Lecture 5
.
......
Syntactic Formalisms for Parsing
Natural Languages
Aleš Horák, Miloš Jakubíček, Vojtěch Kovář
(based on slides by Juyeon Kang)
ia161@nlp.fi.muni.cz
Autumn 2013
IA161 Syntactic Formalisms for Parsing Natural Languages 1 / 56
Lecture 5
.
...... Parsing with (L)TAG and LFG
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Lecture 5
(Lexicalized) Tree Adjoining Grammar (TAG) and
Lexical Functional Grammar (LFG)
A) Same goal
formal system to model human speech
model the syntactic properties of natural language
syntactic frame work which aims to provide a computaionally
precise and psychologically realistic representation of language
B) Properties
Unfication based
Constraint-based
Lexicalized grammar
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Lecture 5
How to parse the sentence in TAG?
by Joshi, A. Levy, L and Takahashi, M. in 1975
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Lecture 5
TAG’s basic component
Representation structure: phrase-structure trees
Finite set of elementary trees
Two kinds of elementary trees
Initial trees (α): trees that can be substituted
Auxiliary trees (β): trees that can be adjoined
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Lecture 5
TAG’s basic component
The tree in (X ∪ Z) are called elementary trees.
Initial tree: Auxiliary tree:
terminal nodes or
substitution nodes
Z
Z*
X
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Lecture 5
TAG’s basic component
An initial tree (α)
all interior nodes are labeled with non-terminal symbols
the nodes on the frontier of initial tree are either labeled with
terminal symbols, or with non-terminal symbols marked for
substitution (↓)
An auxiliary tree (β)
one of its frontier nodes must be marked as foot node (∗)
the foot node must be labeled with a non-terminal symbol which is
identical to the label of the root node.
A derived tree (γ)
tree built by composition of two other trees
the two composition operations that TAG uses adjoining and
substitution.
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Lecture 5
Main operations of combination (1): adjunction
Sentence of the language of a TAG are derived from the
composition of an α and any number of β by this operation.
It allows to insert a complete structure into an interior node of
another complete structure.
Three constraints possible
Null adjunction (NA)
Obligatory adjunction (OA)
Selectional adjunction (SA)
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Lecture 5
Main operations of combination (1): adjunction
Y
S
NP0↓
NP1↓ NP1↓
NP0↓
VP VP VP
VP
V
VV VP*V has
has lovedloved
S
X
X
X*
X
Y
(α)
(α2
)
Adjoining
(β1
)
+ →
(β) (γ)
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Lecture 5
Main operations of combination (2): substitution
It inserts an initial tree or a lexical tree into an elementary tree.
One constraint possible
Selectional substitution
S
NP0↓
NP1↓ N
NP0↓
VP NP VP
VP
V
D↓D↓ NV loved
womanwomanloved
S
X
A↓ A
(α2
)
Substitution
(α3
)
+ →
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Lecture 5
Adjoining constraints
Selective Adjunction (SA(T)): only members of a set T ⊆ A can
be adjoined on the given node, but the adjunction
is not mandatory
Null Adjunction (NA): any adjunction is disallowed for the
given node (NA = SA(ϕ))
Obligatory Adjunction (OA(T)): an auxiliary tree member of
the set T ⊆ A must be adjoined on the given node
for short OA = OA(A)
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Lecture 5
Example 1: selective adjunction (SA)
One possible analysis of “send” could involve selective
adjunction:
α1 β1 β2
S VP VP
NP↓ VPSA(β1,β2,...) VP* away VP* PP
send NP↓ P NP↓
to
send
send away
send to
send something
IA161 Syntactic Formalisms for Parsing Natural Languages 12 / 56
Lecture 5
Example 2: obligatory adjunction
For when you absolutely must have adjunction at a node:
α1 β1 β2
S VP VP
NP↓ VPOA(β1,β2) Aux VP* Aux VP*
V has is
seen
has
is
has seen
is seen
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Lecture 5
Elementary trees (initial trees and auxiliary trees)
Yesterday a man saw Mary
S NP
Adv S* D D↓ N
(βyest) (αa) (αman)
yesterday a man
S
NP0 ↓ VP NP
V NP1 ↓ N
saw Mary
*: foot node/root node
↓: substitution node
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Lecture 5
Elementary trees (initial trees and auxiliary trees)
S
Ad S
yesterday NP VP
D N V NP
a man saw N
(α5)
Mary
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Lecture 5
Derivation tree
Specifies how a derived tree was constructed
The root node is labeled by an S-type initial tree.
Other nodes are labeled by auxiliary trees in the case of adjoining
or initial trees in the case of substitution.
A tree address of the parent tree is associated with each node.
saw
man(1) Mary(2.2) yest (0)
a (1)
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Lecture 5
Derivation tree and derived tree α5
saw
man(1) Mary(2.2) yest (0)
a (1)
S
Ad S
yesterday NP VP
D N V NP
a man saw N
(α5)
Mary
_ _ _ _ : substitution operation
______ : adjunction operation
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Lecture 5
Example 1: Harry likes peanuts passionately
Step 1 NP
Harry
NP
peanuts
S
NP VP
V NP
likes
VP
VP* ADV
passionatelyStep 2: substitution
NP
Harry
S
NP VP
V NP
likes
NP
peanuts
+ +
S
NP VP
V NP
likes
Harry
peanuts
Step 3: adjunction
S
NP VP
V NP
likes
Harry
peanuts
VP
VP* ADV
passionately
+
S
NP
VP
V NP
likes
Harry
peanuts
VP
ADV
passionately
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Lecture 5
Derivation tree and derived tree of Harry likes
peanuts passionately
likes
Harry(1) peanuts(2.2) passionately(2)
S
NP
VP
V NP
likes
Harry
peanuts
VP
ADV
passionately
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Lecture 5
Two important properties of TAG
Elementary trees can be of arbitrary size, so the domain of
locality is increased
Extended domain of locality (EDL)
Small initial trees can have multiple adjunctions inserted within
them, so what are normally considered non-local phenomena
are treated locally
Factoring recursion from the domain of dependency (FRD)
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Lecture 5
Extended domain of locality (EDL): Agreement
The lexical entry for a verb like “loves” will contain a tree like
the following:
S
NP3.sg↓ VP
V NP↓
loves
With EDL, we can easily state agreement between the subject
and the verb in a lexical entry
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Lecture 5
Factoring recursion from the domain of
dependency (FRD): Extraction
S’
NPi[+wh] S’
who COMP S
that NP VP
Bill V NP
likes ei
S’
COMP S
Φ INFL NP VP
did John V NP S’*
tell Sam
.
......
The above trees for the sentence “who did John tell Sam that Bill likes ?” allow the
insertion of the auxiliary tree in between the WH-phrase and its extraction site,
resulting a long distance dependency; yet this is factored out from the domain of
locality in TAG.
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Lecture 5
Factoring recursion from the domain of
dependency (FRD): Extraction
S’
NPi[+wh] S’
who COMP S
Φ INFL NP VP
did John V NP
tell Sam S’
COMP S
that NP VP
Bill V NP
likes ei
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Lecture 5
Variations of TAG
Feature Structure Based TAG (FTAG: Joshi and Shanker, 1988)
each of the nodes of an elementary tree is associated with two
feature structures:
top & bottom Substitution
Substitution with features
Adjoining with features
Y X Xtr
br
t U tr
br
X
Y
t
b
Y
tr
br
tf
bf
X
Y
t U tr
br
tf
b U bf
t
Y
Y*
Y
Y
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Lecture 5
Variations of TAG
Synchronous TAG (STAG: Shieber and Schabes, 1990)
A pair of TAGs characterize correspondences between languages
Semantic interpretation, language generation and translation
Muti-component TAG (MCTAG: Chen-Main and Joshi, 2007)
A set of auxiliary tree can be adjoined to a given elementary tree
Probabilistic TAG (PTAG: Resnik, 1992, Shieber, 2007)
Associating a probability with each elementary tree
Compute the probability of a derivation
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Lecture 5
XTAG Project (UPenn, since 1987 ongoing)
A long-term project to develop a wide-coverage grammar for
English using the Lexicalized Tree-Adjoining Grammar (LTAG)
formalism
Provides a grammar engineering platform consisting of a
parser, a grammar development interface, and a morphological
analyzer
The project extends to variants of the formalism, and languages
other than English
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Lecture 5
XTAG system
Input Sentence
P.O.S Blender
Tree Selection
Derivation Structure
Parser
Morph Analyzer Tagger
Tree Grafting
Morph DB
Stat DB
Trees DB
Syn DB
Lex Prob DB
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Lecture 5
Components in XTAG system
Morphological Analyzer & Morph DB: 317K inflected items
derived from over 90K stems
POS Tagger & Lex Prob DB: Wall Street Journal-trained 3-gram
tagger with N-best POS sequences
Syntactic DB: over 30K entries, each consisting of:
Uninflected form of the word
POS
List of trees or tree-families associated with the word
List of feature equations
Tree DB: 1004 trees, divided into 53 tree families and 221
individual trees
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Lecture 5
(a) Morphology database (b) syntactic database
Interfaces to the database maintenance tools
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Lecture 5
Interface to the XTAG system
Parser evaluation in XTAG Project by [Bangalore,S. et.al, 1998]
http://www.cis.upenn.edu/~xtag/
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Lecture 5
How to parse the sentence in LFG?
by Bresnan, J. and Kaplan, R.M. In 1982
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Lecture 5
Main representation structures
c-structure: constituent structure
level where the surface syntactic form, including categorical
information, word order and phrasal grouping of constituents,
is encoded.
f-structure: functional structure
internal structure of language where grammatical relations
are represented. It is largely invariable across languages.
(e.g. SUBJ, OBJ, OBL, (X)COMP, (X)ADJ)
a-structure: argument structure
They encode the number, type and semantic roles of the
arguments of a predicate.
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Lecture 5
Level of structures and their interaction in LFG
Functional
Projection architecture
semantic
structure
information
structure
phonological
structure
argument
structure
functional
structure
constituent
structure
LFG's
focus
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Lecture 5
Level of structures and their interaction in LFG
In LFG, the parsing result is grammatically correct only if it
satisfies 2 criteria:
1 the grammar must be able to assign a correct c-structure
2 the grammar must be able to assign a correct well-formed
f-structure
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Lecture 5
c-structure
C-structure
PP
P NP
with N
friends
S
NP VP
N V NP
I saw Det N
the girl
The constituent structure represents the organization of overt phrasal syntax
It provides the basis for phonological interpretation
Languages are very different on the c-structure level :external factors that usually vary by language
.
Properties of c-structure
..
......
c-structures are conventional phrase structure trees:
they are defined in terms of syntactic categories, terminal nodes, dominance and precedence.
They are determined by a context free grammar that describes all possible surface strings of the language.
LFG does not reserve constituent structure positions for affixes: all leaves are individual words.
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Lecture 5
f-structure
PRED OBJ
PRED NUM
PLURAL'friend'
'with' PRED 'friend'
NUM PLURAL
PRED 'with'
OBJ
Attribute-Value notation for f-structure
.
......
1 representation of the functional structure of a sentence
2 f-structure match with c-structure
3 it has to satisfy three formal constraints: consistency,
coherence, completeness
4 language are similar on this level: allow to explain
cross-linguistic properties of phenomena
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Lecture 5
Examples of f-structure
OBJ
TENSE
PRED
SUBJ
OBJ2
PRED
PAST
SUBJ, OBJ, OBJ2
PRED
PRED
DEF
NUM SG
SUBJ
TENSE
PRED
PRED
DEF
NUM SG
PAST
PCASE
OBJ PRED
DEF
NUM SG
'homework'
+
OBLon
+
'teacher'
-
'e-mail'
'Sabine'
'Veit'
OBLon
SUBJ, OBJ ''insist OBLon
'send '
1 2
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Lecture 5
Constraint 1: f-structure must be consistent
1 Two paths in the graph structure may designate the same
element-called unification, structure-sharing
Ex: John must leave
PRED XCOMP
PRED SUBJ
PRED
'leave'
'must'
'John'
SUBJ
PRED 'leave'
SUBJ
PRED 'must'
SUBJ
XCOMP
PRED 'John'
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Lecture 5
Constraint 1: f-structure must be consistent
2 attributes are functionally unique - there may not be two arcs
with the same attribute from the same f-structure
OBJOBJ
PRED 'Veit'
PRED 'Tom'
SUBJ
SUBJ
PRED
TENSE
TENSE
SUBJ ''sleep
PAST
FUT
Incosnistent f-structure
*
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Lecture 5
Constraint 1: f-structure must be consistent
3 The symbols used for atomic f-structure are distinct - it is
impossible to have two names for a single atomic f-structure
(“clash”)
PRED SUBJ
PRED NUM
'pro'
'sleep'
*They sleeps
excludedSINGULAR
/PLURAL
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Lecture 5
Constraint 2: f-structure must be coherent
All argument functions in an f-structure must be selected by
the local PRED feature.
SUBJ
PRED
TENSE
PRED
NUM SG
PERS 3
PRES
OBJ
PRED
NUM
PERS 3
SG
'Mary'
'John'
'fall 'SUBJ
SUBJ
PRED
TENSE
PRED
NUM SG
PERS 3
PRES
'John'
'fall 'SUBJ ?
Complete f-structure Incoherent f-structure
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Lecture 5
Constraint 3: f-structure must be complete
All functions specified in the value of a PRED feature must be
present in the f-structure of that PRED.
OBJ
PRED
NUM
PERS 3
SG
'Mary'
SUBJ
PRED
TENSE
PRED
NUM SG
PERS 3
PRES
'John'
'like 'SUBJ OBJ
Complete f-structure Incoherent f-structure
?
SUBJ
PRED
TENSE
PRED
NUM SG
PERS 3
PRES
'John'
'like 'SUBJ OBJ
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Lecture 5
Correspondence between different levels in LFG
C-structure
PP
P NP
Nwith
friends
PRED
OBJ
PRED
NUM PLURAL
'friend'
'with'
+
PP
P NP
Nwith
friends
PRED
OBJ
PRED
NUM PLURAL
'friend'
'with'
1
2
3
4
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Lecture 5
Structural correspondence
c-structures and f-structures represent different properties of an
utterance
How can these structures be associated properly to a particular
sentence?
Words and their ordering carry information about the linguistic
dependencies in thesentence
This is represented by the c-structure (licensed by a CFG)
LFG proposes simple mechanisms that maps between elements
from one structure and those of another: correspondence
functions
A function allows to map c-structures to f-structures Φ : N → F
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Lecture 5
Mapping the c-structure into the f-structure
Since there is no isomorphic relationship between structure and
function LFG assumes c-structure and f-structure
The mapping between c-structure and f-structure is the core of
LFG‘s descriptive power
The mapping between c-structure and f-structure is located in
the grammar (PS) rules
c-structure f-structure
S
NP VP
D N V NP
D Nthe mouse admired
the elephant
SUBJ
TENSE
PRED
OBJ
PRED
DEF
NUM
PERS
PAST
SUBJ OBJ
PRED
DEF
NUM
PERS 3
SG
SG
+
3
'mouse'
+
'elephant'
'admire '
?
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Lecture 5
Mapping mechanism: 6 steps
.
STEP 1: PS rules
..
......
Context-free phrase structure rules
Annotated with functional schemata
- EX.:
mother node
(without functional
schemata)
S NP VP
( SUBJ)= = daughter nodes
(with (a list of)
functional schemata)
- EX.: NP NP NP
= =
VP V (NP)
= ( SUBJ)=
Note:
is sometimes
omitted!
(this means nodes
without functional
schemata percolate
their entire
functional schema
unchanged to the
mother node
=
IA161 Syntactic Formalisms for Parsing Natural Languages 46 / 56
Lecture 5
Mapping mechanism: 6 steps
.
STEP 2: Lexicon entries
..
......
Lexicon entries consists of three parts: representation of the
word, syntactic category, list of functional schemata
Ex.: mouse N (↑PRED)=’mouse’
(↑PERS)=3
(↑NUM)=SG
the D (↑DEF)=+
admire V (↑PRED)=’admire ⟨(↑ SUBJ)(↑ OBJ)⟩’
-ed Aff (↑TENSE)=PAST
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Lecture 5
Mapping mechanism: 6 steps
.
STEP 3: c-structure
..
......
Like the PS rules, each node in the tree is associated with a functional schemata
With the functional schemata of the lexical entries at the leaves we obtain a complete c-structure
↔VP
↑=↓
NP
(↑ SUBJ) =↓
S →
S
(↑ SUBJ) =↓ ↑=↓
NP VP
S
(↑ SUBJ) =↓
NP
↑=↓
VP
↑=↓
D
↑=↓
N
↑=↓
V
(↑ OBJ) =↓
NP
(↑ DEF) = +
the
(↑ PRED) = ’mouse’
(↑ PRED) = 3
(↑ PRED) = SG
mouse
(↑ PRED) =
’admire ⟨(↑ SUBJ)(↑ OBJ)⟩ ’
(↑ TENSE) = PAST
admired
↑=↓
D
(↑ DEF) = +
the
↑=↓
N
(↑ PRED) = ’elephant’
(↑ PRED) = 3
(↑ PRED) = SG
elephant
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Lecture 5
Mapping mechanism: 6 steps
.
STEP 4: Co-indexation
..
......
An f-structure is assigned to each node of the c-structure
Each of these f-structures obtains a name (f1 − fn)
Nodes in the c-structure and associated f-structure are co-indexed, i.e. obtain the same name
F-structure names f1 − fn can be chosen freely but they may not occur twice
S
(↑ SUBJ) =↓
NP
↑=↓
VP
↑=↓
D
↑=↓
N
↑=↓
V
(↑ OBJ) =↓
NP
(↑ DEF) = +
the
(↑ PRED) = ’mouse’
(↑ PRED) = 3
(↑ PRED) = SG
mouse
(↑ PRED) =
’admire ⟨(↑ SUBJ)(↑ OBJ)⟩ ’
(↑ TENSE) = PAST
admired
↑=↓
D
(↑ DEF) = +
the
↑=↓
N
(↑ PRED) = ’elephant’
(↑ PRED) = 3
(↑ PRED) = SG
elephant
f1
f2 f5
f3 f4 f6 f7
f8 f9
f1[ ]
f2[ ] f3[ ] f4[ ]
f5[ ]
f6[ ]
f7[ ] f8[ ] f9[ ]
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Lecture 5
Mapping mechanism: 6 steps
.
STEP 5: Metavariable biding
..
......
All meta-variables are replaced by the names of the f-structure representation
S
(↑ SUBJ) =↓ ↑=↓
NP VP
f1
f2 f5
−→
S
(f1SUBJ) = f2 f1 = f5
NP VP
f1
f2 f5
S
(f1SUBJ) = f2
NP
f1 = f5
VP
f2 = f3
D
f1 = f4
N
f5 = f6
V
(f5OBJ) = f7
NP
(f3DEF) = +
the
(f4PRED) = ’mouse’
(f4PRED) = 3
(f4PRED) = SG
mouse
(f6PRED) =
’admire ⟨(f6SUBJ)(f6OBJ)⟩ ’
(f6TENSE) = PAST
admired
f7 = f8
D
(f8DEF) = +
the
f7 = f9
N
(f9PRED) = ’elephant’
(f9PRED) = 3
(f9PRED) = SG
elephant
f1
f2 f5
f3 f4 f6 f7
f8 f9
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Lecture 5
Mapping mechanism: 6 steps
.
......
We introduce at this point the notion of functional equation
By listing all functional equations from a c-structure we obtain
the functional description, called f-description
(f1SUBJ) = f2 (f6PRED) = ’admire ⟨(f6SUBJ)(f6OBJ)⟩ ’
f2 = f3 (f6TENSE) = PAST
(f3DEF) = + (f5OBJ) = f7
f2 = f4 f7 = f8
(f4PRED) = ’mouse’ (f8DEF) = +
(f4PERS) = 3 f7 = f9
(f4NUM) = SG (f9PRED) = ’elephant’
f1 = f5 (f9PERS) = 3
f5 = f6 (f9NUM) = SG
Table : f-description
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Lecture 5
Mapping mechanism: 6 steps
.
STEP 6: From f-description to f-structure
..
......
Computation of an f-structure is based on the f-description
For the derivation of f-structures from the f-description it is
important that no information is lost and that no information will
be added
The derivation is done by the application of the functional
equations
List of functional equations
a) simple equations of the form: fnA) = B
b) f-equations of the form: fn = fm
c) f-equations of the form: fnA) = fm
→ Functional equations with the same name are grouped into
an f-structure of the same name
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Lecture 5
Application of the functional equation (a): (fnA) = B
DEF =+
PRED ='mouse'
PERS =3
NUM =SG
PRED ='admire SUBJ OBJ '
TENSE =PAST
DEF =+
PRED ='ELEPHANT'
PERS =3
NUM =SG
PRED 'mouse'
PERS 3
NUM SG
PRED 'admire
TENSE PAST
SUBJ OBJ '
DEF +
DEF +
PRED 'elephant'
PERS 3
NUM SG
Application of the functional equation (b): fn = fm
PRED 'admire
TENSE PAST
SUBJ OBJ '
PRED 'mouse'
PERS 3
NUM SG
DEF + DEF +
PRED 'elephant'
PERS 3
NUM SG
DEF + DEF +
unification unification
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Lecture 5
Application of the functional equation (c): (fnA) = fm
SUBJ
OBJ
PRED 'mouse'
PERS 3
NUM SG
DEF +
PRED 'admire
TENSE PAST
SUBJ OBJ '
PRED 'elephant'
PERS 3
NUM SG
DEF +
PRED 'mouse'
PERS 3
NUM SG
DEF +
PRED 'elephant'
PERS 3
NUM SG
DEF +
SUBJ
OBJ
unification
unification
IA161 Syntactic Formalisms for Parsing Natural Languages 54 / 56
Lecture 5
.
STEP 1: lexical entries
..
......
made: V (↑PRED)=’MAKE⟨SUBJ,OBJ,XCOMP⟩’
(↑XCOMP SUBJ)=(↑OBJ)
(↑TENSE)=SIMPLEPAST
gave: V (↑PRED)=’GIVE⟨SUBJ,OBJ,OBJ2⟩’
(↑TENSE)=SIMPLEPAST
had said: V (↑PRED)=’SAY⟨SUBJ,OBJ⟩’
(↑TENSE)=PASTPERFECT
the: D (↑PRED)=’THE’
(↑SPECTYPE)=DEF
about: P (↑PRED)=’ABOUT⟨OBJ⟩’
which: N (↑PRED)=’PRO’
(↑PRONTYPE)=REL
John’s: D (↑PRED)=’JOHN’
(↑SPECTYPE)=POSS
many: D (↑PRED)=’MANY’
(↑SPECTYPE)=QUANT
things: N (↑PRED)=’THINGS’
(↑NUM)=PLURAL
.
STEP 2: c-structure
..
......
a. S →
NP
(↑ SUBJ) =↓
VP
↑=↓
b. NP →
{
A N
↑=↓ ↑=↓
}
c. VP →
V
↑=↓
NP
(↑ SUBJ) =↓
V
(↑ XCOMP) =↓
(↑ XCOMP PRED) = ’be ⟨SUBJ, PREDIC⟩ ’
d. V →
NP
(↑ PREDIC) =↓
IA161 Syntactic Formalisms for Parsing Natural Languages 55 / 56
Lecture 5
.
STEP 3: f-structure
..
......
'John made Peter angry'
S
SUBJ = =
NP
=
N
John
VP
= OBJ = XCOMP =
made
V NP
=
N
Peter
V
PREDIC =
NP
=
A
angry
= =
SUBJ =
=
OBJ =
=
XCOMP =
XCOMP PREDIC ='be SUBJ, PRED '
PREDIC =
=
.
STEP 4: unification
..
......
PRED 'make 'SUBJ, XCOMP
TENSE simplepast
SUBJ , PRED 'John'
, PRED 'Peter'OBJ
PRED 'be SUBJ, PRED '
SUBJ
PREDIC , PRED 'angry'
XCOMP
, ,
IA161 Syntactic Formalisms for Parsing Natural Languages 56 / 56