cpb-us-e1.wpmucdn.com€¦ · Introduction tionalComputa modeling of redutionplica ya2-w FSTs orf redutionplica thematicalMa Typology of Morpho-Phonology Conclusion References Appendix

Introduction

Computational modeling of reduplication

2-way FSTs for reduplication

Mathematical Typology of Morpho-Phonology

Conclusion

References

Appendix

The computational typology and

modeling of reduplication

Hossep Dolatian & Je�rey Heinz

Stony Brook UniversityInstitute of Advanced Computational Science

May 4, 2018

This work was supported by NIH under grant #R01HD87133-01

Introduction




Conclusion

References

Appendix

Table of Contents

Introduction


1-way FSTs in morphology & phonology1-way FSTs for reduplication



Mathematical typology of non-reduplicationMathematical typology of reduplication

Conclusion

Appendix

2

Introduction




Conclusion

References

Appendix

The Message

● Reduplication is well-attested across languages and well-studiedin theoretical linguistics

● Typology is roughly two categories

▸ Indonesian plural: buku → buku∼buku Total (83%)▸ Papago plural: paga → paa∼paga Partial (75%)

● There are numerous patterns in the typology:▸ non-local reduplication (Riggle, 2004)▸ TETU e�ects (McCarthy and Prince, 1995)▸ opacity (underapplication/overapplication) (McCarthy andPrince, 1995; Raimy, 2000b)

▸ internal reduplication (Broselow and McCarthy, 1983)▸ and more (Moravcsik, 1978; Rubino, 2005; Inkelas and Downing,2015a,b; Samuels, 2010)

3

Introduction




Conclusion

References

Appendix

The Message



▸ Indonesian plural: buku → buku∼buku Total (83%)

▸ Papago plural: paga → paa∼paga Partial (75%)



3

Introduction




Conclusion

References

Appendix

The Message






3

Introduction




Conclusion

References

Appendix

The Message




● There are numerous patterns in the typology:

▸ non-local reduplication (Riggle, 2004)▸ TETU e�ects (McCarthy and Prince, 1995)▸ opacity (underapplication/overapplication) (McCarthy andPrince, 1995; Raimy, 2000b)


3

Introduction




Conclusion

References

Appendix

The Message






3

Introduction




Conclusion

References

Appendix

Message

1. How has reduplication been modeled computationally?

Ð→ 1-way �nite-state transducers (FSTs)▸ = reads 1-way from left to right

▸ Does it work? Yes ,+ No /▸ Is it easy to use? Not really /▸ Does it match theory & generalizations ? Not really /→ not well-suited to reduplication /

2. How can you do it instead?Ð→ 2-way FSTs

▸ = reads and rereads in 2 ways (L→R, R→L)

▸ Underdeployed (because overlooked) but �ts all 3 needs ,▸ Developed database (RedTyp), implementations,▸ learnability results,▸ and computational typology!

4

Introduction




Conclusion

References

Appendix

Message

1. How has reduplication been modeled computationally?Ð→ 1-way �nite-state transducers (FSTs)

▸ = reads 1-way from left to right





4

Introduction




Conclusion

References

Appendix

Message



▸ Does it work? Yes ,+ No /▸ Is it easy to use? Not really /▸ Does it match theory & generalizations ? Not really /

→ not well-suited to reduplication /




4

Introduction




Conclusion

References

Appendix

Message







4

Introduction




Conclusion

References

Appendix

Message




2. How can you do it instead?

Ð→ 2-way FSTs▸ = reads and rereads in 2 ways (L→R, R→L)


4

Introduction




Conclusion

References

Appendix

Message







4

Introduction




Conclusion

References

Appendix

Message






▸ Underdeployed (because overlooked) but �ts all 3 needs ,▸ Developed database (RedTyp), implementations,▸ learnability results,

▸ and computational typology!

4

Introduction




Conclusion

References

Appendix

Message







4

Introduction




Conclusion

References

Appendix

1-way FSTs in morphology & phonology


Introduction






Conclusion

Appendix5

Introduction




Conclusion

References

Appendix



Table of Contents

Introduction






Conclusion

Appendix

5

Introduction




Conclusion

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Appendix



Computational modeling

● Most morphology and phonology can be (adequately) modeledwith 1-way �nite-state transducers

● 1-way FSTs are lingua franca of NLP, computational morphology& phonology (Roche and Schabes, 1997; Beesley and Karttunen,2003; Roark and Sproat, 2007)

● FSTs are mathematical devices for modeling transformations(functions) from input to output of a certain complexity

6

Introduction




Conclusion

References

Appendix



What's a 1-way FST?

● Languages have functions that map strings to strings...

likeGerman:

(1) �Häus-er� häuz-er�Haus� haus

7

Introduction




Conclusion

References

Appendix



What's a 1-way FST?

● Languages have functions that map strings to strings...likeGerman:

(2) �Häus-er� häuz-er�Haus� haus

7

Introduction




Conclusion

References

Appendix



Example 1-way FST for phonology

● German �nal z→s● Working example: tad→?

Input: ⋊ t a d ⋉Output:

q0start q1

q2

q3⋊:λ

T:T, V:V

D:λV:DV, D:DD, T:DT

⋉:T

⋉:λ

8

Introduction




Conclusion

References

Appendix




● German �nal z→s● Working example: tad→tat


q0start q1

q2

q3⋊:λ

T:T, V:V


⋉:T

⋉:λ

8

Introduction




Conclusion

References

Appendix






q0start q1

q2

q3⋊:λ

T:T, V:V


⋉:T

⋉:λ

8

Introduction




Conclusion

References

Appendix






q0start q1

q2

q3⋊:λ

T:T, V:V


⋉:T

⋉:λ

8

Introduction




Conclusion

References

Appendix






q0start q1

q2

q3

T:T, V:V


⋉:T

⋉:λ⋊:λ

8

Introduction




Conclusion

References

Appendix





Input: ⋊ t a d ⋉Output: t

q0start q1

q2

q3⋊:λ


⋉:T

⋉:λ

T:T, V:V

8

Introduction




Conclusion

References

Appendix





Input: ⋊ t a d ⋉Output: t a

q0start q1

q2

q3⋊:λ


⋉:T

⋉:λ

T:T, V:V

8

Introduction




Conclusion

References

Appendix





Input: ⋊ t a d ⋉Output: t a

q0start q1

q2

q3⋊:λ

T:T, V:V

V:DV, D:DD, T:DT

⋉:T

⋉:λ

D:λ

8

Introduction




Conclusion

References

Appendix





Input: ⋊ t a d ⋉Output: t a t

q0start q1

q2

q3⋊:λ

T:T, V:V


⋉:λ

⋉:T

8

Introduction




Conclusion

References

Appendix





Input: ⋊ t a d ⋉Output: t a t

,

q0start q1

q2

q3⋊:λ

T:T, V:V


⋉:λ

⋉:T

8

Introduction




Conclusion

References

Appendix



1-way FSTs for phonology

● And virtually all known phonological transformations can bemodeled with 1-way �nite-state transducers (Chandlee, 2014;Kaplan and Kay, 1994)

▸ repairing marked substructures (phonotactics)▸ vowel harmony▸ stress▸ a�xation▸ partial reduplication▸ but...

9

Introduction




Conclusion

References

Appendix



Partial reduplication with 1-way FSTs

● Partial reduplication: can be modeled with 1-way FSTs ifthere is a maximum size for the copied portion (Chandlee andHeinz, 2012)

● Real Sundanese

(3) guyon→gu∼guyon`to jest'→`to jest repeatedly' (Sundanese)

● Mini-Sundanese with Σ = {p, t, a}(4) tappa→ta∼tappa

10

Introduction




Conclusion

References

Appendix





● Real Sundanese



10

Introduction




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Appendix





● Real Sundanese



10

Introduction




Conclusion

References

Appendix




● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→?

Input: ⋊ p a t ⋉Output:

q0start q1

q2

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ

11

Introduction




Conclusion

References

Appendix




● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼pat


q0start q1

q2

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ

11

Introduction




Conclusion

References

Appendix






q0start q1

q2

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ

11

Introduction




Conclusion

References

Appendix






q0start q1

q2

q3

q4 q5

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ⋊:λ

11

Introduction




Conclusion

References

Appendix





Input: ⋊ p a t ⋉Output: p

q0start q1

q2

q3

q4 q5⋊:λ

t:t a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ

p:p

11

Introduction




Conclusion

References

Appendix





Input: ⋊ p a t ⋉Output: p a∼pa

q0start q1

q2

q3

q4 q5⋊:λ

t:t

p:p

a:a∼taΣ ∶ Σ

⋉:λ

a:a∼pa

11

Introduction




Conclusion

References

Appendix





Input: ⋊ p a t ⋉Output: p a∼pa t

q0start q1

q2

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

⋉:λ

Σ ∶ Σ

11

Introduction




Conclusion

References

Appendix






q0start q1

q2

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ

11

Introduction




Conclusion

References

Appendix






,

q0start q1

q2

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ

11

Introduction




Conclusion

References

Appendix




● Partial reduplication: can be modeled with 1-way FSTs ifthere's a maximum size for the copied portion

● But...

bigger alphabet and copied portion size → more states

12

Introduction




Conclusion

References

Appendix




● Partial reduplication: can be modeled with 1-way FSTs ifthere's a maximum size for the copied portion

● But... bigger alphabet and copied portion size → more states

12

Introduction




Conclusion

References

Appendix




● Mini-Sundanese with Σ = {p, t, a}(9) pat→pa∼pat bla

q0start q1

q2

qk

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ

13

Introduction




Conclusion

References

Appendix




● Mini-Sundanese with Σ = {p, t, a}(10) pat→pa∼pat bla

q0start q1

q2

qk

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λ

13

Introduction




Conclusion

References

Appendix



Problems with 1-way FSTs for Partial

● Less-Mini-Sundanese with Σ = {p, t, a, k}(11) pat→pa∼pat(12) kat→ka∼kat

q0start q1

q2

qk

q3

q4 q5⋊:λ

t:t

p:p

a:a∼ta

a:a∼pa

Σ ∶ Σ

⋉:λk:k a:a∼ka

14

Introduction




Conclusion

References

Appendix




● Partial reduplication can be modeled with 1-way FSTs but itcauses an explosion of states (Chandlee, 2014)

▸ "burdensome models" (Roark and Sproat, 2007:54)▸ = too many states to easily design+debug

● Theoretically partial reduplication is understood as copying, butthe 1-way FSTs for it just remember all possible copied portions

→ 1-way FSTs don't capture partial reduplication in a concrete away▸ Explained more technically in next slide via origin semantics

15

Introduction




Conclusion

References

Appendix








15

Introduction




Conclusion

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Appendix








15

Introduction




Conclusion

References

Appendix







→ 1-way FSTs don't capture partial reduplication in a concrete away

▸ Explained more technically in next slide via origin semantics

15

Introduction




Conclusion

References

Appendix








15

Introduction




Conclusion

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Appendix



Matching theory of copying

● Origin information: origin of output symbols in the input● 1-way FSTs remember what to repeat, they don't actively copy

p a t

p a p a t

Input:

Output:

● But linguistic theory says "copy!"

p a t

p a p a t

Input:

Output:

16

Introduction




Conclusion

References

Appendix





p a t

p a p a t

Input:

Output:


p a t

p a p a t

Input:

Output:

16

Introduction




Conclusion

References

Appendix



Problems with 1-way FSTs for Total

● Total reduplication cannot be modeled at all.

● Why?

▸ If copied portion is of unbounded size then no 1-way FST can dothe job

▸ because an in�nite number of states would be needed

17

Introduction




Conclusion

References

Appendix





● Why?



17

Introduction




Conclusion

References

Appendix





● Why?



17

Introduction




Conclusion

References

Appendix





● Can you approximate?

▸ some �nite-state approximations exist... (Hulden, 2009; Beesleyand Karttunen, 2003; Walther, 2000)

▸ But: they impose un-linguistic restrictions (e.g. a �nite bound onword size,...) so don't directly capture reduplication

18

Introduction




Conclusion

References

Appendix








18

Introduction




Conclusion

References

Appendix








18

Introduction




Conclusion

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Appendix





● Therefore:

▸ total reduplication is outside the scope of 1-way FSTs, whilepartial reduplication can be modeled with 1-way FSTs butinelegantly

● Contribution:

▸ show how an extension to 1-way FSTs can do reduplication butstill be �nite-state

19

Introduction




Conclusion

References

Appendix





● Therefore:


● Contribution:


19

Introduction




Conclusion

References

Appendix





● Therefore:


● Contribution:


19

Introduction




Conclusion

References

Appendix

Table of Contents

Introduction






Conclusion

Appendix

20

Introduction




Conclusion

References

Appendix

2-way FSTs

● The previous FSTs can be described as 1-way FSTs because theyread the input once from left to right.

● 2-way FSTs are an enriched class of FSTs that can go back andforth on the input (Engelfriet and Hoogeboom, 2001; Savitch,1982).

● A 2-way FST can do everything a 1-way FST can do, and more.

21

Introduction




Conclusion

References

Appendix

2-way FSTs

● The previous FSTs can be described as 1-way FSTs because theyread the input once from left to right.

● 2-way FSTs are an enriched class of FSTs that can go back andforth on the input (Engelfriet and Hoogeboom, 2001; Savitch,1982).

● A 2-way FST can do everything a 1-way FST can do, and more.

21

Introduction




Conclusion

References

Appendix

2-way FSTs - Total reduplication

● Total reduplication copies an unbounded size

(13) wanita→wanita∼wanita `woman'→`women' (Indo.)

● This 2-way FST reads the input left to right (+1), goes back (-1),and reads the input again (+1)

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

22

Introduction




Conclusion

References

Appendix

2-way FSTs - Total reduplication

● Total reduplication copies an unbounded size

(14) wanita→wanita∼wanita `woman'→`women' (Indo.)

● This 2-way FST reads the input left to right (+1), goes back (-1),and reads the input again (+1)

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

22

Introduction




Conclusion

References

Appendix

2-way FSTs - Total Reduplication

● Indonesian example: wanita→wanita∼wanita● Working example: bye→?

Input: ⋊ b y e ⋉Output:

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

23

Introduction




Conclusion

References

Appendix


● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye


q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

23

Introduction




Conclusion

References

Appendix




q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

23

Introduction




Conclusion

References

Appendix




q0start q1

q2 q3 q4

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

⋊:λ:+1

23

Introduction




Conclusion

References

Appendix



Input: ⋊ b y e ⋉Output: b

q0start q1

q2 q3 q4

⋊:λ:+1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +1

23

Introduction




Conclusion

References

Appendix



Input: ⋊ b y e ⋉Output: b y

q0start q1

q2 q3 q4

⋊:λ:+1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +1

23

Introduction




Conclusion

References

Appendix



Input: ⋊ b y e ⋉Output: b y e

q0start q1

q2 q3 q4

⋊:λ:+1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +1

23

Introduction




Conclusion

References

Appendix



Input: ⋊ b y e ⋉Output: b y e ∼

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

⋉:∼∶ −1

23

Introduction




Conclusion

References

Appendix




q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1Σ ∶ λ ∶ −1

23

Introduction




Conclusion

References

Appendix




q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1Σ ∶ λ ∶ −1

23

Introduction




Conclusion

References

Appendix




q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1Σ ∶ λ ∶ −1

23

Introduction




Conclusion

References

Appendix




q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1

Σ ∶ Σ ∶ +1

⋉:λ:+1⋊:λ ∶ +1

23

Introduction




Conclusion

References

Appendix




b

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1 ⋉:λ:+1

Σ ∶ Σ ∶ +1

23

Introduction




Conclusion

References

Appendix




b y

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1 ⋉:λ:+1

Σ ∶ Σ ∶ +1

23

Introduction




Conclusion

References

Appendix




b y e

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1 ⋉:λ:+1

Σ ∶ Σ ∶ +1

23

Introduction




Conclusion

References

Appendix




b y e

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

23

Introduction




Conclusion

References

Appendix




b y e,

q0start q1

q2 q3 q4

⋊:λ:+1

Σ ∶ Σ ∶ +1

⋉:∼∶ −1

Σ ∶ λ ∶ −1⋊:λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

23

Introduction




Conclusion

References

Appendix

2-way FSTs - Partial Reduplication

● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→?


q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

24

Introduction




Conclusion

References

Appendix


● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat


q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

24

Introduction




Conclusion

References

Appendix




q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

24

Introduction




Conclusion

References

Appendix




q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

24

Introduction




Conclusion

References

Appendix




q0start q1 q2

q3 q4 q5

C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

⋊:λ:+1

24

Introduction




Conclusion

References

Appendix



Input: ⋊ p a t ⋉Output: p

q0start q1 q2

q3 q4 q5

⋊:λ:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

C:C:+1

24

Introduction




Conclusion

References

Appendix



Input: ⋊ p a t ⋉Output: p a

q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

V:V:-1

24

Introduction




Conclusion

References

Appendix




q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1Σ ∶ λ ∶ −1

24

Introduction




Conclusion

References

Appendix




∼q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1

Σ ∶ Σ ∶ +1

⋉:λ:+1

⋊:∼∶ +1

24

Introduction




Conclusion

References

Appendix




∼ p

q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +1

24

Introduction




Conclusion

References

Appendix




∼ p a

q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +1

24

Introduction




Conclusion

References

Appendix




∼ p a t

q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +1

24

Introduction




Conclusion

References

Appendix




∼ p a t

q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

24

Introduction




Conclusion

References

Appendix




∼ p a t,

q0start q1 q2

q3 q4 q5

⋊:λ:+1 C:C:+1

V:V:-1

Σ ∶ λ ∶ −1⋊:∼∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

24

Introduction




Conclusion

References

Appendix



p a t

p a p a t

Input:

Output:


p a t

p a p a t

Input:

Output:

25

Introduction




Conclusion

References

Appendix



p a t

p a p a t

Input:

Output:

● But linguistic theory says "copy!" like a 2-way FST!

p a t

p a p a t

Input:

Output:

25

Introduction




Conclusion

References

Appendix

Mathematical typology of non-reduplication

Mathematical typology of reduplication

Table of Contents

Introduction






Conclusion

Appendix

26

Introduction




Conclusion

References

Appendix



Doing Linguistic Typology

Linguistic typology requires two books:

● �encyclopedia of types�

● �encyclopedia of categories�

Computational linguists look at computa-tional resources needed

● subclasses of FSA/FSTs needed

Wilhelm VonHumboldt

27

Introduction




Conclusion

References

Appendix



FSA & 1-way FST subclasses

● Regular languages (FSAs) & rational functions (1-way FST)consist of subclasses (McNaughton and Papert, 1971)

Regular

SF

LTT

LT

SL

PT

SP

Rational

WD

R-SeqL-Seq

ISL R-OSLL-OSL

● Fruitfully applied to segmental phonology (Chandlee, 2014; Heinzand Lai, 2013)

● Theoretical learnability results (Chandlee et al., 2015)28

Introduction




Conclusion

References

Appendix



OSL subclass

● Relatively weak subclass for segmental phonology is k-OutputStrictly Local (k-OSL) class

▸ = keep track of ONLY last k-1 segments outputted + thecurrent input segment

29

Introduction




Conclusion

References

Appendix



OSL subclass

● Relatively weak subclass for segmental phonology is k-OutputStrictly Local (k-OSL) class

▸ = keep track of ONLY last k-1 segments outputted + thecurrent input segment

29

Introduction




Conclusion

References

Appendix



OSL subclass = truncation

● English nicknames: truncate input to �rst (C)VC

(15) a. /dZEfôi/ →

[dZEf] `Je�rey'→`Je�'b. /deIvId/ →[deIv] `David'→`Dave'c. /æl@n/ →[æl] Àlan→Al'

● 3-OSL because keep track of last 2 segment outputted + thecurrent segment (and skip anything after VC)

30

Introduction




Conclusion

References

Appendix





(16) a. /dZEfôi/ →[dZEf] `Je�rey'→`Je�'b. /deIvId/ →

[deIv] `David'→`Dave'c. /æl@n/ →[æl] Àlan→Al'


30

Introduction




Conclusion

References

Appendix





(17) a. /dZEfôi/ →[dZEf] `Je�rey'→`Je�'b. /deIvId/ →[deIv] `David'→`Dave'c. /æl@n/ →

[æl] Àlan→Al'● 3-OSL because keep track of last 2 segment outputted + thecurrent segment (and skip anything after VC)

30

Introduction




Conclusion

References

Appendix





(18) a. /dZEfôi/ →[dZEf] `Je�rey'→`Je�'b. /deIvId/ →[deIv] `David'→`Dave'c. /æl@n/ →[æl] Àlan→Al'


30

Introduction




Conclusion

References

Appendix



OSL Subclass = Truncation

● English: /dZEfri/→[dZEf]

● Working example: `Samuel' /sæmj@l/→?Input: ⋊ s æ m j @ l ⋉Output:

q0start

λ C CV VC

qf

⋊:λ

C:C V:V C:CΣ ∶ λ

⋉:λ

V:V

31

Introduction




Conclusion

References

Appendix





● Working example: `Samuel' /sæmj@l/→[sæm]Input: ⋊ s æ m j @ l ⋉Output:

q0start

λ C CV VC

qf

⋊:λ


⋉:λ

V:V

31

Introduction




Conclusion

References

Appendix






q0start

λ C CV VC

qf

⋊:λ


⋉:λ

V:V

31

Introduction




Conclusion

References

Appendix






q0start

λ C CV VC

qf

⋊:λ


⋉:λ

V:V

31

Introduction




Conclusion

References

Appendix






q0start

λ C CV VC

qf


⋉:λ

V:V

⋊:λ

31

Introduction




Conclusion

References

Appendix





● Working example: `Samuel' /sæmj@l/→[sæm]Input: ⋊ s æ m j @ l ⋉Output: s

q0start

λ C CV VC

qf

⋊:λ

V:V C:CΣ ∶ λ

⋉:λ

V:V

C:C

31

Introduction




Conclusion

References

Appendix





● Working example: `Samuel' /sæmj@l/→[sæm]Input: ⋊ s æ m j @ l ⋉Output: s æ

q0start

λ C CV VC

qf

⋊:λ

C:C C:CΣ ∶ λ

⋉:λ

V:V

V:V

31

Introduction




Conclusion

References

Appendix





● Working example: `Samuel' /sæmj@l/→[sæm]Input: ⋊ s æ m j @ l ⋉Output: s æ m

q0start

λ C CV VC

qf

⋊:λ

C:C V:VΣ ∶ λ

⋉:λ

V:V

C:C

31

Introduction




Conclusion

References

Appendix






q0start

λ C CV VC

qf

⋊:λ

C:C V:V C:C

⋉:λ

V:V

Σ ∶ λ

31

Introduction




Conclusion

References

Appendix






q0start

λ C CV VC

qf

⋊:λ

C:C V:V C:C

⋉:λ

V:V

Σ ∶ λ

31

Introduction




Conclusion

References

Appendix






q0start

λ C CV VC

qf

⋊:λ

C:C V:V C:C

⋉:λ

V:V

Σ ∶ λ

31

Introduction




Conclusion

References

Appendix






q0start

λ C CV VC

qf

⋊:λ


V:V

⋉:λ

31

Introduction




Conclusion

References

Appendix






,q0start

λ C CV VC

qf

⋊:λ


⋉:λ

V:V

31

Introduction




Conclusion

References

Appendix



What is there?

● No real work on subclasses for 2-way FSTs /

● But... Natural language copying doesn't need full power of 2-wayFSTs

● Solution:▸ Discover subclasses based on descriptive typology= Concatenations/Compositions of 1-way subclasses

32

Introduction




Conclusion

References

Appendix



What is there?



● Solution:

▸ Discover subclasses based on descriptive typology= Concatenations/Compositions of 1-way subclasses

32

Introduction




Conclusion

References

Appendix



What is there?



● Solution:▸ Discover subclasses based on descriptive typology

= Concatenations/Compositions of 1-way subclasses

32

Introduction




Conclusion

References

Appendix



What is there?



● Solution:▸ Discover subclasses based on descriptive typology= Concatenations/Compositions of 1-way subclasses

32

Introduction




Conclusion

References

Appendix



How does it look like?

● Initial-CVC reduplication in Agta

(19) takki→ tak∼takki `leg'→`legs'

● If you focus on input-output relation (not output-output BRCT):

takki

tak ∼ takki

▸ Red(x) = Trunc(x) ∼ ID(x)▸ Red(takki)=Trunc(takki) ∼ ID(takki) = tak ∼ takki▸ Cf. (Steriade, 1988; Inkelas and Zoll, 2005)

● Both Trunc(x) and ID(x) are (1-way) OSL functions!

→ Red(x) is a concatenation of OSL functions... C-OSL

33

Introduction




Conclusion

References

Appendix





(20) takki→ tak∼takki `leg'→`legs'● If you focus on input-output relation (not output-output BRCT):

takki

tak ∼ takki




33

Introduction




Conclusion

References

Appendix






takki

tak ∼ takki

▸ Red(x) = Trunc(x) ∼ ID(x)

▸ Red(takki)=Trunc(takki) ∼ ID(takki) = tak ∼ takki▸ Cf. (Steriade, 1988; Inkelas and Zoll, 2005)



33

Introduction




Conclusion

References

Appendix






takki

tak ∼ takki

▸ Red(x) = Trunc(x) ∼ ID(x)▸ Red(takki)=Trunc(takki) ∼ ID(takki)

= tak ∼ takki▸ Cf. (Steriade, 1988; Inkelas and Zoll, 2005)



33

Introduction




Conclusion

References

Appendix






takki

tak ∼ takki

▸ Red(x) = Trunc(x) ∼ ID(x)▸ Red(takki)=Trunc(takki) ∼ ID(takki) = tak ∼ takki

▸ Cf. (Steriade, 1988; Inkelas and Zoll, 2005)



33

Introduction




Conclusion

References

Appendix






takki

tak ∼ takki




33

Introduction




Conclusion

References

Appendix






takki

tak ∼ takki




33

Introduction




Conclusion

References

Appendix






takki

tak ∼ takki




33

Introduction




Conclusion

References

Appendix



C-OSL: CVC reduplication

● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→?

Input: ⋊ c o p i e s ⋉Output:

q0start λ1 C1 CV1 CV C1

re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

34

Introduction




Conclusion

References

Appendix




● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies



re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

⋊:λ:+1

34

Introduction




Conclusion

References

Appendix





Input: ⋊ c o p i e s ⋉Output: c


re. λ2 qf

⋊:λ:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

C:C:+1

34

Introduction




Conclusion

References

Appendix





Input: ⋊ c o p i e s ⋉Output: c o


re. λ2 qf

⋊:λ:+1 C:C:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

V:V:+1

34

Introduction




Conclusion

References

Appendix





Input: ⋊ c o p i e s ⋉Output: c o p

q0start λ1 C1 CV1 CVC1

re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

C:C:-1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ +1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ +1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ +1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

⋉:∼∶ −1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ −1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ −1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ −1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ −1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ −1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

Σ ∶ λ ∶ −1

34

Introduction




Conclusion

References

Appendix







re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

Σ ∶ Σ ∶ +1

⋉:λ:+1

⋊ ∶ λ ∶ +1

34

Introduction




Conclusion

References

Appendix






c


re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +134

Introduction




Conclusion

References

Appendix






c o


re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +134

Introduction




Conclusion

References

Appendix






c o p


re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +134

Introduction




Conclusion

References

Appendix






c o p i


re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +134

Introduction




Conclusion

References

Appendix






c o p i e


re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +134

Introduction




Conclusion

References

Appendix






c o p i e s


re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

⋉:λ:+1

Σ ∶ Σ ∶ +134

Introduction




Conclusion

References

Appendix






c o p i e s


re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

34

Introduction




Conclusion

References

Appendix






c o p i e s,


re. λ2 qf

⋊:λ:+1 C:C:+1 V:V:+1 C:C:-1

Σ ∶ λ ∶ +1

⋉:∼∶ −1Σ ∶ λ ∶ −1

⋊ ∶ λ ∶ +1

Σ ∶ Σ ∶ +1

⋉:λ:+1

34

Introduction




Conclusion

References

Appendix



What's C-OSL

● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL

● A lot of reduplication is C-OSL:

(27) Total reduplication = unbounded copywanita→wanita∼wanita `woman'→`women' (Indo.)

(28) Partial reduplication = bounded copy

a. C: gen→g∼gen`to sleep'→`to be sleeping' (Shilh)

b. CV: guyon→gu∼guyon`to jest'→`to jest repeatedly' (Sundanese)

c. CVC: takki→ tak∼takki`leg'→`legs' (Agta)

d. CVCV:banagañu→bana∼banagañu`return' (Dyirbal)

35

Introduction




Conclusion

References

Appendix



What's C-OSL









35

Introduction




Conclusion

References

Appendix



What's C-OSL









35

Introduction




Conclusion

References

Appendix



What's C-OSL



(33) Triplication:roar→ roar∼roar-roar`give a shudder' →`continue to shudder' (Mokilese)

(34) Final reduplication:erasi→erasi∼rasi`he is sick'→`he continues being sick' (Siriono)

(35) Non-local reduplication:qanga→qanga∼qan`�re'→`�re (ABS)' (Koryak)

(36) Echo reduplication:kitap→kitap∼mitap`book'→`book schmook' (Turkish)

36

Introduction




Conclusion

References

Appendix



What's C-OSL







36

Introduction




Conclusion

References

Appendix



What's C-OSL







36

Introduction




Conclusion

References

Appendix



What's C-OSL







36

Introduction




Conclusion

References

Appendix



What's C-OSL


● Even subconstituent copying if boundaries are marked!

(49) Subconstituent (total) reduplication:ku-haata→ku-haata∼haata`to ferment'→`to start fermenting' (KiHehe)

(50) Subconstituent (partial) reduplication:na-murak→na-mu∼murak`to �ower'→`decorating with �owers' (Bikol)

(51) Subconstituent (a�x) reduplication:bele-nez→bele∼bele-nezinto-looks→into-into-looks`he looks into it'→`he occasionally...' (Hungarian)

37

Introduction




Conclusion

References

Appendix



What's C-OSL






37

Introduction




Conclusion

References

Appendix



What's C-OSL






37

Introduction




Conclusion

References

Appendix



What's C-OSL






37

Introduction




Conclusion

References

Appendix



What's C-OSL



(61) Subconstituent non-local reduplication:pa-jalan-an→lan∼pa-jalan-an`pedestrian'→`pedestrians' (Madurese)

(62) Iterative reduplication:huang.jang→huang∼huang-jang∼jang`�ustered'→`�ustered (vivid form)' (Mandarin)

38

Introduction




Conclusion

References

Appendix



What's C-OSL





38

Introduction




Conclusion

References

Appendix



What's C-OSL





38

Introduction




Conclusion

References

Appendix



What's still C-OSL


● and with prosodic boundaries...

(67) Stressed Syllable reduplication:hu(gá)ndo→hugá∼gando`play'→`playing' (Chamorro)

(68) Initial foot reduplication:(gindal)ba→gindal∼gindalba`lizard sp.'→`lizards' (Yidiny)

(69) Prosodic stem foot reduplication:s+tSeq→s-tSeq∼tSeqìt is very torn's+ikuk→s+ik∼s-ikuk`he is chopping' (Chumash)

39

Introduction




Conclusion

References

Appendix



What's still C-OSL






39

Introduction




Conclusion

References

Appendix



What's still C-OSL






39

Introduction




Conclusion

References

Appendix



What's still C-OSL






39

Introduction




Conclusion

References

Appendix



What's still C-OSL


● If skipping over �nite chunk...

(79) Place 1st C after 1st V reduplication:tS iko→tS i∼tko`he failed sp.'→`he failed (frequentative)' (Quileute)

(80) Place 1st C after 2nd C reduplication:barad→bar∼b-ad`shave'→`shave unevenly' (Arabic)

(81) CV of �nal CVC reduplication:nalaN→nala∼laN`hungry'→`very hungry' (Chamorro)

40

Introduction




Conclusion

References

Appendix



What's still C-OSL






40

Introduction




Conclusion

References

Appendix



What's still C-OSL






40

Introduction




Conclusion

References

Appendix



What's still C-OSL






40

Introduction




Conclusion

References

Appendix



What's not C-OSL


● But if skipping over a chunk of unbounded size...

(91) Double sided reduplication:lú:t'uxw→lúxw∼lút'uxw`to value'→`to value (plural)' (Nisgha)

(92) non-local internal reduplication:falapk+i:→falap∼fa-k+i:`split (as of wood)'→`... (plural)' (Creek)

● It's not C-OSL so go higher to C-Seq (appendix)

41

Introduction




Conclusion

References

Appendix



What's not C-OSL






41

Introduction




Conclusion

References

Appendix



What's not C-OSL






41

Introduction




Conclusion

References

Appendix



What about phonology?

● Phonology within the reduplicant (templatic simpli�cation) canbe C-OSL...

(97) Complex onset reduction:trabaho→ta∼trabaho`to work'→`just �nished working' (Tagalog)

● But when very complicated...

(98) Complex onset reduction via vocalization:skand→ka∼skand-a `leap'svap→su∼svap-a `sleep' (Sanskrit)

● Looks like copying + rules (Steriade, 1988)

42

Introduction




Conclusion

References

Appendix









42

Introduction




Conclusion

References

Appendix









42

Introduction




Conclusion

References

Appendix




● Especially when there are interactions between the copies...

(103) Overapplication of nasal spread in Madurese:/neyat/→ [�yãt∼n�e�yãt]ìntention'→`'intentions'

(104) Juncture e�ect of coronal dissimilation in Dakota:a. £ap-a →£ap∼£ap-a `trot'b. ºat-a →ºag∼ºat-a `curved'

43

Introduction




Conclusion

References

Appendix







43

Introduction




Conclusion

References

Appendix







43

Introduction




Conclusion

References

Appendix




● From serialist perspective:

Simpli�cation Overapplication Juncture e�ectCopy Phonology Copy(Morpho-)Phonology Copy (Morpho-)Phonology

● Copying is morphological (C-OSL) while the morpho-phonologyis independently ISL/OSL/Sequential

→ Com-C-OSL or Com-C-Seq: composition of C-OSL and eitherOSL or Seq

44

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Appendix




● From serialist perspective:Simpli�cation Overapplication Juncture e�ectCopy Phonology Copy(Morpho-)Phonology Copy (Morpho-)Phonology



44

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References

Appendix




● From serialist perspective:Simpli�cation Overapplication Juncture e�ectCopy Phonology Copy(Morpho-)Phonology Copy (Morpho-)Phonology



44

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References

Appendix




● What about underapplication?

(109) Underapplication of palatalization (Akan)a. /ge/ → [dJI∼dJe] `receive'b. /si/ → [si∼siP] `stand'c. /kaP/ → [kI∼kaP],*[tCI∼kaP] `bite'd. /ge/ → [dJI∼dJe] `receive'

● Very rare (above doesn't exist) and potentially justrule-deactivation /

● Or higher than just composition of functions, but still doablewith 2-way FST

45

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Appendix








45

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Appendix








45

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Appendix








45

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Appendix




● What about backcopying?

(113) Backcopying of nasal spread in Malay/ham@/ → [ham@∼ham@],*[ham@∼ham@] `germ'→`germs'

● Very rare (above doesn't exist) and probably doesn't exist at all(Inkelas and Zoll, 2005; McCarthy et al., 2012) /

● But even if did, it's still doable with 2-way FSTs

● And potentially as Com-C-OSL if certain derivations are assumed(Reiss and Simpson, 2009)

46

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Appendix









46

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Appendix









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Table of Contents

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Appendix

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Appendix

Conclusion

● Reduplication continues to be a fruitful area of study

● Our contribution of 2-way FSTs...

1. o�ers elegant & simple way to computationally modelreduplication

2. computationally demarcates typology of reduplication

● Rings a bell with theoretical linguistics by:

1. Formalizing reduplication as input-to-output functions (contraBRCT),

2. Using templatic associations (Marantz, 1982; Kiparsky et al.,2010; McCarthy et al., 2012),

3. Treating reduplication as essentially getting the same input again(Steriade, 1988; Inkelas and Zoll, 2005)

4. Using window of salient boundary/anchor points to know when tocopy/skip (Raimy, 2000a; Frampton, 2009; Halle, 2008; Reiss andSimpson, 2009)

48

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Appendix

Conclusion










48

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Conclusion

● Close connection between 2-way FSTs & theories of reduplicationmeans

1. we (computational linguists) can directly capture & model theinsights we (theoretical linguists) make about reduplication

2. 2-way FSTs help reveal the computational nature of ourgeneralizations

3. Working Hypothesis: Reduplication is mostly C-OSL.

49

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Conclusion





49

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Appendix

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49

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Appendix

Conclusion





49

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Appendix

Que-Questions?

50

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Conclusion

References

Appendix

Beesley, K. R. and L. Karttunen (2003). Finite-state morphology:Xerox tools and techniques. CSLI, Stanford.

Boja«czyk, M. (2014). Transducers with origin information. InInternational Colloquium on Automata, Languages, andProgramming, pp. 26�37. Springer.

Broselow, E. and J. McCarthy (1983). A theory of internalreduplication. The linguistic review 3(1), 25�88.

Chandlee, J. (2014). Strictly Local Phonological Processes. Ph. D.thesis, University of Delaware.

Chandlee, J., R. Eyraud, and J. Heinz (2015, July). Output strictlylocal functions. In Proceedings of the 14th Meeting on theMathematics of Language (MoL 2015), Chicago, USA, pp. 112�125.

Chandlee, J. and J. Heinz (2012, June). Bounded copying issubsequential: Implications for metathesis and reduplication. InProceedings of the 12th Meeting of the ACL Special Interest Groupon Computational Morphology and Phonology, Montreal, Canada,pp. 42�51. Association for Computational Linguistics.

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References

Appendix

Engelfriet, J. and H. J. Hoogeboom (2001). Mso de�nable stringtransductions and two-way �nite-state transducers. ACMTransactions on Computational Logic (TOCL) 2(2), 216�254.

Frampton, J. (2009). Distributed reduplication. MIT Press.

Halle, M. (2008). Reduplication. Current studies in linguisticsseries 45, 325.

Heinz, J. and R. Lai (2013). Vowel harmony and subsequentiality. InA. Kornai and M. Kuhlmann (Eds.), Proceedings of the 13thMeeting on the Mathematics of Language (MoL 13), So�a,Bulgaria, pp. 52�63.

Hulden, M. (2009). Finite-state machine construction methods andalgorithms for phonology and morphology. Ph. D. thesis, TheUniversity of Arizona.

Inkelas, S. and L. J. Downing (2015a). What is reduplication?Typology and analysis part 1/2: The typology of reduplication.Language and Linguistics Compass 9(12), 502�515.

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Appendix

Inkelas, S. and L. J. Downing (2015b). What is reduplication?Typology and analysis part 2/2: The analysis of reduplication.Language and Linguistics Compass 9(12), 516�528.

Inkelas, S. and C. Zoll (2005). Reduplication: Doubling inMorphology. Cambridge University Press.

Kaplan, R. and M. Kay (1994). Regular models of phonological rulesystems. Computational Linguistics 20(3), 331�378.

Kiparsky, P. et al. (2010). Reduplication in stratal ot. Realityexploration and discovery: pattern interaction in language & life,125�142.

Marantz, A. (1982). Re reduplication. Linguistic inquiry 13(3),435�482.

McCarthy, J. J., W. Kimper, and K. Mullin (2012). Reduplication inharmonic serialism. Morphology 22(2), 173�232.

McCarthy, J. J. and A. Prince (1995). Faithfulness and reduplicativeidentity. GLSA, University of Massachusetts.

McNaughton, R. and S. A. Papert (1971). Counter-Free Automata(MIT research monograph no. 65). The MIT Press.

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References

Appendix

Moravcsik, E. (1978). Reduplicative constructions. In J. Greenberg(Ed.), Universals of Human Language, Volume 1, pp. 297�334.Stanford, California: Stanford University Press.

Raimy, E. (2000a). The Phonology and Morphology of Reduplication.Berlin: Mouton de Gruyter.

Raimy, E. (2000b). Remarks on backcopying. LinguisticInquiry 31(3), 541�552.

Reiss, C. and M. Simpson (2009). Reduplication as projection.

Riggle, J. (2004). Nonlocal reduplication. In Proceedings of the 34thmeeting of the North Eastern Einguistics Society. GLSA, Universityof Massachusetts.

Roark, B. and R. Sproat (2007). Computational Approaches toMorphology and Syntax. Oxford: Oxford University Press.

Roche, E. and Y. Schabes (1997). Finite-state language processing.MIT press.

Rubino, C. (2005). Reduplication: Form, function and distribution.pp. 11�29. Berlin: Mouton de Gruyter.

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References

Appendix

Samuels, B. (2010). The topology of in�xation and reduplication. TheLinguistic Review 27(2), 131�176.

Savitch, W. J. (1982). Abstract machines and grammars. LittleBrown.

Steriade, D. (1988). Reduplication and syllable transfer in sanskritand elsewhere. Phonology 5(01), 73�155.

Walther, M. (2000). Finite-state reduplication in one-level prosodicmorphology. In Proceedings of the 1st North American chapter ofthe Association for Computational Linguistics conference, pp.296�302. Association for Computational Linguistics.

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Table of Contents

Introduction






Conclusion

Appendix

51

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Conclusion

References

Appendix

Appendix guide

● What's the hidden structure of copying? (56)

● What can't 1-way FSTs do total red. 63

● More OSL please (64)

● What's Sequential and C-Seq? (53)

52

Introduction




Conclusion

References

Appendix

Sequential subclass

● Relatively more powerful subclass for segmental phonologySequential (Seq) class

▸ = can keep track of a lot of (�nite) information it has seen before

53

Introduction




Conclusion

References

Appendix

Seq subclass = nasal harmony

● Kikingo nasal harmony: /-ila/ surface as [-ina] with nasals ifstem has nasals

(118) a. /sakid-ila/ →

[sakid-ila]`to congratulate for'

b. /mant-ila/ →[mant-ina]`to climb for'

c. /kudumukis-ila/ →[kudumukis-ila]`to cause to jump for'

● Seq because keeps track if saw a nasal anywhere before the su�x

54

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References

Appendix



(119) a. /sakid-ila/ →[sakid-ila]`to congratulate for'

b. /mant-ila/ →

[mant-ina]`to climb for'



54

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Conclusion

References

Appendix





c. /kudumukis-ila/ →

[kudumukis-ila]`to cause to jump for'


54

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Conclusion

References

Appendix







54

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Conclusion

References

Appendix


● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→?

Input: ⋊ m a r - i l a ⋉Output:

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

Σ ∶ Σ

-:-

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

55

Introduction




Conclusion

References

Appendix


● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]


q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

Σ ∶ Σ

-:-

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

55

Introduction




Conclusion

References

Appendix




q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

Σ ∶ Σ

-:-

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

55

Introduction




Conclusion

References

Appendix




q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

Σ ∶ Σ

-:-

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

55

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Conclusion

References

Appendix




q0start q−n

qn

qila

qina

qf

Σ ∶ Σ

N:N

Σ ∶ Σ

-:-

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

⋊:λ

55

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Conclusion

References

Appendix



Input: ⋊ m a r - i l a ⋉Output: m

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

Σ ∶ Σ

-:-

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

N:N

55

Introduction




Conclusion

References

Appendix



Input: ⋊ m a r - i l a ⋉Output: m a

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

-:-

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

Σ ∶ Σ55

Introduction




Conclusion

References

Appendix



Input: ⋊ m a r - i l a ⋉Output: m a r

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

-:-

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

Σ ∶ Σ55

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Conclusion

References

Appendix



Input: ⋊ m a r - i l a ⋉Output: m a r -

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

-:-

Σ ∶ Σ

Σ ∶ Σ l:n,Σ ∶ Σ

⋉:λ

⋉:λ

-:-

55

Introduction




Conclusion

References

Appendix



Input: ⋊ m a r - i l a ⋉Output: m a r - i

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

-:-

Σ ∶ Σ

Σ ∶ Σ

-:-

⋉:λ

⋉:λ

l:n,Σ ∶ Σ55

Introduction




Conclusion

References

Appendix



Input: ⋊ m a r - i l a ⋉Output: m a r - i n

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

-:-

Σ ∶ Σ

Σ ∶ Σ

-:-

⋉:λ

⋉:λ

l:n,Σ ∶ Σ55

Introduction




Conclusion

References

Appendix



Input: ⋊ m a r - i l a ⋉Output: m a r - i n a

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

-:-

Σ ∶ Σ

Σ ∶ Σ

-:-

⋉:λ

⋉:λ

l:n,Σ ∶ Σ55

Introduction




Conclusion

References

Appendix




q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

-:-

Σ ∶ Σ

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

55

Introduction




Conclusion

References

Appendix




,

q0start q−n

qn

qila

qina

qf⋊:λ

Σ ∶ Σ

N:N

-:-

Σ ∶ Σ

Σ ∶ Σ

-:-

l:n,Σ ∶ Σ

⋉:λ

⋉:λ

55

Introduction




Conclusion

References

Appendix

matching theory of copying

● A lot of Partial reduplication can be done with either 1-way or2-way FSTs

▸ Why go up to 2-way?

● 1-way and 2-way FSTs have di�erent hidden structures

▸ 1-way FSTs remember, 2-way FSTs copy▸ 2-way FST's hidden structure better matches linguistic theory.▸ formalize with origin information (Boja«czyk, 2014)▸ Origin information: The origin of output symbols in the inputstring (TBA)

● But... so what?▸ Important for language modeling,▸ Has cognitive repercussions▸ Formalizes the insight that linguists have

56

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References

Appendix







56

Introduction




Conclusion

References

Appendix







56

Introduction




Conclusion

References

Appendix





▸ 1-way FSTs remember, 2-way FSTs copy▸ 2-way FST's hidden structure better matches linguistic theory.▸ formalize with origin information (Boja«czyk, 2014)

▸ Origin information: The origin of output symbols in the inputstring (TBA)


56

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References

Appendix







56

Introduction




Conclusion

References

Appendix






● But... so what?

▸ Important for language modeling,▸ Has cognitive repercussions▸ Formalizes the insight that linguists have

56

Introduction




Conclusion

References

Appendix







56

Introduction




Conclusion

References

Appendix


● e.g., f(x) = cd if x=ab; otherwise function unde�ned

● 1 function → di�erent FSTs → di�erent origin information

q0start q1 q2a:c b:d q0start q1 q2

a:λ b:cd

● Two 1-way FSTs give di�erent origin information for ab→ cd

a b

c d

Input:

Output:

a b

c d

Input:

Output:

● Weakly equivalent in generative capacity but not strongly fororigin information (=same output, di�erent structures)

57

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References

Appendix


● e.g., f(x) = cd if x=ab; otherwise function unde�ned● 1 function → di�erent FSTs → di�erent origin information


a:λ b:cd


a b

c d

Input:

Output:

a b

c d

Input:

Output:


57

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References

Appendix




a:λ b:cd


a b

c d

Input:

Output:

a b

c d

Input:

Output:


57

Introduction




Conclusion

References

Appendix




a:λ b:cd


a b

c d

Input:

Output:

a b

c d

Input:

Output:


57

Introduction




Conclusion

References

Appendix




a:λ b:cd


a b

c d

Input:

Output:

a b

c d

Input:

Output:


57

Introduction




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References

Appendix


● 1-way and 2-way FSTs for partial reduplication have di�erentorigin information

● Initial-CVC reduplication in Real Agta

(122) takki→ tak∼takki`leg'→`legs'

● Mini-Agta with Σ = {p, t, a}(123) tappa→tap∼tappa

58

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References

Appendix






58

Introduction




Conclusion

References

Appendix






58

Introduction




Conclusion

References

Appendix

Origin information of 1-way FST

● Origin information for patap→

pat∼patap:

p a t a p

p a t p a t a p

Input:

Output:

● Notice the many-to-one-matching: t→t∼pat

59

Introduction




Conclusion

References

Appendix


● Origin information for patap→pat∼patap:

p a t a p

p a t p a t a p

Input:

Output:


59

Introduction




Conclusion

References

Appendix


● Origin information for patap→pat∼patap:

p a t a p

p a t p a t a p

Input:

Output:


59

Introduction




Conclusion

References

Appendix



● 2-way FST won't involve many-to-one association of 1-way FST

60

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Conclusion

References

Appendix



● Origin information for patap→ pat∼patap:

p a t a p

p a t p a t a p

Input:

Output:

● One-to-one mapping between symbols → copying notremembering!

61

Introduction




Conclusion

References

Appendix


● 1-way FSTs remember what to repeat, they don't actively copy● 2-way FSTs actively copy● Informal notion is formalized with origin information

p a t a p

p a t p a t a p

Input:

Output:

p a t a p

p a t p a t a p

Input:

Output:62

Introduction




Conclusion

References

Appendix

1-way FSTs & Total


● How is it non-regular?

▸ FSA for ab→ab∼ab

q0start q1 q2 q3 qf⋊:λ a:a b:b ⋉:∼ab⋉

▸ But if include aba→aba∼aba

q0start q1 q2 q3

q4

qf⋊:λ a:a b:b

a:a ⋉:∼aba⋉

⋉:∼ab⋉

63

Introduction




Conclusion

References

Appendix

1-way FSTs & Total






q0start q1 q2 q3

q4

qf⋊:λ a:a b:b

a:a ⋉:∼aba⋉

⋉:∼ab⋉

63

Introduction




Conclusion

References

Appendix

1-way FSTs & Total






q0start q1 q2 q3

q4

qf⋊:λ a:a b:b

a:a ⋉:∼aba⋉

⋉:∼ab⋉

63

Introduction




Conclusion

References

Appendix

1-way FSTs & Total






q0start q1 q2 q3

q4

qf⋊:λ a:a b:b

a:a ⋉:∼aba⋉

⋉:∼ab⋉

63

Introduction




Conclusion

References

Appendix

1-way FSTs & Total






q0start q1 q2 q3

q4

qf⋊:λ a:a b:b

a:a ⋉:∼aba⋉

⋉:∼ab⋉

63

Introduction




Conclusion

References

Appendix

OSL subclass = nasal spread

● Malay nasal spread: spread nasality from nasal to vowel, skippingglides/P

(128) a. /m@ratappi/ →

[m@ratappi] `to cause to cry'

b. /paNawasan/ →[paNawasan] `supervision'

● 2-OSL because keep track of last 1 segment you outputted + the1 segment you're working on now

64

Introduction




Conclusion

References

Appendix



(129) a. /m@ratappi/ →[m@ratappi] `to cause to cry'

b. /paNawasan/ →

[paNawasan] `supervision'


64

Introduction




Conclusion

References

Appendix



(130) a. /m@ratappi/ →[m@ratappi] `to cause to cry'

b. /paNawasan/ →[paNawasan] `supervision'


64

Introduction




Conclusion

References

Appendix

OSL Subclass = Nasal Spread

● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→?

Input: ⋊ n u j o r k i ⋉Output:

q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

65

Introduction




Conclusion

References

Appendix


● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]


q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

65

Introduction




Conclusion

References

Appendix




q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

65

Introduction




Conclusion

References

Appendix




q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

65

Introduction




Conclusion

References

Appendix




q0start C,V,G

N,�V,�G

qf

C:C, V:V, G:G

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ⋊:λ

65

Introduction




Conclusion

References

Appendix



Input: ⋊ n u j o r k i ⋉Output: n

q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

C:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

N:N

65

Introduction




Conclusion

References

Appendix



Input: ⋊ n u j o r k i ⋉Output: n �u

q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

⋉:λ

⋉:λ

N:N, V:�V, G:�G

65

Introduction




Conclusion

References

Appendix



Input: ⋊ n u j o r k i ⋉Output: n �u �j

q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

⋉:λ

⋉:λ

N:N, V:�V, G:�G65

Introduction




Conclusion

References

Appendix



Input: ⋊ n u j o r k i ⋉Output: n �u �j õ

q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

⋉:λ

⋉:λ

N:N, V:�V, G:�G65

Introduction




Conclusion

References

Appendix



Input: ⋊ n u j o r k i ⋉Output: n �u �j õ r

q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:N

N:N, V:�V, G:�G

⋉:λ

⋉:λ

C:C

65

Introduction




Conclusion

References

Appendix



Input: ⋊ n u j o r k i ⋉Output: n �u �j õ r k

q0start C,V,G

N,�V,�G

qf⋊:λ

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

C:C, V:V, G:G

65

Introduction




Conclusion

References

Appendix



Input: ⋊ n u j o r k i ⋉Output: n �u �j õ r k i

q0start C,V,G

N,�V,�G

qf⋊:λ

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

C:C, V:V, G:G

65

Introduction




Conclusion

References

Appendix




q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

65

Introduction




Conclusion

References

Appendix




,

q0start C,V,G

N,�V,�G

qf⋊:λ

C:C, V:V, G:G

N:NC:C

N:N, V:�V, G:�G

⋉:λ

⋉:λ

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cpb-us-e1.wpmucdn.com€¦ · Introduction tionalComputa modeling of redutionplica ya2-w FSTs orf redutionplica thematicalMa Typology of Morpho-Phonology Conclusion References Appendix