Evolution of Universal Grammar

Pia GöserUniversität Tübingen

Seminar: SprachevolutionDozent: Prof. Jäger

11.02.2010

Structure

• Historical outline• Arguments for Universal Grammar

– Language and Grammar– Learning Theory– Language Acquisition

• Evolutionary Processes– Language– Universal Grammar

Universal GrammarBrief 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

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?

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?

Relationship language-grammar

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

Learning Theory

Classical Learning Theory (Gold)

assumptions: a) learner has to identify the target languageb) learner receives only positive examples

c)learner has access to an arbitrary large number of examplesd) 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 theoryassumptions:

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

Learning Theory

• no learning theory can permit all languages to be learnable

necessity of specific resrictions innate “restricted search space” for languages

Learning a language

• Paradox of language acquisition• Poverty of stimuluspossible answer: UG

argument: there is a learning algorithmlim A (TN) =L

N →∞ Approaches:a) principles and parameters theory (Chomsky)b) optimality theory

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)

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.

Cultural Evolution of Language

starting position: population of individuals with the same UG

UG specifies finite number of languages L1,…,Ln

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)

Cultural Evolution of Language

Model: Two individuals communicating by Li and Lj

Components:

Equation:

Communicative pay-off for user of Li Fij

Relative abundance of speakers of Li xi

Learning Matrix (Probability of an offspring speaking Lj with Li parents)

Qij

Fitness of Li nfi = ∑xjFij j=1

Average fitness (grammatical coherence) of population

𝝓(x)=∑ifi(x)x

i

total population size is consant: ∑ixi=1 - (x)𝝓 xj

Evolution of UG

starting position: population of individuals with different UGs (UI … UM)

each individual uses particular Ueach UI admits a subset of n grammars

selective aspect: ability to generate coherent language

Variation:small search space increases probability of linguistic coherence

Evolution of UG

Model: Two individuals communicating with UI und UJ

Additional Components:

Equation:

in the limit of no mutation: only one UG

Relative abundance of individuals with UJ speaking Lj

xJj

Probability of genetical mutation from UI to UJ WIJ

Linguistic coherence

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

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

Thank you for listening

•Nowak, Martin, Evolutionary Dynamics. Exploring the Equations of Life, Harvard University Press, 2006•Nowak, Martin et al, Computational and evolutionary aspects of language, In:Nature, Vol.417, June 2002, p. 611-617•Grewendorf, G., Hamm, F., Sternefeld, W., Sprachliches Wissen. Eine Einführung in moderne Theorien der grammatischen Beschreibung, Suhrkamp, 1999.