Evolution of Universal Grammar Pia Göser Universität Tübingen Seminar: Sprachevolution Dozent: Prof. Jäger

Structure Historical outline Arguments for Universal Grammar – Language and Grammar – Learning Theory – Language Acquisition Evolutionary Processes – Language – Universal Grammar

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

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 grammarautomata Phrase structure (Unrestricted)Turing machine; description for computable languages with unrestricted rewrite-rules Context sensitiveLinear-bounded; Turing machine can decide every sentence’s belonging to the language; TM has an infinite memory Context freePush-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 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

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 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

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 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)

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 xixi Learning Matrix (Probability of an offspring speaking L j with L i parents) Q ij Fitness of L i n f i = ∑x j F ij j=1 Average fitness (grammatical coherence) of population (x)=∑ i f i (x)x i total population size is consant: ∑ i x i =1- (x)x j

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

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 I to U J W IJ

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 Grewendorf, G., Hamm, F., Sternefeld, W., Sprachliches Wissen. Eine Einführung in moderne Theorien der grammatischen Beschreibung, Suhrkamp, 1999.