Upload
others
View
6
Download
0
Embed Size (px)
Citation preview
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Table of Contents
Introduction
Computational modeling of reduplication
1-way FSTs in morphology & phonology1-way FSTs for reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Mathematical typology of non-reduplicationMathematical typology of reduplication
Conclusion
Appendix
2
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Introduction
Computational modeling of reduplication
1-way FSTs in morphology & phonology1-way FSTs for reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Mathematical typology of non-reduplicationMathematical typology of reduplication
Conclusion
Appendix5
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Table of Contents
Introduction
Computational modeling of reduplication
1-way FSTs in morphology & phonology1-way FSTs for reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Mathematical typology of non-reduplicationMathematical typology of reduplication
Conclusion
Appendix
5
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
What's a 1-way FST?
● Languages have functions that map strings to strings...
likeGerman:
(1) �Häus-er� häuz-er�Haus� haus
7
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
What's a 1-way FST?
● Languages have functions that map strings to strings...likeGerman:
(2) �Häus-er� häuz-er�Haus� haus
7
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
Input: ⋊ t a d ⋉Output:
q0start q1
q2
q3
T:T, V:V
D:λV:DV, D:DD, T:DT
⋉:T
⋉:λ⋊:λ
8
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
Input: ⋊ t a d ⋉Output: t
q0start q1
q2
q3⋊:λ
D:λV:DV, D:DD, T:DT
⋉:T
⋉:λ
T:T, V:V
8
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
Input: ⋊ t a d ⋉Output: t a
q0start q1
q2
q3⋊:λ
D:λV:DV, D:DD, T:DT
⋉:T
⋉:λ
T:T, V:V
8
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
Input: ⋊ t a d ⋉Output: t a t
q0start q1
q2
q3⋊:λ
T:T, V:V
D:λV:DV, D:DD, T:DT
⋉:λ
⋉:T
8
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Example 1-way FST for phonology
● German �nal z→s● Working example: tad→tat
Input: ⋊ t a d ⋉Output: t a t
,
q0start q1
q2
q3⋊:λ
T:T, V:V
D:λV:DV, D:DD, T:DT
⋉:λ
⋉:T
8
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
(5) guyon→gu∼guyon`to jest'→`to jest repeatedly' (Sundanese)
● Mini-Sundanese with Σ = {p, t, a}(6) tappa→ta∼tappa
10
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
(7) guyon→gu∼guyon`to jest'→`to jest repeatedly' (Sundanese)
● Mini-Sundanese with Σ = {p, t, a}(8) tappa→ta∼tappa
10
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output:
q0start q1
q2
q3
q4 q5
t:t
p:p
a:a∼ta
a:a∼pa
Σ ∶ Σ
⋉:λ⋊:λ
11
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼pat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼pat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼pat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼pat
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
Σ ∶ Σ
⋉:λ
11
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● Mini-Sundanese: tappa→ta∼tappa● Working example: pat→pa∼pat
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
Σ ∶ Σ
⋉:λ
11
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Partial reduplication with 1-way FSTs
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Partial
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Partial
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Partial
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Partial
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Partial
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs in morphology & phonology
1-way FSTs for reduplication
Problems with 1-way FSTs for Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Table of Contents
Introduction
Computational modeling of reduplication
1-way FSTs in morphology & phonology1-way FSTs for reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Mathematical typology of non-reduplicationMathematical typology of reduplication
Conclusion
Appendix
20
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output:
q0start q1
q2 q3 q4
Σ ∶ Σ ∶ +1
⋉:∼∶ −1
Σ ∶ λ ∶ −1⋊:λ ∶ +1
Σ ∶ Σ ∶ +1
⋉:λ:+1
⋊:λ:+1
23
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
q0start q1
q2 q3 q4
⋊:λ:+1
Σ ∶ Σ ∶ +1
⋉:∼∶ −1
⋊:λ ∶ +1
Σ ∶ Σ ∶ +1
⋉:λ:+1Σ ∶ λ ∶ −1
23
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
q0start q1
q2 q3 q4
⋊:λ:+1
Σ ∶ Σ ∶ +1
⋉:∼∶ −1
⋊:λ ∶ +1
Σ ∶ Σ ∶ +1
⋉:λ:+1Σ ∶ λ ∶ −1
23
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
q0start q1
q2 q3 q4
⋊:λ:+1
Σ ∶ Σ ∶ +1
⋉:∼∶ −1
⋊:λ ∶ +1
Σ ∶ Σ ∶ +1
⋉:λ:+1Σ ∶ λ ∶ −1
23
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
q0start q1
q2 q3 q4
⋊:λ:+1
Σ ∶ Σ ∶ +1
⋉:∼∶ −1
Σ ∶ λ ∶ −1
Σ ∶ Σ ∶ +1
⋉:λ:+1⋊:λ ∶ +1
23
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
b
q0start q1
q2 q3 q4
⋊:λ:+1
Σ ∶ Σ ∶ +1
⋉:∼∶ −1
Σ ∶ λ ∶ −1⋊:λ ∶ +1 ⋉:λ:+1
Σ ∶ Σ ∶ +1
23
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Total Reduplication
● Indonesian example: wanita→wanita∼wanita● Working example: bye→bye∼bye
Input: ⋊ b y e ⋉Output: b y e ∼
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→?
Input: ⋊ p a t ⋉Output:
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output:
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output:
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output:
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output:
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output: p a
q0start q1 q2
q3 q4 q5
⋊:λ:+1 C:C:+1
V:V:-1
⋊:∼∶ +1
Σ ∶ Σ ∶ +1
⋉:λ:+1Σ ∶ λ ∶ −1
24
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output: p a
∼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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output: p a
∼ 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output: p a
∼ 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output: p a
∼ 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output: p a
∼ 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
2-way FSTs - Partial Reduplication
● Sundanese initial-CV copying: guyon→gu∼guyon● Working example: pat→pa∼pat
Input: ⋊ p a t ⋉Output: p a
∼ 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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:
25
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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!" like a 2-way FST!
p a t
p a p a t
Input:
Output:
25
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
Table of Contents
Introduction
Computational modeling of reduplication
1-way FSTs in morphology & phonology1-way FSTs for reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Mathematical typology of non-reduplicationMathematical typology of reduplication
Conclusion
Appendix
26
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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] `Alan→Al'
● 3-OSL because keep track of last 2 segment outputted + thecurrent segment (and skip anything after VC)
30
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL subclass = truncation
● English nicknames: truncate input to �rst (C)VC
(16) a. /dZEfôi/ →[dZEf] `Je�rey'→`Je�'b. /deIvId/ →
[deIv] `David'→`Dave'c. /æl@n/ →[æl] `Alan→Al'
● 3-OSL because keep track of last 2 segment outputted + thecurrent segment (and skip anything after VC)
30
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL subclass = truncation
● English nicknames: truncate input to �rst (C)VC
(17) a. /dZEfôi/ →[dZEf] `Je�rey'→`Je�'b. /deIvId/ →[deIv] `David'→`Dave'c. /æl@n/ →
[æl] `Alan→Al'● 3-OSL because keep track of last 2 segment outputted + thecurrent segment (and skip anything after VC)
30
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL subclass = truncation
● English nicknames: truncate input to �rst (C)VC
(18) a. /dZEfôi/ →[dZEf] `Je�rey'→`Je�'b. /deIvId/ →[deIv] `David'→`Dave'c. /æl@n/ →[æl] `Alan→Al'
● 3-OSL because keep track of last 2 segment outputted + thecurrent segment (and skip anything after VC)
30
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● Working example: `Samuel' /sæmj@l/→[sæm]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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● Working example: `Samuel' /sæmj@l/→[sæm]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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● Working example: `Samuel' /sæmj@l/→[sæm]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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● Working example: `Samuel' /sæmj@l/→[sæm]Input: ⋊ s æ m j @ l ⋉Output:
q0start
λ C CV VC
qf
C:C V:V C:CΣ ∶ λ
⋉:λ
V:V
⋊:λ
31
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● 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:V C:C
⋉:λ
V:V
Σ ∶ λ
31
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● 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:V C:C
⋉:λ
V:V
Σ ∶ λ
31
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● 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:V C:C
⋉:λ
V:V
Σ ∶ λ
31
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● 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:V C:CΣ ∶ λ
V:V
⋉:λ
31
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
OSL Subclass = Truncation
● English: /dZEfri/→[dZEf]
● 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:V C:CΣ ∶ λ
⋉:λ
V:V
31
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
How does it look like?
● Initial-CVC reduplication in Agta
(20) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
How does it look like?
● Initial-CVC reduplication in Agta
(21) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
How does it look like?
● Initial-CVC reduplication in Agta
(22) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
How does it look like?
● Initial-CVC reduplication in Agta
(23) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
How does it look like?
● Initial-CVC reduplication in Agta
(24) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
How does it look like?
● Initial-CVC reduplication in Agta
(25) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
How does it look like?
● Initial-CVC reduplication in Agta
(26) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output:
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
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 C:C:-1
⋉:∼∶ −1Σ ∶ λ ∶ −1
⋊ ∶ λ ∶ +1
Σ ∶ Σ ∶ +1
⋉:λ:+1
Σ ∶ λ ∶ +1
34
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
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 C:C:-1
⋉:∼∶ −1Σ ∶ λ ∶ −1
⋊ ∶ λ ∶ +1
Σ ∶ Σ ∶ +1
⋉:λ:+1
Σ ∶ λ ∶ +1
34
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
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 C:C:-1
⋉:∼∶ −1Σ ∶ λ ∶ −1
⋊ ∶ λ ∶ +1
Σ ∶ Σ ∶ +1
⋉:λ:+1
Σ ∶ λ ∶ +1
34
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
q0start λ1 C1 CV1 CV C1
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
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
Σ ∶ Σ ∶ +1
⋉:λ:+1
⋊ ∶ λ ∶ +1
34
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
c
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
⋉:λ:+1
Σ ∶ Σ ∶ +134
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
c o
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
⋉:λ:+1
Σ ∶ Σ ∶ +134
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
c o p
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
⋉:λ:+1
Σ ∶ Σ ∶ +134
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
c o p i
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
⋉:λ:+1
Σ ∶ Σ ∶ +134
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
c o p i e
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
⋉:λ:+1
Σ ∶ Σ ∶ +134
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
c o p i e s
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
⋉:λ:+1
Σ ∶ Σ ∶ +134
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
c o p i e s
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
C-OSL: CVC reduplication
● Agta initial-CVC copying: takki→tak∼takki● Working example: copies→cop∼copies
Input: ⋊ c o p i e s ⋉Output: c o p
c o p i e s,
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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:
(29) Total reduplication = unbounded copywanita→wanita∼wanita `woman'→`women' (Indo.)
(30) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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:
(31) Total reduplication = unbounded copywanita→wanita∼wanita `woman'→`women' (Indo.)
(32) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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:
(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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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:
(37) Triplication:roar→ roar∼roar-roar`give a shudder' →`continue to shudder' (Mokilese)
(38) Final reduplication:erasi→erasi∼rasi`he is sick'→`he continues being sick' (Siriono)
(39) Non-local reduplication:qanga→qanga∼qan`�re'→`�re (ABS)' (Koryak)
(40) Echo reduplication:kitap→kitap∼mitap`book'→`book schmook' (Turkish)
36
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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:
(41) Triplication:roar→ roar∼roar-roar`give a shudder' →`continue to shudder' (Mokilese)
(42) Final reduplication:erasi→erasi∼rasi`he is sick'→`he continues being sick' (Siriono)
(43) Non-local reduplication:qanga→qanga∼qan`�re'→`�re (ABS)' (Koryak)
(44) Echo reduplication:kitap→kitap∼mitap`book'→`book schmook' (Turkish)
36
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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:
(45) Triplication:roar→ roar∼roar-roar`give a shudder' →`continue to shudder' (Mokilese)
(46) Final reduplication:erasi→erasi∼rasi`he is sick'→`he continues being sick' (Siriono)
(47) Non-local reduplication:qanga→qanga∼qan`�re'→`�re (ABS)' (Koryak)
(48) Echo reduplication:kitap→kitap∼mitap`book'→`book schmook' (Turkish)
36
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● Even subconstituent copying if boundaries are marked!
(52) Subconstituent (total) reduplication:ku-haata→ku-haata∼haata`to ferment'→`to start fermenting' (KiHehe)
(53) Subconstituent (partial) reduplication:na-murak→na-mu∼murak`to �ower'→`decorating with �owers' (Bikol)
(54) Subconstituent (a�x) reduplication:bele-nez→bele∼bele-nezinto-looks→into-into-looks`he looks into it'→`he occasionally...' (Hungarian)
37
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● Even subconstituent copying if boundaries are marked!
(55) Subconstituent (total) reduplication:ku-haata→ku-haata∼haata`to ferment'→`to start fermenting' (KiHehe)
(56) Subconstituent (partial) reduplication:na-murak→na-mu∼murak`to �ower'→`decorating with �owers' (Bikol)
(57) Subconstituent (a�x) reduplication:bele-nez→bele∼bele-nezinto-looks→into-into-looks`he looks into it'→`he occasionally...' (Hungarian)
37
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● Even subconstituent copying if boundaries are marked!
(58) Subconstituent (total) reduplication:ku-haata→ku-haata∼haata`to ferment'→`to start fermenting' (KiHehe)
(59) Subconstituent (partial) reduplication:na-murak→na-mu∼murak`to �ower'→`decorating with �owers' (Bikol)
(60) Subconstituent (a�x) reduplication:bele-nez→bele∼bele-nezinto-looks→into-into-looks`he looks into it'→`he occasionally...' (Hungarian)
37
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● Even subconstituent copying if boundaries are marked!
(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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● Even subconstituent copying if boundaries are marked!
(63) Subconstituent non-local reduplication:pa-jalan-an→lan∼pa-jalan-an`pedestrian'→`pedestrians' (Madurese)
(64) Iterative reduplication:huang.jang→huang∼huang-jang∼jang`�ustered'→`�ustered (vivid form)' (Mandarin)
38
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● Even subconstituent copying if boundaries are marked!
(65) Subconstituent non-local reduplication:pa-jalan-an→lan∼pa-jalan-an`pedestrian'→`pedestrians' (Madurese)
(66) Iterative reduplication:huang.jang→huang∼huang-jang∼jang`�ustered'→`�ustered (vivid form)' (Mandarin)
38
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's still C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is 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∼tSeq`it is very torn's+ikuk→s+ik∼s-ikuk`he is chopping' (Chumash)
39
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's still C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● and with prosodic boundaries...
(70) Stressed Syllable reduplication:hu(gá)ndo→hugá∼gando`play'→`playing' (Chamorro)
(71) Initial foot reduplication:(gindal)ba→gindal∼gindalba`lizard sp.'→`lizards' (Yidiny)
(72) Prosodic stem foot reduplication:s+tSeq→s-tSeq∼tSeq`it is very torn's+ikuk→s+ik∼s-ikuk`he is chopping' (Chumash)
39
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's still C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● and with prosodic boundaries...
(73) Stressed Syllable reduplication:hu(gá)ndo→hugá∼gando`play'→`playing' (Chamorro)
(74) Initial foot reduplication:(gindal)ba→gindal∼gindalba`lizard sp.'→`lizards' (Yidiny)
(75) Prosodic stem foot reduplication:s+tSeq→s-tSeq∼tSeq`it is very torn's+ikuk→s+ik∼s-ikuk`he is chopping' (Chumash)
39
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's still C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● and with prosodic boundaries...
(76) Stressed Syllable reduplication:hu(gá)ndo→hugá∼gando`play'→`playing' (Chamorro)
(77) Initial foot reduplication:(gindal)ba→gindal∼gindalba`lizard sp.'→`lizards' (Yidiny)
(78) Prosodic stem foot reduplication:s+tSeq→s-tSeq∼tSeq`it is very torn's+ikuk→s+ik∼s-ikuk`he is chopping' (Chumash)
39
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's still C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's still C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● If skipping over �nite chunk...
(82) Place 1st C after 1st V reduplication:tS iko→tS i∼tko`he failed sp.'→`he failed (frequentative)' (Quileute)
(83) Place 1st C after 2nd C reduplication:barad→bar∼b-ad`shave'→`shave unevenly' (Arabic)
(84) CV of �nal CVC reduplication:nalaN→nala∼laN`hungry'→`very hungry' (Chamorro)
40
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's still C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● If skipping over �nite chunk...
(85) Place 1st C after 1st V reduplication:tS iko→tS i∼tko`he failed sp.'→`he failed (frequentative)' (Quileute)
(86) Place 1st C after 2nd C reduplication:barad→bar∼b-ad`shave'→`shave unevenly' (Arabic)
(87) CV of �nal CVC reduplication:nalaN→nala∼laN`hungry'→`very hungry' (Chamorro)
40
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's still C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● If skipping over �nite chunk...
(88) Place 1st C after 1st V reduplication:tS iko→tS i∼tko`he failed sp.'→`he failed (frequentative)' (Quileute)
(89) Place 1st C after 2nd C reduplication:barad→bar∼b-ad`shave'→`shave unevenly' (Arabic)
(90) CV of �nal CVC reduplication:nalaN→nala∼laN`hungry'→`very hungry' (Chamorro)
40
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's not C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's not C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● But if skipping over a chunk of unbounded size...
(93) Double sided reduplication:lú:t'uxw→lúxw∼lút'uxw`to value'→`to value (plural)' (Nisgha)
(94) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What's not C-OSL
● f is C-OSL i�: f(x) = o1(x) ⋅ o2(x) ⋅ ... ⋅ on(x) & oi is OSL
● But if skipping over a chunk of unbounded size...
(95) Double sided reduplication:lú:t'uxw→lúxw∼lút'uxw`to value'→`to value (plural)' (Nisgha)
(96) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● Phonology within the reduplicant (templatic simpli�cation) canbe C-OSL...
(99) Complex onset reduction:trabaho→ta∼trabaho`to work'→`just �nished working' (Tagalog)
● But when very complicated...
(100) Complex onset reduction via vocalization:skand→ka∼skand-a `leap'svap→su∼svap-a `sleep' (Sanskrit)
● Looks like copying + rules (Steriade, 1988)
42
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● Phonology within the reduplicant (templatic simpli�cation) canbe C-OSL...
(101) Complex onset reduction:trabaho→ta∼trabaho`to work'→`just �nished working' (Tagalog)
● But when very complicated...
(102) Complex onset reduction via vocalization:skand→ka∼skand-a `leap'svap→su∼svap-a `sleep' (Sanskrit)
● Looks like copying + rules (Steriade, 1988)
42
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● Especially when there are interactions between the copies...
(103) Overapplication of nasal spread in Madurese:/neyat/→ [�yãt∼n�e�yãt]`intention'→`'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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● Especially when there are interactions between the copies...
(105) Overapplication of nasal spread in Madurese:/neyat/→ [�yãt∼n�e�yãt]`intention'→`'intentions'
(106) Juncture e�ect of coronal dissimilation in Dakota:a. £ap-a →£ap∼£ap-a `trot'b. ºat-a →ºag∼ºat-a `curved'
43
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● Especially when there are interactions between the copies...
(107) Overapplication of nasal spread in Madurese:/neyat/→ [�yãt∼n�e�yãt]`intention'→`'intentions'
(108) Juncture e�ect of coronal dissimilation in Dakota:a. £ap-a →£ap∼£ap-a `trot'b. ºat-a →ºag∼ºat-a `curved'
43
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● What about underapplication?
(110) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● What about underapplication?
(111) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● What about underapplication?
(112) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● What about backcopying?
(114) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● What about backcopying?
(115) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● What about backcopying?
(116) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Mathematical typology of non-reduplication
Mathematical typology of reduplication
What about phonology?
● What about backcopying?
(117) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Table of Contents
Introduction
Computational modeling of reduplication
1-way FSTs in morphology & phonology1-way FSTs for reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Mathematical typology of non-reduplicationMathematical typology of reduplication
Conclusion
Appendix
47
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Que-Questions?
50
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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.
50
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
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.
50
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
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.
50
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
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.
50
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
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.
51
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Table of Contents
Introduction
Computational modeling of reduplication
1-way FSTs in morphology & phonology1-way FSTs for reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Mathematical typology of non-reduplicationMathematical typology of reduplication
Conclusion
Appendix
51
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikingo nasal harmony: /-ila/ surface as [-ina] with nasals ifstem has nasals
(119) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikingo nasal harmony: /-ila/ surface as [-ina] with nasals ifstem has nasals
(120) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikingo nasal harmony: /-ila/ surface as [-ina] with nasals ifstem has nasals
(121) 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
Input: ⋊ m a r - i l a ⋉Output:
q0start q−n
qn
qila
qina
qf
Σ ∶ Σ
N:N
Σ ∶ Σ
-:-
Σ ∶ Σ
-:-
l:n,Σ ∶ Σ
⋉:λ
⋉:λ
⋊:λ
55
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
-:-
l:n,Σ ∶ Σ
⋉:λ
⋉:λ
55
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Seq subclass = nasal harmony
● Kikongo: /kudumukis-ila/→[kudukumis-ina]● Working example: /mar-ila/→[mar-ina]
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
-:-
l:n,Σ ∶ Σ
⋉:λ
⋉:λ
55
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
matching theory of copying
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
matching theory of copying
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
matching theory of copying
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
matching theory of copying
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
matching theory of copying
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Matching theory of copying
● 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
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Matching theory of copying
● 1-way and 2-way FSTs for partial reduplication have di�erentorigin information
● Initial-CVC reduplication in Real Agta
(124) takki→ tak∼takki`leg'→`legs'
● Mini-Agta with Σ = {p, t, a}(125) tappa→tap∼tappa
58
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Matching theory of copying
● 1-way and 2-way FSTs for partial reduplication have di�erentorigin information
● Initial-CVC reduplication in Real Agta
(126) takki→ tak∼takki`leg'→`legs'
● Mini-Agta with Σ = {p, t, a}(127) tappa→tap∼tappa
58
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Matching theory of copying
● 1-way and 2-way FSTs for partial reduplication have di�erentorigin information
● 2-way FST won't involve many-to-one association of 1-way FST
60
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Matching theory of copying
● 1-way and 2-way FSTs for partial reduplication have di�erentorigin information
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
Matching theory of copying
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs & Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs & Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs & Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs & Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
1-way FSTs & Total
● Total reduplication cannot be modeled at all.
● 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL subclass = nasal spread
● Malay nasal spread: spread nasality from nasal to vowel, skippingglides/P
(129) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL subclass = nasal spread
● Malay nasal spread: spread nasality from nasal to vowel, skippingglides/P
(130) 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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
Input: ⋊ n u j o r k i ⋉Output:
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
C:C, V:V, G:G
N:NC:C
N:N, V:�V, G:�G
⋉:λ
⋉:λ
65
Introduction
Computational modeling of reduplication
2-way FSTs for reduplication
Mathematical Typology of Morpho-Phonology
Conclusion
References
Appendix
OSL Subclass = Nasal Spread
● Malay: /paNawasan/→[paNawasan]● Working example: `New Yorkie' /nujorki/→[nujorki]
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
C:C, V:V, G:G
N:NC:C
N:N, V:�V, G:�G
⋉:λ
⋉:λ
65