Markedness Optimization in Grammar and Cognition Paul Smolensky Cognitive Science Department Johns...

Markedness Optimization in Grammar and Cognition

Paul SmolenskyCognitive Science Department

Johns Hopkins University

Elliott MoretonKaren Arnold Donald Mathis

Melanie Soderstrom

Géraldine LegendreAlan Prince

Peter Jusczyk Suzanne Stevenson

with:

Grammar and Cognition

1. What is the system of knowledge? 2. How does this system of

knowledge arise in the mind/brain? 3. How is this knowledge put to use? 4. What are the physical mechanisms

that serve as the material basis for this system of knowledge and for the use of this knowledge?

(Chomsky ‘88; p. 3)

A Grand Unified Theory for the cognitive science of language is enabled by Markedness:

Avoid α①Structure

• Alternations eliminate α• Typology: Inventories lack α

②Acquisition• α is acquired late

③Processing• α is processed poorly

④Neural• Brain damage most easily disrupts α

Jakobson’s Program

Formalize through OT?

OT

①

③

④

②

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The complete story, forthcoming (2003) Blackwell:

The harmonic mind: From neural computation to optimality-theoretic

grammarSmolensky & Legendre

Overview

StructureAcquisition UseNeural

Realization

Theoretical. OT (Prince & Smolensky ’91,

’93): – Construct formal grammars directly from

markedness principles– General formalism/ framework for

grammars: phonology, syntax, semantics; GB/LFG/…

– Strongly universalist: inherent typology Empirical. OT:– Allows completely formal markedness-

based explanation of highly complex data

• Theoretical Formal structure enables OT-general:– Learning algorithms

•Constraint Demotion: Provably correct and efficient (when part of a general decomposition of the grammar learning problem)

– Tesar 1995 et seq. – Tesar & Smolensky 1993, …, 2000

•Gradual Learning Algorithm – Boersma 1998 et seq.

Structure Acquisition UseNeural Realization

Initial state

Empirical – Initial state predictions explored

through behavioral experiments with infants

Structure Acquisition UseNeural

Realization

• Theoretical– Theorems regarding the computational

complexity of algorithms for processing with OT grammars • Tesar ’94 et seq.• Ellison ’94• Eisner ’97 et seq.• Frank & Satta ’98• Karttunen ’98

• Empirical (with Suzanne Stevenson)– Typical sentence processing theory:

heuristic constraints– OT: output for every input; enables

incremental (word-by-word) processing– Empirical results concerning human

sentence processing difficulties can be explained with OT grammars employing independently motivated syntactic constraints

– The competence theory [OT grammar] is the performance theory [human parsing heuristics]

• Empirical

Structure Acquisition UseNeural

Realization

• Theoretical OT derives from the theory of abstract neural (connectionist) networks – via Harmonic Grammar (Legendre, Miyata,

Smolensky ’90)

For moderate complexity, now have general formalisms for realizing– complex symbol structures as distributed

patterns of activity over abstract neurons– structure-sensitive constraints/rules as

distributed patterns of strengths of abstract synaptic connections

– optimization of Harmony

Construction of a miniature, concrete LAD

Program

Structure OT

• Constructs formal grammars directly from markedness principles

• Strongly universalist: inherent typology OT allows completely formal markedness-


AcquisitionInitial state predictions explored through

behavioral experiments with infants

Neural Realization Construction of a miniature, concrete LAD

Program

Structure OT

•Constructs formal grammars directly from markedness principles

•Strongly universalist: inherent typology

OT allows completely formal markedness-based explanation of highly complex data




The Great Dialectic

Phonological representations serve two masters

Phonological Representation Lexico

nPhoneti

cs

Phonetic interface

[surface form]

Often: ‘minimize effort (motoric & cognitive)’;

‘maximize discriminability’

Locked in conflict

Lexical interface

/underlying form/

Recoverability: ‘match this invariant

form’

FAITHFULNESSMARKEDNESS

OT from Markedness Theory

• MARKEDNESS constraints: *α: No α• FAITHFULNESS constraints

– Fα demands that /input/ [output] leave α unchanged (McCarthy & Prince ’95)

– Fα controls when α is avoided (and how)

• Interaction of violable constraints: Ranking – α is avoided when *α ≫ Fα

– α is tolerated when Fα ≫ *α

– M1 ≫ M2: combines multiple markedness dimensions


• MARKEDNESS constraints: *α• FAITHFULNESS constraints: Fα

• Interaction of violable constraints: Ranking – α is avoided when *α ≫ Fα – α is tolerated when Fα ≫ *α – M1 ≫ M2: combines multiple markedness dimensions

• Typology: All cross-linguistic variation results from differences in ranking – in how the dialectic is resolved (and in how multiple markedness dimensions are combined)


• MARKEDNESS constraints• FAITHFULNESS constraints• Interaction of violable constraints: Ranking • Typology: All cross-linguistic variation

results from differences in ranking – in resolution of the dialectic

• Harmony = MARKEDNESS + FAITHFULNESS

– A formally viable successor to Minimize Markedness is OT’s Maximize Harmony (among competitors)

Structure

Explanatory goals achieved by OT• Individual grammars are literally

and formally constructed directly from universal markedness principles

• Inherent Typology : Within the analysis of phenomenon Φ in language L is inherent a typology of Φ across all languages

Program

Structure OT


• Strongly universalist: inherent typology OT allows completely formal

markedness-based explanation of highly complex data




Markedness and Inventories

Theoretical part• An inventory structured by markedness

An inventory I is harmonically complete (HC) iffx I and y is (strictly) less marked than x

impliesy I

• A typology structured by markednessA typology T is strongly Harmonically complete

(SHarC) iffL T if and only if L is harmonically complete

(Prince & Smolensky ’93: Ch. 9)

• Are OT inventories harmonically complete?• Are OT typologies SHarC?

Harmonic Completeness

English obstruent inventory is HC w.r.t. Place/continuancy

1 * *[velar]

2 + velar

t k

* + s x

*[+cont]

cont

… but is not generable by ranking { *[velar], *[+cont]; FPlace, Fcont }

Inventory Bans Only the Worst Of the Worst (BOWOW)

Local conjunction:

*[+cont] &seg *[velar] violated when both violated in same segment

Local Conjunction

• Crucial to distinguish

*[taxi]

[saki]

*x w.r.t segment inventory:

*[+cont], *[velar] fatal in same segment

*[+cont], *[velar]

*[+cont], *[velar]

[saki]

Basic Inventories/Typologies

• Formal analysis of HC/SHarC in OT: Definitions• Basic inventory I [Φ] of elements of type T,

where Φ = {φk}Candidates: {X} = { [φ1, φ2, φ3, φ4, …] }

Con: MARK = { *[+φ1], *[φ2], … }

FAITH = { F[φ1], F[φ2], … }

I [Φ]: a ranking of Con

• Basic typology T [Φ]: All rankings of Con• Basic typology w/ Local Conjunction, T LC[Φ]: All

rankings of ConLC = Con + all conjunctions of constraints in MARK, local to T

SHarC Theorem

• SHarC TheoremT [Φ]:

• each language is HC• SHarC property does not hold

TLC[Φ]:• each language is HC• SHarC property holds

Empirical Relevance

Empirical part• Local conjunction has seen many empirical

applications; here, vowel harmony• Lango (Nilotic, Uganda) ATR harmony

– Woock & Noonan =79– Archangeli & Pulleyblank ‘91 et seq., esp. =94

• Markedness: – *[+ATR, hi/fr]– *[ATR, +hi/fr]– *[+A]/σclosed – HD-L[ATR]

Rather than imposing a parametric superstructure on spreading rules (A&P ’94),

we build the grammar directly from these markedness constraints

marked articulatorily

Lango ATR Harmony• Inventory of ATR domains D [ATR] (~ tiers) • Vowel harmony renders many possibilities

ungrammatical ’yourSING/PLUR stew’:

dk +Cí *d k k í dè kk í * d kk ATR: + [ ] [ +] [ + +0] [ 0 ]

dk+wú dkwú *dèkwú *dkw critical difference:

i[+fr] vs. u[fr]

[fr] ‘worse’ source for [+ATR] spreadviolates *[+ATR, fr] — marked w.r.t. ATR

• Complex system: interaction of 6 dimensions (26 = 64 distinct environments)

VATR (Potential: Source of ATR; Target of ATR )

/ VATR (C).C V ATR/ / V ATR (C).C VATR/ hi hi hi hi

fr fr fr fr fr fr fr fr

Lango

ATR-domain inventory

i _ u _ e _ o/ _ _ i _ u _ e _ o/ hi [i° i] [u° i] [e° i] [o° i] [ i i°] [i u°] e o fr hi [i° e] [u° e] [e° e] [o° e] [e i°] [e u°] e o hi [i° u] [u° u] [e° u] [o° u] [u i°] [u u°] [° ] [° ]

C fr hi / a [i° o] [u° o] [e° o] [o° o] [o i°] [o u°] [° ] [° ]

hi [i° i] [u° i] e o [i i°] [i u°] e o fr hi [i° e] [u° e] e o [e i°] u e o

hi [i° u] [u° u] e o [u i°] [u u°] [° ] [° ]

V A

TR

(Pot

ential

: A

TR

Sou

rce;

A

TR T

arge

t)

C.C

fr hi / a [i° o] [u° o] e o [o i°] u [° ] [° ]

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ VV/ +ATR ATR




Lango





hi [i° u] [u° u] e o [u i°] [u u°] [° ] [° ]

V A

TR

(Pot

ential

: A

TR

Sou

rce;

A

TR T

arge

t)

C.C

fr hi / a [i° o] [u° o] e o [o i°] u [° ] [° ]

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ VV/ +ATR ATR

dk +Cí dèkkí




Lango





hi [i° u] [u° u] e o [u i°] [u u°] [° ] [° ]

V A

TR

(Pot

ential

: A

TR

Sou

rce;

A

TR T

arge

t)

C.C

fr hi / a [i° o] [u° o] e o [o i°] u [° ] [° ]

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ VV/ +ATR ATR

dk+wú dkwú




Lango





hi [i° u] [u° u] e o [u i°] [u u°] [° ] [° ]

V A

TR

(Pot

ential

: A

TR

Sou

rce;

A

TR T

arge

t)

C.C

fr hi / a [i° o] [u° o] e o [o i°] u [° ] [° ]

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ VV/ +ATR ATR

The Challenge

Need a grammatical framework able to handle this nightmarish descriptive complexitywhile staying strictly within the confines of rigidly universal principles

Lango

rulesArchangeli & Pulleyblank ‘94

ATR rules: α β

ATR

V C V

ATR

V (C)C V

ATR rules: a b c

ATR

V C V

hi

ATR

V (C)C V

hi

ATR

V (C)C V

hi fr

ATR rule: x

ATR

V (C)C V

hi fr




Lango

Rule-based

account

i _ u _ e _ o/ _ _ i _ u _ e _ o/ hi α β α β α α a b c a b fr hi α β α β α α a c a hi α β α β α α a b c a b x x

C fr hi / a α β α β α α a c a x x

hi β β b c b fr hi β β c

hi β β b c b x x

V A

TR

(Pot

ential

: A

TR

Sou

rce;

A

TR T

arge

t)

C.C

fr hi / a β β c x x

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ VV/ +ATR ATR



Markedness

of ATR domains


hi fr

hi

hi C

fr hi

hi fr

hi

hi

V A

TR

(Pot

ential

: A

TR

Sou

rce;

A

TR T

arge

t)

C.C

fr hi

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ V V/ +ATR ATR

favors: +ATR ATR


/ VATR (C).C V ATR/ / V ATR (C).C VATR/ hi hi(1) hi hi(1)


Lango 1

*VA C. &D[ATR] *[ hi, A]&*HD[A]

hi fr

hi

hi C

fr hi

hi fr

hi

hi

V A

TR

(Pot

entia

l: A

TR

Sou

rce;

A

TR T

arge

t)

C.C(1)

fr(1) hi

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ VV/ +ATR ATR

* 1 * 1

*[+A]/σclosed &D[A]

*[hi,+A]/HD[A]

“No [ATR] spread into a closed syllable from a [hi] source”

*

*

cont*[+cont]

velar

*[velar]

2

1

xs+

kt

+

*

*

cont

velar2

1

xs+

kt

+

BOWOW

*[+cont] &seg *[velar]


/ VATR (C).C V ATR/ / V ATR (C).C VATR/ hi hi hi hi2


hi fr

hi

hi C

fr hi

hi fr

hi

hi

V A

TR

(Pot

ential

: A

TR

Sou

rce;

A

TR T

arge

t)

C.C

fr hi

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ VV/ +ATR ATR

2 / VATR (C).C V ATR/

/ V ATR (C).C VATR/

hi VATR hi

* 2

* 2

BOWOW*[hi, A] & HD-L[A]

“No regressive [ATR] spread from a [hi] source”

3




hi X Y Z X Y Z X Y X Y Y Z Y Z Y 2 Y 2 fr hi X Y Z X Y Z X Y X Y Y Z Y Z Y 2 Y 2

hi X Z X Z X X Z Z 2 2 C

fr hi X Z X Z X X Z Z 2 2

hi X Y Z X Y Z X Y 1 X Y 1 Y Z Y Z Y 1 2 Y 1 2 fr hi X Y Z X Y Z X Y 1 X Y 1 Y Z Y Z 3 Y 1 2 Y 1 2 3

hi X Z X Z X 1 X 1 Z Z 1 2 1 2

V A

TR

(Pot

ential

: A

TR

Sou

rce;

A

TR T

arge

t)

C.C

fr hi X Z X Z X 1 X 1 Z Z 3 1 2 1 2 3

[° ] [ °] [ °] [ ° ] Key:

/ VV / ATR ATR

/ VV/ +ATR ATR

X,Y,Z: *[A] 1,2,3: *[+A]

≫ AGREE ≫ F[A]

The Challenge

Need a grammatical framework able to handle this nightmarish descriptive complexitywhile staying strictly within the confines of rigidly universal principles

Inherent Typology

• Method applicable to related African languages, where the same markedness constraints govern the inventory (Archangeli & Pulleyblank ’94), but with different interactions: different rankings and active conjunctions

• Part of a larger typology including a range of vowel harmony systems

Structure: Summary

• OT builds formal grammars directly from markedness: MARK, with FAITH

• Inventories consistent with markedness relations are formally the result of OT with local conjunction: TLC[Φ], SHarC theorem

• Even highly complex patterns can be explained purely with simple markedness constraints: all complexity is in constraints’ interaction through ranking and conjunction: Lango ATR harmony

Program

Structure OT




AcquisitionInitial state predictions explored

through behavioral experiments with infants


The Initial State

OT-general: MARKEDNESS ≫ FAITHFULNESS

Learnability demands (Richness of the Base)

(Alan Prince, p.c., ’93; Smolensky ’96a)

Child production: restricted to the unmarked

Child comprehension: not so restricted (Smolensky ’96b)

Experimental Exploration of the Initial

StateCollaborators:

Peter Jusczyk Theresa AlloccoLanguage Acquisition 2002

Karen Arnold Elliott Moretonin progress

Grammar at 4.5 months?

• X/Y/XY paradigm (P. Jusczyk)

un...b...umb

un...b...umb

Experimental Paradigm

p = .006um...b...umb um...b...iŋgu

iŋ…..gu...iŋgu vs. iŋ…..gu…umb

… … ∃FAITH

• Headturn Preference Procedure (Kemler Nelson et al. ‘95; Jusczyk ‘97)

•Highly general paradigm: Main result

ℜ *FNP

Linking Hypothesis

• Experimental results challenging to explain

• Suppose stimuli A and B differ w.r.t. φ. Child: MARK[φ] ≫ FAITH[φ] (‘M ≫ F’). Then:

• If A is consistent with M ≫ F and B is consistent with F ≫ M

then ‘prefer’ (attend longer to) A: ‘A > B’

• MARK[φ] = Nasal Place Agreement

Experimental ResultsIf A is consistent with M ≫ F and

B is consistent with F ≫ M then ‘prefer’ (attend longer to) A: ‘A > B’

m+b mb n+b nb

n+b mb

M≫F?yes (+) no

A

F≫M?

yes()

no

B

>>

>

p < .05 ∃MARKp < .001 nb mb; M ≫ F

p < .05 n m detectable

n+b nd

p > .40 /n+b/: nd ≺UG mbp > .30 *UG unreliability

Program

Structure OT






Neural Realization Construction of a miniature, concrete

LAD

A LAD for OT

Acquisition: • Hypothesis: Universals are

genetically encoded, learning is search among UG-permitted grammars.

• Question: Is this even possible?• Collaborators:

Melanie Soderstrom Donald Mathis

UGenomics

• The game: Take a first shot at a concrete example of a genetic encoding of UG in a Language Acquisition Device¿ Proteins ⇝ Universal grammatical principles ?

Time to willingly suspend disbelief …

UGenomics

• The game: Take a first shot at a concrete example of a genetic encoding of UG in a Language Acquisition Device¿ Proteins ⇝ Universal grammatical principles ?

• Case study: Basic CV Syllable Theory (Prince & Smolensky ’93)

• Innovation: Introduce a new level, an ‘abstract genome’ notion parallel to [and encoding] ‘abstract neural network’

UGenome for CV Theory

• Three levels– Abstract symbolic: Basic CV Theory– Abstract neural: CVNet– Abstract genomic: CVGenome

UGenomics: Symbolic Level

• Three levels– Abstract symbolic: Basic CV

Theory– Abstract neural: CVNet– Abstract genomic: CVGenome

Basic syllabification: Function

• Basic CV Syllable Structure Theory– ‘Basic’ — No more than one segment

per syllable position: .(C)V(C).

• ƒ: /underlying form/ [surface form]• /CVCC/ [.CV.C V C.] /pæd+d/[pædd]

• Correspondence Theory– McCarthy & Prince 1995 (‘M&P’)

• /C1V2C3C4/ [.C1V2.C3 V C4]

• PARSE: Every element in the input corresponds to an element in the output

• ONSET: No V without a preceding C

• etc.

Syllabification: Constraints (Con)

UGenomics: Neural Level


CVNet Architecture

/C1 C2/ [C1 V C2]

CV

/ C1 C2 /

[

C1

V

C2

]

‘1’

‘2’

Connections: PARSE

C

V

3 3

3

3

33

1

11

1

1

1

3 3

3

3

33

3 3

3

3

33

• All connection coefficients are +2

Connections: ONSET

• All connection coefficients are 1

C

V

CVNet Dynamics

• Boltzmann machine/Harmony network– Hinton & Sejnowski ’83 et seq. ; Smolensky ‘83 et

seq.

– stochastic activation-spreading algorithm: higher Harmony more probable

– CVNet innovation: connections realize fixed symbol-level constraints with variable strengths

– learning: modification of Boltzmann machine algorithm to new architecture

UGenomics: Genome Level


Connectivity geometry• Assume 3-d grid geometry (e.g.,

gradients)

V

C

‘E’

‘N’

‘back’

• Correspondence units grow north & west and connect with input & output units.

• Output units grow east and connect

Connectivity: PARSE• Input units grow south and connect

C

V

3 3

3

3

3 3

1

1 1

1

1

1

3 3

3

3

3 3

3 3

3

3

3 3

C

V

3 3

3

3

3 3

1

1 1

1

1

1

3 3

3

3

3 3

3 3

3

3

3 3

C

V

3 3

3

3

3 3

3 3

3

3

3 3

1

1 1

1

1

1

3 3

3

3

3 3

3 3

3

3

3 3

3 3

3

3

3 3

3 3

3

3

3 3

C

V

Connectivity: ONSETx0 segment: | S S VO| N S x0

• VO segment: N&S S VO

Connectivity Genome

• Contributions from ONSET and PARSE:

Source:

CI VI CO VO CC VC xo

Projec-tions:

S LCC S L VC E L CC E L VC

N&S S VO

N S x0

N L CI

W L CO

N L VI

W L VO

S S VO

Key: Direction Extent Target

N(orth) S(outh)E(ast) W(est)F(ront) B(ack)

L(ong) S(hort)

Input: CI VI

Output: CO VO x(0)

Corr: VC CC

CVGenome: Connectivity C-I V-I C-C V-C C-O V-O x

D E T D E T D E T D E T D E T D E T D E T

IDENTITY F Sh V-C B Sh C-C LINEARITY N/E L C-C&V-C N/E L C-C&V-C

S/W L C-C&V-C S/W L C-C&V-C INTEGRITY S L C-C S L V-C

N L C-C N L V-C UNIFORMITY E L C-C E L V-C

W L C-C W L V-C OUTPUTID F Sh V-O B Sh C-O F Sh C-O

B Sh x B Sh x F Sh V-O NOOUTGAPS N Sh x* N Sh x* S Sh C-O&V-O

RESPOND CORRESPOND S L C-C S L V-C N L C-I N L V-I E L C-C E L V-C

W L C-O W L V-O PARSE S L C-C S L V-C N L C-I N L V-I E L C-C E L V-C

W L C-O W L V-O FILL-V S L V-C N L V-I

W L V-O E L V-C FILL-C S L C-C N L C-I E L C-C

W L C-O ONSET N Sh V-O S Sh 1rst V-O

S Sh V-O N Sh 1rst x

NOCODA N Sh C-O N Sh C-O S Sh C-O S Sh x

C-C:

CORRESPOND:

Abstract Gene Map

General Developmental Machinery Connectivity Constraint Coefficients

S L CC S L VC F S VC N/E L CC&VC S/W L CC&VC

direction extent target

C-I: V-I:

G

CO&V&x B 1 CC&VC B 2 CC CI&CO 1 VC VI&VO 1

RESPOND:

G

CVGenome: Connection Coefficients

Constraint From To Strength Constraint From To Strength IDENTITY C-C V-C 1 PARSE C-C&V-C bias 3

LINEARITY C-C&V-C C-C&V-C 1 C-I&V-I bias 1 INTEGRITY C-C&V-C C-C&V-C 1 C-I&C-O C-C 2

UNIFORMITY C-C C-C 1 V-I&V-O V-C 2 OUTPUTID C-O&V-O&x C-O&V-O&x 2 FILL-V V-C bias 3

NOOUTGAPS x C-O&V-O 1 V-O bias 1 RESPOND C-O&V-O&x bias 1 V-I&V-O V-C 2

CORRESPOND C-C&V-C bias 2 FILL-C C-C bias 3 C-C C-I&C-O 1 C-O bias 1 V-C V-I&V-O 1 C-I&C-O C-C 2

NOCODA C-O C-O&x 1 ONSET V-O V-O&x 1

UGenomics

• Realization of processing and learning algorithms in ‘abstract molecular biology’, using the types of interactions known to be biologically possible and genetically encodable

UGenomics

• Host of questions to address– Will this really work?– Can it be generalized to distributed nets?– Is the number of genes [77=0.26%]

plausible?– Are the mechanisms truly biologically

plausible?– Is it evolvable?

How is strict domination to be handled?

Hopeful Conclusion

• Progress is possible toward a Grand Unified Theory of the cognitive science of language– addressing the structure, acquisition, use, and

neural realization of knowledge of language– strongly governed by universal grammar– with markedness as the unifying principle– as formalized in Optimality Theory at the

symbolic level– and realized via Harmony Theory in abstract

neural nets which are potentially encodable genetically

€Thank you for your attention

(and indulgence)

Hopeful Conclusion

• Progress is possible toward a Grand Unified Theory of the cognitive science of language

Still lots of promissory notes, butall in a common currency — Harmony ≈ unmarkedness; hopefullythis will promote further progress by facilitating integration of the sub-disciplines of cognitive science

Markedness Optimization in Grammar and Cognition Paul Smolensky Cognitive Science Department Johns...

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