October 25, 2006

1
October 25, 2006

• 11-721 Grammars and Lexicons
• Lori Levin

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Lexical Functional Grammar

• History
• Joan Bresnan (linguist, MIT and Stanford)
• Ron Kaplan (computational psycholinguist, Xerox
  PARC)
• Around 1978

3
What is Linguistic Theory

• Delimit the range of possible human languages.
• What do all languages have in common?
• Semantic roles, grammatical relations, pragmatic
  relations, some constituent structure only
  subjects can be controllees in matrix coding as
  subject constructions etc.
• What are the ways in which they can differ from
  each other?
• Relative prominence of grammatical or pragmatic
  relations word order reflects grammatical
  relations in English and reflects focus (new
  information) in Hungarian Topic takes precedence
  over subject in Chinese in determining antecedent
  of null pronouns Subject is more prominent in
  English.
• What never happens in a human language?
• Make a question by saying the sentence backwards.

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Universalist view of language

• There is a common organizing structure of all
  languages that underlies their superficial
  variations in modes of expression (Bresnan)
• E.g., Passives that look very different in
  different languages can be described by a
  universal passive rule.
• The common organizing structure is part of human
  biology.

5
Some differences between English and Warlpiri
Aux
V NP
The two small children are chasing that
dog.
S
NP AUX V
NP NP NP
Wita-jarra-rlu ka-pala
wajili-pi-nyi yalumpu kurdu-jarra-rlu maliki.
Small-DU-ERG pres-3duSUBJ chase-NPAST
that.ABS child-DU-ERG dog.ABS
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Possible word orders in Warlpiri that are not
possible in English

• The two small are chasing that children dog.
• The two small are dog chasing that children.
• Chasing are the two small that dog children.
• That are children chasing the two small dog.

7
Non-configurational languages

• Free word order.
• May have discontinuous constituents.
• Tests for constituency do not yield evidence for
  VP constituent.

8
Something that English and Warlpiri have in common

• Lucy is hitting herself.
• Herself is hitting Lucy.
• Napaljarri-rli ka-nyanu paka-rni
• Napaljarri-ERG PRES-REFL hit-NONPAST
• Napaljarri is hitting herself.
• Napaljarri ka-nyanu paka-rni
• Napaljarri.ABS PRES-REFL hit-NONPAST
• Herself is hitting Napaljarri.

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What English and Warlpiri have in common
according to Chomsky
Deep structure
English
Surface Structure
10
What English and Warlpiri have in common
according to Chomsky
Deep structure
Warlpiri
Surface Structure
S
NP Aux V NP NP NP
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What English and Warlpiri have in common
according to Bresnan

• Same grammatical relations and semantic roles
• SUBJECT the two small children AGENT
• PREDICATE are chasing
• OBJECT that dog PATIENT
• Different codings of grammatical relations
• English subject NP immediately under S
• Warlpiri subject Ergative case marked NP (if
  verb is transitive)

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Strength of Chomskys approach

• Proposing that there is a VP in all languages
  explains why there are subject-object asymmetries
  in all languages.

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Strength of Bresnans approach

• Doesnt propose non-existent VPs
• phrase structure is used for representing
  constituency
• A different representation is used for
  grammatical relations

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Challenges for Bresnan and Chomsky

• Bresnan
• explain subject-object asymmetries in the absence
  of a VP
• Explain in a principled way the range of possible
  coding properties of grammatical relations
• Chomsky
• explain in a principled way how the words get
  scrambled out of VP
• The phrase structure tree has to represent both
  grammatical relations and constituent structure,
  which may conflict with each other.

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Levels of Representation in LFG
s np The bear vp ate np a sandwich
constituent structure
Grammatical encoding
SUBJ PRED OBJ
functional structure
Lexical mapping
Agent eat patient
thematic roles
Eat lt agent patient gt lexical
mapping SUBJ OBJ
Grammatical Encoding For English!!!
S
NP
SUBJ
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Syntax

• Syntax is not about the form (phrase structure)
  of sentences.
• It is about how strings of words are associated
  with their semantic roles.
• Phrase structure is only part of the solution.
• Sam saw Sue
• Sam perceiver
• Sue perceived

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Syntax

• Syntax is also about how to tell that two
  sentences are thematic paraphrases of each other
  (same phrases filling the same semantic roles).
• It seems that Sam ate the sandwich.
• It seems that the sandwich was eaten by Sam.
• Sam seems to have eaten the sandwich.
• The sandwich seems to have been eaten by Sam.

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How to associate phrases with their semantic
roles in LFG

• Starting from a constituent structure tree
• Grammatical encoding tells you how to find the
  subject.
• The bear is the subject.
• Lexical mapping tells you what semantic role the
  subject has.
• The subject is the agent.
• Therefore, the bear is the agent.

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Levels of Representation in LFG
s np The sandwich vp was eaten pp by the
bear constituent structure
Grammatical encoding
SUBJ PRED OBL
functional structure
Lexical mapping
patient eat
agent thematic roles
Eat lt agent patient gt lexical
mapping OBL SUBJ
Grammatical Encoding For English!!!
S
NP
SUBJ
20
Active and Passive

• Active
• Patient is mapped to OBJ in lexical mapping.
• Passive
• Patient is mapped to SUBJ in lexical mapping.
• Notice that the grammatical encodings are the
  same for active and passive sentences!!!

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Passive mappings

• Starting from the constituent structure tree.
• The grammatical encoding tells you that the
  sandwich is the subject.
• The lexical mapping tells you that the subject is
  the patient.
• Therefore, the sandwich is the patient.
• The grammatical encoding tells you that the bear
  is oblique.
• The lexical mapping tells you that the oblique is
  the agent.
• Therefore, the bear is the agent.

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How you know that the active and passive have the
same meaning

• In both sentences, the mappings connect the bear
  to the agent role.
• In both sentences, the mappings connect the
  sandwich to the patient role (roll?)
• In both sentences, the verb is eat.

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Levels of Representation in LFG
s-bar np what s did np the bear
eat constituent structure
Grammatical encoding
OBJ SUBJ
PRED functional structure
Lexical mapping
patient agent
eat thematic roles
Eat lt agent patient gt lexical
mapping SUBJ OBJ
Grammatical Encoding For English!!!
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Wh-question

• Different grammatical encoding
• In this example, the OBJ is encoded as the NP
  immediately dominated by S-bar
• Same lexical mappings are used for
• What did the bear eat?
• The bear ate the sandwich.

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Principles

• Variability
• Phrase structures and grammatical encodings vary
  across languages.
• Universality
• Functional structures are largely invariant
  across languages.

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Functional Structure
SUBJ PRED bear
NUM sg PERS
3 DEF PRED
eatlt agent patient gt
SUBJ OBJ TENSE past OBJ
PRED sandwich
NUM sg PERS 3
DEF -

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Functional Structure

• Pairs of attributes (features) and values
• Attributes (in this example) SUBJ, PRED, OBJ,
  NUM, PERS, DEF, TENSE
• Values
• Atomic sg, past, , etc.
• Feature structure
• num sg, pred bear, def , person 3
• Semantic form eatltsubj obgt, bear, sandwich

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Semantic Forms

• Why are they values of a feature called PRED?
• In some approaches to semantics, even nouns like
  bear are predicates (function) that take one
  argument and returns true or false.
• Bear(x) is true when the variable x is bound to a
  bear.
• Bear(x) is false when x is not bound to a bear.

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Why is it called a Functional Structure?

• X squared
• 1
• 4
• 9
• 16
• 25

Each feature has a unique value.
Also, another term for grammtical relation is
grammatical function.
features
values
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We will use the terms functional structure,
f-structure and feature structure
interchangeably.
31
Give a name to each function
f1
SUBJ PRED bear
NUM sg PERS
3 DEF PRED
eatlt agent patient gt
SUBJ OBJ TENSE past OBJ
PRED sandwich
NUM sg PERS 3
DEF -
f2

f3
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How to describe an f-structure

• F1(TENSE) past
• Function f1 applied to TENSE gives the value
  past.
• F1(SUBJ) PRED bear, NUM sg, PERS 3, DEF
• F2(NUM) sg

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Descriptions can be true or false

• F(a) v
• Is true if the feature-value pair a v is in f.
• Is false if the feature-value pair a v is not
  in f.

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This is the notation we really use

• (f1 TENSE) past
• Read it this way
• f1s tense is past.
• (f1 SUBJ) PRED bear, NUM sg, PERS 3, DEF
• (f2 NUM) sg

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Chains of function application

• (f1 SUBJ) f2
• (f2 NUM) sg
• ((f1 SUBJ) NUM) sg
• Write it this way.
• (f1 SUBJ NUM) sg
• Read it this way.
• f1s subjects number is sg.

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More f-descriptions

• (f a) v
• f is something that evaluates to a function.
• a is something that evaluates to an attribute.
• v is something that evaluates to a function,
  symbol, or semantic form.
• (f1 subj) (f1 xcomp subj)
• Used for matrix coding as subject. A subject is
  shared by the main clause and the complement
  clause (xcomp).
• (f1 (f6 case)) f6
• Used for obliques

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SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

S
NP VP
N V VP-bar
COMP VP
V PP
P NP
DET N
Lions seem to live in the forest
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SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f1
f2
S
n1
f3
NP VP
n4
n2
N V VP-bar
n5
n3
n6
f4
COMP VP
n7
n8
f5
f6
V PP
n10
n9
P NP
n12
n11
DET N
n13
n14
Lions seem to live in the forest
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SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f1
f2
S
n1
f3
NP VP
n4
n2
N V VP-bar
n5
n3
n6
f4
COMP VP
n7
n8
f5
f6
V PP
n10
n9
P NP
n12
n11
DET N
n13
n14
Lions seem to live in the forest
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Properties of the mapping from c-structure to
f-structure

• Each c-structure node maps onto at most one
  f-structure node.
• More than one c-structure node can map onto the
  same f-structure node.
• An f-structure node does not have to correspond
  to any c-structure node. (But the information it
  contains does come from somewhere either a
  grammar rule or lexical entry.)

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The formalism for grammatical encoding Local
co-description of partial structures

• F is a mapping from c-structure nodes to
  f-structure nodes.
• There are other mappings to semantic structures,
  argument structures, discourse structures,etc.
• is the current c-structure node (me).
• F() is my f-structure (?)
• m() is my c-structure mother
• F(m()) is my c-structure mothers f-structure
  (?)

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Local co-description of partial structures

• S ? NP VP
• (? SUBJ) ? ? ?
• NP says My mothers f-structure has a SUBJ
  feature whose value is my f-structure.
• VP says My mothers f-structure is my
  f-structure.
• This rule simultaneously describes a piece of
  c-structure and a piece of f-structure.
• It is local because each equation refers only to
  the current node and its mother. (page 119-120)

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Other types of equations

• F-structure composition
• (? SUBJ NUM) sg
• My f-structure has a subj feature, whose value is
  another f-structure, which has a num feature,
  whose value is sg.
• Usually, path names are not longer than two.
• Two features pointing to the same value
• (? SUBJ) (? XCOMP SUBJ)
• (? SUBJ) (? TOPIC)
• (? (? CASE)) ? (Dalrymple pages 152-153)
• Sam walked in the park.
• (? CASE) OBL-loc
• (? OBL-loc) ?

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The minimal solution

• The f-structure for a sentence is the minimal
  f-structure that satisfies all of the equations.
  (page 101).

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Building an F-structure informal, for linguists

• Annotate
• Assign a variable name to the f-structure
  corresponding to each c-structure node.
• May find out later that some of them are the
  same.
• Instantiate
• Replace the arrows with the variable names.
• Solve
• Locate the f-structure named on the left side of
  the equation.
• Locate the f-structure named on the right side of
  the equation
• Unify them.
• Replace both of them with the result of
  unification.

46
Unification

• , empty feature structure, is identity element
• U x x
• Atomic value unified with an atomic value
• x U x x
• x U y fail
• Atomic value unified with a non empty feature
  structure fail

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Unification

• Feature structure f1 unified with feature
  structure f2 to make feature structure f3
• The set of features is the union of the features
  in f1 and f2.
• The value of each feature in f3 is the value of
  that feature in f1 unified with the value of that
  feature in f2.
• Keep going recursively if there are embedded
  feature structures.
• If any unification fails, then the whole thing
  fails.

48
Unification and Grammaticality

• Grammatical sentence
• All unifications succeed and
• Phrase structure derivation succeeds
• Ungrammatical sentence
• At least one unification fails or
• Phrase structure derivation fails

49
Unification Example

• f1 num sg
• gender masc
• person 3
• f2 case nom
• def
• person 3

• f3 num sg
• gender masc
• person 3
• case nom
• def

50
Unification Example

• f1 num sg
• gender masc
• person 3
• f2 case nom
• def
• person 2

• Unification fails. No f-structure is produced.

51
Unification Example

• f1 subj num sg
• gender masc
• person 3
• tense pres
• f2 subj case nom
• def
• person 3
• tense pres
• neg

• f3 subj num sg
• gender masc
• person 3
• case nom
• def
• tense pres
• neg

52
Unification Example

• f1 subj num sg
• gender masc
• person 2
• tense pres
• f2 subj case nom
• def
• person 3
• tense pres
• neg

• Unification fails. No f-structure is produced.

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Rule S ? NP VP (?
SUBJ) ? ??
(?VFORM) fin Instantiated equations (f1
SUBJ) f2 f1 f3
SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f2
f1
f3
S f1
NP f2 VP f3
N V VP-bar
COMP VP
V PP
P NP
DET N
Lions seem to live in the forest
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lion N seem V (? PRED)
lion (? PRED)
seem lt theme gt
SUBJ
XCOMP
(? SUBJ)
(? XCOMP SUBJ) -s (suffix
for nouns) (? NUM) pl - Ø (suffix
for verbs) (? PERS) 3 (? VFORM)
fin (? SUBJ
NUM) pl
SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f4
S
NP VP
f5
f4 N f5 V VP-bar
COMP VP
V PP
P NP
DET N
Lions seem to live in the forest
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lion N seem V (f4
PRED) lion (f5 PRED)
seem lt
theme gt SUBJ
XCOMP
(f5 SUBJ)
(f5 XCOMP SUBJ) -s
(suffix for nouns) (f4 NUM) pl -
Ø (suffix for verbs) (f4 PERS) 3
(f5 VFORM) fin
(f5 SUBJ NUM) pl
SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f4
S
NP VP
f5
f4 N f5 V VP-bar
COMP VP
V PP
P NP
DET N
Lions seem to live in the forest
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What is an XCOMP

• A non-finite clause, predicate nominal, predicate
  adjective, or predicate PP
• Sam seemed to be happy (VP)
• Sam seemed happy (AP)
• Sam became a teacher (NP)
• We had them arrested (VP)
• We kept them in the drawer (PP)
• Has to be an argument of a verb
• Arrested by the police, Sam had no alternative
  but to give up his life of crime.
• This is an adjunct, not an XCOMP
• Gets its subject by sharing with another verb
• I think that Sam is happy.
• This is a COMP, not an XCOMP

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seem V (? PRED) seem lt theme gt SUBJ
XCOMP (? SUBJ) (?
XCOMP SUBJ) (? XCOMP VFORM)
INF - Ø (suffix for verbs) (? VFORM) fin (?
SUBJ NUM) pl
VP ? V VP ?? (? XCOMP) ?

SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f3
S
f5
NP VP f3
f6
f7
N f5 V f8 VP-bar
f8
f6COMP VP f9
f9
f7V PP
P NP
to COMP - Ø (suffix
for verbs) (? VFORM) INF (?
VFORM) INF live V (? PRED) livelttheme
locgt SUBJ OBL
DET N
Lions seem to live in the forest
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seem V (f5 PRED) seem lt theme gt SUBJ
XCOMP (f5 SUBJ)
(f5 XCOMP SUBJ) (f5 XCOMP
VFORM) INF - Ø (suffix for verbs) (f5 VFORM)
fin (f5 SUBJ NUM) pl
VP ? V VP f3f5
(f3 XCOMP) f8
SUBJ PRED lion
NUM pl
PERS 3 PRED seem lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

f3
S
f5
NP VP f3
f6
f7
N f5 V f8 VP-bar
f8
f6COMP VP f9
f9
f7V PP
P NP
to COMP - Ø (suffix
for verbs) (f6 VFORM) INF (f7
VFORM) INF live V (f7 PRED) livelttheme
locgt SUBJ OBL
DET N
Lions seem to live in the forest
59
SUBJ PRED lion
NUM pl
PERS 3 PRED try lt
agent theme gt
SUBJ XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM INF
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

S
NP VP
N V VP-bar
COMP VP
V PP
P NP
DET N
Lions try to live in the forest
60
have V (? PRED) have lt theme gt SUBJ
XCOMP (? SUBJ) (?
XCOMP SUBJ) (? XCOMP VFORM)
PASTPART - Ø (suffix for verbs) (? VFORM) fin
(? SUBJ NUM) pl
SUBJ PRED lion
NUM pl
PERS 3 PRED have lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM PASTPART
PRED livelt theme loc gt
SUBJ
OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

S
NP VP
N V
VP
V PP
P NP
DET N
Lions have lived in the forest
61
were V (? PRED) be lt theme gt SUBJ
XCOMP (? SUBJ) (? XCOMP
SUBJ) (? XCOMP VFORM)
PASSIVE (? VFORM) fin (? SUBJ NUM) pl
SUBJ PRED lion
NUM pl
PERS 3 PRED be lt
theme gt SUBJ
XCOMP TENSE pres VFORM
fin XCOMP SUBJ
VFORM PASSIVE
PRED huntltagent theme loc gt
Ø
SUBJ OBL-loc OBJ
OBL-loc CASE OBL-loc
PRED
inltOBJgt
OBJ PRED forest

NUM sg

PERS 3
DEF

S
NP VP
N V
VP
V PP
P NP
DET N
Lions were hunted in the forest