harmonic grammar growing into optimality theory

OT and HG From HG to OT Cluster simplification Sum learning amp maturation

Harmonic Grammar growing into Optimality TheoryMaturation as the strict domination limit (or vice-versa)

including joint work with Klaas Seinhorst (University of Amsterdam)

Tamaacutes Biroacute

ELTE Eoumltvoumls Loraacutend University

BLINC ELTE June 2 2017

Tamaacutes Biroacute Harmonic Grammar growing into Optimality Theory 1


Learning and maturation

A standard idea in contemporary linguisticsChildren learning a languagesetting parameters or re-ranking constraintsHence because children speak a typologically different languagethat 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





Is it really so




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



Overview







Optimality Theory in a broad sense

Underlying representation 7rarr candidate setSurface representation = optimal element of candidate setOptimality most harmonic What is ldquoharmonyrdquo



Optimality Theory in a narrow sense

Gen(σσσσ) = [suuu] [usuu] [uusu] [uuus]

σσσσ EARLY LATE NONFINAL

+ [s u u u ] 0 3 0[u s u u ] 1 2 0[u u s u ] 2 1 0[u u u s ] 3 0 1

SF(σσσσ) =[suuu]





σσσσ NONFINAL LATE EARLY

[s u u u] 0 3 0[u s u u] 0 2 1

+ [u u s u] 0 1 2[u u u s] 1 0 3

SF(σσσσ) =[uusu]






+ [u u s u] 0 1 2[u s u u] 0 2 1[s u u u] 0 3 0[u u u s] 1 0 3

Harmony in terms of lexicographic order[uusu] [usuu] [suuu] [uuus] Hence SF(σσσσ) =[uusu]



Harmonic Grammar symbolic approach


Constraint Ck is assigned weight wk Harmony H(A) of cand A

σσσσ NONFINAL LATE EARLY minusH(A) =wk = 9 3 1

sumk wk middot Ck [A]

+ [u u s u] 0 1 2 9 middot 0 + 3 middot 1 + 1 middot 2 = 5[u s u u] 0 2 1 9 middot 0 + 3 middot 2 + 1 middot 1 = 7[s u u u] 0 3 0 9 middot 0 + 3 middot 3 + 1 middot 0 = 9[u u u s] 1 0 3 9 middot 1 + 3 middot 0 + 1 middot 3 = 12

By comparing the integerreal numbers in H[uusu] [usuu] [suuu] [uuus] Hence SF(σσσσ) =[uusu]



Harmonic Grammar connectionist approach

si activation of node i Wij connection strengthbetween nodes i and j

Boltzmann machine

The ldquoenergyrdquo (negativeharmony) of the network

minusH(A) =Nsum

ij=1

si middotWij middot sj

Input nodes clamped (fixed)

Output nodes readafter optimization of H(A)




Constraint Ck is a set of W kij

partial connection strengths

Constraint Ck has weight wk

Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1

si middotWij middot sj =

=Nsum

ij=1

si middotnsum

k=1

wk middotW kij middot sj =

nsumk=1

wk middotNsum

ij=1

si middotW kij middot sj =

nsumk=1

wk middot Ck [A]







Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far

We have three approaches

Optimality Theory symbolicoptimization wrt lexicographic order

Symbolic Harmonic Grammaroptimization wrt ge relation among real numbers

Connectionist Harmonic Grammaroptimization wrt ge relation among real numbers

Typological predictions Learnability Cognitive plausibility

Question how to get OT in a ldquoconnectionist brainrdquo(A major issue for Smolenskyrsquos Integrated ConnectionistSymbolic Architecture)



Summary thus far









Summary thus far









Overview







Exponential Harmonic Grammar or q-HG

Optimality Theory minimizes a vector of violations

H(A) =

Cn Cnminus1 Ci C1rn(= n) rnminus1 ri r1(= 1)C1[A] C2[A] Ci [A] Cn[A]

Harmonic Grammar minimizes a weighted sum of violations

H(A) =nsum

i=1

wi middot Ci [A]

ldquoStandardrdquo HG weights wi = ranks ri Exponential HG weights are ranks exponentiated fixed base(e = 27182 ) wi = eri q-HG weights are ranks exponentiated with (variable) base q

wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri



Strict domination in OT is q-HG in the q rarr +infin limit

In q-HG

H(A) = qrn middot Cn[A] + + qri middot Ci [A] + + qr1 middot C1[A]

Or simply (if ri = i minus 1)

H(A) = qnminus1 middot Cn[A] + + q2 middot Ci [A] + q1 middot Ci [A] + q0 middot C1[A]

H(A) = 2nminus1 middot Cn[A] + + 4 middot Ci [A] + 2 middot Ci [A] + 1 middot C1[A]



Main difference between OT and HG is strict domination

If q grows large q-HG turns into OT because




In q-HG












15-HG has ganging-up cumulativity

C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25

15-HG also has counting cumulativity

C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3

(Cf Jaumlger and Rosenbach 2006)




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 Jaumlger and Rosenbach 2006)




3-HG does not have ganging-up cumulativity

C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4

3-HG does not have counting cumulativity either

C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6





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 minus 1 ge Ck [A] for all k and A



Overview







Word initial consonant cluster simplification in Dutch

Klaas Seinhorst collecting data from CHILDES (Laura)

Cf Becker and Tessier (2011)Tamaacutes Biroacute Harmonic Grammar growing into Optimality Theory 21



Using logistic regression or probit regression

cluster simplifies lower upperto boundary boundary

(age in days) (age in days)kl- k - 89432 101055sl- l- 94382 102868st- t- 96260 107623zw- z- 134424 155139

Table 95 confidence intervals of the locations of the inflection points

Differences among kl sl and st statistically not significantBut differences between zw and each of the three others p lt 10minus11



Word initial consonant cluster simplification OT

The traditional account in OT learning = constraint re-ranking

Before learning Markedness FaithfulnessklEin NOCOMPLEX FAITHF [l] [k]

ONSET

[klEin] + [kEin]

[lEin] After learning Faithfulness Markedness

klEin FAITHF NOCOMPLEX [l] [k]ONSET

+ [klEin] [kEin] [lEin]




Questions to the traditional account

Child is exposed to huge amount of evidenceway before correct production Why no learning

If only NoComplexOnset and Faithf are involvedwhy significant difference for zw onset

If cluster-specific constraints factorial typology predicted



Word initial consonant cluster simplification q-HG

An alternative approachChild has acquired FAITHF NOCOMPLEXONSET much earlierprobably already at pre-linguistic ageRelative 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(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2




Before maturation small q eg q = 11 (NB Faithfulness Markedness)

klEin FAITHF NOCOMPLONS [l] [k] Hwi = 214 195 146 121

[klEin] 462+ [kEin] 335

[lEin] 360

After maturation large q eg q = 2


+ [klEin] 148[kEin] 260[lEin] 272




q is a function of age eg age prop log(q)

[xy] produced by q-HG if q is st qc + qx + qy = qf + qy or larger

xy FAITHF COMPLONS [x] [y] H forri = f c x y given q

wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx

Critical age function of deleted segment [x] but not remaining [y]If f gt c x gt y then step function predictedTo get S-shaped curve use Stochastic OT



Word initial consonant clusters stochastic q-HG



Overview







Learning vs Maturation

LearningKnowledge acquired from surrounding linguistic dataSource of cross-linguistic variationFeatures in the childrsquos language shared by other adult languages

MaturationSkills emerging due to general developmentUniversal developmental pathsFeatures in childrsquos language not appearing in any adult language









Learning from surrounding linguistic dataFeatures in the childrsquos language shared by other adult languages

Child learning English produces ldquoItalian-likerdquo pro-droprarr ldquoPro-droprdquo parameter not yet switchedChild learning English deleting codasrarr CODA markedness not yet demoted below FAITHFULNESS

Maturation due to general developmentFeatures in childrsquos language not appearing in any adult language

Long distance place agreement in consonant harmonyErroneous pronoun resolution











Modelling learning and modelling maturationshouldnrsquot they be different

Learning from surrounding linguistic dataSetting parametersRe-ranking constraints

Maturation due to general developmentRestrictions on working memory speed of mental computation Varying q in q-HG









Thank you for your attention

Tamaacutes Biroacutetamas[dot]biro[at]btk[dot]elte[dot]hu

httpbirotwebeltehu

This research was supported by a Veni Grant (project number 275-89-004)offered by the Netherlands Organisation for Scientific Research (NWO)as well as by a Marie Curie FP7 Integration Grant(no PCIG14-GA-2013-631599 ldquoMeMoLIrdquo) 7th EU Framework Programme


Optimality Theory and Harmonic Grammar

From HG to OT the strict domination limit

Consonant cluster simplification in Dutch

Summary learning and maturation




Is it really so






Is it really so




Overview







Overview





















[s u u u] 0 3 0[u s u u] 0 2 1

+ [u u s u] 0 1 2[u u u s] 1 0 3






















Boltzmann machine


minusH(A) =Nsum

ij=1










Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]







Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu










Is it really so




Overview







Overview





















[s u u u] 0 3 0[u s u u] 0 2 1

+ [u u s u] 0 1 2[u u u s] 1 0 3






















Boltzmann machine


minusH(A) =Nsum

ij=1










Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]







Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu








Overview







Overview





















[s u u u] 0 3 0[u s u u] 0 2 1

+ [u u s u] 0 1 2[u u u s] 1 0 3






















Boltzmann machine


minusH(A) =Nsum

ij=1










Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]







Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu








Overview





















[s u u u] 0 3 0[u s u u] 0 2 1

+ [u u s u] 0 1 2[u u u s] 1 0 3






















Boltzmann machine


minusH(A) =Nsum

ij=1










Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]







Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu






















[s u u u] 0 3 0[u s u u] 0 2 1

+ [u u s u] 0 1 2[u u u s] 1 0 3






















Boltzmann machine


minusH(A) =Nsum

ij=1










Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]







Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu


























Boltzmann machine


minusH(A) =Nsum

ij=1










Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]







Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu












Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]







Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu












Wij =nsum

k=1

wk middotW kij


minusH(A) =Nsum

ij=1


=Nsum

ij=1

si middotnsum

k=1


nsumk=1

wk middotNsum

ij=1


nsumk=1

wk middot Ck [A]



Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu








Summary thus far









Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu








Summary thus far









Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu








Summary thus far









Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu








Overview









H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu










H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu










H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu










H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri





H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu










H(A) =



H(A) =nsum

i=1

wi middot Ci [A]


wi = qri




In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu









In q-HG












In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu









In q-HG













C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu










C3 C2 C1 Hw = 225 15 1

+ A1 1 225A2 1 1 25


C3 C2 C1 Hwi = 225 15 1

+ A1 1 225A3 2 3






C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu










C3 C2 C1

A1 + A2


C3 C2 C1

A1 + A3






C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu










C3 C2 C1 H9 3 1

A1 1 9+ A2 1 1 4


C3 C2 C1 H9 3 1

A1 1 9+ A3 2 6











Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu















Overview






















ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu























ONSET

[klEin] + [kEin]
















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu


















ri 8 7 6 5 4 3 2 1(11)ri 214 195 177 161 146 133 121 11

2ri 256 128 64 32 16 8 4 2






[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu











[klEin] 462+ [kEin] 335

[lEin] 360



+ [klEin] 148[kEin] 260[lEin] 272







wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu












wi = qf qc qx qy

[xy] 0 1 1 1 qc + qx + qy

[y] 1 0 0 1 qf + qy

[x] 1 0 1 0 qf + qx







Overview













































httpbirotwebeltehu











Overview













































httpbirotwebeltehu














































httpbirotwebeltehu







harmonic grammar growing into optimality theory

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