You go to jail.

almondpitterpatterAI and Robotics

Feb 23, 2014 (3 years and 1 month ago)

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You drink. You drive.
You go to jail.

Where’s recursion?

Daniel L. Everett

Illinois State University

dlevere@ilstu.edu

http://
www.llc.ilstu.edu/dlevere
/

What is recursion?



1. “An operation that applies to its own output.”


2. “Having the property that in principle a machine
could determine in finite time, for any arbitrary
finite string over the right alphabet, whether the
string is in the language or not.”


I will assume we are interested in (1).


We see family resemblances to recursion all around
us:

One statement of its
importance:


HC&F (1573): “In fact, we
propose in this hypothesis that
FLN comprises only the core
computational mechanisms of
recursion as they appear in
narrow syntax and the
mappings to the interfaces.”




Curious


“Learners are resistant to
recursion”


(paraphrase of
Roeper

and
Hollebrandse
)



Recursion as a non
-
modular
(or general) capacity


1. No one doubts that recursion plays a role in human cognition.


Humans can think thoughts about people thinking certain thoughts,
or about people believing that other people are thinking certain
thoughts, etc.



2. But where is the source of recursion? Grammar? Or cognition more

generally? There are at least three theses one could explore:


2a. Recursion originates in cognition and from there it may perhaps
be manifested in grammar.


2b. Recursion originates in grammar and it is manifested in
nonlinguistic cognitive activities only parasitically on the linguistic
phenomenon.


2c. There are separate recursions for each cognitive module. I WON’T
EXPLORE THIS OPTION IN THIS TALK.




Recursion: grammar or
cognition more generally?


3. It would be at least some evidence for 2b if all grammars
had recursion.





4. It would be evidence for 2a if there were languages that
lack recursion in their syntax but have it in discourse
--

in the
way speakers organize, present, and discuss information.





5. Various researchers have presented evidence from
several languages that seem to lack recursion. If correct,
these tell heavily against 2b

Another way of putting the
matter


"The question is not whether anything at all is
specific to human beings and/or hard wired
into the brain, but whether there exist rules
that are specific to human language and not a
result of our general conceptual/perceptual
apparatus together with our experience of the
world." (Goldberg 2009:117, Cog Ling)

Languages that might lack recursion based
on extant descriptions


1.
Pirahã


2.
Hixkaryana


3. Warlpiri


4.
Teiwa


5. Dutch Sign Language


6. No doubt others if re
-
examined from non
-
recursion committed perspective.


Surprising to find languages
without recursion?


Hilda
Koopman



if there are languages that
have structures for which the basic level of
recursion must be set to 1, 2, 3, etc.
(proliferation of numbers is problematic here),
perhaps languages can set it to zero for all
structures.

One way we might settle
the matter


“We present a Bayesian framework for
performing rational inference that enables us
to quantitatively evaluate grammars with and
without recursive rules and normatively
determine which best describe the sentences
in a corpus…”
Perfors
,
Tenenbaum
, & Gibson
(paper presented at Recursion in Human
Language, ISU, 2007. To appear in van
der

Hulst
, 2009.

Pirahã

(
Hiaiitíihí
): NP
Structure


Possession


John's brother's house.


Xahaigí

kaiíi

xáagahá
.
Xaikáibaí

xahaigí

xaoxaagá
.
Xahaigi

xaisigíai
.


'Brother's house. John has a brother. It is the
same one.'

Pirahã

(
Hiaiitíihí
): NP
Structure
-

Modification


*
Kabogáohoí

biísai

xogií

hoíhio
.


Kabogáohoí

biísai
.
Xogií

píaii
.
Hoí

hiaagá


'Two big red barrels.'


Pirahã

(
Hiaiitíihí
): Restrictive
Reference


Ti
baósaápisí

xoog

-
abagaí
.
Xigi

-
ábií


xaoói
.


Chico hi
goó

baósaápisí

bagá

-
boí
.


Baósaápisí

xais

-
igí


-
ai
.


'I want a hammock. I am like a Brazilian.
Chico
sold a/the hammock (restriction of reference)
.
It is the same one.'


Pirahã

(
Hiaiitíihí
): Complement Clauses
without embedding
-

Imperatives



Ti

xibíib


i


hiab


iig


á
.
Kahaí

kai
-
sai
.


‘I am not ordering you. (We are speaking of) (you) make
an arrow.’



2.
Ti


xibíibihiabiigá
. Ti


xoog
-
i
-
baaí
.

Gíxai

kahaí

kaí

xígiaoaxáí
-
sai
.
Pixái

xíga
.


I am not ordering you. I really want an arrow. OK? You
make an arrow. Now.

Pirahã

(
Hiaiitíihí
): Complement Clauses
without embedding
-

Quotatives


(
i
) Hi

gái

-
sai
.
Tiobáhai

kab

-
iig

-
á
.


'He says
-
sai

there is no child here.’


(ii) Hi



xai


á


b


í

-
sai
.





Tiobáhai

kab

-
í
-
sai
-
áaga
-

.


'He says
-
sai

there is no child here.'


(iii) Hi



xai


á


b


í


sai
.
Tiobáhai

kab

-
í
-
sai
-
áagí
-
sai
.


'He says
-
sai

there is no child here.'


Pirahã

(
Hiaiitíihí
): Adjunct
Clauses:
Temporals


(
i
)
Kohoái
-
kab
-
áo
-
b
-
áo
. Ti



xahoai
-
soog
-
abagaí
.


' (When I) finish eating, I want to speak to you.'


(ii
) K
-
ab


áo


b

-
á
.



'It is finished.' Or 'He/she/it finished.’


(iii
) Ti
soxoá

xísi

kap


áo

-
b
-
a.



'I just/already shot the animal.'




Pirahã

(
Hiaiitíihí
): Adjunct
Clauses:Temporals

(cont.)


(
i
)

Kaógiái

xaaboó


pái


ta


h

-

.


Kaógiái

bíí


oo


ab

-
á
.



'
Kaógiái

returned.
Kaógiái

was tired.'
(free:
'When he returned,
Kaogiai

was tired.')


(ii)

Kaógiái

bííooabá
.
Kaógiái

xaaboópaitahaó
.



Kaógiái

was tired.
Kaógiái

returned.
(free: '
Kaógiái

was tired when he returned.'
)


Wh
-
extraction: Simple
clauses


Kohoibiíhiai

kaoí

xob


áo

-
b

-
á
?


'Who did
Kohoibiíhiai

see?’


Kaoí

Kohoibiíhiai

xobáobá
?



(
i
) 'Who did
Kohoibiíhiai

see?'



(ii) 'Who saw
Kohoibiíhiai
?’


Paóxaisi

hi

goó

koabáipí
?



'What will Dan kill?’


Hi

goó

Paóxaisi


koabáipí
?



(
i
) 'What will Dan kill?'



(ii) 'What will kill Dan?'


Wh
-
Extraction: Simple
Clauses


Hi

goó

kai

-
baaí

-
sai
.



Hi

xo
-
báaxáí
.


'What [thing/kind of] making [does he] know well?' (literally 'He what
associated making sees well?')


Hi
xobáaxáí
.
Hi
goó

kai

baaí
-
sai
.


'He knows well. What does he intensely make?’



Goó

hi/Hi
goó

xobáaxáí
. __
kai


sai
.



'What thing [does he] know well to make?' (literally 'What
associated thing he knows well to make/making?')


*
Who

You came to town yesterday. ___ did Bill see?


Wh
-
extraction


potential
embedding clauses


(1) "When did the boy say he fell?



(2)
Hi
goógíiso

tiobáhai


gáísai
. Hi
bigí

kaobíi
.


(Lit: When did the child talk/speak. He fell to the ground.)


'When did the child SAY he fell?’



(3)
Tiobáhai

hi
goógíiso

gáísai
. Hi
bigí

kaobíi
.


'When did the child say he fell?’


Wh
-
extraction


potential
embedding clauses


(4)
Tiobáhai

gáísai
. Hi
goógíiso

bigí

kaobíi
.


The child said/asked 'When did he fall?'



(5)
Tiobáhai

goó

gáísai
. Hi
goógíiso

bigí

kaobíi
.



(
lit:‘The

child said what/focus. He fell when?’)



‘When did he say he FELL __?


Pirahã

(
Hiaiitíihí
): Adjunct
Clauses

Conditionals



Pii
-
boi
-
baaí
-
hai
. Ti
kahápi
-
hiaba
.


'It is raining a lot. I will not go.’



Pii
-
boi
-
baaí
-
sai
. Ti
kahápi
-
hiaba
.



‘(We are talking about) it raining a lot (at a time also under discussion). I will not go.’



Pii
-
boi
-
baaí
-
sai
. Ti
kahápi
-
hiabí
-
sai
.



‘(We are talking about) it raining a lot (at a time also under discussion). I will not go (as I had
already mentioned).’


Pirahã

(
Hiaiitíihí
): Additional
Evidence


No disjunction



Kohoi

kahápií
.
Xabagi

kahápií
.
Xmh
.
Kosaagá
.


'
Kohoi

came.
Xabagi

came. Hmm. (I) don't
know.’


Kagáíhiaii

Kóhoi

xabáiipi
.
Kagáíhiaii

Xabagi

xabáiipi
.
Xmh
.
Kosaagá
.


'The jaguar jumped on
Kóhoi
. The jaguar
jumped on
Xabagi
. Hmm. I don’t know.’


Pirahã

(
Hiaiitíihí
): Additional
Evidence


No coordination


Kóhoi

kahápií
.
Xabagi

pío

kahápií
. Or
Xabagi

píaii
.


'
Kóhoi

left.
Xabagi

also left.'


The trip to see a plane


Not recorded on tape, Informant:
Tisahai

(written by Steve Sheldon)



This
story was told by
Tisahai

to
Xitaibigai
.
Tisahai

had been to Porto Velho, and had taken
a trip to the airport to look at airplanes. While
there she saw soldiers and lots of Brazilians.
She and her child saw inside a jet and the
steward give them candy
.


Structure of Text


Lines 1 & 2: Setting/beginning/background




Line 3: First event




Line 4 Second event, subordinated to first


Lines
5
-
8: Setting/
resumption



Line
9: Background to 8


Line
10: Setting/resumption




Lines
11 & 12 Third and Fourth Events


Lines 13
-
15 Setting/resumption


Lines 16 & 17: Clarification, new
information


Line 18: Setting/closure

Tests for
some levels of
recursion


Embedding/recursion and
entailments?


1. John said that the price is right.
(But it isn’t.)


2. John hopes that the price is right.


3. John believes that the price is
right.



4. John doubts that the price is
right.


Multiple embeddings



John said that Peter said that the moon is
green cheese.


John believed that Peter believed that the
moon is green cheese.


John said that Peter said that Bill said that
Mary said, etc.

False beliefs without recursion:

One
embedding’s

worth
:


1. The price is right. Or so John said.


2. The price is right. John believes this anyway.


3. The price is right. Actually, John doubts that.


4.The price is right. Or so John hopes.


The price is right. Who said that? John said that.


The price is right. John hopes that(?)/so.


The price is right. John denies that/so.


The price is right. John supposes that/so.

How far can you go?


1. With recursive syntax + recursive reasoning.




2. With recursive reasoning alone.

False beliefs without embedding:
Multiple embeddings’ worth


The moon is green cheese. Or so John said. Maria
reported that anyway.


The Eskimos have 100 words for snow.

That's
Mary's claim.

John told me about it.

Do you
believe it?


You drink. You drive. You go to jail. Rich people
don’t go to jail though. That is what some people
say. (Some people say that if you drink and drive,
then you go to jail, unless you are rich.)


Once upon a time, X. X = entire discourse.



Limbo linguistics
-

How low
can you go?


?
Kóxoí

higáísai
.
Kohoi

hi
goó

gáísai
.
Xaogií

báaxáí
.


(lit:
Koxoi

said (that).
Kohoi

he what said. Foreign
woman is pretty.)



Koxoi

said that.
Kohoi

said THAT. The foreign woman
is pretty.’


??
Kóxoí

higáísai
.
Kohoi

hi
goó

gáísai
.
Xaogií

goó

gáísai
.
Báaxáí
,
tíi
.



Koxoi

said that.
Kohoi

said THAT. Foreign woman said
THAT. I am pretty.’




Some have suggested parataxis is the
general strategy for getting meaning out
of clauses


Davidson & Hobbs


Davidson 1968 “On Saying That”
-

offers
paratactic

theory of
Oratio

obliqua


Theory not widely accepted this days. But
illustrates that even for languages with
recursive syntax, there might be reasons for
preferring a non
-
recursive semantics in some
places.


Jerry Hobbs (2008) ‘Deep lexical semantics’:
the
real
problem is Discourse.

BUT!


We see limitations to expressive power
without syntactic recursion.



Recursive syntax has a utilitarian cognitive
function.

Recursion and relative
expressive power.


Pirahã

easily allows bi
-
clausal structures to
express the semantic effect of what would be
one level of syntactic embedding in other
languages.



After the equivalent of level three embedding,
the translations into
Pirahã

are nearly
impossible.

Expressive power of
languages



Can anything be translated from any language to
any other language?



No. They may have different expressive powers.



The key is the fit between language and
culture/society/situation. The introduction of
recursion into a grammar without it would not be
a difficult step cognitively or linguistically.


Recursion as a cognitive
tool?


Societies of intimates and restricted universe of discourse vs.
societies of strangers and wider ranges of discourse.



Recursion aids interpretation. But where is it in the brain?
I
am betting on (a).


(a) One general recursion tool beginning outside of grammar?


(
b
) One general recursion tool beginning with grammar?


(
c
) Different recursions for different modules


What is it, after all?


We are still puzzled, I think. But that’s OK.
Lot’s of things can require lots of thinking. Like
simple things we see.

‘Whoa, Dan’s plane is coming. We
gotta

talk baby talk without
recursion again!