Harmonic Grammar growing into Optimality Theory Maturation as the - - PowerPoint PPT Presentation

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Harmonic Grammar growing into Optimality Theory Maturation as the - - PowerPoint PPT Presentation

OT and HG From HG to OT Cluster simplification Sum: learning & maturation Harmonic Grammar growing into Optimality Theory Maturation as the strict domination limit (or vice-versa) including joint work with Klaas Seinhorst (University of


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SLIDE 1

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Harmonic Grammar growing into Optimality Theory

Maturation as the strict domination limit (or vice-versa) including joint work with Klaas Seinhorst (University of Amsterdam) Tamás Biró

ELTE Eötvös Loránd University

BLINC @ ELTE, June 2, 2017

Tamás Biró Harmonic Grammar growing into Optimality Theory 1

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SLIDE 2

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Learning and maturation

A standard idea in contemporary linguistics: Children learning a language: setting parameters or re-ranking constraints. Hence / because: children speak a typologically different language that resides in the typology of adult languages. Is it really so? Goal of this talk: to show how maturation (as opposed to learning) can be included into OT.

Tamás Biró Harmonic Grammar growing into Optimality Theory 2

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SLIDE 3

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Learning and maturation

A standard idea in contemporary linguistics: Children learning a language: setting parameters or re-ranking constraints. Hence / because: children speak a typologically different language that resides in the typology of adult languages. Is it really so? Goal of this talk: to show how maturation (as opposed to learning) can be included into OT.

Tamás Biró Harmonic Grammar growing into Optimality Theory 2

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SLIDE 4

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Overview

1

Optimality Theory and Harmonic Grammar

2

From HG to OT: the strict domination limit

3

Consonant cluster simplification in Dutch

4

Summary: learning and maturation

Tamás Biró Harmonic Grammar growing into Optimality Theory 3

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SLIDE 5

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Overview

1

Optimality Theory and Harmonic Grammar

2

From HG to OT: the strict domination limit

3

Consonant cluster simplification in Dutch

4

Summary: learning and maturation

Tamás Biró Harmonic Grammar growing into Optimality Theory 4

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SLIDE 6

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Optimality Theory in a broad sense

Underlying representation → candidate set. Surface representation = optimal element of candidate set. Optimality: most harmonic. What is “harmony”?

Tamás Biró Harmonic Grammar growing into Optimality Theory 5

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SLIDE 7

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Optimality Theory in a narrow sense

Gen(σσσσ) = {[suuu], [usuu], [uusu], [uuus]}. /σσσσ/ EARLY LATE NONFINAL

[s u u u ] 3 [u s u u ] 1! 2 [u u s u ] 2! 1 [u u u s ] 3! 1 SF(σσσσ) =[suuu].

Tamás Biró Harmonic Grammar growing into Optimality Theory 6

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SLIDE 8

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Optimality Theory in a narrow sense

Gen(σσσσ) = {[suuu], [usuu], [uusu], [uuus]}. /σσσσ/ NONFINAL LATE EARLY [s u u u] 3! [u s u u] 2! 1

[u u s u] 1 2 [u u u s] 1! 3 SF(σσσσ) =[uusu].

Tamás Biró Harmonic Grammar growing into Optimality Theory 7

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SLIDE 9

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Optimality Theory in a narrow sense

Gen(σσσσ) = {[suuu], [usuu], [uusu], [uuus]}. /σσσσ/ NONFINAL LATE EARLY

[u u s u] 1 2 [u s u u] 2 1 [s u u u] 3 [u u u s] 1 3 Harmony in terms of lexicographic order: [uusu] ≻ [usuu] ≻ [suuu] ≻ [uuus]. Hence, SF(σσσσ) =[uusu].

Tamás Biró Harmonic Grammar growing into Optimality Theory 8

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SLIDE 10

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Harmonic Grammar, symbolic approach

Gen(σσσσ) = {[suuu], [usuu], [uusu], [uuus]}. Constraint Ck is assigned weight wk. Harmony H(A) of cand. A: /σσσσ/ NONFINAL LATE EARLY −H(A) = wk = 9 3 1

  • k wk · Ck[A]

[u u s u] 1 2

9 · 0 + 3 · 1 + 1 · 2 =

5 [u s u u] 2 1

9 · 0 + 3 · 2 + 1 · 1 =

7 [s u u u] 3

9 · 0 + 3 · 3 + 1 · 0 =

9 [u u u s] 1 3

9 · 1 + 3 · 0 + 1 · 3 = 12

By comparing the integer/real numbers in H: [uusu] ≻ [usuu] ≻ [suuu] ≻ [uuus]. Hence, SF(σσσσ) =[uusu].

Tamás Biró Harmonic Grammar growing into Optimality Theory 9

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SLIDE 11

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Harmonic Grammar, connectionist approach

si: activation of node i. Wi,j: connection strength between nodes i and j. Boltzmann machine: The “energy” (negative harmony) of the network: −H(A) =

N

  • i,j=1

si · Wi,j · sj Input nodes clamped (fixed). Output nodes read after optimization of H(A).

Tamás Biró Harmonic Grammar growing into Optimality Theory 10

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SLIDE 12

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Harmonic Grammar, connectionist approach

Constraint Ck is a set of W k

i,j

partial connection strengths. Constraint Ck has weight wk: Wi,j =

n

  • k=1

wk · W k

i,j

The “energy” (negative harmony) of the network: −H(A) =

N

  • i,j=1

si · Wi,j · sj = =

N

  • i,j=1

si ·

n

  • k=1

wk · W k

i,j · sj = n

  • k=1

wk ·

N

  • i,j=1

si · W k

i,j · sj = n

  • k=1

wk · Ck[A].

Tamás Biró Harmonic Grammar growing into Optimality Theory 11

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SLIDE 13

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Harmonic Grammar, connectionist approach

Constraint Ck is a set of W k

i,j

partial connection strengths. Constraint Ck has weight wk: Wi,j =

n

  • k=1

wk · W k

i,j

The “energy” (negative harmony) of the network: −H(A) =

N

  • i,j=1

si · Wi,j · sj = =

N

  • i,j=1

si ·

n

  • k=1

wk · W k

i,j · sj = n

  • k=1

wk ·

N

  • i,j=1

si · W k

i,j · sj = n

  • k=1

wk · Ck[A].

Tamás Biró Harmonic Grammar growing into Optimality Theory 11

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SLIDE 14

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Summary thus far:

We have three approaches: Optimality Theory: symbolic,

  • ptimization w.r.t. lexicographic order.

Symbolic Harmonic Grammar:

  • ptimization w.r.t. ≥ relation among real numbers.

Connectionist Harmonic Grammar:

  • ptimization w.r.t. ≥ relation among real numbers.

Typological predictions? Learnability? Cognitive plausibility? Question: how to get OT in a “connectionist brain”?

(A major issue for Smolensky’s Integrated Connectionist/Symbolic Architecture.)

Tamás Biró Harmonic Grammar growing into Optimality Theory 12

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SLIDE 15

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Summary thus far:

We have three approaches: Optimality Theory: symbolic,

  • ptimization w.r.t. lexicographic order.

Symbolic Harmonic Grammar:

  • ptimization w.r.t. ≥ relation among real numbers.

Connectionist Harmonic Grammar:

  • ptimization w.r.t. ≥ relation among real numbers.

Typological predictions? Learnability? Cognitive plausibility? Question: how to get OT in a “connectionist brain”?

(A major issue for Smolensky’s Integrated Connectionist/Symbolic Architecture.)

Tamás Biró Harmonic Grammar growing into Optimality Theory 12

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SLIDE 16

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Summary thus far:

We have three approaches: Optimality Theory: symbolic,

  • ptimization w.r.t. lexicographic order.

Symbolic Harmonic Grammar:

  • ptimization w.r.t. ≥ relation among real numbers.

Connectionist Harmonic Grammar:

  • ptimization w.r.t. ≥ relation among real numbers.

Typological predictions? Learnability? Cognitive plausibility? Question: how to get OT in a “connectionist brain”?

(A major issue for Smolensky’s Integrated Connectionist/Symbolic Architecture.)

Tamás Biró Harmonic Grammar growing into Optimality Theory 12

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SLIDE 17

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Overview

1

Optimality Theory and Harmonic Grammar

2

From HG to OT: the strict domination limit

3

Consonant cluster simplification in Dutch

4

Summary: learning and maturation

Tamás Biró Harmonic Grammar growing into Optimality Theory 13

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SLIDE 18

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Exponential Harmonic Grammar, or q-HG

Optimality Theory minimizes a vector of violations:

H(A) = Cn Cn−1 . . . Ci . . . C1 rn(= n) rn−1 ri r1(= 1) C1[A] C2[A] . . . Ci[A] . . . Cn[A]

Harmonic Grammar minimizes a weighted sum of violations: H(A) =

n

  • i=1

wi · Ci[A]. “Standard” HG: weights wi = ranks ri. Exponential HG: weights are ranks exponentiated, fixed base

(e = 2.7182 . . .)

wi = eri. q-HG: weights are ranks exponentiated, with (variable) base q wi = qri.

Tamás Biró Harmonic Grammar growing into Optimality Theory 14

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SLIDE 19

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Exponential Harmonic Grammar, or q-HG

Optimality Theory minimizes a vector of violations:

H(A) = Cn Cn−1 . . . Ci . . . C1 rn(= n) rn−1 ri r1(= 1) C1[A] C2[A] . . . Ci[A] . . . Cn[A]

Harmonic Grammar minimizes a weighted sum of violations: H(A) =

n

  • i=1

wi · Ci[A]. “Standard” HG: weights wi = ranks ri. Exponential HG: weights are ranks exponentiated, fixed base

(e = 2.7182 . . .)

wi = eri. q-HG: weights are ranks exponentiated, with (variable) base q wi = qri.

Tamás Biró Harmonic Grammar growing into Optimality Theory 14

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SLIDE 20

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Exponential Harmonic Grammar, or q-HG

Optimality Theory minimizes a vector of violations:

H(A) = Cn Cn−1 . . . Ci . . . C1 rn(= n) rn−1 ri r1(= 1) C1[A] C2[A] . . . Ci[A] . . . Cn[A]

Harmonic Grammar minimizes a weighted sum of violations: H(A) =

n

  • i=1

wi · Ci[A]. “Standard” HG: weights wi = ranks ri. Exponential HG: weights are ranks exponentiated, fixed base

(e = 2.7182 . . .)

wi = eri. q-HG: weights are ranks exponentiated, with (variable) base q wi = qri.

Tamás Biró Harmonic Grammar growing into Optimality Theory 14

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SLIDE 21

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Exponential Harmonic Grammar, or q-HG

Optimality Theory minimizes a vector of violations:

H(A) = Cn Cn−1 . . . Ci . . . C1 rn(= n) rn−1 ri r1(= 1) C1[A] C2[A] . . . Ci[A] . . . Cn[A]

Harmonic Grammar minimizes a weighted sum of violations: H(A) =

n

  • i=1

wi · Ci[A]. “Standard” HG: weights wi = ranks ri. Exponential HG: weights are ranks exponentiated, fixed base

(e = 2.7182 . . .)

wi = eri. q-HG: weights are ranks exponentiated, with (variable) base q wi = qri.

Tamás Biró Harmonic Grammar growing into Optimality Theory 14

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SLIDE 22

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Strict domination in OT is q-HG in the q → +∞ limit

In q-HG: H(A) = qrn · Cn[A] + . . . + qri · Ci[A] + . . . + qr1 · C1[A] Or simply (if ri = i − 1): H(A) = qn−1 · Cn[A] + . . . + q2 · Ci[A] + q1 · Ci[A] + q0 · C1[A] H(A) = 2n−1 · Cn[A] + . . . + 4 · Ci[A] + 2 · Ci[A] + 1 · C1[A] H(A) = 3n−1 · Cn[A] + . . . + 9 · Ci[A] + 3 · Ci[A] + 1 · C1[A] H(A) = 10n−1 · Cn[A] + . . . + 100 · Ci[A] + 10 · Ci[A] + 1 · C1[A] Main difference between OT and HG is strict domination. If q grows large, q-HG turns into OT, because. . .

Tamás Biró Harmonic Grammar growing into Optimality Theory 15

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SLIDE 23

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Strict domination in OT is q-HG in the q → +∞ limit

In q-HG: H(A) = qrn · Cn[A] + . . . + qri · Ci[A] + . . . + qr1 · C1[A] Or simply (if ri = i − 1): H(A) = qn−1 · Cn[A] + . . . + q2 · Ci[A] + q1 · Ci[A] + q0 · C1[A] H(A) = 2n−1 · Cn[A] + . . . + 4 · Ci[A] + 2 · Ci[A] + 1 · C1[A] H(A) = 3n−1 · Cn[A] + . . . + 9 · Ci[A] + 3 · Ci[A] + 1 · C1[A] H(A) = 10n−1 · Cn[A] + . . . + 100 · Ci[A] + 10 · Ci[A] + 1 · C1[A] Main difference between OT and HG is strict domination. If q grows large, q-HG turns into OT, because. . .

Tamás Biró Harmonic Grammar growing into Optimality Theory 15

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SLIDE 24

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Strict domination in OT is q-HG in the q → +∞ limit

1.5-HG has ganging-up cumulativity: C3 C2 C1 H w = 2.25 1.5 1

A1 1 2.25 A2 1 1 2.5 1.5-HG also has counting cumulativity: C3 C2 C1 H wi = 2.25 1.5 1

A1 1 2.25 A3 2 3

(Cf. Jäger and Rosenbach 2006)

Tamás Biró Harmonic Grammar growing into Optimality Theory 16

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SLIDE 25

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Strict domination in OT is q-HG in the q → +∞ limit

But OT does not have ganging-up cumulativity: C3 C2 C1 A1 *

A2 * * OT does not have counting cumulativity either: C3 C2 C1 A1 *

A3 **

(Regarding Stochastic OT, cf. Jäger and Rosenbach 2006)

Tamás Biró Harmonic Grammar growing into Optimality Theory 17

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SLIDE 26

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Strict domination in OT is q-HG in the q → +∞ limit

3-HG does not have ganging-up cumulativity: C3 C2 C1 H 9 3 1 A1 1 9

A2 1 1 4 3-HG does not have counting cumulativity, either: C3 C2 C1 H 9 3 1 A1 1 9

A3 2 6

(Cf. Jäger and Rosenbach 2006)

Tamás Biró Harmonic Grammar growing into Optimality Theory 18

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SLIDE 27

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Strict domination in OT is q-HG in the q → +∞ limit

As we have known it since Prince and Smolensky 1993, strict domination in OT can be reproduced using q-HG with sufficiently large q: q − 1 ≥ Ck[A] for all k and A.

Tamás Biró Harmonic Grammar growing into Optimality Theory 19

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SLIDE 28

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Overview

1

Optimality Theory and Harmonic Grammar

2

From HG to OT: the strict domination limit

3

Consonant cluster simplification in Dutch

4

Summary: learning and maturation

Tamás Biró Harmonic Grammar growing into Optimality Theory 20

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SLIDE 29

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Word initial consonant cluster simplification in Dutch

Klaas Seinhorst collecting data from CHILDES (Laura):

  • Cf. Becker and Tessier (2011)

Tamás Biró Harmonic Grammar growing into Optimality Theory 21

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OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Word initial consonant cluster simplification in Dutch

Using logistic regression or probit regression: cluster simplifies lower upper to boundary boundary (age in days) (age in days) kl- k- 894.32 1010.55 sl- l- 943.82 1028.68 st- t- 962.60 1076.23 zw- z- 1344.24 1551.39

Table: 95% confidence intervals of the locations of the inflection points.

Differences among kl, sl and st: statistically not significant. But differences between zw and each of the three others: p < 10−11!

Tamás Biró Harmonic Grammar growing into Optimality Theory 22

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OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Word initial consonant cluster simplification: OT

The traditional account in OT: learning = constraint re-ranking. Before learning: Markedness ≫ Faithfulness /klEin/ NOCOMPLEX FAITHF *[l] *[k] ONSET [klEin] *! * *

[kEin] * * [lEin] * *! After learning: Faithfulness ≫ Markedness /klEin/ FAITHF NOCOMPLEX *[l] *[k] ONSET

[klEin] * * * [kEin] *! * [lEin] *! *

Tamás Biró Harmonic Grammar growing into Optimality Theory 23

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SLIDE 32

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Word initial consonant cluster simplification: OT

Questions to the traditional account: Child is exposed to huge amount of evidence way before correct production. Why no learning? If only NoComplexOnset and Faithf are involved, why significant difference for zw onset? If cluster-specific constraints: factorial typology predicted.

Tamás Biró Harmonic Grammar growing into Optimality Theory 24

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SLIDE 33

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Word initial consonant cluster simplification: q-HG

An alternative approach: Child has acquired FAITHF ≫ NOCOMPLEXONSET much earlier, probably already at pre-linguistic age. Relative ranks *[w] ≫ *[s] ≫ *[l] ≫ *[z] ≫ *[k] ≫ *[t] motivated by natural phonology (? feedback appreciated!). No more ranking needed. For instance, Ci FAITHF NOCOMPL *[w] *[s] *[l] *[z] *[k] *[t] ONSET ri 8 7 6 5 4 3 2 1 (1.1)ri 2.14 1.95 1.77 1.61 1.46 1.33 1.21 1.1 2ri 256 128 64 32 16 8 4 2

Tamás Biró Harmonic Grammar growing into Optimality Theory 25

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SLIDE 34

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Word initial consonant cluster simplification: q-HG

Before maturation: small q, e.g., q = 1.1 (NB: Faithfulness ≫ Markedness!)

/klEin/ FAITHF NOCOMPLONS *[l] *[k] H wi = 2.14 1.95 1.46 1.21 [klEin] * * * 4.62

[kEin] *! * 3.35 [lEin] *! * 3.60

After maturation: large q, e.g., q = 2

/klEin/ FAITHF NOCOMPLONS *[l] *[k] H wi = 256 128 16 4

[klEin] * * * 148 [kEin] *! * 260 [lEin] *! * 272

Tamás Biró Harmonic Grammar growing into Optimality Theory 26

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SLIDE 35

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Word initial consonant cluster simplification: q-HG

q is a function of age, e.g. age ∝ log(q). [xy] produced by q-HG, if q is s.t. qc + qx + qy = qf + qy or larger: /xy/ FAITHF *COMPLONS *[x] *[y] H for ri = f c x y given q wi = qf qc qx qy [xy] 1 1 1 qc + qx + qy [y] 1 1 qf + qy [x] 1 1 qf + qx Critical age function of deleted segment [x], but not remaining [y]. If f > c, x > y, then: step function predicted. To get S-shaped curve, use Stochastic OT.

Tamás Biró Harmonic Grammar growing into Optimality Theory 27

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SLIDE 36

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Word initial consonant clusters: stochastic q-HG

Tamás Biró Harmonic Grammar growing into Optimality Theory 28

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SLIDE 37

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Overview

1

Optimality Theory and Harmonic Grammar

2

From HG to OT: the strict domination limit

3

Consonant cluster simplification in Dutch

4

Summary: learning and maturation

Tamás Biró Harmonic Grammar growing into Optimality Theory 29

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SLIDE 38

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Learning vs. Maturation?

Learning: Knowledge acquired from surrounding linguistic data Source of cross-linguistic variation Features in the child’s language shared by other adult languages Maturation: Skills emerging due to general development Universal developmental paths Features in child’s language not appearing in any adult language

Tamás Biró Harmonic Grammar growing into Optimality Theory 30

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SLIDE 39

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Learning vs. Maturation?

Learning: Knowledge acquired from surrounding linguistic data Source of cross-linguistic variation Features in the child’s language shared by other adult languages Maturation: Skills emerging due to general development Universal developmental paths Features in child’s language not appearing in any adult language

Tamás Biró Harmonic Grammar growing into Optimality Theory 30

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SLIDE 40

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Learning vs. Maturation?

Learning from surrounding linguistic data: Features in the child’s language shared by other adult languages

Child learning English produces “Italian-like” pro-drop → “Pro-drop” parameter not yet switched. Child learning English deleting codas → *CODA markedness not yet demoted below FAITHFULNESS.

Maturation due to general development: Features in child’s language not appearing in any adult language

Long distance place agreement in consonant harmony? Erroneous pronoun resolution?

Tamás Biró Harmonic Grammar growing into Optimality Theory 31

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SLIDE 41

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Learning vs. Maturation?

Learning from surrounding linguistic data: Features in the child’s language shared by other adult languages

Child learning English produces “Italian-like” pro-drop → “Pro-drop” parameter not yet switched. Child learning English deleting codas → *CODA markedness not yet demoted below FAITHFULNESS.

Maturation due to general development: Features in child’s language not appearing in any adult language

Long distance place agreement in consonant harmony? Erroneous pronoun resolution?

Tamás Biró Harmonic Grammar growing into Optimality Theory 31

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SLIDE 42

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Learning vs. Maturation!

Modelling learning and modelling maturation: shouldn’t they be different? Learning from surrounding linguistic data: Setting parameters Re-ranking constraints Maturation due to general development: Restrictions on working memory, speed of mental computation. . . Varying q in q-HG?

Tamás Biró Harmonic Grammar growing into Optimality Theory 32

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SLIDE 43

OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Learning vs. Maturation!

Modelling learning and modelling maturation: shouldn’t they be different? Learning from surrounding linguistic data: Setting parameters Re-ranking constraints Maturation due to general development: Restrictions on working memory, speed of mental computation. . . Varying q in q-HG?

Tamás Biró Harmonic Grammar growing into Optimality Theory 32

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OT and HG From HG to OT Cluster simplification Sum: learning & maturation

Thank you for your attention!

Tamás Biró: tamas[dot]biro[at]btk[dot]elte[dot]hu http://birot.web.elte.hu/

This research was supported by a Veni Grant (project number 275-89-004)

  • ffered by the Netherlands Organisation for Scientific Research (NWO),

as well as by a Marie Curie FP7 Integration Grant (no. PCIG14-GA-2013-631599, “MeMoLI”), 7th EU Framework Programme.

Tamás Biró Harmonic Grammar growing into Optimality Theory 33