Introduction to Lexical Functional Grammar
Mary Dalrymple, John Lowe, & Louise Mycock
Centre for Linguistics and Philology
Oxford University
Konstanz, November/December 2012
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• “Semantic roles, syntactic constituents, and grammatical functions belong to parallel
information structures of very different formal character. They are related not by
proof-theoretic derivation but by structural correspondences, as a melody is related to the
words of a song. The song is decomposable into parallel melodic and linguistic structures,
which jointly constrain the nature of the whole. In the same way, the sentences of human
language are themselves decomposable into parallel systems of constraints – structural,
functional, semantic, and prosodic – which the whole must jointly satisfy.” (Bresnan, 1990)
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LFG
Two aspects of syntactic structure:
• Functional structure is the abstract functional syntactic organisation of the sentence,
familiar from traditional grammatical descriptions, representing syntactic predicate-argument
structure and functional relations like subject and object.
• Constituent structure is the overt, more concrete level of linear and hierarchical
organisation of words into phrases.
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LFG’s c-structure and f-structure
IP
NP
I′
N
VP
David
V′

V
NP
greeted
N
PRED

 SUBJ



OBJ

‘ GREEThSUBJ , OBJi’
h
i 

PRED ‘DAVID ’

h
i 

PRED ‘C HRIS ’
Chris
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1
Functional structure

PRED

 TENSE PAST

"


PRED
 SUBJ
NUM
•
•
•
•

‘ GOhSUBJ i’


#

‘DAVID ’ 

SG
PRED , TENSE NUM :
attributes
‘ GOhSUBJ i’, DAVID, SG: values
PAST , SG : symbols (a kind of value)
‘ BOY ’, ‘ GOhSUBJ i’: semantic forms
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F-structures


PRED ‘ GO hSUBJ i’


 TENSE PAST



"
#




PRED ‘DAVID ’
 SUBJ



NUM SG




nh
io


PRED ‘ QUICKLY ’
ADJ
An f-structure can be the value of an attribute. Attributes with f-structure values are the
grammatical functions: SUBJ , OBJ , OBJθ , COMP, XCOMP, ...
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F-structures

PRED

‘ GOhSUBJ i’


 TENSE PAST



"
#




PRED ‘DAVID ’
 SUBJ



NUM SG




nh
io


PRED ‘ QUICKLY ’
ADJ
A set of f-structures can also be a value of an attribute.
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Sets of f-structures

PRED
‘ GOhSUBJ i’

 TENSE PAST

h




 PRED

 SUBJ

h



 PRED



nh

ADJ
PRED






‘DAVID ’




i 


‘G EORGE ’  

io 

‘ QUICKLY ’
i
Sets of f-structures represent:
• adjuncts (there can be more than one adjunct) or
• coordinate structures (there can be more than one conjunct)
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2
C- and F-Structure
V
φ
greeted
"
PRED
TENSE
‘ GREEThSUBJ , OBJ i’
PAST
#
φ function relates c-structure nodes to f-structures.
(Function: Every c-structure node corresponds to exactly one f-structure.)
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Constraining the c-structure/f-structure correspondence
V′
φ
V
"
PRED
TENSE
‘ YAWNhSUBJ i’
PAST
#
yawned
V′
−→ V
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Local F-Structure Reference
V′
φ
V
"
PRED
TENSE
‘ YAWNhSUBJ i’
PAST
#
yawned
V′
−→ V
the current c-structure node (“self”):
the immediately dominating node (“mother”):
the c-structure to f-structure function:
∗
b
∗
φ
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Rule Annotation
V′
V
φ
"
PRED
TENSE
‘ YAWNhSUBJ i’
PAST
#
yawned
V′
−→
V
φ(b
∗) = φ(∗)
mother’s (V′ ’s) f-structure = self’s (V’s) f-structure
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3
Simplifying the Notation
φ(b
∗)
φ(∗)
(mother’s f-structure)
(self’s f-structure)
φ
V′
"
V
=↑
=↓
‘ YAWNhSUBJ i’
PRED
TENSE
PAST
#
yawned
−→
V′
V
↑= ↓
mother’s f-structure = self’s f-structure
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Using the Notation
−→
V′
V
↑= ↓
mother’s f-structure = self’s f-structure
[]
V′
V
↑ =↓
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More rules
−→
V′
V
φ(b
∗) = φ(∗)
NP
(φ(b
∗) OBJ ) = φ(∗)
mother’s f-structure’s
OBJ
= self’s f-structure
In simpler form:
−→
V′
V
↑= ↓
NP
(↑
OBJ )
=↓
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Using the Notation
−→
V′
h
′
V
V
V
↑= ↓
NP
(↑
OBJ
OBJ )
[]
=↓
i
NP
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4
Terminal nodes
"
V
yawned
‘ YAWNhSUBJ i’
PRED
TENSE
PAST
#
Expressible as:
V
−→
(↑
yawned
= ‘ YAWNhSUBJ i’
(↑ TENSE) = PAST
PRED )
Standard form:
yawned V
(↑
(↑
PRED )
= ‘ YAWNhSUBJ i’
TENSE ) = PAST
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Phrase structure rules: English
IP
−→
NP
(↑
I′
SUBJ )
=↓
I
VP
↑= ↓
↑= ↓
−→
I′
↑= ↓
V
↑= ↓
VP −→
N
↑= ↓
NP −→
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Lexical entries: English
yawned V
David
N
(↑
(↑
(↑
PRED )
= ‘ YAWNhSUBJ i’
TENSE ) = PAST
PRED )
= ‘DAVID ’
(Standard LFG practice: include only features relevant for analysis under discussion.)
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5
Analysis: English
IP
(↑ fip
I′
↑ fip = ↓fi′
NP
SUBJ ) = ↓fnp
N
↑ fnp = ↓fn
VP
↑ fi′ = ↓fvp
David
(↑ fn PRED ) = ‘DAVID ’
V
↑ fvp = ↓fv
yawned
(↑ fv PRED ) = ‘ YAWNhSUBJ i’
(↑ fv TENSE) = PAST
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Solving the Description
(fip SUBJ ) = fnp
fnp = fn
(fn PRED ) = ‘DAVID ’
fip = fi′
fi′ = fvp
fvp = fv
(fv PRED ) = ‘ YAWNhSUBJ i’
(fv TENSE) = PAST
fip
fi′
fvp
fv

PRED

‘ YAWNhSUBJ i’
 TENSE PAST



fnp h
SUBJ
PRED
fn
‘DAVID ’


i

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Final result

IP
NP
(fip SUBJ ) = fnp
I′
fip = fi′
N
fnp = fn
VP
fi′ = fvp
(fn
David
= ‘DAVID ’
PRED )
(fv

PRED ‘ YAWN hSUBJ i’


 TENSE PAST



h
i


SUBJ
PRED ‘DAVID ’
V
fvp = fv
yawned
= ‘ YAWNhSUBJ i’
(fv TENSE) = PAST
PRED )
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6
Semantics in LFG
IP
NP
I′
N′
VP
N
V′
John

V
NP
married
N′
PRED

 SUBJ



OBJ

‘ MARRYhSUBJ , OBJ i’
h
i 

PRED ‘J OHN ’


h
i

PRED ‘R OSA ’
N
Rosa
Meaning: marry(john, rosa)
How is this meaning composed?
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Glue: Composing meanings via deduction
Glue (Asudeh, 2004, 2012; Dalrymple, 1999, 2001): Meaning assembly and linear logic
• Logic of meanings (semantic level):
the level of meanings of utterances and phrases
• Logic for composing meanings (‘glue’ level):
the level responsible for assembling the meanings of parts to get the meaning of the whole
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Meanings
Meanings are expressions like David , yawn(David) , yawn ...
Function: when applied to an argument, yields a unique value.
yawn : applied to David , yields “true”.
applied to Fred , yields “true”.
applied to George , yields “false”.
...
Function application:
yawn applied to David = yawn(David)
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7
Application and abstraction
Lambda abstraction:
λX.P represents a function from entities represented by X to entities represented by P .
Usually, the expression P contains at least one occurrence of the variable X, and we say that
these occurrences are bound by the λ lambda operator.
Function application:
[λX.P ](a)
The function λX.P is applied to the argument a.
Equivalent to the expression that results from replacing all occurrences of X in P with a.
Example: [λX.yawn (X)](David ) ≡ yawn (David )
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Meaning contributions

PRED


 SUBJ



OBJ

‘ MARRYhSUBJ , OBJ i’
h
i 


PRED ‘J OHN ’


h
i

PRED ‘R OSA ’
• The word John contributes the meaning john.
• The word Rosa contributes the meaning rosa.
• The word married contributes meaning assembly instructions of the following form: When
given a meaning x for my subject and a meaning y for my object, I produce a meaning
marry(x, y) for my sentence.
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Contribution of ‘John’
NP
N′
N
john:[ ]
h
PRED
‘J OHN ’
i
John
• Every f-structure has a corresponding semantic structure, related to it by the projection
function σ (represented by a dotted line).
• john:[ ] is a meaning constructor.
• In the lexicon: john:↑σ
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8
Meaning assembly: Gluing meanings together

PRED

 SUBJ

OBJ
‘ MARRYhSUBJ , OBJ i’
[]
[]




λy .λx.marry(x, y):oσ −◦(sσ −◦mσ )
λy.λx .marry(x, y ): a relation between two individuals x and y that holds if x marries y
oσ −◦(sσ −◦mσ ): If I am provided with the semantic structure of my object and then the semantic
structure of my subject, I produce the semantic structure of the sentence.
In the lexicon: λy .λx.marry(x, y):(↑
OBJ )σ −◦((↑ SUBJ )σ −◦↑σ )
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Proof rules
X : fσ
P : fσ −◦ gσ
P (X) : gσ
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Meaning proof for ‘married Rosa’
X : fσ
P : fσ −◦ gσ
P (X) : gσ
rosa:oσ
λy.λx.marry(x, y ):oσ −◦(sσ −◦mσ )
λx.marry(x, rosa):sσ −◦mσ
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Meaning proof for ‘John married Rosa’
X : fσ
P : fσ −◦ gσ
P (X) : gσ
rosa:oσ
λy.λx.marry(x, y ):oσ −◦(sσ −◦mσ )
λx.marry(x, rosa):sσ −◦mσ
marry(john, rosa): mσ
john:sσ
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9
Details are not important for theory of information structure and prosody
Our theory of meaning composition, to be explained in the following:
rosa:oσ
λy.λx.marry(x, y ):oσ −◦(sσ −◦mσ )
λx.marry(x, rosa):sσ −◦mσ
marry(john, rosa): mσ
john:sσ
In fact, however, the details won’t be important for our discussion of information structure. We
can use abbreviations like the following, where Rosa stands for any reasonable theory of the
meaning of Rosa and how it combines with the rest of the sentence:
Rosa
married
married-Rosa
marry(john, rosa): mσ
John
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Bibliography
Asudeh, Ash. 2004. Resumption as Resource Management. Ph.D. thesis, Stanford University.
Asudeh, Ash. 2012. The Logic of Pronominal Resumption. Oxford: Oxford University Press.
Bresnan, Joan. 1990. Parallel constraint grammar project. CSLI Calendar, 4 October 1990,
volume 6:3.
Dalrymple, Mary (editor). 1999. Semantics and Syntax in Lexical Functional Grammar: The
Resource Logic Approach. Cambridge, MA: The MIT Press.
Dalrymple, Mary. 2001. Lexical Functional Grammar , volume 34 of Syntax and Semantics. New
York: Academic Press.
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