical items that plays an imp ortant role in the recursiveness pro of pre

AFormal System for Grammatical Representation

sented in Section For each domain ro ot there must b e a distinct word

in the terminal string This word is called the lexical signature of the

domain ro ot The domain ro ot must dominate its lexical signature The

eect of f is that each domain ro ot and thus eachcontrol domain

must b e reected in the string in some unique way One p ossible in

terpretation of this formal condition is that a control domain must have



a lexically realized head The head can b e dened in terms of the X

category system It can also b e dened purely in functional terms a

lexical head is the lexical item that contributes the pred semantic form

to a constituents fstructure

According to corresp onding metavariables of a grammatical sen

tence must b e in a cstructure conguration as outlined in

x

r

y r

c

z

c

b

w

c

lexical

signature

In this cstructure and in the illustrations b elow b ounding no des are

enclosed in b oxes The dashed line passes by the domain ro ot to connect

the corresp onding controller and controllee The lower in cannot

c

corresp ond to the controller b ecause the b ounding no de b lies on the path

to the ro ot r



The lexical signature requirement and its formal implications are somewhat remi

niscentofPeters Survivor prop ertyandWasows Subsistence prop erty

two restrictions that have b een prop osed to guarantee the recursiveness of transfor

mational grammars Those conditions are imp osed on the input and output trees of a

transformational cycle whereas f stipulates a prop ertythatmust hold of a single cstructure

Ronald M Kaplan and Joan Bresnan

Bounding no des dene islands of the cstructure that constituent

control dep endencies may not p enetrate They serve the same descrip

tive purp ose as Ross constraints on transformational variables and

Chomskys notion of cyclic or b ounding categories Those theo

ries however have descriptive inadequacies Ross hyp othesized that con

straints such as the Complex NP Constraint apply to all human languages

but this has proved not to b e the case All Scandinavian languages for

example p ermit longdistance dep endencies to cross the b oundaries of

indirect questions and all except for Icelandic p ermit them to cross the

b oundaries of relative clauses as well for illustrations see Erteschik

Allwo o d Engdahl ab Maling and Zaenen Moreover al

though dep endencies into English relative clauses a are unacceptable

Ross himself noted that extractions from phrases within the lexicallylled

NPs in examples like bc are p ossible even in English

talked to saw Mary a I wonder who the man that

b Iwonder who John saw a picture of

c Who was it that John denied the claim that he dated

The restrictions on constituentcontrol into English sentential comple

ments and relative clauses seem to b e governed by dierent generaliza

tions Go dard convincingly argues that a similar pattern holds for

complements and relatives in French In Chomskys theory the sub ja

cency convention provides a general limitation on syntactic rules The

domains of rule application are thereby restricted by the o ccurrence of

no des in sp ecied categories Chomsky shows that many of the prop er



ties of English dep endencies follow from the assumption that S and NP

and p ossibly S are b ounding categories One reasonable extension to

Chomskys theory denes b ounding categories on a languagebylanguage

basis stipulating a smaller or p erhaps empty set of b ounding categories

in the grammarofSwedish mightgive an account of the freer dep enden

cies exhibited by that language However the English sentences bc

have no natural description in Chomskys system if al l NPs in English

are b ounding no des

Bounding no de sp ecications in lexicalfunctional grammar acknowl

edge the fact that restrictions on longdistance dep endencies mayvary

between languages and b etween dierent no des of the same category in

particular languages This exibility do es not diminish the explanatory

p otential of our formal system We exp ect that a substantivetheoryof



Chomsky prop oses to derivesuch examples by restructuring rules that move

the of prep ositional phrase and that complement outside of the picture and claim NPs

b efore the wh movement rule applies But such a reanalysis in all the relevant cases

cannot b e justied as Go dard shows for French

AFormal System for Grammatical Representation

human language based on our formalism will stipulate a small principled

set of cstructure congurations in which b ounding no des may app ear

The grammars of particular languages must draw from this universal in

ventory of p ossible b ounding no des to identify the b ounding categories

in individual cstructure rules see Zaenen for some partial prop os

als Further work will of course b e needed to formulate and justify a

universal b ounding no de theory Our goal at present is only to illustrate

the notation and formal prop erties of our constituent control mechanisms

A simple notational device is used to indicate that constituentcontrol is

blo cked by no des in particular cstructure congurations enclosing a cat

egory on the righthand side of a cstructure rule in a b ox sp ecies that

the no des derived by that rule element are b ounding no des

We incorp orate this notation into our treatment of indirect questions

for the variety of English in which they form islands The S in these

constructions is a b ounding no de as shown in the revised rule



S S NP

NP

q

wh

focus

S

NP

Notice rst that the b ounding no de intro duced by this rule do es not

blo ck the simple indirect question sentence b As shown in

this is b ecause the S is the ro ot no de of the controllers control domain

Therefore in accordance with the b ounding convention it do es not

interfere with the metavariable corresp ondence

Ronald M Kaplan and Joan Bresnan

S

NP VP



Det N V S

NP S

S NP

wh NP

N NP VP

wh

Det N V NP

The girl wondered who the baby saw e

NP

The dashed line in this illustration runs b etween the corresp onding

metavariables not b etween the no des they are attached to The con

nected metavariables will b e instantiated with the same actual variable

The situation is dierent for the more complicated string Nei

ther of the gaps inside the asked question b elongs to the control domain

whose ro ot no de is the sister of what This is b ecause the who domain

ro ot is a b ounding no de on the path from eachofthecontrollees to the

S

ro ot for the what NP

AFormal System for Grammatical Representation



S

NP S

NP S

wh NP

N NP VP

wh



Det N V S

NP S

S NP

wh NP

N NP VP

wh

V NP

what the nurse asked who e saw e

NP NP

Conditions cd are not satised and the string is marked ungram

matical

Our b ox notation also p ermits an account of the apparent dierence in



NP b ounding prop erties illustrated in The S in the relative clause

expansion rule is b oxed thus intro ducing a b ounding no de that

separates b oth of the gaps in example a from the who controller

S NP NP

A prop er instantiation for this example is therefore imp ossible Con

stituent control into the other NP constructions in is acceptable b e

cause they are derived by alternative rules which do not generate b ound

ing no des This distribution of b ounding no des has a further consequence

Together with our hyp othesis that the interrogativeword inside a fronted

NP is sub ject to constituentcontrol it explains certain restrictions on

the lo cation of the interrogative Sentence a shows that a fronted

NP maycontain a relative clause but example b demonstrates that

the interrogative pronoun may not app ear inside the relative This is just

what wewould predict since the relative clause b ounding no de that sepa

rates the NP metavariables in c also blo cks the wh corresp ondence in b

Ronald M Kaplan and Joan Bresnan

a The girl whose pictures of the man that called Mary I saw

talked to John

b The girl the pictures of the man that called whom I saw talked

to John

c The girl who I saw pictures of the man that called talked to

John

Though similar in these examples there are English constructions in

which NP and wh metavariables do not have the same privileges of

o ccurrence We see in and that a controlled interrogative

maybutacontrolled e may not b e lo cated in the p ossessive mo dier of

an NP

The girl wondered whose nurse the babysaw

s nurse The girl wondered who the babysaw

The ungrammaticality of follows from making the prenominal gen

itive NP b e a b ounding no de as in the revised NP rule

NP NP N

case gen

c

poss

The genitive b ounding no de also blo cks a direct corresp ondence for the

wh metavariables in but a simple schema can b e added to rule

to circumventtheblocking eect just for interrogative dep endencies

NP

splits what seems to b e a single control This schema

wh

wh

domain into two separate domains one emb edded inside the other It

equates a wh controllee for the upp er domain with a wh controller

for a lower domain

NP N NP

case gen

c

poss

NP

wh

wh

Because this schema links only wh metavariables constituentcontrol

only for interrogatives is p ossible inside the genitiveNP control for

empty NPs is prohibited The relevant cstructure relations for sentence

are illustrated in



Constituent control dep endencies for relative pronouns also p enetrate the genitive

NP This would follow automatically from the hyp othesis that relative metavariables

share the whsubscript The w ellknown distributional dierences b etween relative

and interrogative items would b e accounted for by additional features in the categorial

subscripts for the relative and interrogative dep endencies and more selective sp ecica

tions on the linking schemata asso ciated with other b ounding no des

AFormal System for Grammatical Representation



S

S

NP S

wh

NP

wh

NP N NP VP

NP

wh

N Det N V NP

wh

whose nurse the baby saw e

NP

Sp ecial constraints have b een prop osed in transformational theory eg

the Left Branch Condition of Ross to account for the asymmetry in

and The lexicalfunctional description of these facts is stated

within the grammar for English without p ostulating extragrammatical

universal constraints It thus predicts that this is an area of variation

among languages

In contrast to the nonuniform b ounding characteristics of NPs it can

b e argued that in languages like English Icelandic and French all Ss are

b ounding no des see the discussions of verb inversion in control domains

in Bresnan and Grimshaw and Zaenen If so the Bounding

Convention would also blo ck the derivation of sentences such as

where the controllee is inside a verb phrase that complement

The girl wondered who the nurse claimed that the babysaw



The linking schema app earing in the alternativeS rule will let the

dep endency go through in this case



S that S

S

Neither of the metavariables in this linking schema has a categorial sub

script This is an abbreviation for a nite set of alternativeschemata of

S

the form where c is one of the typ es NP wh PP etc Thus

c

c

this schema will link metavariables of anytyp e passing on to the lower

controller the compatibility requirement of the upp er one With this rule

the following cstructure is assigned to the sentential complement in

Ronald M Kaplan and Joan Bresnan



S

NP S

NP S

wh NP

N NP VP

wh



Det N V S

S

S

NP VP

Det N V NP

who the nurse claimed that the baby saw e

NP

S

Observe that the that no de b elongs to the control domain of the who

NP

controller since there is no b ounding no de on the path leading down to

it The on the left of the linking schema is thus instantiated with the

S S

variable of the who no de A separate variable is intro duced for the

NP

on the right and this is substituted for the of the emptyNPwhich

NP

b elongs to the domain ro oted in the complement S The semantically

appropriate connections for are thus established

The denitions of our theory place controllees in a onetoone cor

resp ondence with domain ro ots and hence with lexical signatures Our

denitions do not establish such a corresp ondence b etween controllees and

arbitrary constituents there is nothing to preventcontrol domains from

overlapping and any constituent in several domains maycontain several



Our use of linking schemata has some of the avor of Chomskys sub jacency con

dition and COMP to COMP movement eg Chomsky We mentioned ab ove

that our sp ecication of b ounding no des diers from Chomskys but there are other

signicant dierences in our approaches For one we do not move constituents from

place to place we merely assert that a functional equivalence obtains That equiva

lence enters into the fdescription and is reected in the ultimate fstructure but it

is never visible in the cstructure Thus wehave a simple account of cases where

unmoved constituents are sub ject to the b ounded domination constraints as in Chi

nese interrogatives Huang in such cases the theory of Chomsky fails to

provide a uniform explanation

AFormal System for Grammatical Representation

controllees Control domains will overlap whenever a domain ro ot b e

longing to the domain of a higher controller is not marked as a b ounding

no de The p otential for multiple dep endencies into a single constituentis

greater for languages whose grammars sp ecify fewer b ounding no des The

hyp othesis that Swedish has fewer b ounding no des than English would

thus account for the less restrictive patterns of Swedish dep endencies

There are examples of multiple dep endencies in English however

whichwe will use to illustrate the op eration of our formal mechanism The

recent literature contains many discussions of the interaction of tough

movement and questions see Chomsky and Fo dor for ex

ample and the references cited therein

on Iwonder which violin the sonata is tough for her to play



As we will see the no des in the VP in this example lie within twocontrol



domains one ro oted in the VP in the sentential complementoftough

and the other ro oted in the S after which Before exploring the interac

tions in this sentence wesketch a grammar for simple tough movement

constructions

A predicate like tough is an adjective that can o ccur as the head of an

adjective phrase Among the alternative expansions for AP is one that

allows the adjectivetobefollowed by a sentential complement



AP A S

scomp

TheVPmust of course p ermit APs as complements to copular verbs

but the details of the VP grammar do not concern us here Tough pred



icates take innitival sentential complements so the category S must



also have an alternative expansion Rule allows S to expand as a



for complementizer followed by a sub ject NP and a VP



We also leave op en the p ossibilitythata given controller has several domain ro ots

If several daughters of the controller no des mother are lab eled with the controllers

categorial sup erscript then eachsuch daughter b ecomes the ro ot of a domain that

must contain one corresp onding controllee This distributes the instantiation require

ment to each of the domains indep endently This suggests a plausible accountforthe

acrosstheb oard prop erties of co ordinate structures but more intensiveinvestigation

of co ordination within the lexicalfunctional framework is needed b efore a denitive

analysis can b e given



Chomsky has prop osed an analysis of these sentences that do es not involve

a double dep endency He suggests an alternative phrase structure for examples of

this typ e wherebytheon prep ositional phrase b elongs somewhere outside the play

VPBach and Bresnan p oint out that this prop osal has a number of

empirical shortcomings

Ronald M Kaplan and Joan Bresnan

 

S for NP VP

subj

VP

topic

NP

The topic schema identies the topic with an NP controller metavari



able whose corresp onding controllee must b e inside the VP Sentences

such as where the sub ject of tough has a clauseinternal function

in an emb edded that complement justify treating this as a constituent

control dep endency

Mary is tough for me to b elievethatJohnwould ever marry

In some resp ects the topic function is likethe focus function intro duced

earlier for indirect questions It raises an entity with a clauseinternal

function to a canonical p osition in the fstructure hierarchy providing an

alternative access path for various anaphoric rules cf note There are

substantive dierences b etween topic and focus however The focus

relation marks new information in the sentence or discourse and therefore

is not identied with any other elements The topic function is a place

holder for old information its value must b e linked either functionally or

anaphorically to some other element For tough predicates the topic is

functionally controlled bya schema in the adjectives lexical entry

tough A pred toughh scompi

scomp topic subj

With these sp ecications the fstructure for the simple tough movement

sentence is as shown in and its cstructure is displayed in

The sonata is tough for her to play on the violin

We are now ready to examine the double dep endency in In

this sentence violin has b ecome the focus of an indirect question The c



structure for the complementof wonder is shown in Since the VP

domain is intro duced without a b ounding no de there is nothing to blo ck

the corresp ondence b etween the ob ject NP of on and the NP controller for

which violin The corresp ondence for the topic metavariables in tough s

complement is established just as in the simpler example ab ove Thus

the metavariables can b e prop erly instantiated and the intuitively correct

fstructure will b e assigned to this sentence

As has frequently b een noted the acceptability of these double de

p endencies is sensitive to the relative order of controllees and controllers



The prep osed item in relative clauses is also a topic Although the relative topic

might b e functionally controlled when the clause is emb edded next to the NP that it

mo dies it must b e linked anaphorically when the relative is extrap osed

AFormal System for Grammatical Representation i on obj obj violin the sg subj i her on spec num pred h y scomp pred pla pcase obj h i to inf obj on topic subj pred tough comp sonata the sg a scomp subj pred h spec num pred pres b e comp subj a tense pred

Ronald M Kaplan and Joan Bresnan N violin NP the Det PP P on NP e NP VP V NP  y V S VP pla to N her NP  S AP for A VP tough S is V N sonata NP the Det

AFormal System for Grammatical Representation NP e NP PP P on NP e NP VP V NP  y V S VP pla to N her NP  S AP for A VP tough is V S N sonata NP the Det  S NP S N NP wh violin wh NP h Det whic

Ronald M Kaplan and Joan Bresnan

If sonata is questioned and violin is the tough sub ject the result is the

ungrammatical string

I wonder which sonata the violin is tough for her to play on

The reading of this sentence in which which sonata is the ob ject of on and

violin is the ob ject of play is semantically unacceptable but the semanti

cally wellformed reading of our previous example is not available

SimilarlyBach observes that p otentially ambiguous sentences are

rendered unambiguous in these constructions Sentence can b e as

signed only the reading in which doctor is understo o d as the ob ject of to

and patient is the ob ject of about even though the alternativeinterpre

tation is equally plausible

ab out Which patient is that do ctor easiest to talk to

As Baker Fo dor and others havepointed out there is a

simple and intuitivewayofcharacterizing the acceptable dep endencies in

these examples If a line is drawn from each gap to the various lexical

items that are candidates for lling it then the p ermissible dep endencies

are just those in which the lines for the separate gaps do not cross Or

to use Fo dors terminology only nested dep endencies seem to b e allowed

The nested pattern of acceptable dep endencies is an empirical con

sequence of the requirement e that corresp onding metavariables b e

nearly nested However this restriction in our denition of prop er instan

tiation is strongly motivated by indep endent theoretical considerations

as wepoint out in Section this requirementprovides a sucient condi

tion for proving that lexicalfunctional languages are included within the

set of contextsensitive languages Thus our restriction oers not only

a description of the observed facts but also a formal basis for explaining

them

As the rst step in formalizing the notion of a nearly nested corre

sp ondence we establish an ordering on the b ounded domination metavari

ables attached to a cstructure We order the cstructure no des so that

each no de comes b efore its daughters and rightsister if any and all its

daughters precede its rightsister If the no de that one metavariable is

attached to precedes another metavariables no de then wesay that the

rst metavariable precedes the second The ordering of metavariables can

b e describ ed more p erspicuously in terms of a lab eledbracket representa

tion of the cstructure tree If metavariables are asso ciated with the open

brackets for the no des they are attached to then the lefttoright sequence

in the lab eled bracketing denes the metavariable ordering This is illus

trated with the partial bracketing for sentence shown in Figure

AFormal System for Grammatical Representation

S

sentence a We see from this representation that the on the fronted

NP

VP

noun phrase is ordered b efore the and that play s direct ob ject

NP

NP

is ordered b efore the controllee after on

Drawing lines b etween corresp onding metavariables as ordered in Fig

ure sentence a illustrates the intuitivecontrast b etween nested and

crossed dep endencies The lines are shown in b for the acceptable nested

reading of and in c for the unacceptable crossed dep endency

A precise formulation of this intuitive distinction can b e given in terms

of the denition of a crossed corresp ondence

Denition of CrossedCorrespondence

The corresp ondence of two metavariables m and m is crossed by

acontroller or controllee m if and only if all three variables have

compatible categorial subscripts and m but not its corresp onding

controllee or controller is ordered b etween m and m

Obviously a corresp ondence is nested if and only if it is not crossed All

the corresp ondences in the acceptable readings for the examples ab ove

are nested according to this denition but the corresp ondences in the

unacceptable readings are not

Metavariable corresp ondences can b e allowed limited departures from

strict nesting without undermining the contextsensitivity of lexical func

tional languages We asso ciate with eachmetavariable corresp ondence an

integer called its crossing degree This is simply the numb er of controllers

and controllees by which that corresp ondence is crossed A corresp on

dence is strictly nested if its crossing degree is zero Further for each

lexicalfunctional grammar we determine another numb er the crossing

limit of the grammar A nearly nested corresp ondence is then dened as

follows

Denition of Nearly NestedCorrespondence

A metavariable corresp ondence is nearly nested if its crossing de

gree do es not exceed the grammars crossing limit

The signicant formal implication of this denition and the nearly nested

restriction on prop er instantiation is that for any string the degree of

departure from strict nesting is b ounded by a constant that is indep endent

of the length of that string

The examples ab ove suggest that the crossing limit for English is zero

This limit can b e maintained even in the face of apparentcounterexamples

to the nesting prop osals of other theories Since our denition of crossed

corresp ondence only involves metavariables with compatible catego

rial subscripts wehave no diculty with acceptable sentences containing

crossed dep endencies of dierent categories Other classes of counterex

Ronald M Kaplan and Joan Bresnan NP NP NP e e e NP NP NP on on on NP NP NP e e e NP NP NP y y y to pla to pla to pla VP NP VP NP VP NP VP VP VP the sonata is tough for her the sonata is tough for her the sonata is tough for her FIGURE S S S h violin h violin h violin whic whic whic wh wh wh Det Det Det NP wh S NP NP wh S NP NP wh S NP NP NP NP S S S onder onder onder Iw Iw Iw S S S c a b

AFormal System for Grammatical Representation

amples involveinteractions of functional and constituentcontrol but our

restrictions are imp osed only for constituentcontrol dep endencies Thus

there is no real crossover in sentences such as

How nice a man would John b e to marry

The man NP is linked to the rst gap while John is linked to the second

In our theory there is a functional identication b etween John the subj

of the complex predicate how niceaman and the topic of its scomp

The controller for the second dep endency is thus ordered after the rst

gap Icelandic stands in contrast to English in having constituentcontrol

dep endencies that can b e describ ed correctly only on the hyp othesis that

the crossing limit for that language is one Maling and Zaenen

Wehave presented in this section the ma jor formal mechanisms for

characterizing the longdistance dep endencies of natural language We

have motivated and illustrated our formal apparatus with simple and

plausible fragments of English grammar Constituentcontrol is a syntac

tic phenomenon of considerable complexity and there are many empirical

and theoretical issues that wehave not touched on and some that are still

to b e resolved No doubt future research in this area will lead to b oth sub

stantive and formal renements of our theoryHowever we exp ect the

broad outline of our approachtoremainunchanged lexicalfunctional

grammar treats longdistance dep endencies as part of the pro cedure for

pro ducing prop erly instantiated fdescriptions These dep endencies are

governed by cstructure congurations and are not directly sensitiveto

the fstructures that are ultimately constructed

Generativepower

Wehave seen that lexicalfunctional grammar oers considerable expres

sivepower for describing linguistic phenomena In this section weex

amine the p osition of LFG in the Chomsky hierarchy of generativeca

pacity The most imp ortant result is that our formal system with two

wellmotivated restrictions on cstructure derivations that we discuss b e

low is not as p owerful as a general rewriting system or Turing machine In

fact lexicalfunctional languages are included within the class of context

sensitive languages On the lower end of the scale weshowthatLFGhas

greater generativepower than the class of contextfree grammars

For a string to b e a memb er of the language generated by a lexical

functional grammar it must satisfy ve requirements

a It must b e the terminal string of a valid cstructure derivation

b There must b e a prop erly instantiated fdescription asso ciated

with that derivation

Ronald M Kaplan and Joan Bresnan

c The fdescription must b e consistent and determinate with a

unique minimal solution

d The minimal fstructure solution must satisfy all constraints

in the fdescription

e The fstructure must b e complete and coherent

Given a single cstructure derivation for a string of length n a tree to

whose no des the appropriate functional schemata are attached there are

nite pro cedures for deciding whether be hold Determining

prop er instantiation for immediate domination metavariables is trivial

Since the given tree has only a nite numb er of nite control domains

it is also computable whether the b ounded domination metavariables are

prop erly instantiated The instantiated fdescription has a nite number

of statements in it so the algorithm outlined in Section and in the

App endix pro duces its unique minimal solution if it is consistent and

determinate Evaluating a constraining statement requires only a nite

traversal of the fstructure and the Completeness and Coherence Con

ditions can similarly b e checked by a nite computation on the fstructure

Thus all that is needed to prove that the grammaticalityofany string

is decidable is a terminating pro cedure for enumerating all p ossible c

structures for the string so that the functional correctness of eachone

can then b e veried Cstructures are generated bycontextfree gram

mars and there are wellknown decision pro cedures for the memb ership

problem of grammars in this class That is there exist algorithms for

determining whether there is at least one way of deriving the string De

ciding that a string is derivable however is not the same as enumerating

for insp ection all of its derivations Indeed there are grammars for which

neither the numb er of derivations that a given string mighthave nor the

numb er of no des in a single derivation is b ounded While it maybede

termined that such a string has one derivation and thus b elongs to the

language of the cstructure grammar there is no way of deciding whether

or not there exists among all of its derivations one that satises the func

tional requirements of our theory Supp ose that at some p ointwehave

examined all derivations with less than m no des and found them all to

b e functionally deviant This do es not mean that all derivations with

m no des will also b e unsatisfactory Since this can b e true for any m

the grammaticality of that string cannot b e decided in a nite number of

steps



The evaluation uses op erators similar to Lo cate Merge and Include except that

they return False whenever the corresp onding solution op erators would mo dify the

fstructure



This diculty arises not just with our formalism but with any system in whichthe

AFormal System for Grammatical Representation

A contextfree grammar can pro duce an unb ounded numb er of deriva

tions of arbitrary size for a string either b ecause its rules p ermit a single

category to app ear twice in a nonbranching chain or b ecause expansions

involving the empty string are not suciently restricted The rules in

illustrate the rst situation

X Y

Y Z

Z X

Any string which has a derivation including the category X will b e in

nitely ambiguous There is a larger derivation with the domination chain

XYZX replacing the single X and a still larger one with one of those

Xs replaced by another chain and so on The derivations that result from

rules of this sort are in a certain sense p eculiar The nonbranching recur

sive cycles p ermit a sup erstructure of arbitrary size to b e constructed over

a single terminal or group of terminals or even over the empty string

The cstructure is thus highly rep etitive and the fdescription whichis

based on a xed set of lexical schemata and arbitrary rep etitions of a

nite set of grammatical schemata is also While the cstructure and

fstructure can b e of unb ounded size they enco de only a nite amountof

nonredundant information that is relevant to the functional or semantic

interpretation of the string

Suchvacuously rep etitive structures are without intuitive or empirical

motivation Presumably neither linguists nor language learners would

p ostulate rules of grammar whose purp ose is to pro duce these deriva

tions However linguists and language learners b oth are likely to prop ose

rules whose purp ose is to express certain surface structure generalizations

but whichhave derivations of this sort as unintended consequences For

example supp ose that the grammar that includes also has a large

numb er of alternative rules for expanding Y and Z Supp ose further that

except for the undesired cyclic XYZX chain X can dominate every

thing that Y and Z dominate Only the intended derivations are p ermitted



if X expands to a new category Y whose rules are exactly the same as



the rules for Y except that another new category Z app ears in place of



Z in The rules for Z are those of Z without the X alternative

This much more complicated grammar do es not make explicit the almost

 

complete equivalence of the YY and ZZ categories Except for the one

spurious derivation the original grammar is a much more revealing

description of the linguistic facts

denition of grammaticalityinvolves an evaluation or interpretation of the contextfree

derivations

Ronald M Kaplan and Joan Bresnan

The following rules illustrate how derivations of arbitrary size may

also result from unrestricted empty string expansions

P PP

P e

If a P dominates either directly or indirectly a lexical item in one

derivation there will b e another derivation in which that P has a mother

and sister which are b oth P with the sister expanding to the empty string

Without further stipulations rules of this sort can apply an indenite

numb er of times Weintro duced empty strings in Section to represent

the lower end of longdistance dep endencies These e s havecontrollee

metavariables and thus are uniquely asso ciated with the lexical signature

of a control domain The p ossibility of arbitrary rep etitions do es not

arise b ecause derivations for a string of length n can havenomorethan

n controlled e s An empty string may app ear in a cstructure rule for

another reason however It can alternate with other rule elements in

order to mark them as optional An optionality e is a generalization of

the standard parenthesis notation for cstructure optionality it p ermits

functional schemata to b e intro duced when the optional constituents are

omitted An optionality e do es not have the controllee metavariable that

inhibits rep etitions of controlled e s and according to the standard in

terpretation of contextfree rules may app ear in derivations indenitely

many times with no intervening lexical items These derivations are re

dundant and unmotivated just like those with nonbranching dominance

cycles The p ossibility of rep eating rule elements with xed schema sets

and no new lexical information is again an unintended consequence of a

simple notational device for conating sets of closely related rules

Having argued that the vacuous derivations involving nonbranching

dominance chains and rep eated optionality e s are unmotivated and un

desired wenow simply exclude them from functional consideration We

do this by restricting what it means to b e a valid cstructure derivation

in the sense of a

Denition of Valid Derivation

A cstructure derivation is valid if and only if no category ap

pears twice in a nonbranching dominance chain no nonterminal

exhaustively dominates an optionality e and at least one lexical

item or controlled e app ears b etween two optionality e s derived

by the same rule element

This denition together with the fact that controlled e s are asso ciated

with unique lexical signatures implies that for any string the size and

numb er of cstructure derivations relevant to our notion of grammaticality

AFormal System for Grammatical Representation

is b ounded as a function of neven though no such b ounds exist according

to the standard interpretation for contextfree grammars Note that this

restriction on derivations do es not aect the language of the cstructure

grammar it is well known that a string has a valid cstructure with no

cycles and no e s if and only if it has any cstructure at all see Hop croft

and Ullman

With the validity of a derivation dened as in the following

theorem can b e proved

Decidability Theorem

For any lexicalfunctional grammar G and for any string sitis

decidable whether s b elongs to the language of G

We observe that algorithms exist for enumerating just the nite num

ber of valid derivations if anythatG assigns to s Aconventional

contextfree parsing algorithm for example can easily b e mo died to

notice and avoid nonbranching cycles to keep track of the source of op

tionality e s and avoid rep etitions and to p ostulate no more controlled

e s than there are words in the string With the valid derivations in hand

there are algorithms as outlined ab ove for determining whether anyof

them satises the functional conditions be Theorem is

thus established

Theorem sets an upp er b ound on the generative capacityof

lexicalfunctional grammar only the recursive as opp osed to recursively

enumerable languages are generable It is p ossible to set a tighter b ound

on the generativepower of our formalism Because of the nearly nested

restriction on prop er instantiation for any lexicalfunctional grammar

G a nondeterministic linear b ounded automaton can b e constructed that

accepts exactly the language of G Lexicalfunctional languages are there



Given the functional apparatus of our theorywe can demonstrate that the restric

tions in are necessary as well as sucient for recursiveness If nonbranching

dominance cycles are allowed there is a straightforward wayofsimulating the com

putation of an arbitrary Turing machine The Turing machine tap e is enco ded in the

fstructure eachlevel of which corresp onds to one cell and has up to three attributes

contents whose value is drawn from the TMs tap e vo cabulary leftcell whose

value is an enco ding of the cell to the left and rightcellEach state of the TM

is represented by a nonterminal category and a transition from state q to q is rep

i j

resented by a rule rewriting q as q A single rule expands the starting category

i j

of the grammar to the initial state of the machine and that rule has schemata that

describ e the TMs input tap e Starting at the top of the cstructure eachnodeinthe

nonbranching tree represents the next transition of the machine and the fstructure

at each no de is the tap e at that transition The tap e op erations of a transition app ear

as schemata on the corresp onding cstructure rule They insp ect the contents of the

mother fstructure and pro duce an appropriate daughter fstructure The lexical cate

gories corresp ond to the nal states of the machine and the fstructure for a prelexical no de is an enco ding of the TMs output tap e

Ronald M Kaplan and Joan Bresnan

fore included within the contextsensitive languages The details of this

construction are quite complicated and will b e presented in a separate

pap er In brief the cstructure with attached schemata for any string

of length n can b e discovered and represented by an automaton with

aworking tap e whose size is b ounded by a linear function of n This

automaton however cannot intro duce actual variables and substitute

them for metavariables as the instantiation pro cedure sp ecies since that

would require a nonlinear amount of space roughly prop ortional to n log

n Instead it uses the arrangementofmetavariables in the cstructure

to determine the implicit synonymy relations that the actual variables

would simply make explicit The nearly nested restriction guarantees

that these relations can b e computed using a linear amountofworking

storage With synonymous metavariables identied the functional well

formedness conditions ce can also b e veried in a linear amount

of space

The generativepower of lexicalfunctional grammarisobviously

b ounded from b elowbytheclassofcontextfree grammars Anygiven

contextfree grammar is a legitimate cstructure grammar with no gram

matical schemata As noted ab ove the strings with valid cstructure

derivations are exactly those that b elong to the contextfree language

The sets of schemata for those derivations are emptyandarevacuously

instantiated to pro duce an empty fdescription whose unique minimal so

lution is the null fstructure The functional comp onentthus do es no

ltering and the cstructure grammar under our interpretation is weakly

equivalent to the grammar interpreted in the ordinary contextfree way

In fact LFG has greater generativepower than the class of context

free grammars for it allows grammars for languages that are known not

n n n

to b e contextfree The language a b c is a classic example of sucha

language Its strings consist of a sequence of as followed by the same

number of bs and then cs A grammar for this language is shown in

S A B C



Certain other restrictions on metavariable corresp ondences will also provide this

guarantee For example a nearly crossed restriction would also suce but it would

entail more cumb ersome mo dels of pro cessing Formallywhatmust b e excluded is arbitrary degrees of nesting and crossing

AFormal System for Grammatical Representation

a

count

A

a A

count

b

count

B

b B

count

c

count

C

c C

count

The cstructure rules pro duce as bs and cs in sequences of arbitrary

length as illustrated by the cstructure for aaabbc in

Sf

Af Bf Cf

a A b B c

a A b

a

The lengths of those sequences however are enco ded in the fstructure

For each of the A B and C no des in the tree the number of count

attributes in the fstructure of that no de is a count of the elements in

that no des terminal sequence Thus the fstructures shown in for

the f f and f no des havethreetwo and one counts resp ectively

count count count

f

count count

f

count

f

Ronald M Kaplan and Joan Bresnan

The attempt to equate these three fstructures in accordance with the

schemata on the S rule leads to a violation of the Uniqueness Condition

and the string is marked ungrammatical Only if the terminal sequences

are all of the same length can the fstructures b e combined

The fstructure in this grammar records the one string prop erty se

quence length that is crucially needed for this particular contextsensitive

test If instead we let the fstructure b e a complete isomorphic image of

the cstructure tree we can describ e a rep etition language another clas

sical example of a noncontextfree language This is a language whose

sentences are all of the form where stands for an arbitrary string

over some vo cabularyWe start with a simple contextfree grammarfor

the strings for example the rule in a

a W L

W

w

b S W W

All words in the vo cabulary are assumed to b elong to the lexical cate

gory L so this rule generates arbitrary strings under rightbranching tree

structures If for every word x there is a distinct symbol xandifx has

lx as its only lexical schema the fstructure of a W no de will b e

an exact image of its subtree For example shows the cstructure

that this grammar would assign to the ungrammatical string abcdbc and

gives the fstructures for the two topmost W no des

Sf

Wf Wf

L W L W

a L W d L W

b L b L

c c

AFormal System for Grammatical Representation

l a

l b

f

w

l c

w

l d

l b

f

w

l c

w

These fstructures contradict the schemata on the S rule whichassert

that they are identical The fstructures for the two Ws in sequence will

b e the same only if their subtrees and hence their terminal strings are

also the same

We can thus characterize within our formalism at least some of the

noncontextfree contextsensitive languages There is nothing devious

or obscure ab out the grammars for these languages they use ordinary

functional mechanisms in p erfectly straightforward ways The additional

generativepower comes from two features of LFG function comp osition

and the equality predicate Function comp osition p ermits fstructures to

enco de a wide range of tree prop erties while the equality predicate can

enforce a matchbetween the prop erties enco ded from dierent no des We

can b e even more sp ecic ab out the source of our contextsensitivepower

If all schemata in a grammar equate attribute values only to constants

eg schemata of the form d d where d designates a symbol or

semantic form then a weakly equivalentcontextfree grammar can b e

constructed In this grammar the information contained in the fstructure

is enco ded in an enlarged set of contextfree categories The additional

power of lexicalfunctional grammar stems from schemata that equate

two fstructures for example the identication schemata in the examples

ab ove

Wehaveshown that lexicalfunctional languages prop erly include the

contextfree languages and are included within the contextsensitive lan

guages LFGs generative capacity is b oth a strong p oint of our theory

and also something of an embarrassment Huybregts has argued

that dep endencies of the sort illustrated by are quite pro ductivein

Dutch and such phenomena have b een claimed to exist in other lan

guages as well eg Mohawk Postal and the English respectively

construction Mechanisms of this p ower must therefore b e a part of any

adequate theory of human language

On the other hand the problem of recognizing languages with con

text sensitivities can b e computationally much more complex than the



Bresnan et al discuss the formal consequences of the Dutch dep endencies

and provide a simple lexicalfunctional description of them

Ronald M Kaplan and Joan Bresnan

recognition problem for contextfree languages If our system turns out

to have full contextsensitivepower then there are no known solutions to

the recognition problem that require less than exp onential computational

resources in the worst case It might therefore seem that contrary to the

Comp etence Hyp othesis lexicalfunctional grammars cannot b e naturally

incorp orated into p erformance mo dels that simulate the apparenteaseof

human comprehension

There are several reasons why this conclusion do es not necessarily

follow First an explanatory linguistic theory undoubtedly will imp ose

avariety of substantive constraints on how our formal devices maybe

employed in grammars of human languages Some candidate constraints

have b een mentioned in passing eg the constraints on functional control

schemata and the principle of functional lo cality and others are under

currentinvestigation It is quite p ossible that the worst case computa

tional complexity for the subset of lexicalfunctional grammars that con

form to such constraints will b e plausibly subexp onential Second while

the Comp etence Hyp othesis asserts that a grammar will b e a signicant

comp onent of a p erformance mo del the grammar is not identied with

the pro cessor that interprets it An adequate theory of p erformance might

imp ose certain space and time limitations on the pro cessors capabilities

or sp ecify certain nongrammatical heuristic strategies to guide the pro

cessors computations see for example the scheduling heuristics describ ed

byFord Bresnan and Kaplan Given these further assumptions

the p erformance mo del might actually exhibit the worst case b ehavior

very rarely and then only under sp ecial circumstances Finallyitisquite

p ossible that the exp onential explosion is in fact psychologically realistic

For our formal system this pro cessing complexity is not the result of a

lengthy search along erroneous paths of computation Rather it comes

ab out only when the cstructure grammar assigns an exp onential num

b er of cstructure ambiguities to a string To the extent that cstructure

is a psychologically real level of representation it seems plausible that

ambiguities at that level will b e asso ciated with increased cognitive load

We conjecture then that the generativepower of our system is not

only necessary for adequate linguistic descriptions but is also compatible

with realistic mo dels of psycholinguistic p erformance In keeping with the

Comp etence Hyp othesis we b elieve that p erformance mo dels that incor

p orate linguistically justied lexicalfunctional grammars will ultimately

provide an explanatory account of the mental op erations that underlie

human linguistic abilities

AFormal System for Grammatical Representation

App endix Fdescription solution op erators

An intuitive description of our fdescription solution algorithm was pre

sented in Section The algorithm involves three basic op erators Lo cate

Merge and Include If d and d are designators then an fdescription

equality of the form d d is pro cessed by p erforming

MergeLo cated Lo cated

and a memb ership statement of the form d d is pro cessed by p erform

ing

IncludeLo cated Lo cated

Wenow give the formal denitions of these op erators

Lo cate Merge and Include all cause mo dications to a collection of

entities and variable assignments C either by mo difying an already ex

isting entityorby substituting one entityforevery o ccurrence of another

We sp ecify substitution as a separate sub op erator since it is common to

all three op erators

Denition of Substitute

For twoentities ol d and new Substitutenew ol d replaces all

o ccurrences of ol d in C with new assigns new as the value of

variables that previously had ol d as their assignment in addition

to anyvariables that had new as their value previously and

removes ol d from C

Applying the Substitute op erator makes all previous designators of ol d

and new b e designators of new

The Lo cate op erator takes a designator d as input If successful it

nds a value for d in a p ossibly mo died entity collection

Ronald M Kaplan and Joan Bresnan

Denition of Locate

a If d is an entityin C then Lo cated is simply d

b If d is a symb ol or semantic form character string Lo cated

is the symb ol or semantic form with that representation

c If d is a variable

If d is already assigned a value in C Lo catedisthat

value

Otherwise a new placeholder is added to C and assigned

as the value of d Lo cated is that new placeholder

d Otherwise d is a functionapplication expression of the form

fs Let F and S b e the entities Lo catef and Lo cates

resp ectively

IfSisnotasymb ol or placeholder or if F is not an

fstructure or placeholder the fdescription has no solu

tion

If F is an fstructure

If S is a symb ol or placeholder with a value dened

in F then Lo catedisthatvalue

Otherwise S is a placeholder or a symb ol for which

F has no value F is mo died to dene a new place

holder as the value of S Lo cated is that placeholder



Otherwise F is a placeholder A new fstructure F is

constructed with a single pair that assigns a new place



holder value to S and SubstituteF F is p erformed

Lo cated is then the new placeholder value

a provides closure by allowing an entity to serve as a designator of

itself The recursiveinvo cations of Lo cate that yield F and S in d

enable the values of all functional comp ositions to b e obtained The con

sistency check is sp ecied in the rst clause of d A Lo cate attempt

fails if it requires an entity already known not to b e an fstructure to b e

applied as a function or an entity knownnottobeasymboltobeused

as an argument The Merge op erator is also dened recursivelyIttakes

twoentities e and e as input Its result is an entity e which mightbe

newly constructed The new entity is substituted for b oth e and e in C

so that all designators of e and e b ecome designators of e instead

AFormal System for Grammatical Representation

Denition of Merge

a If e and e are the same entity then Mergee e isthat

entity and C is not mo died

b If e and e are b oth symb ols or b oth semantic forms the

fdescription has no solution

c If e and e are b oth fstructures let A and A b e the sets of

attributes of e and e resp ectively Then a new fstructure

e is constructed with

e fha v ija A A and v Merge Lo catee a

Lo catee ag

Substitutee e and Substitutee e are b oth p erformed and

the result of Mergee e isthen e

d If e and e are b oth sets then a new set e e e is

constructed Substitutee e and Substitutee e areboth

p erformed and the result of Mergee e is then e

e If e is a placeholder then Substitutee e is p erformed

and the result of Mergee e ise

f If e is a placeholder then Substitutee e is p erformed

and the result of Mergee e ise

g Otherwise e and e are entities of dierenttyp es and the

fdescription has no solution

The consistency check in b ensures that nonidentical symb ols and

semantic forms are not combined and the checks in cd guarantee

that entities of dierentknown typ es ie excluding placeholders cannot

b e merged The recursion in c propagates these checks to all the

substructures of two fstructures building compatible values for common

function names as it pro ceeds down level bylevel until it reaches nonf

structure values



The recursive sp ecication in c must b e slightly complicated if fstructures are

allowed to b e cyclic that is to contain themselves as one of their attribute values

either directly or indirectly through some intervening fstructure levels Structures of

this kind would b e induced by equations of the form f f IfaMergeoftwosuch

structures is attempted the recursive sequence mightnever reach a nonfstructure

and terminate However any innitely recursive sequence must rep eat the merger

of the same two fstructures within a nite numb er of steps Merges after the rst

will have no eect so the sequence can b e truncated b efore attempting step c

for the second time The Merge op erator must simply keep a record of which pairs

of fstructures it is still in the pro cess of merging The Lo cate op erator is immune

to this problem since the numb er of its recursions is determined bythenumber of

functionapplications in the designator which b eing derived from the grammar or

lexicon is nite While presenting no ma jor formal diculties cyclic structures seem

to b e linguistically unmotivated

References

The Include op erator has a particularly simple sp ecication in terms

of the Merge op erator It takes twoentities e and s as input and is dened

as follows

Denition of Include

Perform Mergefegs

The rst entity given to Merge is a new set with e as its only member

The setrelevant clauses of the Merge denition are thus applicable if s

is also a set for example d indicates how its other elements will b e

combined with e

With these op erator denitions the fundamental theorem that our

algorithm pro duces solutions for all and only consistent fdescriptions

can easily b e proved by induction on the numb er of statements in the

fdescription Supp ose an entity collection C is a solution for an f

description of n statements Then the collection after successfully

p erforming MergeLo cated Lo cated is a solution for the description

formed by adding d d as an nth statement and the collection af

ter successfully p erforming IncludeLo cated Lo cated is a solution

for the description formed by adding d d as an nth statement If

the Lo cate Merge or Include op erators fail the larger fdescription is

inconsistent and has no solution at all

Acknowledgments

We are indebted to Martin Kay Beau Sheil and Tom Wasow for valuable

suggestions and fruitful discussions over a p erio d of several years We

also wish to thank Ken Church Elisab et Engdahl Kris Halvorsen and

Annie Zaenen for commenting on earlier drafts of this pap er This work

was supp orted in part by a grant from the Alfred P Sloan Foundation for

research in cognitive science at the Massachusetts Institute of Technology

References

Ackermann Wilhelm Solvable Cases of the Decision Problem Amster

dam NorthHolland

Akma jian Adrian Susan M Steele and Thomas Wasow The Category

AUX in Universal Grammar Linguistic Inquiry

Allwo o d J The Complex NP Constraint as a nonuniversal rule and

some semantic factors inuencin g the acceptabilityofSwedish sentences

which violate the CNPC Construction In University of Massachusetts Oc

casional Papers in Linguistics ed J Stillings Amherst MA Universityof

Massachusetts at Amherst

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