1. Chapter 3 Language Acquisition: A Linguistic Treatment Jang, HaYoung Biointelligence Laborotary Seoul National University

2. Arguments in the Previous Chapters Languages have a formal structure and in this sense may be viewed as sets of well-formed expressions. On exposure to finite amounts of data, children are able to learn a language. Language acquisition does not depend upon the order of presentations of sentences and it largely proceeds on the basis of positive examples alone. All naturally occurring languages are learnable by children.

3. Arguments in the Previous Chapters In Gold theorem, Chomsky hierarchy

4. Objectives of This Chapter In the complete absence of prior information, successful generalization to novel expressions is impossible. Explanation for how successful language acquisition may come about.  The range of grammatical hypotheses  Learning algorithm that children may plausibly use

5. Contents 3.1 Language Learning and the Poverty of Stimulus 3.2 Constrained Grammars – Principles and Parameters 3.3 Learning in the Principles and Parameters Framework 3.4 Formal Analysis of the triggering Learning Algorithm 3.5 Conclusions

6. 3.1 Language Learning and the Poverty of Stimulus Question formation in English  John is bald.  Is John bald? Two rules that the learner may logically infer  Move the second word in the sentence to the front  Move the first ‘is’ to the front

7. 3.1 Language Learning and the Poverty of Stimulus Novel statement where there are multiple instances of ‘is’  The man who is running is bald. What is the appropriate interrogative form?  Is the man who is running bald?  Is the man who running is bald? Grammatical sequences have an internal structure  is

8. Poverty of Stimulus Two main conclusions from the examples  Given a finite amount of data, there are always many grammatical rules consistent with the data.  Sentences have an internal structure and these constituents play an important role. Poverty of Stimulus  There are patterns in all natural languages that cannot be learned by children using positive evidence alone. Children are only ever presented with positive evidence for these particular patterns.  Children do learn the correct grammars for their native languages.  Conclusion: Therefore, human beings must have some form of innate linguistic capacity which provides additional knowledge to language learners.

9. 3.2 Constrained Grammars – Principles and Parameters Principles and Parameters (Chomsky 1981)  A finite set of fundamental principles that are common to all languages.  A finite set of parameters that determine syntactic variability amongst languages.

10. Example: A Three Parameter System from Syntax X-bar theory (Chomsky 1970)  Parameterized phrase structure grammar  It claims that among their phrasal categories, all languages share certain structural similarities. Two X-bar parameters  Spec: short for specifier  Roughly like the old in the noun phrase, the old book  Comp: short for complement, roughly a phrase’s argument  Like an ice-cream in the verb phrase ate an ice-cream  Or with envy in the adjective phrase green with envy

11. Example: A Three Parameter System from Syntax Parameterized production rules  Parameter settings of English are Spec-first and Comp- final (p 1 =0, p 2 =1) Example X-bar

12. Example: A Three Parameter System from Syntax Different derivation tree between English (Spec-first, Comp-final) and Bengali (Spec-first, Comp-first)

13. Example: A Three Parameter System from Syntax One transformational parameter (V2)  Finite verbs must move so as to appear in exactly the second position in root declarative clauses (p 3 =1)  German: p 3 =1  English: p 3 =0

14. Example: Parameterized Metrical Stress in Phnology

15. 3.3 Learning in the Principles and Parameters Framework Learnability and the sample complexity of the finite hypothesis classes suggested by the Principles and Parameters theory.  Parameterization of the language space  Distribution of the input data  Noise in examples  Type of learning algorithm  Use of memory

16. 3.4 Formal Analysis of the Triggering Learning Algorithm Triggering learning algorithm

17. Markov Formulation Parameterized grammar family with 3 parameters  Target language  Absorbing State  Loop to itself  No exit arcs  Closed set of states  No arc from any states in set  Absorbing set is a closed set with one state

18. Markov Chain Criteria for Learnability Memoryless learning system  Triple (A, G, g f )  A: memoryless learning algorithm  G: family of grammars  g f : target grammar Gold learnability

19. Markov Chain Criteria for Learnability Proof  Gold learnable ↔ every closed set includes the target state  →: by contradiction  ←: first, show that every non-target state must be transient. Then, show that the learner must converge to the target grammar in the limit with probability 1

20. The Markov Chain for the Three- parameter Example

21. Derivation of the Transition Probabilities for the Markov TLA Structure Target language L t consist of the strings TLA will move from state s to k only if the following conditions are met  Next sentence ω with probability P(ω) is analyzable by the parameter settings corresponding to k and not by the parameter settings corresponding to s  TLA happens to pick and change the one parameter (out of n) that would move it to state k

22. Derivation of the Transition Probabilities for the Markov TLA Structure Total probability of transition from s to k after one step Probability of remaining s after one step

23. Derivation of the Transition Probabilities for the Markov TLA Structure Procedeur for constructing Markov chain

24. Conclusions In order to learn language, certain kinds of prior information is required. How can we formulate such information? Under what condition is grammar learnable? There are many variants in algorithm, the possibility of noise, memory and so on.