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Transcript of Evolution of Universal Grammar Pia Göser Universität Tübingen Seminar: Sprachevolution Dozent:...
![Page 1: Evolution of Universal Grammar Pia Göser Universität Tübingen Seminar: Sprachevolution Dozent: Prof. Jäger 11.02.2010.](https://reader035.fdocuments.net/reader035/viewer/2022070408/56649e675503460f94b63581/html5/thumbnails/1.jpg)
Evolution of Universal Grammar
Pia GöserUniversität Tübingen
Seminar: SprachevolutionDozent: 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 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
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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 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
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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 stimuluspossible answer: UG
argument: there is a learning algorithmlim A (TN) =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 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)
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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
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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
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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
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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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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.