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Computational perspectives on phonological constituency and recursion

krisyu
November 22, 2019

Computational perspectives on phonological constituency and recursion

Talk at RecPhon 2019: Recursivity in Phonology below and above the word.
21-22 November 2019, Universitat Autònoma de Barcelona, Bellaterra.
Website: http://filcat.uab.cat/pagines_clt/recphon2019/

krisyu

November 22, 2019
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  1. Factoring prosodic recursion
    Computing with trees
    Computational perspectives on
    phonological constituency
    and recursion
    Kristine M. Yu
    [email protected]
    RecPhon 2019, UAB, Barcelona / Nov. 22, 2019
    K.M. Yu [email protected] Phonological constituency and recursion 1/ 41

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  2. Factoring prosodic recursion
    Computing with trees
    A common idea
    A reason not to admit prosodic recursion:
    Adding prosodic recursion into phonological descriptions and
    computations blows up the complexity of
    description/computation.
    Why should we do this if recursion is shallow, e.g., 1 or two
    layers?
    No complexity blowup, and gains in capturing gener-
    alizations.
    K.M. Yu [email protected] Phonological constituency and recursion 2/ 41

    View full-size slide

  3. Factoring prosodic recursion
    Computing with trees
    1 Factoring prosodic recursion
    Recursion in phonology
    Prosodic constituents in phonology
    2 Computing with trees
    K.M. Yu [email protected] Phonological constituency and recursion 3/ 41

    View full-size slide

  4. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Table of Contents
    1 Factoring prosodic recursion
    Recursion in phonology
    Prosodic constituents in phonology
    2 Computing with trees
    K.M. Yu [email protected] Phonological constituency and recursion 4/ 41

    View full-size slide

  5. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

    View full-size slide

  6. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite) length
    K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

    View full-size slide

  7. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite) length
    With recursion, we can write grammars that recognize that
    a constituent shares properties with one of its parts
    K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

    View full-size slide

  8. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite) length
    With recursion, we can write grammars that recognize that
    a constituent shares properties with one of its parts
    2 Controversial but widely assumed: Phonological grammars
    refer to constituents
    K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

    View full-size slide

  9. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite) length
    With recursion, we can write grammars that recognize that
    a constituent shares properties with one of its parts
    2 Controversial but widely assumed: Phonological grammars
    refer to constituents
    Phonological patterns distinguish right-branching from
    left-branching
    K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

    View full-size slide

  10. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite) length
    With recursion, we can write grammars that recognize that
    a constituent shares properties with one of its parts
    2 Controversial but widely assumed: Phonological grammars
    refer to constituents
    Phonological patterns distinguish right-branching from
    left-branching
    There are phonological patterns defined over trees
    K.M. Yu [email protected] Phonological constituency and recursion 5/ 41

    View full-size slide

  11. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Table of Contents
    1 Factoring prosodic recursion
    Recursion in phonology
    Prosodic constituents in phonology
    2 Computing with trees
    K.M. Yu [email protected] Phonological constituency and recursion 6/ 41

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  12. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    What is recursion (informal)?
    Recursion: structure/operation being defined used in its own
    definition
    Recursive structure: string defined as an extension of
    another string
    Recursive operation: ω → σ ω
    K.M. Yu [email protected] Phonological constituency and recursion 7/ 41

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  13. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Simplest definition of strings is recursive
    Given an alphabet of symbols, Σ, define a string over Σ as
    follows:
    1 Base case: The empty symbol λ is a string.
    2 Recursive case: If w is a string and s is a symbol (s ∈ Σ),
    then ws is a string.
    Note that this defines unbounded recursion.
    K.M. Yu [email protected] Phonological constituency and recursion 8/ 41

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  14. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Finite physical realization of unbounded recursion
    Maximum length of a string in Python on a 64-bit system:
    9223372036854775807
    1 import sys
    2 print(sys.maxsize)
    3 9223372036854775807
    K.M. Yu [email protected] Phonological constituency and recursion 9/ 41

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  15. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Finite physical realization of unbounded recursion
    Maximum length of a string in Python on a 64-bit system:
    9223372036854775807
    1 import sys
    2 print(sys.maxsize)
    3 9223372036854775807
    Recursion unbounded in definition of data structure,
    but finite realization of structure in physical systems.
    K.M. Yu [email protected] Phonological constituency and recursion 9/ 41

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  16. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α
    α → C β α → C β
    β → V γ β → V α
    γ → λ
    K.M. Yu [email protected] Phonological constituency and recursion 10/ 41

    View full-size slide

  17. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α (immediate recursion)
    α → C β α → C β
    β → V γ β → V α
    γ → λ
    K.M. Yu [email protected] Phonological constituency and recursion 10/ 41

    View full-size slide

  18. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α
    α → C β α → C β (recursion)
    β → V γ β → V α
    γ → λ
    K.M. Yu [email protected] Phonological constituency and recursion 10/ 41

    View full-size slide

  19. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α
    α → C β α → C β
    β → V γ β → V α
    γ → λ
    Generates {λ, V , CV } Generates {λ, V , CV ,
    VV , VCV , CVV , CVCV , . . .}
    K.M. Yu [email protected] Phonological constituency and recursion 10/ 41

    View full-size slide

  20. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α
    α → C β α → C β
    β → V γ β → V α
    γ → λ
    Generates {λ, V , CV } Generates {λ, V , CV ,
    VV , VCV , CVV , CVCV , . . .}
    Recursive operations are necessary for generalization
    to strings of arbitrary (finite) length.
    K.M. Yu [email protected] Phonological constituency and recursion 10/ 41

    View full-size slide

  21. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Non-recursive grammars generate finite sets
    (a) Non-recursive grammar (b) (Non-recursive) list grammar
    α → λ α → λ
    α → V γ α → V
    α → C β α → CV
    β → V γ
    γ → λ
    K.M. Yu [email protected] Phonological constituency and recursion 11/ 41

    View full-size slide

  22. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Non-recursive grammars generate finite sets
    (a) Non-recursive grammar (b) (Non-recursive) list grammar
    α → λ α → λ
    α → V γ α → V
    α → C β α → CV
    β → V γ
    γ → λ
    Generates {λ, V , CV } Generates {λ, V , CV }
    K.M. Yu [email protected] Phonological constituency and recursion 11/ 41

    View full-size slide

  23. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Non-recursive grammars generate finite sets
    (a) Non-recursive grammar (b) (Non-recursive) list grammar
    α → λ α → λ
    α → V γ α → V
    α → C β α → CV
    β → V γ
    γ → λ
    Generates {λ, V , CV } Generates {λ, V , CV }
    Without recursion, we can only write grammars that
    can be modeled as finite lists of words up to some
    upper bound in length.
    K.M. Yu [email protected] Phonological constituency and recursion 11/ 41

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  24. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Strings of arbitrary (finite) length
    Words and sentences can be arbitrarily long, (though finite)
    K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

    View full-size slide

  25. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Strings of arbitrary (finite) length
    Words and sentences can be arbitrarily long, (though finite)
    Winnepesaukee, Halicarnassus (Dabouis et al., this
    conference)
    K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

    View full-size slide

  26. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Strings of arbitrary (finite) length
    Words and sentences can be arbitrarily long, (though finite)
    Winnepesaukee, Halicarnassus (Dabouis et al., this
    conference)
    Winnehalipecarnasaukeessus
    K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

    View full-size slide

  27. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Strings of arbitrary (finite) length
    Words and sentences can be arbitrarily long, (though finite)
    Winnepesaukee, Halicarnassus (Dabouis et al., this
    conference)
    Winnehalipecarnasaukeessus
    There are infinitely many possible words/sentences. . .
    K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

    View full-size slide

  28. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Strings of arbitrary (finite) length
    Words and sentences can be arbitrarily long, (though finite)
    Winnepesaukee, Halicarnassus (Dabouis et al., this
    conference)
    Winnehalipecarnasaukeessus
    There are infinitely many possible words/sentences. . .
    . . . so we need grammars that can generate infinite set of
    arbitrarily long words, i.e., grammars with recursive
    operations
    K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

    View full-size slide

  29. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Strings of arbitrary (finite) length
    Words and sentences can be arbitrarily long, (though finite)
    Winnepesaukee, Halicarnassus (Dabouis et al., this
    conference)
    Winnehalipecarnasaukeessus
    There are infinitely many possible words/sentences. . .
    . . . so we need grammars that can generate infinite set of
    arbitrarily long words, i.e., grammars with recursive
    operations
    Bounds on recursion could come from factors outside
    phonological grammar, e.g., processing, memory, lexi-
    con, or elsewhere in phonological grammar, e.g., con-
    straint interactions
    K.M. Yu [email protected] Phonological constituency and recursion 12/ 41

    View full-size slide

  30. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α
    α → C β α → C β
    β → V γ β → V α
    γ → λ
    K.M. Yu [email protected] Phonological constituency and recursion 13/ 41

    View full-size slide

  31. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α (immediate recursion)
    α → C β α → C β
    β → V γ β → V α
    γ → λ
    K.M. Yu [email protected] Phonological constituency and recursion 13/ 41

    View full-size slide

  32. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α
    α → C β α → C β (recursion)
    β → V γ β → V α
    γ → λ
    K.M. Yu [email protected] Phonological constituency and recursion 13/ 41

    View full-size slide

  33. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α
    α → C β α → C β
    β → V γ β → V α
    γ → λ
    Generates {λ, V , CV } Generates {λ, V , CV ,
    VV , VCV , CVV , CVCV , . . .}
    K.M. Yu [email protected] Phonological constituency and recursion 13/ 41

    View full-size slide

  34. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → V γ α → V α
    α → C β α → C β
    β → V γ β → V α
    γ → λ
    Generates {λ, V , CV } Generates {λ, V , CV ,
    VV , VCV , CVV , CVCV , . . .}
    Recursive operations are necessary for generalization
    to strings of arbitrary (finite) length.
    K.M. Yu [email protected] Phonological constituency and recursion 13/ 41

    View full-size slide

  35. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Two derivations of CV
    With non-recursive grammar With recursive grammar
    α
    C β
    V γ
    λ
    α
    C β
    V α
    λ
    α γ
    V
    β
    C V
    α
    V
    β
    C
    V
    K.M. Yu [email protected] Phonological constituency and recursion 14/ 41

    View full-size slide

  36. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars II
    (a) Non-recursive grammar
    α → λ
    α → λ, α → V γ, α → C β, β → V γ
    γ → λ, γ → V , γ → C δ, δ → V
    Generates {λ,
    α γ
    V
    β
    C ε
    V
    δ
    C
    V V
    K.M. Yu [email protected] Phonological constituency and recursion 15/ 41

    View full-size slide

  37. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars II
    (a) Non-recursive grammar
    α → λ
    α → λ, α → V γ, α → C β, β → V γ
    γ → λ, γ → V , γ → C δ, δ → V
    Generates {λ, (C)V ,
    α γ
    V
    β
    C ε
    V
    δ
    C V
    V
    K.M. Yu [email protected] Phonological constituency and recursion 15/ 41

    View full-size slide

  38. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars II
    (a) Non-recursive grammar
    α → λ
    α → λ, α → V γ, α → C β, β → V γ
    γ → λ, γ → V , γ → C δ, δ → V
    Generates {λ, (C)V ,
    (C)V (C)V ,
    α γ
    V
    β
    C ε
    V
    δ
    C
    V V
    K.M. Yu [email protected] Phonological constituency and recursion 15/ 41

    View full-size slide

  39. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars II
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → λ, α → V γ, α → C β, β → V γ α → V α
    γ → λ, γ → V , γ → C δ, δ → V α → C β
    β → V α
    Generates {λ, (C)V , Generates {(C)V }∗
    (C)V (C)V , (C)V (C)V (C)V }
    α γ
    V
    β
    C ε
    V
    δ
    C
    V V
    α
    V
    β
    C
    V
    K.M. Yu [email protected] Phonological constituency and recursion 15/ 41

    View full-size slide

  40. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Two derivations of VCV
    With non-recursive grammar With recursive grammar
    α
    V γ
    C δ
    V
    λ
    α
    V β
    C α
    V α
    λ
    K.M. Yu [email protected] Phonological constituency and recursion 16/ 41

    View full-size slide

  41. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Two derivations of VCV
    With non-recursive grammar With recursive grammar
    α
    V γ
    C δ
    V
    λ
    α
    V β
    C α
    V α
    λ
    Non-recursive derivation can’t assign same category to
    different (C)V chunks in string. The fact that (C)V
    can be repeated appears accidental.
    K.M. Yu [email protected] Phonological constituency and recursion 16/ 41

    View full-size slide

  42. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars III
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → λ, α → V γ, α → C β, β → V γ α → V α
    γ → λ, γ → V , γ → C δ, δ → V α → C β
    → λ, → V η, → C ζ, η → V λ β → V α
    Generates {λ, Generates {(C)V }∗
    α γ
    V
    β
    C ε
    V
    δ
    C η
    V
    ζ
    C
    V V V
    α
    V
    β
    C
    V
    K.M. Yu [email protected] Phonological constituency and recursion 17/ 41

    View full-size slide

  43. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars III
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → λ, α → V γ, α → C β, β → V γ α → V α
    γ → λ, γ → V , γ → C δ, δ → V α → C β
    → λ, → V η, → C ζ, η → V λ β → V α
    Generates {λ, (C)V , Generates {(C)V }∗
    α γ
    V
    β
    C ε
    V
    δ
    C η
    V
    ζ
    C
    V V
    V
    α
    V
    β
    C
    V
    K.M. Yu [email protected] Phonological constituency and recursion 17/ 41

    View full-size slide

  44. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars III
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → λ, α → V γ, α → C β, β → V γ α → V α
    γ → λ, γ → V , γ → C δ, δ → V α → C β
    → λ, → V η, → C ζ, η → V λ β → V α
    Generates {λ, (C)V , Generates {(C)V }∗
    (C)V (C)V ,
    α γ
    V
    β
    C ε
    V
    δ
    C η
    V
    ζ
    C V
    V V
    α
    V
    β
    C
    V
    K.M. Yu [email protected] Phonological constituency and recursion 17/ 41

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  45. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in phonological grammars III
    (a) Non-recursive grammar (b) Recursive grammar
    α → λ α → λ
    α → λ, α → V γ, α → C β, β → V γ α → V α
    γ → λ, γ → V , γ → C δ, δ → V α → C β
    → λ, → V η, → C ζ, η → V λ β → V α
    Generates {λ, (C)V , Generates {(C)V }∗
    (C)V (C)V , (C)V (C)V (C)V }
    α γ
    V
    β
    C ε
    V
    δ
    C η
    V
    ζ
    C
    V V V
    α
    V
    β
    C
    V
    K.M. Yu [email protected] Phonological constituency and recursion 17/ 41

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  46. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Two derivations of VCVCV
    With non-recursive grammar With recursive grammar
    α
    V γ
    C δ
    V
    C ζ
    V η
    λ
    α
    V β
    C α
    V β
    C α
    V α
    λ
    K.M. Yu [email protected] Phonological constituency and recursion 18/ 41

    View full-size slide

  47. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Two derivations of VCVCV
    With non-recursive grammar With recursive grammar
    α
    V γ
    C δ
    V
    C ζ
    V η
    λ
    α
    V β
    C α
    V β
    C α
    V α
    λ
    Recursive grammar: restriction to (C)V chunks not an
    accident.
    K.M. Yu [email protected] Phonological constituency and recursion 18/ 41

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  48. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Strategic labelling doesn’t capture generalization
    With non-recursive grammar With recursive grammar
    α1
    V α2
    C β2
    V α3
    C β3
    V α4
    λ
    α
    V β
    C α
    V β
    C α
    V α
    λ
    α1 α2
    V
    β1
    C α3
    V
    β2
    C α4
    V
    β3
    C
    V V V
    α
    V
    β
    C
    V
    K.M. Yu [email protected] Phonological constituency and recursion 19/ 41

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  49. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in grammar is always an
    analytic choice
    α1 α2
    V
    β1
    C
    α3
    V
    β2
    C
    α4
    V
    β3
    C
    V V V
    α
    V
    β
    C
    V
    Humans are finite machines so recursion in human language
    is always bounded (in phonology and morphosyntax)
    We can always model bounded recursion without recursive
    operations
    K.M. Yu [email protected] Phonological constituency and recursion 20/ 41

    View full-size slide

  50. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursive operations in grammar is always an
    analytic choice
    α1 α2
    V
    β1
    C
    α3
    V
    β2
    C
    α4
    V
    β3
    C
    V V V
    α
    V
    β
    C
    V
    Humans are finite machines so recursion in human language
    is always bounded (in phonology and morphosyntax)
    We can always model bounded recursion without recursive
    operations
    Recursion is the analytic choice to make if we want to
    explain why repeatedly observed patterns are not accidental
    K.M. Yu [email protected] Phonological constituency and recursion 20/ 41

    View full-size slide

  51. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Interim summary: factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology.
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite)
    length. . .
    . . . regardless of what lexical elements and categories we
    define phonological grammars over
    K.M. Yu [email protected] Phonological constituency and recursion 21/ 41

    View full-size slide

  52. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Interim summary: factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology.
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite)
    length. . .
    . . . regardless of what lexical elements and categories we
    define phonological grammars over
    With recursion, we can write grammars that recognize that
    that a constituent shares properties with one of its parts
    K.M. Yu [email protected] Phonological constituency and recursion 21/ 41

    View full-size slide

  53. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Interim summary: factoring prosodic recursion
    1 Uncontroversial: Recursion is in phonology.
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite)
    length. . .
    . . . regardless of what lexical elements and categories we
    define phonological grammars over
    With recursion, we can write grammars that recognize that
    that a constituent shares properties with one of its parts
    Whether or not we have identified the right constituents is
    an independent, empirical issue
    K.M. Yu [email protected] Phonological constituency and recursion 21/ 41

    View full-size slide

  54. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Table of Contents
    1 Factoring prosodic recursion
    Recursion in phonology
    Prosodic constituents in phonology
    2 Computing with trees
    K.M. Yu [email protected] Phonological constituency and recursion 22/ 41

    View full-size slide

  55. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursion over the “wrong” constituents
    With recursion, we can write grammars that recognize that the
    properties of a constituent is similar to one of its parts. . .
    α
    V β
    C α
    V β
    C α
    V α
    λ
    α category: {[VCVCV], VC[VCV],
    VCVC[V] } are V-initial
    K.M. Yu [email protected] Phonological constituency and recursion 23/ 41

    View full-size slide

  56. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursion over the “wrong” constituents
    With recursion, we can write grammars that recognize that the
    properties of a constituent is similar to one of its parts. . .
    α
    V β
    C α
    V β
    C α
    V α
    λ
    α category: {[VCVCV], VC[VCV],
    VCVC[V] } are V-initial
    β category: { V[CVCV], VCV[CV] }
    are C-initial
    K.M. Yu [email protected] Phonological constituency and recursion 23/ 41

    View full-size slide

  57. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursion over the “wrong” constituents
    With recursion, we can write grammars that recognize that the
    properties of a constituent is similar to one of its parts. . .
    α
    V β
    C α
    V β
    C α
    V α
    λ
    α category: {[VCVCV], VC[VCV],
    VCVC[V] } are V-initial
    β category: { V[CVCV], VCV[CV] }
    are C-initial
    Neither category picks out
    [V][CV][CV] or [VC][VC][V]
    K.M. Yu [email protected] Phonological constituency and recursion 23/ 41

    View full-size slide

  58. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Recursion over the “wrong” constituents
    With recursion, we can write grammars that recognize that the
    properties of a constituent is similar to one of its parts. . .
    α
    V β
    C α
    V β
    C α
    V α
    λ
    α category: {[VCVCV], VC[VCV],
    VCVC[V] } are V-initial
    β category: { V[CVCV], VCV[CV] }
    are C-initial
    Neither category picks out
    [V][CV][CV] or [VC][VC][V]
    If we want syllables, the gram-
    mars we wrote won’t give us
    them: only suffixes!
    K.M. Yu [email protected] Phonological constituency and recursion 23/ 41

    View full-size slide

  59. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Constituents captured by recursive grammar
    α
    V β
    C α
    V β
    C α
    V α
    λ
    VCVC[V]
    K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

    View full-size slide

  60. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Constituents captured by recursive grammar
    α
    V β
    C α
    V β
    C α
    V α
    λ
    VCVC[V]
    VCV[C[V]]
    K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

    View full-size slide

  61. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Constituents captured by recursive grammar
    α
    V β
    C α
    V β
    C α
    V α
    λ
    VCVC[V]
    VCV[C[V]]
    VC[V[C[V]]]
    K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

    View full-size slide

  62. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Constituents captured by recursive grammar
    α
    V β
    C α
    V β
    C α
    V α
    λ
    VCVC[V]
    VCV[C[V]]
    VC[V[C[V]]]
    V[C[V[C[V]]]]
    K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

    View full-size slide

  63. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Constituents captured by recursive grammar
    α
    V β
    C α
    V β
    C α
    V α
    λ
    VCVC[V]
    VCV[C[V]]
    VC[V[C[V]]]
    V[C[V[C[V]]]]
    [V[C[V[C[V]]]]]
    K.M. Yu [email protected] Phonological constituency and recursion 24/ 41

    View full-size slide

  64. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Trees as additional data structures for phonology
    Simply put, if the representations are right, then the
    rules will follow. (McCarthy 1988: 84)
    K.M. Yu [email protected] Phonological constituency and recursion 25/ 41

    View full-size slide

  65. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Trees as additional data structures for phonology
    Simply put, if the representations are right, then the
    rules will follow. (McCarthy 1988: 84)
    With trees over categories as phonological data structures (in
    addition to strings):
    Prosodic constituents follow (with definition of prosodic
    categories)
    Behavior referencing prosodic constituents (including that a
    constituent shares properties with one of its parts) follows
    Distinctions between left- and right-branching phonological
    structures follow
    Behavior referencing (non-) maximal/minimal projections in
    phonological trees follows
    K.M. Yu [email protected] Phonological constituency and recursion 25/ 41

    View full-size slide

  66. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Trees as a data structure is always an analytic choice
    Modeling (recursion over) prosodic constituents using
    trees rather than strings is always an analytic choice.
    Humans are finite machines so recursion in human language
    is always bounded (in phonology and morphosyntax)
    We can always model bounded recursion over constituents
    without recursive operations by marking up strings with
    boundary symbols (and this is commonly done in natural
    language processing)
    K.M. Yu [email protected] Phonological constituency and recursion 26/ 41

    View full-size slide

  67. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Trees as a data structure is always an analytic choice
    Modeling (recursion over) prosodic constituents using
    trees rather than strings is always an analytic choice.
    Humans are finite machines so recursion in human language
    is always bounded (in phonology and morphosyntax)
    We can always model bounded recursion over constituents
    without recursive operations by marking up strings with
    boundary symbols (and this is commonly done in natural
    language processing)
    Trees are the analytic choice to make if we want to explain
    why repeatedly observed patterns conditioned on different
    natural properties of trees are not accidental
    K.M. Yu [email protected] Phonological constituency and recursion 26/ 41

    View full-size slide

  68. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Prosodic constituents with string markup
    Yu (2019): computation of Samoan prosodic and syntax-prosody
    interface constraints implemented prosodic constituents with
    string markup
    K.M. Yu [email protected] Phonological constituency and recursion 27/ 41

    View full-size slide

  69. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Prosodic constituents with string markup
    Yu (2019): computation of Samoan prosodic and syntax-prosody
    interface constraints implemented prosodic constituents with
    string markup
    K.M. Yu [email protected] Phonological constituency and recursion 27/ 41

    View full-size slide

  70. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Prosodic tree candidates
    K.M. Yu [email protected] Phonological constituency and recursion 28/ 41

    View full-size slide

  71. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Prosodic tree candidates as strings
    +-U[L,na]+ZYX<{U[L,la](P[L,la]W[L,ga])}+U[L,e]>+U[L,le]x+X<{U[L,ma](P[L,li]W[L,ni])}+U[L,hi]>+U[L,le]xy+{U[L,
    +-ZU[L,na]+YX<{U[L,la](P[L,la]W[L,ga])}+U[L,e]>+U[L,le]x+X<{U[L,ma](P[L,li]W[L,ni])}+U[L,hi]>+U[L,le]xyz+{U[L
    K.M. Yu [email protected] Phonological constituency and recursion 29/ 41

    View full-size slide

  72. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Prosodic tree candidates as strings
    +-U[L,na]+ZYX<{U[L,la](P[L,la]W[L,ga])}+U[L,e]>+U[L,le]x+X<{U[L,ma](P[L,li]W[L,ni])}+U[L,hi]>+U[L,le]xy+{U[L,
    +-ZU[L,na]+YX<{U[L,la](P[L,la]W[L,ga])}+U[L,e]>+U[L,le]x+X<{U[L,ma](P[L,li]W[L,ni])}+U[L,hi]>+U[L,le]xyz+{U[L
    Modeling (recursion over) prosodic constituents using
    strings makes the constituents appear accidental.
    K.M. Yu [email protected] Phonological constituency and recursion 29/ 41

    View full-size slide

  73. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Putting it together: prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite) length
    With recursion, we can write grammars that recognize that
    a constituent shares properties with one of its parts
    K.M. Yu [email protected] Phonological constituency and recursion 30/ 41

    View full-size slide

  74. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Putting it together: prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite) length
    With recursion, we can write grammars that recognize that
    a constituent shares properties with one of its parts
    2 Controversial but widely assumed: Phonological grammars
    refer to constituents
    There are phonological patterns defined over trees
    K.M. Yu [email protected] Phonological constituency and recursion 30/ 41

    View full-size slide

  75. Factoring prosodic recursion
    Computing with trees
    Recursion in phonology
    Prosodic constituents in phonology
    Putting it together: prosodic recursion
    1 Uncontroversial: Recursion is in phonology
    Without recursive operations, phonological knowledge
    cannot be generalized to strings of arbitrary (finite) length
    With recursion, we can write grammars that recognize that
    a constituent shares properties with one of its parts
    2 Controversial but widely assumed: Phonological grammars
    refer to constituents
    There are phonological patterns defined over trees
    Analytic choices of recursive operations over trees as
    data structures make empirical generalizations non-
    accidental.
    K.M. Yu [email protected] Phonological constituency and recursion 30/ 41

    View full-size slide

  76. Factoring prosodic recursion
    Computing with trees
    Table of Contents
    1 Factoring prosodic recursion
    Recursion in phonology
    Prosodic constituents in phonology
    2 Computing with trees
    K.M. Yu [email protected] Phonological constituency and recursion 31/ 41

    View full-size slide

  77. Factoring prosodic recursion
    Computing with trees
    Computing with strings for finitely bounded
    recursion
    So long as there is a finite bound on recursion, we have the
    choice of computing on strings to approximate computing on
    trees
    K.M. Yu [email protected] Phonological constituency and recursion 32/ 41

    View full-size slide

  78. Factoring prosodic recursion
    Computing with trees
    Computing with strings for finitely bounded
    recursion
    So long as there is a finite bound on recursion, we have the
    choice of computing on strings to approximate computing on
    trees
    But we have to count each additional layer and it becomes
    an accident if a subpart of a constituent shares properties
    with the constituent
    K.M. Yu [email protected] Phonological constituency and recursion 32/ 41

    View full-size slide

  79. Factoring prosodic recursion
    Computing with trees
    Computing with strings for finitely bounded
    recursion
    So long as there is a finite bound on recursion, we have the
    choice of computing on strings to approximate computing on
    trees
    But we have to count each additional layer and it becomes
    an accident if a subpart of a constituent shares properties
    with the constituent
    What about a potential blowup in complexity from
    computing over trees?
    K.M. Yu [email protected] Phonological constituency and recursion 32/ 41

    View full-size slide

  80. Factoring prosodic recursion
    Computing with trees
    Computing operations on trees
    Two or more, use a for.
    Operations on trees are computed using tree transducers
    that transduce input trees into output trees
    Many tree transducers can be computed in linear time in the
    size of the tree
    Case study: syntax-prosody mapping in Japanese nominals
    (Ito and Mester 2013)
    K.M. Yu [email protected] Phonological constituency and recursion 33/ 41

    View full-size slide

  81. Factoring prosodic recursion
    Computing with trees
    TATA tree transducer reference
    K.M. Yu [email protected] Phonological constituency and recursion 34/ 41

    View full-size slide

  82. Factoring prosodic recursion
    Computing with trees
    Syntax-prosody mapping in Japanese nominals
    [ [NPposs
    ] NP ] structures (Ito and Mester 2013)
    N-gen N conj ‘and Hiroshima/Okayama fish/eggs’
    A = accented ω, U = unaccented ω
    [[U]U] [[hiroshima no ] sakana to] (ϕ
    U U)
    [[A]A] [[okayama no ] tamago to] (ϕ
    U A)
    [[U]A] [[hiroshima no ] tamago to] (ϕ

    A) (ϕ
    A))
    [[A]U] [[okayama no ] sakana to] (ϕ

    A) (ϕ
    U))
    K.M. Yu [email protected] Phonological constituency and recursion 35/ 41

    View full-size slide

  83. Factoring prosodic recursion
    Computing with trees
    Analysis: interleaved phonological and interface
    constraints
    Task: given an input like U U, determine the prosodic structure by
    computing the violations incurred by the following constraints
    Accent-as-Head, Lapse(ϕ) prosody
    Minimal Binarity(ϕ) prosody
    Match XP to ϕ syntax-prosody interface
    NoRecursion prosody
    K.M. Yu [email protected] Phonological constituency and recursion 36/ 41

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  84. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    conceptual
    DP
    NP
    NPposs
    Nposs
    okayama-no
    N
    sakana-to
    D
    K.M. Yu [email protected] Phonological constituency and recursion 37/ 41

    View full-size slide

  85. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    conceptual
    DP/NP
    NPposs
    Nposs
    okayama-no
    N
    sakana-to
    K.M. Yu [email protected] Phonological constituency and recursion 37/ 41

    View full-size slide

  86. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    conceptual
    ϕ
    ϕ
    ω
    okayama-no
    ω
    sakana-to
    K.M. Yu [email protected] Phonological constituency and recursion 37/ 41

    View full-size slide

  87. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  88. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  89. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  90. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  91. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  92. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  93. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  94. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  95. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  96. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  97. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  98. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  99. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  100. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  101. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  102. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  103. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  104. Factoring prosodic recursion
    Computing with trees
    Computation of syntax-prosody mapping over trees:
    implementation
    Idea: transduce from syntactic tree to candidate prosodic trees,
    with some transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 38/ 41

    View full-size slide

  105. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Idea: transduce from input candidate prosodic tree to output
    candidate prosodic tree (identity transduction), but with some
    transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

    View full-size slide

  106. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Idea: transduce from input candidate prosodic tree to output
    candidate prosodic tree (identity transduction), but with some
    transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

    View full-size slide

  107. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Idea: transduce from input candidate prosodic tree to output
    candidate prosodic tree (identity transduction), but with some
    transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

    View full-size slide

  108. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Idea: transduce from input candidate prosodic tree to output
    candidate prosodic tree (identity transduction), but with some
    transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

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  109. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Idea: transduce from input candidate prosodic tree to output
    candidate prosodic tree (identity transduction), but with some
    transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

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  110. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Idea: transduce from input candidate prosodic tree to output
    candidate prosodic tree (identity transduction), but with some
    transduction rules incurring violations
    K.M. Yu [email protected] Phonological constituency and recursion 39/ 41

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  111. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Accent-as-Head, Minimal Binarity(ϕ), NoRecursion
    K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

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  112. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Accent-as-Head, Minimal Binarity(ϕ), NoRecursion
    K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

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  113. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Accent-as-Head, Minimal Binarity(ϕ), NoRecursion
    K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

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  114. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Accent-as-Head, Minimal Binarity(ϕ), NoRecursion
    K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

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  115. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Accent-as-Head, Minimal Binarity(ϕ), NoRecursion
    K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

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  116. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Accent-as-Head, Minimal Binarity(ϕ), NoRecursion
    K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

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  117. Factoring prosodic recursion
    Computing with trees
    Computation of phonological constraints over trees
    Accent-as-Head, Minimal Binarity(ϕ), NoRecursion
    K.M. Yu [email protected] Phonological constituency and recursion 40/ 41

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  118. Factoring prosodic recursion
    Computing with trees
    Conclusion
    Prosodic recursion in human language is always finitely
    bounded and can always be modeled over strings
    K.M. Yu [email protected] Phonological constituency and recursion 41/ 41

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  119. Factoring prosodic recursion
    Computing with trees
    Conclusion
    Prosodic recursion in human language is always finitely
    bounded and can always be modeled over strings
    Analytic choices of recursive operations over trees as data
    structures make empirical generalizations non-accidental
    K.M. Yu [email protected] Phonological constituency and recursion 41/ 41

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  120. Factoring prosodic recursion
    Computing with trees
    Conclusion
    Prosodic recursion in human language is always finitely
    bounded and can always be modeled over strings
    Analytic choices of recursive operations over trees as data
    structures make empirical generalizations non-accidental
    Computation of syntax-prosody interface and phonological
    constraints over trees is feasible and may lead to new insights
    K.M. Yu [email protected] Phonological constituency and recursion 41/ 41

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