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Reduplication and Finite-State Machinery Hossep Dolatian & - - PowerPoint PPT Presentation

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References Reduplication and Finite-State Machinery Hossep Dolatian & Jeffrey Heinz University of Delaware May

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication and Finite-State Machinery

Hossep Dolatian & Jeffrey Heinz

University of Delaware

May 26, 2017

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Table of Contents

Introduction FSTs in Phonology FSTs & Reduplication 2-way FSTs & Reduplication Reduplication typology Conclusion

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

The Message

  • Reduplication is well-attested across languages and well-studied

in theoretical linguistics

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

The Message

  • Reduplication is well-attested across languages and well-studied

in theoretical linguistics

  • There are numerous patterns in the typology:

▸ total reduplication ▸ initial/final CV, CVC, CVCV ▸ non-local reduplication (Riggle, 2004) ▸ TETU effects (McCarthy and Prince, 1995) ▸ opacity (underapplication/overapplication) (McCarthy and

Prince, 1995; Raimy, 2000)

▸ internal reduplication (Broselow and McCarthy, 1983) ▸ and more (Moravcsik, 1978; Rubino, 2005; Inkelas and Downing,

2015a,b; Samuels, 2010)

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

The Message

  • Reduplication is difficult to handle in computational &

mathematical linguistics

▸ state-of-the-art: reduplication is beyond finite-state machinery 4 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

The Message

  • Reduplication is difficult to handle in computational &

mathematical linguistics

▸ state-of-the-art: reduplication is beyond finite-state machinery

  • However, that is false

▸ reduplication is not a regular transduction ▸ But a certain understudied and enriched class of finite-state

machinery (2FSTs) can model virtually all reduplication patterns

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Introduction FSTs in Phonology FSTs & Reduplication 2-way FSTs & Reduplication Reduplication typology Conclusion

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Table of Contents

Introduction FSTs in Phonology FSTs & Reduplication 2-way FSTs & Reduplication Reduplication typology Conclusion

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Models in Phonology

  • Phonological processes can be modeled using various theoretical

and descriptive tools

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Models in Phonology

  • Phonological processes can be modeled using various theoretical

and descriptive tools

  • Post-nasal consonant voicing:

▸ Prose: consonants after nasals are voiced ▸ Infinite set of UR-SR pairs: {(anpa, anba), (anba, anba), ...} ▸ Rules: [+cons] → [+voice] / N _ ▸ Constraints: *NT » IDENT(VOICE) 6 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Models in Phonology

  • Each description has its own conceptual implications and baggage

▸ Prose: purely descriptive ▸ Infinite set of pairs: purely descriptive ▸ Rules: SPE, rule ordering, derivational/serial phonology ▸ Constraints: OT, Richness of the Base, optimization 7 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology

  • Mathematical and computational phonology utilizes its own

devices in industry and mathematical modeling

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology

  • Mathematical and computational phonology utilizes its own

devices in industry and mathematical modeling

▸ Finite-State Accepters and Transducers 8 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology

  • Mathematical and computational phonology utilizes its own

devices in industry and mathematical modeling

▸ Finite-State Accepters and Transducers

  • Acceptors are used to model phonotactic constraints: *NT

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology

  • Mathematical and computational phonology utilizes its own

devices in industry and mathematical modeling

▸ Finite-State Accepters and Transducers

  • Acceptors are used to model phonotactic constraints: *NT
  • Transducers are used for transformations from input (UR) to
  • utput (SR): NT→ND
  • Finite-State Transducers (FSTs) will be the main focus of the talk

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology

  • Finite-State Transducer (FST) for post-nasal voicing:
  • Word boundaries ⋊,⋉ are used on both sides of input:

q0 start q1 q2 q3

⋊:⋊ T:T, D:D, V:V N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→?

Input: ⋊ b a m p i ⋉ Output: q0 start q1 q2 q3

⋊:⋊ T:T, D:D, V:V N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: q0 start q1 q2 q3

⋊:⋊ T:T, D:D, V:V N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: ⋊ q0 start q1 q2 q3

T:T, D:D, V:V N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉ ⋊:⋊

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: ⋊ b q0 start q1 q2 q3

⋊:⋊ N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉ T:T, D:D, V:V

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: ⋊ b a q0 start q1 q2 q3

⋊:⋊ N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉ T:T, D:D, V:V

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: ⋊ b a m q0 start q1 q2 q3

⋊:⋊ T:T, D:D, V:V V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉ N:N

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: ⋊ b a m b q0 start q1 q2 q3

⋊:⋊ T:T, D:D, V:V N:N N:N ⋉:⋉ ⋉:⋉ V:V, D:D, T:D

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: ⋊ b a m b i q0 start q1 q2 q3

⋊:⋊ N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉ T:T, D:D, V:V

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: ⋊ b a m b i ⋉ q0 start q1 q2 q3

⋊:⋊ T:T, D:D, V:V N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology - examples

  • Working example: /bampi/→[bambi]

Input: ⋊ b a m p i ⋉ Output: ⋊ b a m b i ⋉ q0 start q1 q2 q3

⋊:⋊ T:T, D:D, V:V N:N V:V, D:D, T:D N:N ⋉:⋉ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Phonology

  • And virtually all known transformations from UR to SR can be

modeled with finite-state transducers (Chandlee, 2014; Kaplan and Kay, 1994)

▸ repairing marked substructures (phonotactics) ▸ vowel harmony ▸ stress ▸ affixation ▸ partial reduplication ▸ but... 20 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Reduplication

  • Only robust exception is (total) reduplication,

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Reduplication

  • Only robust exception is (total) reduplication,
  • Why? Because FSAs and FSTs have a finite memory.

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Reduplication

  • Only robust exception is (total) reduplication,
  • Why? Because FSAs and FSTs have a finite memory.

post-nasal voicing: can remember if a nasal was recently seen

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Reduplication

  • Only robust exception is (total) reduplication,
  • Why? Because FSAs and FSTs have a finite memory.

post-nasal voicing: can remember if a nasal was recently seen partial CV-reduplication: can remember the first 2 segments

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Finite-State Machinery & Reduplication

  • Only robust exception is (total) reduplication,
  • Why? Because FSAs and FSTs have a finite memory.

post-nasal voicing: can remember if a nasal was recently seen partial CV-reduplication: can remember the first 2 segments total reduplication: can’t remember all the segments in the word if the word has no maximum size

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Table of Contents

Introduction FSTs in Phonology FSTs & Reduplication 2-way FSTs & Reduplication Reduplication typology Conclusion

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Partial reduplication: can be modeled in FST if there is a

maximum size for the reduplicant (Chandlee and Heinz, 2012)

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Partial reduplication: can be modeled in FST if there is a

maximum size for the reduplicant (Chandlee and Heinz, 2012)

  • Initial CV-RED with small alphabet: Σ = {p,t,a}

q0 start q1 q2 q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→?

Input: ⋊ p a t ⋉ Output: q0 start q1 q2 q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→[pa∼pat]

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→[pa∼pat]

Input: ⋊ p a t ⋉ Output: q0 start q1 q2 q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→[pa∼pat]

Input: ⋊ p a t ⋉ Output: ⋊ q0 start q1 q2 q3 q4 q5

t:t p:p a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉ ⋊:⋊

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→[pa∼pat]

Input: ⋊ p a t ⋉ Output: ⋊ p q0 start q1 q2 q3 q4 q5

⋊:⋊ t:t a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉ p:p

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→[pa∼pat]

Input: ⋊ p a t ⋉ Output: ⋊ p a∼pa q0 start q1 q2 q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta Σ ∶ Σ ⋉:⋉ a:a∼pa

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→[pa∼pat]

Input: ⋊ p a t ⋉ Output: ⋊ p a∼pa t q0 start q1 q2 q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta a:a∼pa ⋉:⋉ Σ ∶ Σ

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→[pa∼pat]

Input: ⋊ p a t ⋉ Output: ⋊ p a∼pa t ⋉ q0 start q1 q2 q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Working example: /RED+pat/→[pa∼pat]

Input: ⋊ p a t ⋉ Output: ⋊ p a∼pa t ⋉ q0 start q1 q2 q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Partial reduplication: can be modeled in FST if there’s a

maximum size for the reduplicant

  • But...

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Partial reduplication: can be modeled in FST if there’s a

maximum size for the reduplicant

  • But... bigger alphabet and RED size → more states

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Partial reduplication: can be modeled in FST if there’s a

maximum size for the reduplicant

  • But... bigger alphabet and RED size → more states
  • Σ = {p,t,a}...

q0 start q1 q2 qk q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Partial RED

  • Partial reduplication: can be modeled in FST if there’s a

maximum size for the reduplicant

  • But... bigger alphabet and RED size → more states
  • Σ = {p,t,a,k}...

q0 start q1 q2 qk q3 q4 q5

⋊:⋊ t:t p:p a:a∼ta a:a∼pa Σ ∶ Σ ⋉:⋉ k:k a:a∼ka

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs- Deadend

  • Partial reduplication can be modeled in FSTs but it causes an

explosion of states (Chandlee, 2014)

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs- Deadend

  • Partial reduplication can be modeled in FSTs but it causes an

explosion of states (Chandlee, 2014)

▸ They are thus "burdensome models" (Roark and Sproat, 2007, 54) 34 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs- Deadend

  • Partial reduplication can be modeled in FSTs but it causes an

explosion of states (Chandlee, 2014)

▸ They are thus "burdensome models" (Roark and Sproat, 2007, 54)

  • Theoretically partial reduplication is understood as copying, but

the FSTs for it just remember all possible reduplicants

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs- Deadend

  • Partial reduplication can be modeled in FSTs but it causes an

explosion of states (Chandlee, 2014)

▸ They are thus "burdensome models" (Roark and Sproat, 2007, 54)

  • Theoretically partial reduplication is understood as copying, but

the FSTs for it just remember all possible reduplicants

▸ "The model is naive in that it simply remembers what was

inserted, and then imposes the requirement that the base match appropriately." (Roark and Sproat, 2007, 54)

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs- Deadend

  • Partial reduplication can be modeled in FSTs but it causes an

explosion of states (Chandlee, 2014)

▸ They are thus "burdensome models" (Roark and Sproat, 2007, 54)

  • Theoretically partial reduplication is understood as copying, but

the FSTs for it just remember all possible reduplicants

▸ "The model is naive in that it simply remembers what was

inserted, and then imposes the requirement that the base match appropriately." (Roark and Sproat, 2007, 54)

→ FSTs don’t capture partial reduplication in a concrete away

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Deadend

  • Total reduplication cannot be modeled at all.

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Deadend

  • Total reduplication cannot be modeled at all.

▸ Why?: If reduplicant is of unbounded size → no FST could do

the job because an infinite number of states would be needed

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Deadend

  • Total reduplication cannot be modeled at all.

▸ Why?: If reduplicant is of unbounded size → no FST could do

the job because an infinite number of states would be needed

▸ So?: some finite-state approximations exist... (Hulden, 2009;

Beesley and Karttunen, 2003; Walther, 2000)

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Deadend

  • Total reduplication cannot be modeled at all.

▸ Why?: If reduplicant is of unbounded size → no FST could do

the job because an infinite number of states would be needed

▸ So?: some finite-state approximations exist... (Hulden, 2009;

Beesley and Karttunen, 2003; Walther, 2000)

▸ But: they impose un-linguistic restrictions (e.g. a finite bound on

word size,...) and don’t directly capture reduplication

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication & FSTs - Deadend

  • Total reduplication cannot be modeled at all.

▸ Why?: If reduplicant is of unbounded size → no FST could do

the job because an infinite number of states would be needed

▸ So?: some finite-state approximations exist... (Hulden, 2009;

Beesley and Karttunen, 2003; Walther, 2000)

▸ But: they impose un-linguistic restrictions (e.g. a finite bound on

word size,...) and don’t directly capture reduplication

→ total reduplication is outside the scope of FSTs, while partial reduplication can be modeled with FSTs but unelegantly

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Table of Contents

Introduction FSTs in Phonology FSTs & Reduplication 2-way FSTs & Reduplication Reduplication typology Conclusion

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs

  • The previous FSTs can be described as one-way FSTs because

they read the input once from left to right.

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs

  • The previous FSTs can be described as one-way FSTs because

they read the input once from left to right.

  • 2-way FSTs are an enriched class of FSTs that can go back and

forth on the input (Engelfriet and Hoogeboom, 2001; Savitch, 1982).

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

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • To model total reduplication, the below 2FST reads the input left

to right (1st copy), goes back, and reads the input again (2nd copy) q0 start q1 q2 q3 q4

⋊:⋊+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

38 / 97

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SLIDE 64

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→?

Input: ⋊ b y e ⋉ Output: q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

39 / 97

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SLIDE 65

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

40 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

40 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ q0 start q1 q2 q3 q4

Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 ⋊:⋊:+1

41 / 97

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SLIDE 68

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b q0 start q1 q2 q3 q4

⋊:⋊:+1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

42 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y q0 start q1 q2 q3 q4

⋊:⋊:+1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

43 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e q0 start q1 q2 q3 q4

⋊:⋊:+1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

44 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 ⋉:∼∶ −1

45 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 Σ ∶ ǫ ∶ −1

46 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 Σ ∶ ǫ ∶ −1

47 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 Σ ∶ ǫ ∶ −1

48 / 97

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SLIDE 75

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 ⋊:ǫ ∶ +1

49 / 97

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SLIDE 76

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ b q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

50 / 97

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SLIDE 77

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ b y q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

51 / 97

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SLIDE 78

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ b y e q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

52 / 97

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SLIDE 79

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ b y e ⋉ q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

53 / 97

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SLIDE 80

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Total RED

  • Working example: /bye+RED/→[bye∼bye]

Input: ⋊ b y e ⋉ Output: ⋊ b y e ∼ b y e ⋉ q0 start q1 q2 q3 q4

⋊:⋊:+1 Σ ∶ Σ ∶ +1 ⋉:∼∶ −1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

54 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • To model initial-CVC reduplication, the below 2FST reads the

input (1st copy), goes back, and reads the input again (2nd copy) q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:ǫ ∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

55 / 97

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SLIDE 82

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→?

Input: ⋊ c

  • p

i e s ⋉ Output: q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

56 / 97

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SLIDE 83

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

57 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

57 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ q0 start q1 q2 q3 q4 q5 q6

C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 ⋊:⋊:+1

58 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 C:C:+1

59 / 97

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SLIDE 87

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • q0

start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 V:V:+1

60 / 97

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SLIDE 88

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 C:C:-1

61 / 97

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SLIDE 89

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 Σ ∶ ǫ ∶ −1

62 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 Σ ∶ ǫ ∶ −1

63 / 97

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SLIDE 91

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 ⋊:∼∶ +1

64 / 97

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SLIDE 92

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ c q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

65 / 97

slide-93
SLIDE 93

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ c

  • q0

start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

66 / 97

slide-94
SLIDE 94

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ c

  • p

q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

67 / 97

slide-95
SLIDE 95

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ c

  • p

i q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

68 / 97

slide-96
SLIDE 96

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ c

  • p

i e q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

69 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ c

  • p

i e s q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

70 / 97

slide-98
SLIDE 98

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ c

  • p

i e s ⋉ q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

71 / 97

slide-99
SLIDE 99

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Partial RED

  • Working example: /RED+copies/→[cop∼copies]

Input: ⋊ c

  • p

i e s ⋉ Output: ⋊ c

  • p

∼ c

  • p

i e s ⋉ q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:C:+1 V:V:+1 C:C:-1 Σ ∶ ǫ ∶ −1 ⋊:∼∶ +1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

72 / 97

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SLIDE 100

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • RED processes may interact opaquely with phonological

processes.

  • Akan palatalization without RED (McCarthy and Prince, 1995;

Raimy, 2000):

▸ Prose: Dorsal segments palatalize before a non-low front vowel

/wi/ ‘nibble’ → [4i]

▸ Rule: [+cons, +dorsal] →[+cor] / _ [+syll, -low, +front] ▸ Constraint: PAL » IDENT-IO-(-cor) 73 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • RED processes may interact opaquely with phonological

processes.

  • Akan palatalization with Initial CV-RED (McCarthy and Prince,

1995; Raimy, 2000):

▸ The V in the CV reduplicant is pre-specified as [I] ▸ /RED+saP/→[sI∼saP] ‘cure’ not *[sa∼saP] 74 / 97

slide-102
SLIDE 102

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • RED processes may interact opaquely with phonological

processes.

  • Akan palatalization with Initial CV-RED (McCarthy and Prince,

1995; Raimy, 2000):

▸ The V in the CV reduplicant is pre-specified as [I] ▸ /RED+saP/→[sI∼saP] ‘cure’ not *[sa∼saP] ▸ Palatalization underapplies in reduplicant ... ▸ /RED+kaP/→[kI∼kaP] not *[>

tcI∼kaP] or *[> tcI∼> tcaP] ‘bite’

74 / 97

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SLIDE 103

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • RED processes may interact opaquely with phonological

processes.

  • Akan palatalization with Initial CV-RED (McCarthy and Prince,

1995; Raimy, 2000):

▸ The V in the CV reduplicant is pre-specified as [I] ▸ /RED+saP/→[sI∼saP] ‘cure’ not *[sa∼saP] ▸ Palatalization underapplies in reduplicant ... ▸ /RED+kaP/→[kI∼kaP] not *[>

tcI∼kaP] or *[> tcI∼> tcaP] ‘bite’

▸ Unless BOTH of the initial C’s two copies precede non-low front

vowels: ID-BR, OCP » PAL » ID-IO

▸ /RED+kaP/→[kI∼kaP] ‘bite’ ▸ /RED+ge/→[>

dzI∼> dze] ‘receive’

74 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • To model initial Ci reduplication with palatalization:

q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:ǫ ∶ +1 I:ǫ:-1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

75 / 97

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SLIDE 105

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→?

Input: ⋊ g e ⋉ Output: q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:ǫ ∶ +1 I:ǫ:-1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

76 / 97

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SLIDE 106

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

77 / 97

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SLIDE 107

Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

Input: ⋊ g e ⋉ Output: q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:ǫ ∶ +1 I:ǫ:-1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

77 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

Input: ⋊ g e ⋉ Output: ⋊ q0 start q1 q2 q3 q4 q5 q6

C:ǫ ∶ +1 I:ǫ:-1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 ⋊:⋊:+1

78 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

Input: ⋊ g e ⋉ Output: ⋊ q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 I:ǫ:-1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 C:ǫ ∶ +1

79 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

Input: ⋊ g e ⋉ Output: ⋊ q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:ǫ ∶ +1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 I:ǫ:-1

80 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

Input: ⋊ g e ⋉ Output: ⋊ dzI∼dz q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:ǫ ∶ +1 I:ǫ:-1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1 C:PI∼P:+1

81 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

Input: ⋊ g e ⋉ Output: ⋊ dzI∼dz e q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:ǫ ∶ +1 I:ǫ:-1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 ⋉:⋉:+1 Σ ∶ Σ ∶ +1

82 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

Input: ⋊ g e ⋉ Output: ⋊ dzI∼dz e ⋉ q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:ǫ ∶ +1 I:ǫ:-1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

83 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

2-way FSTs - Opacity

  • Working example: /RED+ge/→[dzI∼dzE]

Input: ⋊ g e ⋉ Output: ⋊ dzI∼dz e ⋉ q0 start q1 q2 q3 q4 q5 q6

⋊:⋊:+1 C:ǫ ∶ +1 I:ǫ:-1 C:PI∼P:+1 A:ǫ:-1 C:CI∼C:+1 Σ ∶ Σ ∶ +1 ⋉:⋉:+1

84 / 97

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Table of Contents

Introduction FSTs in Phonology FSTs & Reduplication 2-way FSTs & Reduplication Reduplication typology Conclusion

85 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology

  • Almost all forms of partial and total reduplication seen so far can

be modeled with 2FSTS

▸ initial/final CV, CVC, CVCV ▸ non-local reduplication (Riggle, 2004) ▸ TETU effects (McCarthy and Prince, 1995) ▸ opacity (underapplication/overapplication) (McCarthy and

Prince, 1995; Raimy, 2000)

▸ internal reduplication (Broselow and McCarthy, 1983) ▸ and almost everything in the typology (Moravcsik, 1978; Rubino,

2005; Inkelas and Downing, 2015a,b; Samuels, 2010)

86 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - database

  • To my knowledge, there is only existing reduplication database

(Graz) but it’s currently offline because of technical difficulties

  • I’m currently going through the literature and making my own

database of 2FSTs

87 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - database

  • To my knowledge, there is only existing reduplication database

(Graz) but it’s currently offline because of technical difficulties

  • I’m currently going through the literature and making my own

database of 2FSTs

  • As of now almost all 138+ reduplicative processses (RED

morphemes) in the surveys can be modeled with FSTs.

  • These RED morphemes cover 93+ languages

87 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - distinct 2FSTs?

  • These 138+ RED processes can be lumped together and be

modeled with 59+ distinct 2FSTs

  • Distinctness is subjective but it’s about how certain effects in the

reduplicant are crosslinguistically common

88 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - distinct 2FSTs?

  • These 138+ RED processes can be lumped together and be

modeled with 59+ distinct 2FSTs

  • Distinctness is subjective but it’s about how certain effects in the

reduplicant are crosslinguistically common

  • For example in an initial-CV RED morpheme, a language may

specify that the reduplicant:

88 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - distinct 2FSTs?

  • These 138+ RED processes can be lumped together and be

modeled with 59+ distinct 2FSTs

  • Distinctness is subjective but it’s about how certain effects in the

reduplicant are crosslinguistically common

  • For example in an initial-CV RED morpheme, a language may

specify that the reduplicant:

▸ must have a short V 88 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - distinct 2FSTs?

  • These 138+ RED processes can be lumped together and be

modeled with 59+ distinct 2FSTs

  • Distinctness is subjective but it’s about how certain effects in the

reduplicant are crosslinguistically common

  • For example in an initial-CV RED morpheme, a language may

specify that the reduplicant:

▸ must have a short V ▸ must have a long V 88 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - distinct 2FSTs?

  • These 138+ RED processes can be lumped together and be

modeled with 59+ distinct 2FSTs

  • Distinctness is subjective but it’s about how certain effects in the

reduplicant are crosslinguistically common

  • For example in an initial-CV RED morpheme, a language may

specify that the reduplicant:

▸ must have a short V ▸ must have a long V ▸ can’t be a diphthong 88 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - distinct 2FSTs?

  • These 138+ RED processes can be lumped together and be

modeled with 59+ distinct 2FSTs

  • Distinctness is subjective but it’s about how certain effects in the

reduplicant are crosslinguistically common

  • For example in an initial-CV RED morpheme, a language may

specify that the reduplicant:

▸ must have a short V ▸ must have a long V ▸ can’t be a diphthong ▸ copies from the root 88 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - distinct 2FSTs?

  • These 138+ RED processes can be lumped together and be

modeled with 59+ distinct 2FSTs

  • Distinctness is subjective but it’s about how certain effects in the

reduplicant are crosslinguistically common

  • For example in an initial-CV RED morpheme, a language may

specify that the reduplicant:

▸ must have a short V ▸ must have a long V ▸ can’t be a diphthong ▸ copies from the root ▸ copies from the prosodic word 88 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - distinct 2FSTs?

  • These 138+ RED processes can be lumped together and be

modeled with 59+ distinct 2FSTs

  • Distinctness is subjective but it’s about how certain effects in the

reduplicant are crosslinguistically common

  • For example in an initial-CV RED morpheme, a language may

specify that the reduplicant:

▸ must have a short V ▸ must have a long V ▸ can’t be a diphthong ▸ copies from the root ▸ copies from the prosodic word

  • Each of these TETU effects & morpho-prosodic sensitivities can

be done with their own 2FSTs with minor differences.

88 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - Overgenerate?

  • In fact, 2FSTs can a) copy any specified substring b) for a

specified number of times and c) place it at any specified location.

  • 2FSTs treat reduplicative processes as mathematical objects

▸ They are mathematical translations of RED, not theories, 89 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - Overgenerate?

  • In fact, 2FSTs can a) copy any specified substring b) for a

specified number of times and c) place it at any specified location.

  • 2FSTs treat reduplicative processes as mathematical objects

▸ They are mathematical translations of RED, not theories,

  • But 2FSTs can also describe objects which marginally occur in

language (but they still do):

89 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - Overgenerate?

  • In fact, 2FSTs can a) copy any specified substring b) for a

specified number of times and c) place it at any specified location.

  • 2FSTs treat reduplicative processes as mathematical objects

▸ They are mathematical translations of RED, not theories,

  • But 2FSTs can also describe objects which marginally occur in

language (but they still do):

▸ triplication 89 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - Overgenerate?

  • In fact, 2FSTs can a) copy any specified substring b) for a

specified number of times and c) place it at any specified location.

  • 2FSTs treat reduplicative processes as mathematical objects

▸ They are mathematical translations of RED, not theories,

  • But 2FSTs can also describe objects which marginally occur in

language (but they still do):

▸ triplication ▸ quadruplication, e.g. Twi: /fe/ ‘fine’ →[fe∼fe∼fe∼fe] ‘very nicely’

(Moravcsik, 1978)

89 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - Overgenerate?

  • In fact, 2FSTs can a) copy any specified substring b) for a

specified number of times and c) place it at any specified location.

  • 2FSTs treat reduplicative processes as mathematical objects

▸ They are mathematical translations of RED, not theories,

  • But 2FSTs can also describe objects which marginally occur in

language (but they still do):

▸ triplication ▸ quadruplication, e.g. Twi: /fe/ ‘fine’ →[fe∼fe∼fe∼fe] ‘very nicely’

(Moravcsik, 1978)

▸ truncating the base (Hamilton-Kager conundrum), e.g.

Rihanna+RED → Ri∼Ri (Inkelas 2014: 139)

89 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - Undergenerate?

  • Reduplication occurs at the interface of morphology & phonology

→ sensitive to morpho-lexical and phonetic/perceptual systems

  • These systems have to be encoded into the 2FSTs in order to

capture effects such as the following:

90 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - Undergenerate?

  • Reduplication occurs at the interface of morphology & phonology

→ sensitive to morpho-lexical and phonetic/perceptual systems

  • These systems have to be encoded into the 2FSTs in order to

capture effects such as the following:

  • 1. Morphological copying (Inkelas and Downing, 2015a)

90 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - Undergenerate?

  • Reduplication occurs at the interface of morphology & phonology

→ sensitive to morpho-lexical and phonetic/perceptual systems

  • These systems have to be encoded into the 2FSTs in order to

capture effects such as the following:

  • 1. Morphological copying (Inkelas and Downing, 2015a)
  • 2. anti-homophony effects (Moravcsik, 1978)

90 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - undergenerate?

  • Reduplication occurs at the interface of morphology & phonology

→ sensitive to morpho-lexical and phonetic/perceptual systems

  • These systems have to be encoded into the 2FSTs in order to

capture effects such as the following:

  • 1. Morphological copying (Inkelas and Downing, 2015a)

▸ In Sye, a stem may have multiple suppletive allomorphs used in

different contexts, e.g. amol & omol ‘fall’

91 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - undergenerate?

  • Reduplication occurs at the interface of morphology & phonology

→ sensitive to morpho-lexical and phonetic/perceptual systems

  • These systems have to be encoded into the 2FSTs in order to

capture effects such as the following:

  • 1. Morphological copying (Inkelas and Downing, 2015a)

▸ In Sye, a stem may have multiple suppletive allomorphs used in

different contexts, e.g. amol & omol ‘fall’

▸ Total reduplication can return a different allomorph instead of a

phonological copy, e.g. /cw-RED+omol/→[cw-amol∼omol] *[cw-omol∼omol] ‘they will fall all over’

  • 2. anti-homophony effects (Moravcsik, 1978)

91 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - undergenerate?

  • Reduplication occurs at the interface of morphology & phonology

→ sensitive to morpho-lexical and phonetic/perceptual systems

  • These systems have to be encoded into the 2FSTs in order to

capture effects such as the following:

  • 1. Morphological copying (Inkelas and Downing, 2015a)
  • 2. anti-homophony effects (Moravcsik, 1978)

▸ In Kanuri, total reduplication is blocked if it creates sequence of

identical syllables/feet

▸ /kan@mbu-RED/→ [kan@mbu∼kan@mbu] "language of the

Kanembu tribe"

92 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Reduplication typology - undergenerate?

  • Reduplication occurs at the interface of morphology & phonology

→ sensitive to morpho-lexical and phonetic/perceptual systems

  • These systems have to be encoded into the 2FSTs in order to

capture effects such as the following:

  • 1. Morphological copying (Inkelas and Downing, 2015a)
  • 2. anti-homophony effects (Moravcsik, 1978)

▸ In Kanuri, total reduplication is blocked if it creates sequence of

identical syllables/feet

▸ /kan@mbu-RED/→ [kan@mbu∼kan@mbu] "language of the

Kanembu tribe" /karekare-RED/→ *[karekare∼karekare]"language of the Karekare tribe"

92 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Table of Contents

Introduction FSTs in Phonology FSTs & Reduplication 2-way FSTs & Reduplication Reduplication typology Conclusion

93 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Conclusion - Gist

  • RED processes can’t be elegantly or feasibly modeled with the
  • ne class of FSM (1-FST) that people have used so far
  • But RED can be handled with another more richer class (2-FSTs)

94 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Conclusion - Future

  • A lot of work left to do...

95 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Conclusion - Future

  • A lot of work left to do...
  • 1. Slowly grow my database of canonical and

theoretically-significant reduplication pattern (and hopefully make it public and online soon)

95 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Conclusion - Future

  • A lot of work left to do...
  • 1. Slowly grow my database of canonical and

theoretically-significant reduplication pattern (and hopefully make it public and online soon)

  • 2. Categorize and convert more data into ‘distinct’ 2FSTs

95 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Conclusion - Future

  • A lot of work left to do...
  • 1. Slowly grow my database of canonical and

theoretically-significant reduplication pattern (and hopefully make it public and online soon)

  • 2. Categorize and convert more data into ‘distinct’ 2FSTs
  • 3. Determine subclasses of complexity in RED

95 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Conclusion - Future

  • A lot of work left to do...
  • 1. Slowly grow my database of canonical and

theoretically-significant reduplication pattern (and hopefully make it public and online soon)

  • 2. Categorize and convert more data into ‘distinct’ 2FSTs
  • 3. Determine subclasses of complexity in RED
  • 4. Go higher level and convert 2FSTs into more abstract logical

structures (First Order logical transductions) in order to better understand/model opacity effects

95 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

Que-Questions?

96 / 97

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Introduction FSTs in Phonology FSTs & Reduplication 2-w ay FSTs & Reduplication Reduplication typology Conclusion References

References

Beesley, K. and L. Karttunen (2003). Finite-state morphology: Xerox tools and techniques. CSLI Publications. Broselow, E. and J. McCarthy (1983). A theory of internal

  • reduplication. The Linguistic Review 3(1), 25–88.

Chandlee, J. (2014). Strictly Local Phonological Processes. Ph. D. thesis, University of Delaware, Newark, DE. Chandlee, J. and J. Heinz (2012, June). Bounded copying is subsequential: Implications for metathesis and reduplication. In Proceedings of the 12th Meeting of the ACL Special Interest Group

  • n Computational Morphology and Phonology, SIGMORPHON

’12, Montreal, Canada, pp. 42–51. Association for Computational Linguistics. Engelfriet, J. and H. J. Hoogeboom (2001, April). MSO definable string transductions and two-way finite-state transducers. ACM

  • Trans. Comput. Logic 2(2), 216–254.

Hulden, M. (2009). Finite-state machine construction methods and algorithms for phonology and morphology. Ph. D. thesis, The University of Arizona, Tucson, AZ.

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