Evolution of Universal Grammar

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Evolution of Universal Grammar

Pia Göser

Universität Tübingen Seminar: Sprachevolution

Dozent: Prof. Jäger

11.02.2010

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Structure

• Historical outline

• Arguments for Universal Grammar

– Language and Grammar – Learning Theory

– Language Acquisition

• Evolutionary Processes

– Language

– Universal Grammar

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Universal Grammar

Brief history of a theory...

• Basic: Researches on language acquisition

• From ‘20s: behavioristic approach

 Problem: „poverty of stimulus“

• ‘60s/‘70s: Alternative model: nativistic approach

 Noam Chomsky: innate human mechanism

• Still controversial topic

 mathematical approach tries to explain it

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What is language?

Formal language theory:

• Generative system

• Set of sentences

– A sentence is a string of symbols

– there are infinite many sentences (countable)

• Finite Languages (are infinite – countable)

• Infinite Languages (are infinite – uncountable)

 set of languages is uncountable

Biologically: extended phenotype of population

What is language?

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What is grammar?

• Finite list of rules specifying a language

• There are infinitely many grammars (countable)

 only small subset of languages can be described by a grammar (=computable languages)

What is grammar?

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Relationship language-grammar

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Languages, grammars and machines

Chomsky hierarchy of formal grammar automata

Phrase structure (Unrestricted) Turing machine;

description for computable languages with unrestricted rewrite-rules

Context sensitive Linear-bounded;

Turing machine can decide every sentence’s belonging to the language; TM has an infinite memory

Context free Push-down;

language can be described with computers with only one memory task

Regular (Finite State) Finite-State;

generate regular languages; subset of regular languages contains all finite languages

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Learning Theory

Classical Learning Theory (Gold)

assumptions:

a) learner has to identify the target language

b) learner receives only positive examples

c)learner has access to an arbitrary large number of examples

d) learner is not limited by any consideration of computational complexity

Gold’s theorem: no algorithm can learn the set of all regular language; only by memorization

Statistical learning theory

assumptions:

a) learner will come very close to the right language with a high probability b) learner receives both positive and negative examples (distribution P) c) after a Number of “empirical data”

the learner guesses a language out of a set of languages

Theorem:

-> set of all regular and finite languages cannot be learnt

-> subsets of regular languages with finite-state automata can be learnt Basically: generalizing rules beyond one’s own experience

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Learning Theory

• no learning theory can permit all languages to be

learnable

 necessity of specific resrictions

 innate “restricted search space” for languages

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Learning a language

• Paradox of language acquisition

• Poverty of stimulus

 possible answer: UG

argument: there is a learning algorithm lim A (T

_N

) =L

^{N →∞}

Approaches:

a) principles and parameters theory (Chomsky)

b) optimality theory

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Chomsky Hierarchy

UG as a restricted search space:

Natural languages

• finite state grammar is not capable of representing “if…then”-sentences

• at least context-free grammars are necessary

•no phrase structure (is unrestricted)

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Summary: Arguments for UG

• Language acquisition

– Paradox of Language acquisition

• Learning theory:

– necessity of restricted search space

Human brain contains of an algorithm that can learn grammar  there is no algorithm that can learn an unrestricted set of

grammars  Human brain can only learn a certain subset of

all possible languages  The theory of this subset is UG.

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Cultural Evolution of Language

starting position:

population of individuals with the same UG UG specifies finite number of languages L

₁

,…,L

_n

each individual uses particular language

selective aspect:

successful communication (coherent language) results in pay-off

 increased fitness

Variation:

Offspring inherit a mechanism to learn language and UG (mutation)

Offspring use this mechanism to learn the language of their parents etc

(mistakes)

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Cultural Evolution of Language

Model: Two individuals communicating by L

_i

and L

_j

Components:

Equation:

Communicative pay-off for user of L_i F_ij Relative abundance of speakers of L_i x_i Learning Matrix (Probability of an offspring

speaking L_j with L_i parents) Q_ij

Fitness of L_i n

f_i= ∑x_jF_ij

j=1

Average fitness (grammatical coherence) of population

�(x)=∑_if_i(x)x_i total population size is consant: ∑_ix_i=1 - (x) � x_j

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Evolution of UG

starting position:

population of individuals with different UGs (U

I

… U

M

) each individual uses particular U

each U

I

admits a subset of n grammars

selective aspect:

ability to generate coherent language

Variation:

small search space increases probability of linguistic coherence

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Evolution of UG

Model: Two individuals communicating with U

_I

und U

_J

Additional Components:

Equation:

 in the limit of no mutation: only one UG

Relative abundance of individuals with U_J speaking L_j

x_Jj Probability of genetical mutation from U_Ito U_J W_IJ

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Linguistic coherence

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Combination

• Evolution of the algorithm of UG as a prerequisitional

mechanism for distinction between humans and apes

• UG specifies the mechanisms of language acquisition

and allows cultural evolution of

language

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Possible Criticism

• theory of UG is not falsifiable

• Daniel Everett: Non-recursive languages:

Pirahã language (!)

• Tomasello: Language acquisition can be explained by development of cognitive abilities

 Remains a theory

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