“For instance, on the planet Earth, man had always …ajyu/Teaching/Cogs160_sp10/Week6/tomoki...Agenda Background Noam Chomsky CTF and Chomsky hierarchy Universal grammar Experiment

“For instance, on the planet Earth, man had always assumed that he was more intelligent than dolphins because he had achieved so much -- the wheel, New York, wars and so on -- whilst all the dolphins had ever done was muck about in the water having a good time. But conversely, the dolphins had always believed that they were far more intelligent than man -- for precisely the same reasons.”

-- Douglas Adams

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Recursive syntactic pattern learning by

Gentner, Fenn, Margoliash, Nusbaum 2006Presented by Tomoki TsuchidaCOGS 160May 4, 2010

+Agenda

Background Noam Chomsky CTF and Chomsky hierarchy Universal grammar

Experiment

Results

Conclusions

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+Background: Noam Chomsky

Formal Grammars Rules for transforming strings

Universal Grammar “Principle of grammar

shared by all languages, innate to humans”

Nativistic view of language acquisition

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+Background: Chomsky hiearchy

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+Background: Chomsky hiearchy

Grammar Language Automaton

Type-0 Recursively enumerable

Turing machine

Type-1 (aSb dEf) Context-sensitive Linear-bounded TM

Type-2 (S aBc) Context-free Pushdown

Type-3 (S aB) Regular Finite-state

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+Background: Regular Grammar

Represented by a finite number of states and transitions

Regular expressions: ab (ab)|(aabb)|(aaabbb) a*b*

Cannot have infinite number of states.

In particular, can’t “count infinitely”: anbn

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+Background: Context-Free Grammar

FSA plus an (infinite) stack

Can now “count” matching patterns “Recusive center embedding”

Example: parentheses matching S SS S aSb S ab

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+Background: Universal Grammar

Universal grammar Shared by all languages Innate to humans (“poverty of stimulus”) Recursive center-embedding is usually part of UG (one of formal universals)

Faculty of language — broad sense (FLB). FLB includes an internal computational system (FLN, below) combined with at least two other organism-internal systems, which we call “sensory-motor” and “conceptual-intentional.” ...we take as uncontroversial the existence of some biological capacity of humans that allows us (and not, for example, chimpanzees) to readily master any human language without explicit instruction.

Faculty of language — narrow sense (FLN). FLN is the abstract linguistic computational system alone, independent of the other systems with which it interacts and interfaces. FLN is a component of FLB, and the mechanisms underlying it are some subset of those underlying FLB.

(Chomsky et al., 2002)

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+Agenda

Background Noam Chomsky CTF and Chomsky hierarchy Nonhuman communications

Experiment

Results

Conclusions

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+Experiment

European starlings: one of the best mimics (Eens, et al) Repertoire ranges from 15 to 70 phrases

Two motifs: ‘rattle’ (A) and ‘warble’ (B)

Goal: Can European starlings learn context-free grammars?

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(AB)2 A2B2

a1b6a5b2 a1a3b6b2

a2b5a6b7 a2a1b7b5

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+Experiment

Apparatus

(center hole = for food reward)

Performance measured in d’

d’ = Z(hit rate) – Z(false alarm rate)

Higher d’: better discrimination; d’ = 0 : chance

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+Experiment: Learning

Eleven starlings learned to classify “FSG” – (AB)n – and “CFG” – AnBn – grammars.

(Half had FSG as S+ and CFG as S-; vice versa for the other half.)

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+Agenda

Background Noam Chomsky CTF and Chomsky hierarchy Nonhuman communications

Experiment

Results

Conclusions

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+Results: Learning

Different learning rates

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+Results: Generalization

Was it rote memorization or grammatical learning?

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w/ reinforcement w/o reinforcement

+Results: Rejecting alternate explanations

Was FSG learned as compliment of CFG? (binary choice?) Probed with “agrammatical” motif discrimination (AAAA vs ABBA) (d’=0.99), (BBBB vs BAAB) (d’=0.02) both lower

than d’=1.63

Was AnBn approximated as A*B*? A1B3, A3B1 different from A2B2, A4B4

AA* vs AB* classification? B/A transitions? A/B transitions? AA pairs? Ruled out by comparing with various agrammatical patterns.

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+Agenda

Background Noam Chomsky CTF and Chomsky hierarchy Nonhuman communications

Experiment

Results

Conclusions

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+Conclusions

Starlings can recognize AnBn grammar rules. Does that mean starlings can learn / communicate using context-

free grammar rules? Do humans use context-free grammars?

Species differences as quantitative rather than qualitative distinctions in cognitive mechanisms.

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+Extra: Non-human cognition

Non-human communications Washoe (Chimpanzee) – ASL, categorization (Gardner, 1998) Koko (Gorilla) – ASL, 100 English words (Patterson, 1978) Alex (Parrot) – Color / shape adjectives, object permanence,

counting, word formation (Pepperberg, 1981)

Human language without recursion Pirahã (Everett, 2009)

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