CML 2010 DUBROVNIK THE ARGUMENT-BASED COMPUTATION: SOLVING THE BINDING PROBLEM Velina Slavova, NBU...

CML 2010 DUBROVNIK

THE ARGUMENT-BASED COMPUTATION: SOLVING THE BINDING PROBLEM

Velina Slavova, NBU

Alona Soschen, MIT

CML 2010 DUBROVNIK

We offer an experimental support of the developed formal model of Argument Based Syntax.

In this paper, we further developed the argument-based model of syntactic operations that is argued to represent the key to basic mental representations.

The binding problem arises when the same noun occupies either a Subject or an

Object position.

The cat chases the mouse

The mouse chases the cat

The results of our experiments confirmed that semantic relations between the images in conceptual nets influence syntactic computation.

We use the absence of of Accusative Case marker in Bulgarian and its rather free word order, and we show how the syntactic structure of ambiguous sentences is interpreted by means of other cognitive mechanisms.

CML 2010 DUBROVNIK

by the (formal) semantic system (Hauser et al., 2002).

Introduction

LanguageSemantic

system

Following one of the widely accepted linguistic theories, the key component of Faculty of Language is a computational system (narrow syntax)

that generates internal representations

and maps them into the conceptual-intentional interface

CML 2010 DUBROVNIK

Language

SYNTACTIC RULES ?

Semantic knowledge

COMPUTATION

There is a consensus that the core property of FL is recursion, which is attributed to narrow syntax.

The claim is that this computation is based on a primitive operation that takes already constructed objects to create a new object. This basic operation, called

“Merge”, provides a “language of thought”, an internal system to allow preexistent conceptual resources to construct expressions (Chomsky, 2006).

Introduction

CML 2010 DUBROVNIK

One step in this direction was provided in Slavova and Soschen (2007). Syntactic structures, presented in the traditional sense of Chomskyan theory (Bare Phrase Structures, XP-structures), were re-defined in terms of finite recursive binary trees.

XP

XP

XXP

X’

S : The boy likes the girl

The boy/ NPV’/ likes the girl

NP/ The girlSpecifier

Head X Complement

The study of syntactic recursion by mathematical means may provide valuable insights into the principles underlying the human language.

Introduction

CML 2010 DUBROVNIK

X’XP

XXPX’ XP

X XP XPX’ XPX’

XPX’ X XPX’ X XP X’

XP XP

X XP XP X’

X XPX’ XXPX’

XPX’ XPXP X’

XP

X’XP

XXPX’ XP

X XP XPX’ XPX’


XP XP

X XP XP X’

X XPX’ XXPX’

XPX’ XPXP X’

XP

X’XP

XXPX’ XP

X

XP XPX’XP

X’


XP XP

XXP XP X

’X XPX’ XXPX

’

XPX’ XPXP X’

XP

X’XP

XXPX’XP

X

XP XPX’ XPX’

XPX’X

XPX’ X XP X’

XP XP

X XP XP X’

X XPX’ XXPX’

XPX’ XPXPX’

XP

X

X

X X

X X X

X’XP

XPX’ XP

XP XPX’ XPX’

XPX’ XPX’ XP X’

XP XP

XP XP X’

XPX’ XPX’

XPX’ XPXP X’

XP

XP

The “traditional syntactic tree” was modified:

the nodes related to syntactic role of verbs were discarded.

Introduction

CML 2010 DUBROVNIK

X

X

X

X X

X X X

X’XP

XPX’ XP

XP XPX’ XPX’


XP XP

XP XP X’

XPX’ XPX’

XPX’ XPXP X’

XP

XP

One reason to introduce this modification was to build a structure that complies with the principles of optimization, namely with the principle of efficient growth (Soschen 2006, 2008).

Introduction

http://britton.disted.camosun.bc.ca/fibslide/fib09.gif

CML 2010 DUBROVNIK

X

X

X X

X X X

X’XP

XPX’ XP

XP XPX’ XPX’


XP XP

XP XP X’

XPX’ XPX’

XPX’ XPXP X’

XP

XP

http://britton.disted.camosun.bc.ca/fibslide/fib09.gif

CML 2010 DUBROVNIK

XP

X’XP

XXPX’ XP

X XP XPX’ XPX’

XPX’ X XPX’ X XPX’

XP XP

X XP XPX’

X XPX’ X XPX’

XPX’ XPXPX’

XP

The structure obtained in this way is a tree of Fibonacci Introduction

CML 2010 DUBROVNIK

XP

XP

XP XP

XP XP XP

XP XP XPXP XP

XP XP XP XPXP XPXP XP

Introduction

CML 2010 DUBROVNIK

XP

XP XP

X3

Ø

Ø

XPXP XPXP

XPXP XPXP

X4

Ø

Ø

X5

Ø

XP

X2

ØX1

Ø Ø

Introduction

CML 2010 DUBROVNIK

XP

XP XP

X3

Ø

Ø -merge

Ø -merge

ØØ -merge

Ø -merge

XPXP XPXP

XPXP XPXP

X4

Ø

Ø

Ø -merge

X5

Ø

Ø -merge

XP

X2

Ø

Ø -merge

X1

ØØ -merge

Ø

merge merge

merge

merge

Language of thought?

This tree can be seen as is an operator – it “performs” a bottom-up Merge, its nodes are the results of Merge. The tree shows the patterns of relating arguments Xs.

CML 2010 DUBROVNIK

This maximal configuration corresponds to thematic roles agent, recipient, and theme (the arguments in a sentence).

These schemes represent all possible configurations and relations between arguments in the human theta-role Semantic Space.

Introduction

CML 2010 DUBROVNIK

The difficulty of designing an appropriate experiment is that mental computation runs on a deep (pre-linguistic) level and cannot be captured on the lexical level by a standard experiment.

EXPERIMENT 1

One possible way to extract some information about the primary mechanisms is to force the mental system to solve ambiguities on the lexical level and to analyze the system’s response.

Language

Rules,Operators

Semantic knowledge

“computation”

Introduction

CML 2010 DUBROVNIK

EXPERIMENT 1

In Bulgarian, sentences of type:

are ambiguous where the used verb allows a Recipient (to whom).

Subject Verb the Object на the Z

NB Bulgarian exhibits certain peculiarities that set it apart from other Slavic languages, such as elimination of Case marking and the development of a suffixed definite article.

They assign two different meanings to Z - Recipient and Possessor:

Subject Verb the Object to the Z

Subject Verb the Object of the Z

Introduction

CML 2010 DUBROVNIK

Test statement

Анна подаде стола на директора.

Анна продаде ябълките на момчето.

Елена продаде къщата на кучето.

Иван показа пътеката на баща си.

Иван продаде къщата на баща си.

Кумчо Вълчо продаде къщата на кучето.

Мария показа колата на съседката.

Мария продаде колата на съседката.

Михаил продаде къщата на съседа си.

Монтьорът показа колата на съседката.

Петър донесе стола на директора.

Петър показа къщата на баща си.

Тапицерът донесе стола на директора.

In normal listening or reading-comprehension conditions, native Bulgarian speakers are never mistaken about the conveyed meaning - they interpret one of these two senses depending on the context.

EXPERIMENT 1

Introduction

CML 2010 DUBROVNIK

The subjects of our experiment wore 62 students with different backgrounds (economists, sociologists, biologists, linguists, engineers etc.) all of them fluent speakers of French

Test statement














Translate into French!

(Quickly, please)

The 124 written translations of the test statements were stored in a database.

EXPERIMENT 1

In order to understand which meaning is captured first by the subjects in our experiment, we used the fact that the sentence structure, including word order, is exactly the same in French.

Introduction

CML 2010 DUBROVNIK

Test statement















(Quickly, please)

EXPERIMENT 1

The crucial difference is that the preposition на is translated in French as

“à” (to) for the Recipient-meaning and as “de” (of) for the Possessor-meaning.

Introduction

CML 2010 DUBROVNIK

Here the result:

The important observation is that these changes do not depend on the verb.

Introduction

CML 2010 DUBROVNIK

The Z The Y Verb X на

Concept Achievement

Concept Preposition

Concept

SYNTACTIC PROCEDURE WITH SEMANTIC MERGE

CML 2010 DUBROVNIK


Semantic Merge (M) is modeled as binary operation, performed in sequential progression between concepts

verbY*X* Z*

The result of M consists of a couple, in which each element obtains an image , representing the concept in the semantic context of the other member of the couple.

For example, the image of the concept X* within the couple [X*V] is the image of X* as Subject, performing V.

verbX* X Acts V

CML 2010 DUBROVNIK

Z*= Recipient ( X*)

X* =

M (X*,V) = [X*,V]

X* = X*V (Y*, ?R)

X* V (?O, ?R) Y* Z*

M ([X*,Y* ], [X*,Z*])

X*= X*V (Y*, Z*)

Y* = Object of X* to Z*Z*= Recipient of X* Acts Y*

1.

4.

на

M (X*, Y*) = [X*, Y*] 3.

= X*V (?O, ?R)

Y* = Object X* V

M (X*, Z*) = [ X*, Z*] 2.

SEMANTIC MERGE – experimental results 1

Recipient scheme

PRIMARY

CML 2010 DUBROVNIK

X* =

M (X*,V*) = [X*,V*]

X* = X* Acts (?what, to Ø)

X* V*( ?O, ?R) Y* Z*

M ([X*, Y* ], [X*, Ø ])

X*= X* Acts Y* of Z*Y* = belongs to Z* and Acted by X* Z*= Possessor of Y*

1.

4.

на

M (X*, Ø) = [X*, Ø]2b.

= X* Acts (?O, ?R)

M (X*, Y*) = [ X*, Y*] 3.

Z* = (Z*Y*) = Poss of Y*

Y* = (Z*Y*) = belongs to Z*

Ø2a.

Y* = X* Acts Y*, to Ø)

= X* Acts (?O)

Possessor scheme

IF RECIPIENT IS REJECTED


CML 2010 DUBROVNIK

Z*= Recipient ( X*)

X* =

M (X*,V) = [X*,V]

X* = X*V (Y*, ?R)

X* V (?O, ?R) Y* Z*

M ([X*,Y* ], [X*,Z*])

X*= X*V (Y*, Z*)


1.

4.

на

M (X*, Y*) = [X*, Y*] 3.

= X*V (?O, ?R)

Y* = Object X* V

M (X*, Z*) = [ X*, Z*] 2.

Recipient scheme

The experimental results show that if in the semantic space there exists a previous knowledge about Z* as a natural Possessor of Y*, that influences the process on step 2.

Z Y Previous semantic knowledge


CML 2010 DUBROVNIK

X* [X*, V] =

M (X*,V) = [X*,V]

X* V (?O, ?R) Y* Z*

1.

на

= X*V (?O, ?R)

The experimental results show that if in the semantic space there exists a previous knowledge about Z* as a natural Possessor of Y*, that influences the process on step 2.

Z Y



2a.


M ([X*, Y* ], [X*, Ø ])


4.

M (X*, Ø) = [X*, Ø]2b.

M (X*, Y*) = [ X*, Y*] 3. Y* = X* Acts Y*, to Ø)

= X* Acts (?O)

Possessor scheme


CML 2010 DUBROVNIK

Z*= Recipient ( X*)

X* =

M (X*,V) = [X*,V]

X* = X*V (Y*, ?R)

X* V (?O, ?R) Y* Z*

M ([X*,Y* ], [X*,Z*])

X*= X*V (Y*, Z*)


1.

4.

на

M (X*, Y*) = [X*, Y*] 3.

= X*V (?O, ?R)

Y* = Object X* V

M (X*, Z*) = [ X*, Z*] 2.

X* Y* на

Recipient scheme

Y X

The knowledge about Y* as usual Object of actions of X* forms in the semantic space a relation X*-Y*.

Previous knowledge


CML 2010 DUBROVNIK

Z*= Recipient ( X*)

X* =

M (X*,V) = [X*,V]

X* = X*V (Y*, ?R)

X* V (?O, ?R) Y* Z*

1.

на

M (X*, Y*) = [X*, Y*] 3.

= X*V (?O, ?R)

Y* = Object X* V

M (X*, Z*) = [ X*, Z*] 2.

X* Y* на

Recipient scheme

Y X


M ([X*, Y* ], [X*, Ø ])4.


CML 2010 DUBROVNIK

X* [X*, V] =

M (X*,V) = [X*,V]

X* V (?O, ?R) Y* Z*

1.

на

= X*V (?O, ?R)

Possessor scheme


Y



2a.


M ([X*, Y* ], [X*, Ø ])


4.

M (X*, Ø) = [X*, Ø]2b.

M (X*, Y*) = [ X*, Y*] 3. Y* = X* Acts Y*, to Ø)

= X* Acts (?O)

X


CML 2010 DUBROVNIK

Z*= Recipient ( X*)

X* =

M (X*,V) = [X*,V]

X* = X*V (Y*, ?R)

X* V (?O, ?R) Y* Z*

M ([X*,Y* ], [X*,Z*])

X*= X*V (Y*, Z*)


1.

4.

на

M (X*, Y*) = [X*, Y*] 3.

= X*V (?O, ?R)

Y* = Object X* V

M (X*, Z*) = [ X*, Z*] 2.

X* Y* на

Recipient scheme

ZX

When between X* and Z* exists a strong semantic relation, Z* takes the (natural) role of Recipient of the actions of X*.


CML 2010 DUBROVNIK

The general conclusion is that people very much construct the meaning of what has been said.

CML 2010 DUBROVNIK

(SVO): децата прочетоха писмoто.

‘The children have read the letter’.

(SOV): децата писмoто прочетоха.

‘The children the letter have read’.

(OSV): писмoто децата прочетоха.

‘The letter the children have read’.

(OVS): писмoто прочетоха децата.

‘The letter have read the children’.

(VOS): прочетоха писмoто децата.

‘Have read the letter the children’.

(VSO): прочетоха децата писмoто.

‘Have read the children the letter’.

EXPERIMENT 2

Subject

Verb

Object

(Bulgarian)

Although the Bulgarian nouns are not marked for Case, the word order is rather free.

Thus, in a Bulgarian the sentence ‘The children have read the letter’ can be expressed as the following:

the Noun 1 Verb the Noun 2

The children

have read

the letter


CML 2010 DUBROVNIK

EXPERIMENT 2

Subject

Verb

Object

(Bulgarian)

The children

have read

the letter


Although SVO is the basic WO, all permutations are possible; they are grammatically correct, even thought some are used mostly in poetry.

According to the Institute of Bulgarian at the Bulgarian Academy of Sciences, this grammatical particularity of permutation is possible because of the agreement between Subject and Verb which clarifies the role of Object.

But whatIf the Verb is in agreement with both nouns?

s

There exists in Bulgarian a particular grammatical operation (clitic doubling) that marks Object in cases of a reverse word order, as in:

(OVS): Иван го поздрави Мария.

Ivan him congratulated Maria

‘Maria congratulated Ivan’.

CML 2010 DUBROVNIK

EXPERIMENT 2

Subject

Verb

Object

(Bulgarian)

Noun 1

Noun 2

Noun 1 Verb Noun 2

The clitic (го/ги) is obligatory only when the subject and the object are in the third person, and they are both either singular or plural.

According to the Institute of Bulgarian at the Bulgarian Academy of Sciences, When the meaning is clear from the context, the clitic can be omitted.

(OVS): Иван го поздрави Мария.

Ivan him congratulated Maria

‘Maria congratulated Ivan’.

го/ги

(OVS): Ролите озвучиха артистите: (list).

The roles sound-screened the artists:

‘The artists (from the list) sound-screened the roles’.

for example:

CML 2010 DUBROVNIK

EXPERIMENT 2 (Merge patterns)

M (X*,V) = [X*,V]

X* = X*V (Y)

X* V (?O) Y*

1.

M (X*, Y*) = [X*, Y*] 2.

X Acts (?O)

Y* = Object X* V

Noun 1 Noun 2verb The first mental operator in this treatment is to merge nouns with V*

Stage I : Merge Subject-Verb

M (X*V*) = [X*, V] (?O)

X* = X* Acts (?O)

Y*

X*

Stage II : Merge Acting Subject with Object

Y* [ X*, Y*] = Object X* V

X*

X* V Object Y*

CML 2010 DUBROVNIK


M (Y*,V) = [Y*,V]

X* V (?O) Y*

1.

M (Y*, X*) = [Y*, X*] 2.

= Y Acts (?O)

Y* = X*V (Y)

X* = Object Y* V


M (Y*V*) = [Y*, V] (?O)

Y* = Y* Acts (?O)

Stage II : Merge Acting Subject with Object

X*

Y*

Y*

Y* V Object X*

CML 2010 DUBROVNIK


X*

M (X*,V) = [X*,V]

X* = X*V (Y)

X* V (?O) Y*

1.

M (X*, Y*) = [X*, Y*] 2.

= X*V (?O)

Y* = Object X* V

Y*

M (Y*,V) = [Y*,V]

Y* = Y*V (X)

X* V (?O) Y*

1.

M (Y*, X*) = [Y*, X*] 2.

= Y*V (?O)

X* = Object Y* V

We assume that these operations are semantically supported by the meaning of the concepts X* and Y*.

X* Y*

IF THERE ARE NOT GRAMMATICAL MARKERS…

CML 2010 DUBROVNIK

EXPERIMENT 2 (Bulgarian)

In this case, either X or Y can appear as Object:

We used Bulgarian sentences of type:

Where V is in agreement with both X and Y.

X(noun) VerbY(noun)

Subject

Verb

Object

X(noun)

Verb

Y(noun)

CML 2010 DUBROVNIK

EXPERIMENT 2 (Bulgarian)

The following folk verses that contain sentences of the above kind were used in our experiment:

CML 2010 DUBROVNIK

Живееше мишка, сива и красиваOnce upon a time there lived a mouse, grey and beautifulнейде на тавана, дето бе дивана. Somewhere in the attic, where the sofa wasПояви се тук Котанчо, котаракът на Стоянчо.There appeared Kotantcho, the cat of SoyantchoМишката Котанчо хвана и изчезна под дивана.The mouse Kotantcho caught and disappeared under the sofa

CML 2010 DUBROVNIK

Живееше куче, сиво и красивоOnce upon a time there lived a dog, grey and beautifulнейде на тавана, дето бе дивана. Somewhere in the attic, where the sofa wasПояви се тук Котанчо, котаракът на Стоянчо.There appeared Kotantcho, the cat of SoyantchoКучето Котанчо хвана и изчезна под дивана.The dog Kotantcho caught and disappeared under the sofa

CML 2010 DUBROVNIK


X(noun) VerbY(noun)

CML 2010 DUBROVNIK


X(noun) VerbY(noun)

The two sentences in the verses have identical structure X* Y* V* and there are no grammatical markers indicating which noun is Subject and which is Object.

CML 2010 DUBROVNIK

The subjects of our experiment wore 36 students with different backgrounds (economists, sociologists, biologists, linguists, engineers etc.) all of them fluent speakers of French


(Quickly, please)

The written translations of the test statements were stored in a database.

We designed our experiment as a translation (from Bulgarian to French) task.

In French the word order is fixed.

Thus, our subjects had to assign a fixed word order to their French translations, thus bringing out their interpretation of the same noun as either Subject or Object.



Subject

Verb

Object

Noun 1

Noun 2

CML 2010 DUBROVNIK

EXPERIMENT: RESULTS AND ANALYSIS

Кучето Котанчо хвана и изчезна под дивана.The dog Kotantcho caught and disappeared under the sofa

X(noun) VerbY(noun)

The dog

Caught(activity)

Kotantcho (cat)

SUBJECT Verb OBJECT

Result: 17 (100%)

CML 2010 DUBROVNIK


Мишката Котанчо хвана и изчезна под дивана.The mouse Kotantcho caught and disappeared under the sofa

X(noun) VerbY(noun)

The mouse

Caught(activity)

Kotantcho (cat)

Result: 12 (100%)

‘retell the story in two sentences’ condition

SUBJECT Verb OBJECT All translations were structured as S V O (le chat a attrapé la sourris).

CML 2010 DUBROVNIK



X(noun) VerbY(noun)

The mouse

Caught(activity)

Kotantcho (cat)

Result: 16 (72,7%)

‘translate the story’ condition

SUBJECT Verb OBJECT

CML 2010 DUBROVNIK



X(noun) VerbY(noun)

The mouse

Caught(activity)

Kotantcho (cat)

Result: 4 (18,2%)


SUBJECT Verb OBJECT

CML 2010 DUBROVNIK



X(noun) VerbY(noun)

The mouse

Caught(activity)

Kotantcho (cat)

NOT CLEAR Result: 2


SUBJECT Verb OBJECT

The cases which are not clear represent mot-à-mot translations: the result in French does not make sense because of the fixed word order.

CML 2010 DUBROVNIK



X(noun) VerbY(noun)

The mouse

Caught(activity)

Kotantcho (cat)


SUBJECT Verb OBJECT

An attempt to comply with the original word order is seen in a couple of cases where the “subject first” rule is respected, leading to the translation of sentences in a passive form

“La sourris a été par Kotantcho attrapée” (The mouse has been by the cat caught).

CML 2010 DUBROVNIK

Following our model, the cognitive system first assembles a fractional representation of the sentence-meaning structure (coupled words for example) and uses working memory loops for checking the semantic consistency.

EXPERIMENT : ANALYSIS

Long

Term

Memory

ConceptsEvents

verbs

Attributes

Semantic primitives

Syntactic categories prep.

Semantic Operators

Syntactic rules

….

…

nouns adjectives

SentenceWorking memory

Z24

Z25

Z26

Z27

λ

l81

l105

l70l89

l87

l85 l86

l84

l83

l82

l100

l88

l94

l95

l96

l91

l92

l93

l90

λ

l12

l69

l49

φ φ

φ

CML 2010 DUBROVNIK

Z24

Z25

Z26

Z27

λ

l81

l105

l70l89

l87

l85 l86

l84

l83

l82

l100

l88

l94

l95

l96

l91

l92

l93

l90

l12

l69

l49

φ φ

φ

Verb

Y

X

λ

The grammatical information is not sufficient to build the syntactic structure.

The treatment can continue only by applying other mechanisms.

verbYX

Concept Concept Achievement

EXPERIMENT : ANALYSIS

CML 2010 DUBROVNIK


verbYX

Mouse Cat Caught


M (X*V*) = [X*, V] (?O)

X* = X* Acts (?O)

TheMouseCaught

CML 2010 DUBROVNIK


verbYX Stage I : Merge Subject-Verb

M (Y*V*) = [Y*, V] (?O)

Y* = Y* Acts (?O)

TheCatCaught

Mouse Cat Caught

CML 2010 DUBROVNIK



M (X*V*) = [X*, V] (?O)

X* = X* Acts (?O)

TheMouseCaught

Stage II Merge Acting Subject with Object

The Mouse Caught the Cat

Mouse Cat Caught

The Cat is the Object of TheMouseCaught

REJECTED

CML 2010 DUBROVNIK



M (Y*V*) = [Y*, V] (?O)

Y* = Y* Acts (?O)

TheCatCaught

Mouse Cat Caught

Stage II Merge Acting Subject with Object

The CatCaught the Mouse

The Mouse is the Object of TheCatCaught

ACCEPTED

CML 2010 DUBROVNIK

CONCLUSIONS

Experimental evidence is provided in support of the argument-based model. The semantic role of entities (nouns) is primary in syntax.

The analysis provided here is based on the assumption that the syntactic treatment includes a Merge operation between the images of the concepts. The obtained formal description of the stages of syntactic treatment explains the experimental results.

CML 2010 DUBROVNIK

The Mouse is the Object of TheCatCaught

THANK YOU!

CML 2010 DUBROVNIK THE ARGUMENT-BASED COMPUTATION: SOLVING THE BINDING PROBLEM Velina Slavova, NBU...

Documents

Transcript of CML 2010 DUBROVNIK THE ARGUMENT-BASED COMPUTATION: SOLVING THE BINDING PROBLEM Velina Slavova, NBU...