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Using networks to infer sound correspondence patterns across multiple languages

Using networks to infer sound correspondence patterns across multiple languages

Talk held at the Symposium on Networks and Evolution (Université Pierre et Marie Curie, 2017-10-24, Paris).

Johann-Mattis List

October 24, 2017
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  1. Using networks to infer sound-correspondence patterns
    across multiple Languages
    Johann-Mattis List
    Research Group “Computer-Assisted Language Comparison”
    Department of Linguistic and Cultural Evolution
    Max-Planck Institute for the Science of Human History
    Jena, Germany
    2017-10-24
    very
    long
    title
    P(A|B)=P(B|A)...
    1 / 29

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  2. Comparative Linguistics
    2 / 29

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  3. "All languages change, as long as they exist."
    (August Schleicher 1863)
    walkman
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    Germanic
    German English
    iPod
    Comparative Linguistics
    2 / 29

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  4. iPod
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    Germanic
    German English
    walkman
    "All languages change, as long as they exist."
    (August Schleicher 1863)
    Comparative Linguistics
    2 / 29

    View Slide

  5. walkman
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    Germanic
    German English
    iPod
    "All languages change, as long as they exist."
    (August Schleicher 1863)
    Comparative Linguistics
    2 / 29

    View Slide

  6. walkman
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    Germanic
    German English
    iPod
    "All languages change, as long as they exist."
    (August Schleicher 1863)
    Comparative Linguistics
    2 / 29

    View Slide

  7. iPod
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    walkman
    L₁
    L₁ L₁
    L₁
    L₁
    "All languages change, as long as they exist."
    (August Schleicher 1863)
    Comparative Linguistics
    2 / 29

    View Slide

  8. iPod
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    walkman
    L₁
    L₁
    L₁
    L₁
    L₁
    "All languages change, as long as they exist."
    (August Schleicher 1863)
    Comparative Linguistics
    2 / 29

    View Slide

  9. iPod
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    walkman
    L₁
    L₁
    L₁
    L₁
    L₁
    "All languages change, as long as they exist."
    (August Schleicher 1863)
    Comparative Linguistics
    2 / 29

    View Slide

  10. iPod
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    walkman
    L₁
    L₁
    L₁
    "All languages change, as long as they exist."
    (August Schleicher 1863)
    Comparative Linguistics
    2 / 29

    View Slide

  11. iPod
    Indo-European
    Germanic
    Old English
    English
    p
    f
    f
    f
    ə
    a
    æ
    ɑː
    t
    d
    d
    ð


    e
    ə
    r
    r
    r
    r
    walkman
    L₂
    L₁
    L₃
    "All languages change, as long as they exist."
    (August Schleicher 1863)
    Comparative Linguistics
    2 / 29

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  12. Comparative Linguistics Background
    Background
    3 / 29

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  13. Comparative Linguistics Background
    Background
    3 / 29

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  14. Comparative Linguistics Background
    Background
    3 / 29

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  15. Comparative Linguistics Background
    Background
    3 / 29

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  16. Comparative Linguistics Background
    Background
    3 / 29

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  17. Comparative Linguistics Comparative Method
    The Comparative Method
    COMPA-
    RATIVE
    METHOD
    4 / 29

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  18. Comparative Linguistics Comparative Method
    The Comparative Method
    COMPA-
    RATIVE
    METHOD
    4 / 29

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  19. Comparative Linguistics Comparative Method
    The Comparative Method
    COMPA-
    RATIVE
    METHOD
    4 / 29

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  20. Comparative Linguistics Comparative Method
    The Comparative Method
    COMPA-
    RATIVE
    METHOD
    4 / 29

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  21. Comparative Linguistics Comparative Method
    The Comparative Method
    COMPA-
    RATIVE
    METHOD
    4 / 29

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  22. Comparative Linguistics Computational Linguistics
    Computational Historical Linguistics
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    5 / 29

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  23. Comparative Linguistics Computational Linguistics
    Computational Historical Linguistics
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    5 / 29

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  24. Comparative Linguistics Computational Linguistics
    Computational Historical Linguistics
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    5 / 29

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  25. Comparative Linguistics Computational Linguistics
    Computational Historical Linguistics
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    5 / 29

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  26. Comparative Linguistics Computational Linguistics
    Computational Historical Linguistics
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    5 / 29

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  27. Comparative Linguistics Computational Linguistics
    Classical vs. Computational Language Comparison
    LC
    CA
    COMPA-
    RATIVE
    METHOD
    lacks
    efficiency
    lacks
    consistency
    lacks
    efficiency
    lacks
    accuracy
    lacks
    flexibility
    high
    efficiency
    high
    consistency
    high
    flexibility
    high
    accuracy
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    6 / 29

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  28. Comparative Linguistics Computational Linguistics
    Classical vs. Computational Language Comparison
    LC
    CA
    COMPA-
    RATIVE
    METHOD
    lacks
    efficiency
    lacks
    consistency
    lacks
    efficiency
    lacks
    accuracy
    lacks
    flexibility
    high
    efficiency
    high
    consistency
    high
    flexibility
    high
    accuracy
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    6 / 29

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  29. Comparative Linguistics Computational Linguistics
    Classical vs. Computational Language Comparison
    LC
    CA
    lacks
    efficiency
    lacks
    consistency
    lacks
    efficiency
    lacks
    accuracy
    lacks
    flexibility
    high
    efficiency
    high
    consistency
    high
    flexibility
    high
    accuracy
    COMPA-
    RATIVE
    METHOD accuracy
    flexibility
    consistency
    efficiency
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    6 / 29

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  30. Comparative Linguistics CALC
    Computer-Assisted Language Comparison LC
    CA
    LC
    CA
    lacks
    efficiency
    lacks
    consistency
    lacks
    efficiency
    lacks
    accuracy
    lacks
    flexibility
    high
    efficiency
    high
    consistency
    high
    flexibility
    high
    accuracy
    COMPA-
    RATIVE
    METHOD accuracy
    flexibility
    consistency
    efficiency
    COMPUTA-
    TIONAL
    HISTORICAL
    LINGUISTICS
    7 / 29

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  31. Comparative Linguistics CALC
    Computer-Assisted Language Comparison LC
    CA
    7 / 29

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  32. Historical Language Comparison
    8 / 29

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  33. Historical Language Comparison Sequences in Biology and Linguistics
    Alphabets in Biology and Linguistics
    9 / 29

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  34. Historical Language Comparison Sequences in Biology and Linguistics
    Alphabets in Biology and Linguistics
    • universal • language-specific
    9 / 29

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  35. Historical Language Comparison Sequences in Biology and Linguistics
    Alphabets in Biology and Linguistics
    • universal • language-specific
    • limited • widely varying
    9 / 29

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  36. Historical Language Comparison Sequences in Biology and Linguistics
    Alphabets in Biology and Linguistics
    • universal • language-specific
    • limited • widely varying
    • constant • mutable
    9 / 29

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  37. Historical Language Comparison Sound Correspondences
    Inferring Correspondences
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    10 / 29

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  38. Historical Language Comparison Sound Correspondences
    Inferring Correspondences
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    10 / 29

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  39. Historical Language Comparison Sound Correspondences
    Inferring Correspondences
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    10 / 29

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  40. Historical Language Comparison Sound Correspondences
    Inferring Correspondences
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    10 / 29

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  41. Historical Language Comparison Sound Correspondences
    Inferring Correspondences
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    10 / 29

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  42. Historical Language Comparison Sound Correspondences
    Inferring Correspondences
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    10 / 29

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  43. Historical Language Comparison Sound Correspondences
    Inferring Correspondences
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    10 / 29

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  44. Historical Language Comparison Sound Correspondences
    Inferring Correspondences
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    10 / 29

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  45. Historical Language Comparison Homolog Detection
    Inferring Homologs
    Cognate List Alignment Correspondences
    Bola six kʰ j a u ʔ ⁵⁵ Bola Maru Freq.
    a(a̰) a(a̰) 3 x
    u u 3 x
    ʔ k 3 x
    j j 2 x
    k(ʰ) k(ʰ) 2 x
    ⁵⁵ ⁵⁵ 2 x
    ³¹ ³¹ 1 x
    Maru six kʰ j a u k ⁵⁵
    Bola lip k a̰ u ʔ ⁵⁵
    Maru lip k a̰ u k ⁵⁵
    Bola man j a u ʔ ³¹
    Maru man j a u k ³¹
    11 / 29

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  46. Historical Language Comparison Correspondence Patterns
    Inferring Patterns
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ

    tsʰ
    t


    12 / 29

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  47. Historical Language Comparison Correspondence Patterns
    Inferring Patterns
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ

    tsʰ
    t


    "salt"
    Bola tʰ a ³⁵
    Maru tsʰ ɔ ³⁵
    Rangoon sʰ ɑ ⁵⁵
    12 / 29

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  48. Historical Language Comparison Correspondence Patterns
    Inferring Patterns
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    t
    ts
    t


    12 / 29

    View Slide

  49. Historical Language Comparison Correspondence Patterns
    Inferring Patterns
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    t
    ts
    t


    "tooth"
    Bola t u i ⁵⁵
    Maru ts ɔ i ³¹
    Rangoon tθ w a ⁵⁵
    12 / 29

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  50. Historical Language Comparison Correspondence Patterns
    Inferring Patterns
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    tʰ tʰ
    t


    12 / 29

    View Slide

  51. Historical Language Comparison Correspondence Patterns
    Inferring Patterns
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    tʰ tʰ
    t


    "sharp"
    Bola tʰ a ʔ ⁵⁵
    Maru tʰ ɔ ʔ ⁵⁵
    Rangoon tʰ ɛ ʔ ⁴
    12 / 29

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  52. Historical Language Comparison Correspondence Patterns
    Inferring Patterns
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    t t
    t

    t
    12 / 29

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  53. Historical Language Comparison Correspondence Patterns
    Inferring Patterns
    Ø
    Sound Bola Maru Rangoon
    d Ø Ø d
    t t t t
    tʰ tʰ tʰ tʰ
    tθ Ø Ø tθ
    ts ts ts Ø
    tsʰ tsʰ tsʰ Ø
    tʃ tʃ tʃ Ø
    tʃʰ tʃʰ tʃʰ Ø
    s s s s
    sʰ Ø Ø sʰ
    ɕ Ø Ø ɕ
    ʃ ʃ ʃ
    t t
    t

    t
    "wing"
    Bola t a u ŋ ⁵⁵
    Maru t a u ŋ ³¹
    Rangoon t ɑ u ∼ ²²
    12 / 29

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  54. Inferring Correspondence Patterns
    13 / 29

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  55. Inferring Correspondence Patterns Sound Correspondence Patterns
    Sound Correspondence Patterns
    PIE Hittite Sanskrit Avestan Greek Latin Gothic
    Old
    Church
    Slavonic
    Lithuanian Old Irish Armenian Tocharian
    *p p p p f p p f b p p Ø h w Ø p
    *b b p b bβ b b p b b b p p
    *bʰ b p bʱ/bh bβ pʰ/ph f b b b b b b p
    *t t t t θ t t θ/þ d t t t tʼ j/y t tʃ/c
    *d d t d d ð d d t d d d t ts ʃ/ś
    *dʰ d t dʰ/dh h d ð tʰ/th f d b d d d d t t tʃ/c
    ... ... ... ... ... ... ... ... ... ... ... ...
    *kʷ kʷ/ku k c k c k p t kʷ/qu hʷ/hw g k tʃ/č k c kʼ tʃʼ/čʼ k ʃʲ/ś
    *gʷ kʷ/u g j g j g b d gʷ/gu u q g ʒ/ž z g b k k ś
    *gʷʰ kʷ/ku gʷ/gu gʱ/gh h g j pʰ/ph tʰ/th kʰ/kh f gʷ/gu u g b g ʒ/ž z g g g dʒ/ǰ k ʃʲ/ś
    Clackson (2007: 37)
    14 / 29

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  56. Inferring Correspondence Patterns Sound Correspondence Patterns
    Sound Correspondence Patterns
    15 / 29

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  57. Inferring Correspondence Patterns Sound Correspondence Patterns
    Sound Correspondence Patterns
    correspondence patterns in linguistics are a way to encode mappings
    across several different alphabets
    15 / 29

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  58. Inferring Correspondence Patterns Sound Correspondence Patterns
    Sound Correspondence Patterns
    correspondence patterns in linguistics are a way to encode mappings
    across several different alphabets
    they are usually inferred manually, by inspecting “correspondence
    sets” (Clackson 2007: 29f) of words (i.e., cognate sets with recurring
    sounds)
    15 / 29

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  59. Inferring Correspondence Patterns Sound Correspondence Patterns
    Sound Correspondence Patterns
    correspondence patterns in linguistics are a way to encode mappings
    across several different alphabets
    they are usually inferred manually, by inspecting “correspondence
    sets” (Clackson 2007: 29f) of words (i.e., cognate sets with recurring
    sounds)
    the main problem of correspondence pattern identification is the
    handling of missing data, since not all cognate sets will necessarily
    contain reflexes from each of the languages under investigation
    15 / 29

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  60. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Inference of Correspondence Patterns
    16 / 29

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  61. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Inference of Correspondence Patterns
    the main idea for the correspondence pattern inference algorithm is to
    derive a graph from correspondence sets in which each individual
    correspondence set (a site in an aligned cognate set) is a node, and
    links between nodes are drawn between compatible correspondence
    sets
    16 / 29

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  62. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Inference of Correspondence Patterns
    the main idea for the correspondence pattern inference algorithm is to
    derive a graph from correspondence sets in which each individual
    correspondence set (a site in an aligned cognate set) is a node, and
    links between nodes are drawn between compatible correspondence
    sets
    if two correspondence sets are compatible, this means that they have
    identical non-missing values for at least one language and no
    conflicting data for any of the languages
    16 / 29

    View Slide

  63. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Inference of Correspondence Patterns
    the main idea for the correspondence pattern inference algorithm is to
    derive a graph from correspondence sets in which each individual
    correspondence set (a site in an aligned cognate set) is a node, and
    links between nodes are drawn between compatible correspondence
    sets
    if two correspondence sets are compatible, this means that they have
    identical non-missing values for at least one language and no
    conflicting data for any of the languages
    if two or more correspondence sets are compatible, we can impute
    missing values by combining them
    16 / 29

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  64. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compabitility of Alignment Sites
    Cognate Set L1 L2 L3 L4 L5 L6 L7 L8
    “hand-1” p p p Ø f f Ø p
    “foot-1” p p p p f f p p
    ⊠ compatible
    □ incompatible
    17 / 29

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  65. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compabitility of Alignment Sites
    Cognate Set L1 L2 L3 L4 L5 L6 L7 L8
    “hand-1” p p p Ø f f Ø p
    “foot-1” p p p p f f p p
    ⊠ compatible
    □ incompatible
    Cognate Set L1 L2 L3 L4 L5 L6 L7 L8
    “hand-1” p p p Ø f f Ø p
    “leg-1” p p f pf f f p p
    □ compatible
    ⊠ incompatible
    17 / 29

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  66. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compatibility Graphs
    8 Burmish languages (spoken in China and Myanmar, taken from Hill
    and List 2017)
    18 / 29

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  67. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compatibility Graphs
    8 Burmish languages (spoken in China and Myanmar, taken from Hill
    and List 2017)
    240 concepts
    855 partial cognate sets
    18 / 29

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  68. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compatibility Graphs
    8 Burmish languages (spoken in China and Myanmar, taken from Hill
    and List 2017)
    240 concepts
    855 partial cognate sets
    728 cross-semantic partial cognate sets (covering one and more
    concepts)
    18 / 29

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  69. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compatibility Graphs
    8 Burmish languages (spoken in China and Myanmar, taken from Hill
    and List 2017)
    240 concepts
    855 partial cognate sets
    728 cross-semantic partial cognate sets (covering one and more
    concepts)
    218 valid cognate sets (residues in more than one language)
    18 / 29

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  70. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compabitility Graphs
    A "gums"
    Achang ʂ - u a ³¹
    Rangoon tθ w - ɑ ⁵⁵
    Atsi Ø Ø Ø Ø Ø
    Bola Ø Ø Ø Ø Ø
    Maru Ø Ø Ø Ø Ø
    B "die"
    Achang Ø Ø Ø Ø
    Rangoon tθ e - ²²
    Atsi Ø Ø Ø Ø
    Bola ʃ ɿ - ⁵⁵
    Maru ʃ i k ³¹
    C "daughter"
    Achang Ø Ø Ø
    Rangoon tθ ɑ ⁵³
    Atsi Ø Ø Ø
    Bola Ø Ø Ø
    Maru ts o ⁰
    A B A C B C
    ʂ Ø ʂ Ø Ø Ø
    tθ tθ tθ tθ tθ tθ
    Ø Ø Ø Ø Ø Ø
    Ø ʃ Ø Ø ʃ Ø
    Ø ʃ Ø ts ʃ ts
    identical
    compatible
    incompatible
    A
    C
    B
    A
    B C
    19 / 29

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  71. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compatibility Graphs











    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    tsʰ
    tʃʰ
    tsʰ
    tʃʰ
    tʃʰ
    tsʰ
    tsʰ
    tsʰ
    v
    j f j
    v v
    n◌̥
    ŋ
    -
    ŋ
    ŋ
    ŋ
    ŋ
    ʃ
    ʃ
    ʃ ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    s
    s


    s







    x
    x

    x
    x
    x
    t
    t
    t
    t
    t
    t
    ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    t
    t
    t t
    t
    t
    t
    t
    p

    m
    m
    p
    m
    m

    p
    m
    s
    s
    s
    s
    s
    s
    s
    s
    s
    s
    n
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    s
    s
    s
    s
    s
    s
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p

    p
    p
    p p
    p
    p
    m
    m
    m
    m
    m
    m
    m
    l
    l
    l
    l
    l
    l
    l
    l
    j
    j
    -
    j
    -
    j
    j
    -
    j
    k
    ɣ
    ɣ
    ɣ
    ɣ
    ʐ
    ɣ
    j
    j
    v
    j
    -
    w
    v
    j
    k k
    k
    k
    k
    k
    k
    k
    k

    kʰ kʰ




    k
    k
    k k
    k











    x
    x
    x
    x
    n◌̥ n
    n
    n
    n
    n
    n
    n
    n
    n
    ŋ
    n
    n
    n
    n
    n
    n
    n
    n n
    k
    k
    k
    k
    k
    k
    m
    m
    m
    m
    m
    m
    m
    m
    m
    n◌̥
    n
    n n
    -
    ŋ
    n
    ŋ

    m m
    m
    m
    m
    m
    m
    m
    20 / 29

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  72. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compatibility Graphs











    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    tsʰ
    tsʰ
    tʃʰ
    tsʰ
    tsʰ
    tʃʰ
    tʃʰ
    tsʰ
    j v f j
    v v
    ŋ
    -
    ŋ
    n◌̥
    ŋ
    ŋ
    ŋ
    ʃ
    ʃ
    s
    ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    s





    s




    x
    x

    x
    x
    x
    t
    t
    t
    t
    t
    t
    ʃ ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    t
    t
    t
    t
    t t
    t
    t
    m
    m
    m


    p
    p
    p
    m
    m
    s
    s
    s s
    s
    s
    s
    s
    s
    s
    n
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    s
    s
    s
    s
    s
    s
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p

    p
    m
    m
    m
    m
    m
    m
    m
    l
    l
    l
    l
    l
    l
    l
    l
    -
    -
    j
    j
    j
    j
    j
    -
    j
    k
    ɣ
    ɣ
    ɣ
    ɣ
    ʐ
    ɣ
    w
    j
    -
    v
    v
    j
    j
    j
    k
    k k k
    k
    k
    k
    k
    k







    k
    k
    k
    k
    k











    x
    x
    x
    x
    n
    n◌̥
    n
    n
    n
    n
    n
    ŋ
    n
    n n
    n
    n
    n
    n
    n
    n
    n
    n
    n
    k k
    k
    k
    k k
    m
    m
    m
    m
    m
    m
    m
    m
    -
    n
    n
    ŋ
    ŋ
    n
    n◌̥
    n

    m
    m
    m
    m
    m
    m
    m
    m
    m
    20 / 29

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  73. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compatibility Graphs
    x
    x
    x
    x
    x
    x
    x
    x
    x
    x
    good
    correspondence
    set
    bad
    correspondence
    set
    20 / 29

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  74. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Compatibility Graphs
    Only fully compatible clusters (i.e., only cliques in our net-
    work of correspondence sets) can represent true sound corre-
    spondence patterns (if sound change is regular).
    20 / 29

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  75. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Correspondence Pattern Inference as Clique Cover Problem
    21 / 29

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  76. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Correspondence Pattern Inference as Clique Cover Problem
    The clique cover problem (also called clique partitioning problem, see
    Bhasker 1991) is the inverse of the famous graph coloring problem
    and has been shown to be NP-hard.
    21 / 29

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  77. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Correspondence Pattern Inference as Clique Cover Problem
    The clique cover problem (also called clique partitioning problem, see
    Bhasker 1991) is the inverse of the famous graph coloring problem
    and has been shown to be NP-hard.
    The goal of the problem is to split a graph into the smallest number
    of cliques in which each node is represented by exactly one clique.
    21 / 29

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  78. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Correspondence Pattern Inference as Clique Cover Problem
    The clique cover problem (also called clique partitioning problem, see
    Bhasker 1991) is the inverse of the famous graph coloring problem
    and has been shown to be NP-hard.
    The goal of the problem is to split a graph into the smallest number
    of cliques in which each node is represented by exactly one clique.
    We assume (but we cannot formally prove it) that the clique cover of
    our graph of compatible correspondence sets will correspond to the
    optimal set of sound correspondence patterns in our data.
    21 / 29

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  79. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Correspondence Pattern Inference as Clique Cover Problem
    The clique cover problem (also called clique partitioning problem, see
    Bhasker 1991) is the inverse of the famous graph coloring problem
    and has been shown to be NP-hard.
    The goal of the problem is to split a graph into the smallest number
    of cliques in which each node is represented by exactly one clique.
    We assume (but we cannot formally prove it) that the clique cover of
    our graph of compatible correspondence sets will correspond to the
    optimal set of sound correspondence patterns in our data.
    By applying an approximation algorithm to infer a near-optimal clique
    cover of our data of aligned cognate sets, we can infer the most
    frequently recurring correspondence patterns in our data.
    21 / 29

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  80. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Graph with Clique Cover
    tʃʰ
    s ʃ tʃʰ x
    j
    n◌̥
    n
    n
    ŋ
    tsʰ
    tsʰ
    tsʰ
    tʃʰ


    pʰ j
    w
    x
    v
    x
    v
    x
    j
    x
    n
    n
    x
    x
    x
    n◌̥
    x
    n
    m
    m
    m
    n
    kʰ kʰ









    -
    -
    -


    p
    j
    ɣ
    ɣ
    ɣ
    ɣ
    j
    j
    j
    n
    n
    n
    n
    m
    n
    n
    n
    n
    m
    m
    m
    m
    m
    m
    m
    m
    m
    m
    l
    l
    l
    p
    l
    l
    l
    l
    l
    l
    l










    ʃ
    s
    s
    s
    k
    ʃ
    ʃ
    k
    s
    s
    k s
    ʃ
    ʃ
    ʃ
    t
    t
    t
    t
    t
    t
    t
    t
    t
    t
    t
    m
    m
    m
    m m
    m
    m
    m
    m
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    k
    k s kʰ
    kʰ k
    ʃ
    ŋ n m l t t l -
    tsʰ f tʃ k n n
    l
    ʃ
    tsʰ
    l
    s
    m
    t p
    k
    n
    kʰ m j
    m
    v j
    s

    n
    ts
    m
    l ŋ
    k kʰ
    v ʃ
    ʐ ʃ n
    k
    j -
    tʃ pʰ
    s
    v m
    k ŋ ŋ - n n l
    n◌̥
    ŋ
    ŋ
    l
    l
    l
    l
    ʃ
    ʃ
    ts
    ʃ k
    s
    k
    s
    s
    s
    s
    s
    ts
    ts
    ts
    ts
    ts
    ts
    j k
    j
    ɣ
    k
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    s
    s







    k
    k
    k
    k
    k
    ts p

    ts

    ŋ
    n ŋ
    k
    22 / 29

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  81. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Graph with Clique Cover











    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    ŋ
    tsʰ
    tsʰ
    tʃʰ
    tsʰ
    tsʰ
    tʃʰ
    tʃʰ
    tsʰ
    j v f j
    v v
    ŋ
    -
    ŋ
    n◌̥
    ŋ
    ŋ
    ŋ
    ʃ
    ʃ
    s
    ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    s





    s




    x
    x

    x
    x
    x
    t
    t
    t
    t
    t
    t
    ʃ ʃ
    ʃ
    ʃ
    ʃ
    ʃ
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    ts
    t
    t
    t
    t
    t t
    t
    t
    m
    m
    m


    p
    p
    p
    m
    m
    s
    s
    s s
    s
    s
    s
    s
    s
    s
    n
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    l
    s
    s
    s
    s
    s
    s
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p
    p

    p
    m
    m
    m
    m
    m
    m
    m
    l
    l
    l
    l
    l
    l
    l
    l
    -
    -
    j
    j
    j
    j
    j
    -
    j
    k
    ɣ
    ɣ
    ɣ
    ɣ
    ʐ
    ɣ
    w
    j
    -
    v
    v
    j
    j
    j
    k
    k k k
    k
    k
    k
    k
    k







    k
    k
    k
    k
    k











    x
    x
    x
    x
    n
    n◌̥
    n
    n
    n
    n
    n
    ŋ
    n
    n n
    n
    n
    n
    n
    n
    n
    n
    n
    n
    k k
    k
    k
    k k
    m
    m
    m
    m
    m
    m
    m
    m
    -
    n
    n
    ŋ
    ŋ
    n
    n◌̥
    n

    m
    m
    m
    m
    m
    m
    m
    m
    m
    22 / 29

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  82. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Graph with Clique Cover
    tʃʰ
    tʃʰ
    tsʰ
    tsʰ
    tsʰ
    tsʰ


    tsʰ
    tʃʰ





    22 / 29

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  83. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Graph with Clique Cover
    tʃʰ
    tʃʰ
    tʃʰ
    tsʰ
    tsʰ
    tsʰ
    tsʰ
    tsʰ







    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    41 659 "goat" Ø Ø Ø Ø tʃʰ tsʰ sʰ Ø
    41 672 "armpit" Ø Ø tʃʰ tʃʰ tʃʰ Ø Ø Ø
    41 433 "rice" tsʰ tʃʰ tʃʰ tʃʰ tʃʰ Ø sʰ tsʰ
    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    74 55 "ten" Ø Ø tʰ tsʰ Ø Ø Ø tsʰ
    42 53 "ten" tɕʰ tsʰ Ø Ø Ø tsʰ sʰ Ø
    42 421 "salt" tɕʰ tsʰ tʰ tsʰ tsʰ tsʰ sʰ cʰ
    42 129 "twenty" Ø tsʰ tʰ tsʰ tsʰ tsʰ sʰ Ø
    83 287 "hair" Ø tsʰ tsʰ tsʰ tsʰ tsʰ sʰ Ø
    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    17 639 "above" Ø tʰ tʰ Ø tʰ tʰ tʰ Ø
    17 472 "sing" Ø tʰ tʰ Ø tʰ Ø Ø Ø
    17 61 "that" tʰ Ø Ø tʰ tʰ tʰ tʰ tʰ
    17 323 "sharp" tʰ tʰ tʰ tʰ tʰ tʰ tʰ Ø
    17 66 "there" tʰ Ø tʰ tʰ tʰ Ø tʰ tʰ
    17 547 "firewood" tʰ tʰ tʰ tʰ tʰ tʰ tʰ tʰ
    17 74 "thick" Ø tʰ tʰ tʰ tʰ Ø tʰ Ø
    22 / 29

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  84. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Graph with Clique Cover
    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    41 659 "goat" Ø Ø Ø Ø tʃʰ tsʰ sʰ Ø
    41 672 "armpit" Ø Ø tʃʰ tʃʰ tʃʰ Ø Ø Ø
    41 433 "rice" tsʰ tʃʰ tʃʰ tʃʰ tʃʰ Ø sʰ tsʰ
    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    74 55 "ten" Ø Ø tʰ tsʰ Ø Ø Ø tsʰ
    42 53 "ten" tɕʰ tsʰ Ø Ø Ø tsʰ sʰ Ø
    42 421 "salt" tɕʰ tsʰ tʰ tsʰ tsʰ tsʰ sʰ cʰ
    42 129 "twenty" Ø tsʰ tʰ tsʰ tsʰ tsʰ sʰ Ø
    83 287 "hair" Ø tsʰ tsʰ tsʰ tsʰ tsʰ sʰ Ø
    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    17 639 "above" Ø tʰ tʰ Ø tʰ tʰ tʰ Ø
    17 472 "sing" Ø tʰ tʰ Ø tʰ Ø Ø Ø
    17 61 "that" tʰ Ø Ø tʰ tʰ tʰ tʰ tʰ
    17 323 "sharp" tʰ tʰ tʰ tʰ tʰ tʰ tʰ Ø
    17 66 "there" tʰ Ø tʰ tʰ tʰ Ø tʰ tʰ
    17 547 "firewood" tʰ tʰ tʰ tʰ tʰ tʰ tʰ tʰ
    17 74 "thick" Ø tʰ tʰ tʰ tʰ Ø tʰ Ø
    tʃʰ
    tʃʰ
    tʃʰ
    tsʰ
    tsʰ
    tsʰ
    tsʰ
    tsʰ







    22 / 29

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  85. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Results
    23 / 29

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  86. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Results
    104 initial consonant patterns (48 with more than one reflex, the rest
    highly irregular)
    23 / 29

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  87. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Results
    104 initial consonant patterns (48 with more than one reflex, the rest
    highly irregular)
    many patterns correspond to well-known proto-sounds in the data
    23 / 29

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  88. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Results
    104 initial consonant patterns (48 with more than one reflex, the rest
    highly irregular)
    many patterns correspond to well-known proto-sounds in the data
    some cliques are unintuitive
    23 / 29

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  89. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Problems
    Irregular patterns:
    24 / 29

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  90. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Problems
    Irregular patterns:
    result in part from problems in cognate coding (homology assessment)
    24 / 29

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  91. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Problems
    Irregular patterns:
    result in part from problems in cognate coding (homology assessment)
    result in part from sparseness of data
    24 / 29

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  92. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Problems
    Irregular patterns:
    result in part from problems in cognate coding (homology assessment)
    result in part from sparseness of data
    result in part from the exactness of the algorithm
    24 / 29

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  93. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Problems
    Irregular patterns:
    result in part from problems in cognate coding (homology assessment)
    result in part from sparseness of data
    result in part from the exactness of the algorithm
    Unintuitive patterns:
    24 / 29

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  94. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Summary on Problems
    Irregular patterns:
    result in part from problems in cognate coding (homology assessment)
    result in part from sparseness of data
    result in part from the exactness of the algorithm
    Unintuitive patterns:
    result in part from the greediness of the algorithm
    24 / 29

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  95. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Possible Improvements
    25 / 29

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  96. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Possible Improvements
    catch the greediness of the algorithm by adding a secondary check of
    cliques (calculate consensus, re-assign all alignment sites to all
    compatible consensus sequences, count the instances)
    25 / 29

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  97. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Possible Improvements
    catch the greediness of the algorithm by adding a secondary check of
    cliques (calculate consensus, re-assign all alignment sites to all
    compatible consensus sequences, count the instances)
    allow for non-perfect cliques in which compatibility is allowed to
    deviate to a certain degree (e.g., one irregular cell)
    25 / 29

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  98. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Possible Improvements
    catch the greediness of the algorithm by adding a secondary check of
    cliques (calculate consensus, re-assign all alignment sites to all
    compatible consensus sequences, count the instances)
    allow for non-perfect cliques in which compatibility is allowed to
    deviate to a certain degree (e.g., one irregular cell)
    provide a more fine-grained checking of proposed cliques by counting
    columns suffering from missing data
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  99. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Possible Improvements
    catch the greediness of the algorithm by adding a secondary check of
    cliques (calculate consensus, re-assign all alignment sites to all
    compatible consensus sequences, count the instances)
    allow for non-perfect cliques in which compatibility is allowed to
    deviate to a certain degree (e.g., one irregular cell)
    provide a more fine-grained checking of proposed cliques by counting
    columns suffering from missing data
    allow for a direct checking and correcting of patterns by the experts
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  100. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Possible Improvements
    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    41 659 "goat" Ø Ø Ø Ø tʃʰ tsʰ sʰ Ø
    41 672 "armpit" Ø Ø tʃʰ tʃʰ tʃʰ Ø Ø Ø
    41 433 "rice" tsʰ tʃʰ tʃʰ tʃʰ tʃʰ Ø sʰ tsʰ
    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    74 55 "ten" Ø Ø tʰ tsʰ Ø Ø Ø tsʰ
    42 53 "ten" tɕʰ tsʰ Ø Ø Ø tsʰ sʰ Ø
    42 421 "salt" tɕʰ tsʰ tʰ tsʰ tsʰ tsʰ sʰ cʰ
    42 129 "twenty" Ø tsʰ tʰ tsʰ tsʰ tsʰ sʰ Ø
    83 287 "hair" Ø tsʰ tsʰ tsʰ tsʰ tsʰ sʰ Ø
    Clique Cogn. Concept Achang Atsi Bola Lashi Maru Old B. Rang. Xiand.
    17 639 "above" Ø tʰ tʰ Ø tʰ tʰ tʰ Ø
    17 472 "sing" Ø tʰ tʰ Ø tʰ Ø Ø Ø
    17 61 "that" tʰ Ø Ø tʰ tʰ tʰ tʰ tʰ
    17 323 "sharp" tʰ tʰ tʰ tʰ tʰ tʰ tʰ Ø
    17 66 "there" tʰ Ø tʰ tʰ tʰ Ø tʰ tʰ
    17 547 "firewood" tʰ tʰ tʰ tʰ tʰ tʰ tʰ tʰ
    17 74 "thick" Ø tʰ tʰ tʰ tʰ Ø tʰ Ø
    tʃʰ
    tʃʰ
    tʃʰ
    tsʰ
    tsʰ
    tsʰ
    tsʰ
    tsʰ







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  101. Outlook
    27 / 29

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  102. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Outlook
    28 / 29

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  103. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Outlook
    the proposed inference of correspondence patterns is a first attempt
    to account for systemic aspects of sound change in a rigorous manner
    28 / 29

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  104. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Outlook
    the proposed inference of correspondence patterns is a first attempt
    to account for systemic aspects of sound change in a rigorous manner
    in contrast to many approaches proposed so far, it does not require
    family trees in any form, networks are just enough, but the patterns
    inferred can be used to study tree-like aspects of evolution (Chacon
    and List 2015),
    28 / 29

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  105. Inferring Correspondence Patterns Inference of Correspondence Patterns
    Outlook
    the proposed inference of correspondence patterns is a first attempt
    to account for systemic aspects of sound change in a rigorous manner
    in contrast to many approaches proposed so far, it does not require
    family trees in any form, networks are just enough, but the patterns
    inferred can be used to study tree-like aspects of evolution (Chacon
    and List 2015),
    the algorithm is surely a good start, but it needs to be improved in
    several ways
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  106. Merci Pour Votre Attention!
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