Introduction C-structure F-structure Licensing a string Phenomena References

Lexical-Functional Grammar (LFG)

Linguistics 614

Based primarily on Dalrymple (2006) and Kaplan and Bresnan (1995)

Spring 2015

Introduction C-structure F-structure Licensing a string Phenomena References

Motivation for LFG

Lexical = (not transformational) richly structured lexicon,where relations between, e.g., verbal alternations, are stated

Functional = (not configurational) abstract grammaticalfunctions like subject and object are primitives, i.e., notdefined by the phrase structure configurations

Introduction C-structure F-structure Licensing a string Phenomena References

LFG in a nutshell

LFG (minimally) distinguishes two kinds of representation:

c-structure (constituent structure):overt linear and hierarchical organization of words into phrases

f-structure (functional structure):abstract functional organization of the sentence, explicitlyrepresenting syntactic predicate-argument structure andfunctional relations

These are two separate levels of representation and formalisms:trees (c-structure) and attribute-value matrices (f-structure).

Use of both structures allows, e.g., information from differentparts of the tree to connect to the same function

A range of other levels have been proposed, e.g., A-structureand σ-structure.

Introduction C-structure F-structure Licensing a string Phenomena References

Part I: C-structure

C-structure corresponds to a fairly traditional notion of phrasestructure.

X-Bar Theory: heads with complements, adjuncts, specifierCategories: lexical (N, P, V, A, Adv) and functional (I, C)categories—not universally fixed

Slightly different notions:

Endocentric category S: has no lexical head (for “internalsubject” languages)Optionality: all constituent structure positions can beconsidered optional

Introduction C-structure F-structure Licensing a string Phenomena References

Example

Example of c-structure

(1) kogdawhen

rodilsjaborn

Lermontov?Lermontov

‘When was Lermontov born?’

Introduction C-structure F-structure Licensing a string Phenomena References

Example

Example c-structureCP

NP

N

kogda

C’

IP

I

I

rodilsja

VP

NP

N

Lermontov

Introduction C-structure F-structure Licensing a string Phenomena References

Rules

C-structure rules

C-structure rules are essentially CFG rules, but :

interpreted as node admissibility conditions,i.e., trees must meet c-structure rule descriptionsallow for regular expressions (Kleene star, disjunction,optionality, etc.) on the right-hand sidecan be specified as ID/LP rules

Introduction C-structure F-structure Licensing a string Phenomena References

ID/LP Rules

ID/LP Rules

Rules can be in ID/LP format (Gazdar et al., 1985, cf. alsoGPSG): ID = immediate dominance, LP = linear precedence

Examples:

(2) No LP rules:

a. VP → V, NP

b. VP → {V NP | NP V}

(3) One LP rule:

a. VP → V, NP V < NP

b. VP → V NP

(4) Interacting LP rules:

a. VP → V, NP, PP V < NP, V < PP

b. VP → {V NP PP | V PP NP}

Introduction C-structure F-structure Licensing a string Phenomena References

Part II: F-structure

F-structure maps more closely to meaning and encodesabstract grammatical relations like subject & object asprimitives, i.e. not reducible to tree structure.

Motivation:

Study of grammatical relations predates modern linguistictheoryCategories like subject and object are cross-linguistic→ languages vary less in their f-structuree.g., Keenan-Comrie Hierarchy (for relative clause formation,passivization): subj > do > io > obl > gen > ocomp

Introduction C-structure F-structure Licensing a string Phenomena References

Grammatical functions

Grammatical functions

Governable functions: subj, obj, obj2, comp, xcomp,oblθ

A predicate can govern these functions, i.e., subcategorize forthem.

Non-governable functions: adj, xadj

adj: David devoured a sandwich yesterday.xadj: Having opened the window, David took a deep breath.

Discourse functions: topic, focus

For topic-oriented languages (e.g., Russian)Potentially useful for UDC handling

Introduction C-structure F-structure Licensing a string Phenomena References

Grammatical functions

Governable & non-governable grammatical functions

Overview:

Governable Non-governable

Unrestricted Restricted

subj oblθobj comp adjobj2 xcomp xadj

Semantically restricted = thematic restrictions (θ) can beplaced on function

oblθ: thematically restricted oblique functions (e.g., Englishto-PPs)

Open clausal functions (no internal subject): xcomp, xadjcomp: sentential or closed (nonpredicative) infinitivalcomplementxcomp: open (predicative) complement with subjectexternally controlled

Introduction C-structure F-structure Licensing a string Phenomena References

Subcategorization

Subcategorization

Subcategorization is done at f-structure

Verbs select for grammatical functions

Use the pred (predicate) feature to specify the semanticform, e.g.,

yawn: pred ’yawn<subj>’hit: pred ’hit<subj,obj>’give: pred ’give<subj,obj,objtheme>’eat: pred ’eat<subj,(obj)>’

Notationally, you may also see, e.g., pred ’yawn<(↑subj)>’

Introduction C-structure F-structure Licensing a string Phenomena References

F-structure features

F-structure representation: Simple F-structures

F-structure is a function from attributes to values

For the proper noun David, pred and num are attributes;’David’ and sg are the corresponding values

(5)[

pred ’David’num sg

]

F-structures within f-structures: David yawned

(6)

pred ’yawn<subj>’tense past

subj

[

pred ’David’num sg

]

Introduction C-structure F-structure Licensing a string Phenomena References

F-structure features

F-structure features

What sorts of features can be used?

Decision is up to the grammar writer.Commonly used features in LFG include aspect, prontype,vform, cf. Dalrymple (2006, Table 2)

Note:

LFG does not have a mechanism to define a set of features orvalues that must be included in an f-structure.For example, one verb may define vform, while another mightleave it undefined.

This is different from HPSG, as we’ll see.

Introduction C-structure F-structure Licensing a string Phenomena References

F-structure features

F-structure: Sets

Values can be sets, in order to handle phenomena with anunbounded number of elements, e.g., adjuncts, coordinates

(7) David yawned quietly yesterday.

(8)

pred ’yawn<subj>’tense past

subj

[

pred ’David’num sg

]

adj

{[

pred ’quietly’]

[

pred ’yesterday’]

}

Introduction C-structure F-structure Licensing a string Phenomena References

F-structure features

F-structure: Attributes with Common Values

Attributes can share the same values, to describe phenomena suchas raising.

(9) David seemed to yawn.

(10)LFG notation: Equivalent HPSG-style notation:

pred ’seem<xcomp>subj’tense past

subj

[

pred ’David’num sg

]

xcomp

[

pred ’yawn<subj>’subj

]

pred ’seem<xcomp>subj’tense past

subj 1

[

pred ’David’num sg

]

xcomp

[

pred ’yawn<subj>’subj 1

]

Introduction C-structure F-structure Licensing a string Phenomena References

General constraints

The nature of f-structure

An f-structure is restricted by the principles of

Completeness: A predicate and all its arguments must be apart of the structure.

Coherence: All arguments in the structure must be requiredby a predicate.

Introduction C-structure F-structure Licensing a string Phenomena References

General constraints

Completeness

Argument list of a semantic form = list of governablegrammatical functions

Completeness: All governable grammatical functionsmentioned in the predicate must be present in the f-structure.

Example:

(11) a. pred ’devour<subj,obj>’

b. * David devoured.

Definition (Kaplan and Bresnan, 1995, p. 65):

An f-structure is locally complete iff it contains all thegovernable grammatical functions that its predicate governs.An f-structure is complete iff it and all its subsidiaryf-structures are locally complete.(subsidiary f-structures = f-structures contained in it)

Introduction C-structure F-structure Licensing a string Phenomena References

General constraints

Coherence

Coherence: All governable grammatical functions present inthe f-structure must be mentioned in the argument list of thepredicate.Like completeness, but in the other direction.

Example:

(12) a. * David yawned the sink.

b.

pred ’yawn<subj>’

subj[

pred ’David’]

obj[

pred ’sink’]

Definition (Kaplan and Bresnan, 1995, p. 65):An f-structure is locally coherent iff all the governablegrammatical functions that it contains are governed by a localpredicate.An f-structure is coherent iff it and all its subsidiaryf-structures are locally coherent.

Introduction C-structure F-structure Licensing a string Phenomena References

General constraints

Uniqueness (consistency)

A third condition is often mentioned: Uniqueness(Consistency)

= Every attribute has a single value.

This does not need to be explicitly stated or enforced, though.It follows from interpreting attributes as functions (cf.unification).

Example: Ensuring subject-verb agreeement:

(13) a. * The boys yawns.

b.

pred ’yawn<subj>’

subj

[

pred ’boys’num sg/pl

]

Definition:In a given f-structure, a particular attribute may have at mostone value.

Introduction C-structure F-structure Licensing a string Phenomena References

Functional constraints

Constraining f-structures

We use functional equations (defining equations) on wordsand phrases to describe acceptable f-structures.

F-description with a single equation:

(14) (g num) = sg

Different f-structures which satisfy this f-description:

(15) a.[

num sg]

b.

pred ’Charlie’gend mascnum sg

Introduction C-structure F-structure Licensing a string Phenomena References

Functional constraints

Functional Constraints (formally)

(16) (fa) = v holds iff f is an f-structure, a is a symbol, and thepair 〈a, v〉 ∈ f

⇒ The f-structure for an utterance is the minimal solutionsatisfying the constraints introduced by the words and phrasestructure of the utterance.

minimal solution: satisfies all constraints in the f-descriptionand has no additional structure

Introduction C-structure F-structure Licensing a string Phenomena References

Functional constraints

Constraining equations

Can also use constraining equations to check the propertiesof the minimal solution

For example, the subj of f must meet certain conditions: (fsubj num) =c sg

Defining equations and constraining equations are similarenough to ignore the distinction in the following.

Introduction C-structure F-structure Licensing a string Phenomena References

Functional constraints

Functional constraints example

Lexical constraints:

John

(g pred) = ’John’(g num) = sg

runs

(f pred) = ’run<subj>’(f subj case) = nom(f subj num) = sg

Phrasal constraints (more on this later):

(f subj) = g

Introduction C-structure F-structure Licensing a string Phenomena References

Functional constraints

Functional constraints example (cont.)

Combining lexical and phrasal constraints, we have:

(f subj) = g(g pred) = ’John’(g num) = sg(f pred) = ’run<subj>’(g case) = nom(g num) = sg

Minimal solution:

f :

pred ’run<subj>’

subj g:

pred ’John’case nomnum sg

Introduction C-structure F-structure Licensing a string Phenomena References

More functional constraints

More functional constraints

We want more ways to define the set of acceptable f-structures

DisjunctionNegationExistential ConstraintsOptionality

Introduction C-structure F-structure Licensing a string Phenomena References

More functional constraints

Disjunction

Disjunction: different options can be used to satisfy anf-description

(17) I met/have met him.

Lexical entry for met:

(f pred) = ’meet<subj,obj>’{(f tense) = past | (f form) = pastpart}

Introduction C-structure F-structure Licensing a string Phenomena References

More functional constraints

Negation

Negation: an f-description is specified that cannot be true

(18) a. I know whether/if David yawned.

b. You have to justify whether/*if your journey is reallynecessary.

⇒ if is not allowed with justify (unlike know)

justify V (f comp compform) 6= if

Introduction C-structure F-structure Licensing a string Phenomena References

More functional constraints

Existential Constraints

Existential constraint: an f-structure must have some attribute,but the value of that attribute is unconstrained.

(19) a. The man who yawns/yawned/will yawn.

b. * The man who yawning.

⇒ In a relative clause, yawn must be tensed, but which tense isnot important

Relative clause constraint is simply: (f tense)

Can also specify negative existential constraints, e.g., ¬ (f tense)

Introduction C-structure F-structure Licensing a string Phenomena References

More functional constraints

OptionalityOptionality: an f-description may (or may not) be satisfied(20) a. Juan

Juancomprobought

una

relojwatch

aprep

Pedro.Pedro

b. JuanJuan

lehim

comprobought

una

reloj.watch

c. JuanJuan

lehim

comprobought

una

relojwatch

aprep

Pedro.Pedro

‘Juan bought a watch for Pedro.’

By specifying the semantic information contributed by le asoptional, both Pedro and le can appear in the same sentence.

Pedro N (f pred) = ’Pedro’

le Pro ((f pred) = ’pro’)

Note: Which objects can be doubled or dropped in Spanish iscomplex and depends on the semantic role (e.g., the abovecase is for benefactive/experiencer objects).

Introduction C-structure F-structure Licensing a string Phenomena References

Part III: How a string is licensed

A context-free c-structure grammar licenses the c-structure ofa string.

The grammar is augmented with functional equations, whichmap the c-structure to an f-structure representation.

A function φ (phi) maps the c-structure to the f-structure of asentence.

It is a function, so each c-structure is related to only onef-structure (but not necessarily vice versa, i.e., it can be amany-to-one mapping)

V

yawned

φ(V ):

[

pred ’yawn<subj>’tense past

]

Introduction C-structure F-structure Licensing a string Phenomena References

The Head Convention

Multiple c-structures can map onto the same f-structure → thisallows nodes to inherit properties from their head

VP

V’

V

yawned

φ(VP) = φ(V’) = φ(V):

[

pred ’yawn<subj>’tense past

]

Introduction C-structure F-structure Licensing a string Phenomena References

F-structure/C-structure Regularities

Can have set mappings for particular positions, e.g., the specifierof IP in English maps to subj

the same position in Russian maps to topic and in Bulgarianto focus

IP

NP

N

David

I’

VP

V

yawned

φ(IP):

[

pred ’yawn<subj>’

subj[

pred ’David’]

]

φ(NP):[

pred ’David’]

Introduction C-structure F-structure Licensing a string Phenomena References

Notation

Notation

A way to specify this constraint on the specifier of IP is thefollowing:

(21) IP → XP(↑subj) = ↓

I’↑ = ↓

This says: The value of subj for XP’s mother is equal to XP’sf-structure

IP and I’ have the same f-structure

Introduction C-structure F-structure Licensing a string Phenomena References

Notation

Annotated Phrase Structure Rules

(22) V’ → V↑ = ↓

NP(↑obj) = ↓

(23) VP → V↑ = ↓

NP(↑obj) = ↓

NP(↑obj2) = ↓

(24) VP → V↑ = ↓

NP(↑obj) = ↓

PP(↑obj2) = ↓(↑pform) = to

Introduction C-structure F-structure Licensing a string Phenomena References

Notation

Lexical Entries

Can use the same notation to express lexical entries

(25) a. yawned V (↑pred) = ’yawn<subj>’(↑tense) = past

b. David N (↑pred) = ’David’

The complete setup is best illustrated with an example.

Introduction C-structure F-structure Licensing a string Phenomena References

Example

Example grammar: C-structure rules with annotations(based on Kaplan and Bresnan, 1995, pp. 40ff)

(26) a. S → NP(↑subj) = ↓

VP↑ = ↓

b. NP → Det↑ = ↓

N↑ = ↓

c. VP → V↑ = ↓

NP(↑obj) = ↓

NP(↑obj2) = ↓

Introduction C-structure F-structure Licensing a string Phenomena References

Example

Example grammar: Lexicon

(27) a. a Det (↑spec) = a(↑num) = sg

b. girl N (↑num) = sg(↑pred) = ’girl’

c. handed V (↑tense) = past(↑pred) = ’hand<(↑subj),

(↑obj), (↑obj2)>’

d. the Det (↑spec) = the

e. baby N (↑num) = sg(↑pred) = ’baby’

f. toy N (↑num) = sg(↑pred) = ’toy’

Introduction C-structure F-structure Licensing a string Phenomena References

Example

A sentence licensed by the example grammar

f1:S

↑ = ↓

f3:VP

(↑obj2)=↓

f5:NP

(↑num)=sg(↑pred)=‘to

N

toy

(↑spec)=a(↑num)=sg

Det

a

(↑obj)=↓

f4:NP

(↑num)=sg(↑pred)=‘baby’

N

baby

(↑det)=theDet

the

(↑tense)=past(↑pred)=‘hand<. . .>’

V

handed

(↑subj)=↓

f2:NP

(↑n)=sg(↑pred)=‘girl’

N

girl

(↑spec)=a(↑num)=sg

Det

A

Introduction C-structure F-structure Licensing a string Phenomena References

Example

The resulting f-structure for the example sentence

f1, f3:

subj f2:

spec anum sgpred ’girl’

tense pastpred ‘hand <(↑subj), (↑obj), (↑obj2)>’

obj f4:

spec thenum sgpred ‘baby’

obj2 f5 :

spec anum sgpred ‘toy’

Introduction C-structure F-structure Licensing a string Phenomena References

Example

Computational issues

Processing c-structure by itself is essentially equivalent toprocessing CFGs, which is very efficient

How does one account for f-structures?

Can be interleaved, which requires sophisticated algorithms todo this efficiently.

Can post-processc-structures with f-structure constraints.

It has been shown that if an f-structure is acyclic, the set of stringsit corresponds to are equivalent to a context-free language.

This can help constrain both parsing and generation.

Introduction C-structure F-structure Licensing a string Phenomena References

Part IV: Phenomena

Head mobility

Passives

Unbounded dependency phenomena (Extraction)

Nonfinite Constructions

Introduction C-structure F-structure Licensing a string Phenomena References

Head mobility

Head mobility

Phenomenon: The position of a main verb w.r.t. adverbsdepending upon the presence of an auxiliary

Solution: use different categories

(28) a. mange T (↑pred) = ’eat<(↑subj),(↑obj)>’

(↑tense) = present

b. mange T (↑pred) = ’eat<(↑subj),(↑obj)>’

c. ai T (↑tense) = present

Introduction C-structure F-structure Licensing a string Phenomena References

Head mobility

Head mobility: main verb as T

TP

NP

Je

T’

T

mange

VP

V’

AdvP

souvent

V’

NP

des pommes

Introduction C-structure F-structure Licensing a string Phenomena References

Head mobility

Head mobility: main verb as V

TP

NP

J’

T’

T

ai

VP

V’

AdvP

souvent

V’

V

mange

NP

des pommes

Introduction C-structure F-structure Licensing a string Phenomena References

Passives

Passives

Passives are handled entirely via the lexicon

Lexical rules (or the like) relate one lexical entry to another,e.g., a +en rule:

(29) a. kiss V (↑pred) = ’kiss<(↑subj),(↑obj)>’

b. (↑subj) ⇒ ∅,(↑obj) ⇒ (↑subj)

c. kiss V (↑pred) = ’kiss<∅ (↑subj)>’

Introduction C-structure F-structure Licensing a string Phenomena References

Extraction

Extraction: Functional uncertainty

Extraction is handled in LFG by functional uncertainty:

a functional equation sets up a relation between some initial,extracted object with an OBJ grammatical function later inthe sentence.

(30) CP → XP(↑topic) = ↓(↑topic) = (↑comp* obj)

C’↑ = ↓

This says that the topic element is equated with an objfound under some path of comp functions.

Introduction C-structure F-structure Licensing a string Phenomena References

Extraction

Extraction example

(31) What do you think Chris bought?

(32)

topic[

pred ’what’]

pred ’think<subj,comp>

subj[

pred ’pro’]

comp

pred ’buy<subj,obj>

subj[

pred ’Chris’]

obj

The principle of completeness ensures that bought has arealized object, and the functional equation fills it in.

Introduction C-structure F-structure Licensing a string Phenomena References

Extraction

Extraction example 2

(33) What do you think Chris hoped David bought?

(34)

topic[

pred ’what’]

pred ’think<subj,comp>

subj[

pred ’pro’]

comp

pred ’hope<subj,comp>

subj[

pred ’Chris’]

comp

pred ’buy<subj,obj>

subj[

pred ’David’]

obj

Introduction C-structure F-structure Licensing a string Phenomena References

Nonfinite constructions

Nonfinite constructions

(35) John tries to smile.

(36) John seems to smile.

Equi: Verb embedding infinitive assigns two thematic roles.

(37) tries V (↑pred) = ’try<(↑subj),(↑xcomp)>’

(↑subj) = (↑xcomp subj)

Raising: Verb embedding infinitive assigns one thematic role.

(38) seems V (↑pred) =’seem<(↑xcomp)>’

(↑subj) = (↑xcomp subj)

Introduction C-structure F-structure Licensing a string Phenomena References

Nonfinite constructions

Nonfinite constructions (cont.)

Depending on the interface to semantics employed, sometimes thefunctions not assigned to a semantic role are notated after theangled brackets<>:

(39) seems V (↑pred) = ’seem<(↑xcomp)>(↑subj)’

(↑subj) = (↑xcomp subj)

Introduction C-structure F-structure Licensing a string Phenomena References

Nonfinite constructions

Dalrymple, Mary (2006). Lexical Functional Grammar. In KeithBrown (ed.), Encyclopedia of Language and Linguistics. SecondEdition, Oxford: Elsevier, vol. 7, pp. 82–94.

Gazdar, Gerald, Ewan Klein, Geoffrey K. Pullum and Ivan A. Sag(1985). Generalized Phrase Structure Grammar . Cambridge,MA: Harvard University Press.

Kaplan, Ronald M. and Joan Bresnan (1995). Lexical-FunctionalGrammar: A Formal System for Grammatical Representations.In Mary Dalrymple, Ronald M. Kaplan, III Maxwell, John t. andAnnie Zaenen (eds.), Formal issues in Lexical-FunctionalGrammar , Stanford, CA: CSLI Publications, pp. 29–130.