Colin Wilson UCLA Current Perspectives on Phonology ...Colin Wilson UCLA Current Perspectives on Phonology Bloomington, Indiana June 23 Unbounded spreading is myopic – p.1/?? Unbounded

Unbounded spreading is myopicColin Wilson

UCLA

Current Perspectives on Phonology

Bloomington, Indiana June 23

Unbounded spreading is myopic – p.1/??

Unbounded nasal spreading in Arabela

‘A vowel, a sequence of vowels, or a sequence ofvowels separated by y [j] or w have nasalizedallophones when following nasals’ (Rich 1963)

"mjænu ‘swallow’ "huwaP ‘a yellow bird’"hanuP ‘to fly’ "ninjuP ‘to come’"maanuP ‘to come’ "nuwaP ‘partridge’"hijæniP ‘old woman’ "njææ"riP ‘he laid it down’"heeGiP ‘termites’ cf. "tukuru ‘palm leaf’

Note: h always surfaces as nasal


Unbounded spreading

• In principle, any number of segments canundergo spreading from a single triggerex. "huwaP ‘a yellow bird’

• Spreading applies until it reaches the edge ofits domain (e.g., PrWd) or a blocking segex. "hijæ p2"ham2"hinjEP

‘where the sun comes up’ex. "ka"naa"kIP ‘our (excl.) father’


Contribution of Optimality Theory

• Rule-based analyses must build the blockingconditions into the spreading rules (or addfilters / constraint on top of the rule system)ex. [–consonantal]→ [+nasal] / [+nasal]

“spread [+nasal] to a following segmentexcept when it is [+consonantal]”

• Given strict-domination ranking, it is possibleto explain blocking with constraints that areindependently motivated and activeex. *NASOBSTR/LIQUID ≫ “Spread nasal”


Contribution of Optimality Theory

Hierarchical blocking effects (terminology fromWalker 2000) are explained with substantivelymotivated constraint sets that potentially regulatemultiple spreading processes (McCarthy 1997),govern the distribution of contrastive values forthe spreading feature (Bakovic 2000, Kaun 1995,Walker 2000), and play other roles in phonology

ex. *NASOBSTRSTOP ≫ *NASFRIC ≫*NASLIQUID ≫ *NASGLIDE ≫ *NASVOWEL ≫*NASSONSTOP (hierarchy from Walker 2000)


Outline of the talk

• GeneralizationUnbounded spreading is myopic

• Formal analysisPositive and negative harmony in OptimalityTheory with Targeted Constraints (TCOT)

nawa−

ta → nawa+

t−

a ≻ nawa−

ta

• General properties of TCOT grammars [andconnection to opacity and the P-map]


Typology of unbounded spreading

• Nasal (Cohn 1993, Homer 1998, Hyman1982, Piggott 1992, Safir 1979, Walker 2000)

• Vowel harmony (Beckman 1997, Clements1980, Goldsmith 1985, Kaun 1995, Ringen1975, Vago 1976, Walker 2001)

• ATR (Archangeli & Pulleyblank 1994,Bakovic 2000, Kaye 1982, Noske 2000)

• Emphasis (Bessell 1998, Davis 1995,McCarthy 1997, Watson 2002, Younes 1993)


Typology of unbounded spreading

• Long-distance consonant agreement(Gafos 1999, Hansson 2001, 2004, Poser1982, Rose & Walker 2004)

• Regrettably nothing to say about tonespreading here — suggestions welcome!


Unbounded spreading is myopic

All attested unbounded spreading processesobey a myopia (“no look ahead”) generalization

• LR→ spreading from T to U is independentof whether spreading can proceed into Z

. . . T X U Z . . .

• ←RL spreading from T to U is independentof whether spreading can extend into Z

. . . Z U X T . . .


Unbounded spreading is myopic

• A generalization similar to myopia was firstnoted by Anderson (1982)

• Related to claims that certain feature values,such as [–nasal] and [–round], never spreadunboundedly (Steriade 1995)

• Bakovic (2000) analyzes several cases ofmyopia with stem control


Myopic spreading in Arabela

• LR→ unbounded nasal spreadingTriggers: nasal consonants [m n h]Undergoers: vowels [i e a o u], glides [j w]Blockers: obstruents [p t k s S], rhotic [r]

• Spreading is myopic"heegiP ‘termites’ *"heegiP, *"heegiP

"hjuuS:"SænoP ‘where I fished’"po"konaGiP ‘yellow’"tinja"kari ‘afternoon’ (cf. "na"iP ‘stinging ant’)


AGREE is inconsistent with myopia

• AGREE(F) requires adjacent segments tohave the same specification for [F] (Bakovic2000, Butska 1999, Lombardi 1999)

• Because AGREE(F) cannot be satisfied in thepresence of a blocker, it incorrectly fails toprefer myopic spreading (McCarthy 2003)/heegiP/ AGREE(nas) IDENT(nas)heegiP -1heegiP -1 -2 / -3!


ALIGN is consistent with myopia

• ALIGN-L/R(F) (variously named) assigns oneviolation for every segment before/after thetrigger that has not undergone spreading(Akinlabi 1994, Cole & Kisseberth 1994,Kaun 1995, Kirchner 1993, McCarthy 1997,Padgett 1995, Pulleyblank 1996, Ringen &Vago 1995, Walker 2000)

• ALIGN correctly prefers myopic spreading,but predicts a range of unattested non-localeffects, such as long-distance blocking ofepenthesis (McCarthy 2004, Wilson 2003)


ALIGN blocks epenthesis non-locally

• Partial rankingALIGN-R([+nasal])≫ *C#≫ DEP-V

• Normal application of word-final epenthesisin words that contain no [+nasal] segment

/latak/→ lataki

• Blocking of epenthesis when [+nasal]spreading cannot be complete/natak/ ALIGN-R(nas) *C# DEP-Vnatak -3 -1nataki -4! -1


Additional approaches to spreading

• Directional evaluation (Eisner 2000)LR→ evaluation prefers violations later in theword,←RL evaluation prefers earlier violns

Non-myopic [+nasal] spreading predicted by*[+nasal][-nasal] (←RL) ex. nawata ≻ nawata*[-nasal][+nasal] (LR→)


Additional approaches to spreading

• Headed Span Theory (Key to appear,McCarthy 2004, O’Keefe to appear)Spreading preferred by constraints againstadjacent spans, with directionality governedby span-headedness constraints

Non-myopic [+nasal] spreading predicted by*A-SP(nas)≫SPHDR(+nas)≫SPHDL(-nas)⇒ (na) ≻ (n)(a) but (n)(ata) ≻ (na)(ta)


Summary

• Myopia follows from iterative application ofrules such as [–cons]→ [+nasal]/[+nasal]ex. /huwaP/→ huwaP→ huwaP→ · · ·

• Strict-domination ranking has the potential toreduce blocking to independent constraints

• None of the viable OT approaches tospreading predict myopia under all rankings


Targeted constraints

• A targeted constraint specifies both amarked configuration and a repair (Bakovic &Wilson 2000, Hansson 2001, Wilson 2001)

• Targeted constraints are formalized here asfinite-state machines (see Hopcroft & Ullman1979, Mohri 1997, Pereira & Riley 1997)

• Targeted spreading constraints resemblespreading rules but without built-in blocking


Targeted spreading constraint

±SPREAD-R(+nasal)

0

[-nasal]0

1

[+nasal]0

[-nasal] : [+nasal]+1

[-nasal]-1

[+nasal]0

Negative marks (–1) are identical to OT viol’nsPositive marks (+1) reward the designated repair


Harmonic ordering with pos marks

• Let C(X) stand for the sum of the marks(positive or negative) that C assigns to X

• Greater harmony is betterC: X ≻ Y ⇔ C(X) > C(Y)

• ExampleC(X) = +1 C(Y) = 0 C(Z) = -1⇒ C: X ≻ Y ≻ Z


Targeted constraint as evaluator

EVAL(C, A) is the evaluation function, definedessentially as in classic finite-state OT (Albro2003, Eisner 1997, Ellison 1994, Riggle 2004)

Ex. A =

0 1

n0

42

a0

3

t0

a0

EVAL(±SPREAD-R(+nasal), A) =

(0,0) (1,1)

n0

(0,4)(0,2)

a-1

(0,3)

t0

a0


Definition of EVAL

Targeted constraintfor every transition (q, c, d, v, r) in Ci s.t. v ≤ 0

for every transition (q′, x, y, w, r′) in A s.t. y ⊔ c

construct ((q, q′), x, y, w[i←v if v<0], (r, r′))

Mark indelibilityExisting positive and negative marks of atargeted constraint are not changed by EVAL


Definition of EVAL

Markedness constraint (non-targeted)for every transition (q, c, d, v, r) in Ci

for every transition (q′, x, y, w, r′) in A s.t. y ⊔ c

construct ((q, q′), x, y, w[i←v], (r, r′))

Faithfulness constraintfor every (q, c, d, v, r) in Ci

for every (q′, x, y, w, r′) in A s.t. x ⊔ c and y ⊔ d

construct ((q, q′), x, y, w[i←v], (r, r′))

(This definition ignores ǫ-transitions; see finite-state refs)


Extension to hierarchy evaluation

EVAL([C0, C1, . . . , Cn], A)

= EVAL(Cn, . . . EVAL(C1, EVAL(C0,A)))

= EVAL(C0, EVAL(C1, . . . EVAL(Cn,A)))


Targeted constraint as generator

GEN(C,A) is the generation function, anothervariant of finite-state intersection / composition

A =

0 1

n0

42

a-1

3

t0

a0

GEN(±SPREAD-R(+nasal), A) =

(0,0) (1,1)

n0

(0,4)(0,2)

a-1

A+1

(0,3)

t0

a0


Definition of GEN

Targeted constraintfor every transition (q, c, d, v, r) in Ci

for every transition (q′, x, -, w, r′) in A s.t. x ⊔ c

if v ≤ 0 // faithful mappingconstruct ((q, q′), x, x, w, (r, r′))

else // repairconstruct ((q, q′), x, d(x), w[i←v], (r, r

′))

Mark conversionApplication of the designated repair converts anegative mark (–1) to a positive mark (+1)


TCOT framework

• CON = T ∪M∪F

• GEN is replaced by T except perhaps forcreation of alternative prosodic parses

• H-EVAL is defined exactly as in OT(lexicographic ordering of viol’n vectors)

• I/O mapping is achieved by a version ofharmonic serialism (see Prince & Smolensky1993/2004, McCarthy 2000, 2006) . . .


TCOT framework

Given hierarchy H = [C0, C1, . . . , Cn] and input in

out0 ← in

k ← 0do

k ← k + 1outk−1 ← EVAL(H, RESET(outk−1))for each targeted constraint Ci

out← H-MAX(EVAL(H, GEN(Ci, outk−1)))outk ← H-MAX({outk, out})

while outk ≻ outk−1

return outk


TCOT framework

in out_{k-1}

Eval(H)

Gen(T_1)

Gen(T_2)

...

Gen(T_n)

Eval(H)

out_{k}


Example: constraints

±NONASOBSTR ±SPREAD-R(+nasal)

0

[-nasal]0

[+son]0

[-son,+nasal]-1

[-son,+nasal] : [-nasal]+1

0

[-nasal]0

1

[+nasal]0

[-nasal] : [+nasal]+1

[-nasal]-1

[+nasal]0


Example: constraints

±NONASVOC IDENT(nasal)

0

[-nasal]0

[+cons]0

[-cons,+nasal]-1

[-cons,+nasal] : [-nasal]+1

0

[+nasal] : [+nasal]0

[-nasal] : [-nasal]0

[+nasal] : [-nasal]-1

[-nasal] : [+nasal]-1


Example: hierarchy and inputs

Hierarchy±NONASOBSTR ≫ ±SPREAD-R(+nasal)≫ ±NONASVOC ≫ IDENT(nasal)

Inputs/nawa/

0 1

n0

42

a0

3

w0

a0

/nawata/

0 1

n0

62

a0

3

w0

4

a0

5

t0

a0


Example: unbounded spreading

±NONASOBS ≫ ±SPRD-R(+nas)≫ ±NONASV ≫ ID(nas)




out0 = EVAL(H, nawa) =

0 2

n : n[0, 0, 0, 0]

13

a : a[0, -1, 0, 0]

4

w : w[0, 0, 0, 0]

a : a[0, 0, 0, 0]




EVAL(H, GEN(±SPRD-R(+nas), out0)) =

0 2

n : n[0, 0, 0, 0]

1

3a : a

[0, -1, 0, 0]

4

a : A[0, 1, -1, -1]

5

w : w[0, 0, 0, 0]

w : w[0, -1, 0, 0]

a : a[0, 0, 0, 0]

/nawa/ ±NONASOBS ±SPRD-R(+nas) ±NONASV ID(nas)

nawa -1!

nAwa (+1) + (-1) = 0 -1 -1




out1 = EVAL(H, nAwa) =

0 2

n : n[0, 0, 0, 0]

13

A : A[0, 0, -1, 0]

4

w : w[0, -1, 0, 0]

a : a[0, 0, 0, 0]





0 2

n : n[0, 0, 0, 0]

13

A : A[0, 0, -1, 0]

4w : w

[0, -1, 0, 0]

5

w : W[0, 1, -1, -1]

a : a[0, 0, 0, 0]

a : a[0, -1, 0, 0]

/nAwa/ ±NONASOBS ±SPRD-R(+nas) ±NONASV ID(nas)

nAwa -1! -1

nAWa (+1) + (-1) = 0 -2 -1




EVAL(H, GEN(±NONASV, out1)) =

0 2

n : n[0, 0, 0, 0]

1

3A : a

[0, -1, 1, -1]

4

A : A[0, 0, -1, 0]

5

w : w[0, -1, 0, 0]

w : w[0, -1, 0, 0]

a : a[0, 0, 0, 0]

/nAwa/ ±NONASOBS ±SPRD-R(+nas) ±NONASV ID(nas)

nawa -2! +1 -1

nAwa -1 -1




out2 = EVAL(H, nAWa) =

0 4

n : n[0, 0, 0, 0]

12 3

W : W[0, 0, -1, 0]

a : a[0, -1, 0, 0]

A : A[0, 0, -1, 0]





0 5

n : n[0, 0, 0, 0]

2

1

3 4

W : W[0, 0, -1, 0]

a : A[0, 1, -1, -1]

a : a[0, -1, 0, 0]

A : A[0, 0, -1, 0]

/nAWa/ ±NONASOBS ±SPRD-R(+nas) ±NONASV ID(nas)

nAWA +1 -3 -1

nAWa -1! -2





0 6

n : n[0, 0, 0, 0]

1

2 3

W : W[0, 0, -1, 0]

4

W : w[0, -1, 1, -1]

a : a[0, -1, 0, 0]

a : a[0, -1, 0, 0]

5

W : W[0, 0, -1, 0]

W : w[0, 0, 1, -1]

A : A[0, 0, -1, 0]

A : a[0, -1, 1, -1]




out3 = EVAL(H, nAWA) =

0 4

n : n[0, 0, 0, 0]

12 3

W : W[0, 0, -1, 0]

A : A[0, 0, -1, 0]

A : A[0, 0, -1, 0]


How it works

• ±SPREAD-R(+nasal) assigns -1 to a [-nasal]segment immed. after a [+nasal] segment

na−wa

• Application of the spreading repair convertsthe negative mark to a positive mark +1

na−wa → nA

+wa

• Negative and positive marks cancel, makingpartial spreading better than “sour grapes”

na−wa → nA

+w−

a ≻ na−wa


Example: myopia



Example: myopia


out3 = EVAL(H, nAWAta) =

0 5

n : n[0, 0, 0, 0]

12 3

W : W[0, 0, -1, 0]

4

A : A[0, 0, -1, 0]

6

t : t[0, -1, 0, 0]

A : A[0, 0, -1, 0]

a : a[0, 0, 0, 0]


Example: myopia



0 5

n : n[0, 0, 0, 0]

12 3

W : W[0, 0, -1, 0]

4

A : A[0, 0, -1, 0]

6t : T

[-1, 1, 0, -1]

7

t : t[0, -1, 0, 0]

A : A[0, 0, -1, 0]

a : a[0, -1, 0, 0]

a : a[0, 0, 0, 0]

/nAWAta/ ±NONASOBS ±SPRD-R(+nas) ±NONASV ID(nas)

nAWATa -1! -3 -1

nAWAta -1 -3


Example: myopia



0 8

n : n[0, 0, 0, 0]

1

23

W : W[0, 0, -1, 0]

4

W : w[0, -1, 1, -1] 5

A : A[0, 0, -1, 0]

6

A : a[0, -1, 1, -1]

A : A[0, 0, -1, 0]

A : a[0, 0, 1, -1]

9

t : t[0, -1, 0, 0]

t : t[0, -1, 0, 0]

7

W : W[0, 0, -1, 0]

W : w[0, 0, 1, -1]

A : A[0, 0, -1, 0]

A : a[0, -1, 1, -1]

a : a[0, 0, 0, 0]


How it works

• Evaluation by ±SPRD-R(+nas) does not “lookahead” to the blocking segment

• Mark conversion ensures that partialspreading beats non-spreading

nAWa−ta → nAWA

+t−a ≻ nAWa

−ta

• Mark indelibility ensures that retraction ofpartial spreading is worse than no change

nAWAt−a → nAWAt

−a ≻ nAWa

−t−a


Factorial typology

• Blockers±NOX[αF]≫ ±SPREAD-R(αF)

• Undergoers±SPREAD-R(αF)≫ ±NoY[αF]

• Transparent segments require additionalassumptions of the TCOT account of opacity


Ranking for Arabela

±NONASOBSTRSTOP|

±NONASFRIC|

±NONASLIQUID|

±SPREAD-R(+nasal)|

±NONASGLIDE|

±NONASVOWEL


Summary

• Myopia is a universal property of unboundedspreading not accounted for within OT

• TCOT combines the strengths of rule-basedanalyses, which easily capture myopia, andOT, which is more explanatory w.r.t. blocking

• Key to the TCOT analysis is the regulation ofpositive and negative marks, and iterative opt


General properties of TCOT

• No global constraints on derivations

• Computational complexity

• Proving convergence


No global constraints

• Optimization in TCOT is strictly iterative: noconstraint evaluates entire derivations

in out_{k-1}

Eval(H)

Gen(T_1)

Gen(T_2)

...

Gen(T_n)

Eval(H)

out_{k}

• This is a point of difference between TCOTand Candidate Chain OT (McCarthy 2006)


Computational complexity

• OT: Exponential in |CON|, polynomial in|input| (at best; see Eisner 2000); somegrammars can be compiled to linear-timetransducers (Riggle 2004)

• TCOT: Exponential in |CON|, polynomial in|input| at each iteration (at best); should bepossible to extend grammar compilation tothis case — working on the details


Computational complexity

• CC-OT: Literal implementation of Becker(2006) is easily factorial in |input| (becauseit enumerates all n! orderings of n steps)

10! ≈ 3, 600, 00 > 210 ≈ 1024 > 102

20! ≈ 2.4× 1018 > 220 ≈ 1× 106 > 202

• Candidate sets in CC-OT and TCOT (undersensible conditions) are finite — but currentimplementations are either demonstrablyintractable (NP) or not known to be tractable


Proving convergence

• Proof of convergence follows from a boundon iteration by individual targeted constraints

• For every targeted constraint T and everyrepresentation A, there must be a k ≥ 0 s.t.H-MAX(GENk+1(T,A)) = H-MAX(GENk(T,A))

• Equivalently, for every targeted constraint Tthere is a function f bounded below by 0 s.t.for all A, f (GEN(T,A)) < f (A) or GEN(T,A)=A


Proving convergence

• ±SPREAD-R(+nasal)A suitable function f sums the number ofsegments intervening between each [+nasal]segment and the right edge of the domain(= the eval function for ALIGN-R(+nasal)!)

• ±NONASGLIDEObvious function f counts the number ofnasal glides (= –(negative violations))


Thank you!

Selected referencesHopcroft, J.E. and J.D. Ullman. 1979. Introduction to automata,

languages and computation. Reading, MA: Addison-Wesley

McCarthy, John. 2006. Hidden Generalizations: Phonological

Opacity in Optimality Theory. London: Equinox Publishing

Rich, Furne. 1963. Arabela Phonemes and High-Level

Phonology. In Benjamin F. Elson (ed.), Studies in Peruvian

Indian Languages: I. University of Oklahoma: SIL

Walker, Rachel. 2000. Nasalization, Neutral Segments and

Opacity Effects. New York: Garland

Wilson, Colin. 2001. Consonant cluster neutralizaton and

targeted constraints. Phonology 18: 147-197


Extensions

Phonological opacity in TCOT

Projecting targeted constraints from the P-map


Phonological opacity in TCOT

• Conservation of harmony (assumed above)

Positive and negative marks occupy thesame position in the hierarchy

• Phonological opacity results from rankings inwhich harmony is not conserved

• A monotonicity condition prevents iterativeoptimization from cycling endlessly


Example: transparent obstruents

+NONASVOC|

+SPREAD-R(+nasal)|

±NONASOBSTR|

−SPREAD-R(+nasal)|

−NONASVOC|

IDENT(nasal)



+SPREAD-R(+nasal)≫ ±NONASOBSTR

0 2

n : n[0, 0, 0, 0, 0, 0, 0]

13

A : A[0, 0, 0, 0, 0, -1, 0]

4

t : T[0, 1, 0, -1, -1, 0, -1]

5

t : t[0, 0, 0, 0, -1, 0, 0]

a : a[0, 0, 0, 0, -1, 0, 0]

a : a[0, 0, 0, 0, 0, 0, 0]



±NONASOBSTR ≫ −SPREAD-R(+nasal)

0 5

n : n[0, 0, 0, 0, 0, 0, 0]

1

2A : A

[0, 0, 0, 0, 0, -1, 0]

3

T : t[0, 0, 1, -1, -1, 0, -1]

4

T : T[0, 0, 0, -1, 0, 0, 0] A : A

[0, 0, 0, 0, 0, -1, 0]

A : A[0, 0, 0, 0, 0, -1, 0]


Monotonicity condition

• A single extrinsic order (ranking) controlsboth harmonic ordering and generation

• Given derivation out0, out1, . . . , outn andcorresponding sequence T1, . . . , Tn ofgenerating constraints

Ti ≫ Ti+1 or Ti = Ti+1 for all 1 ≤ i < n

• Computational cost is trivial: store a pointerto the most recent generating constraint


Projecting targeted constraints

• P-map (Steriade 2001) encodes perceptualsimilarity relations in phonological contexts

• Targeted constraints can be projected fromthe P-map if the latter is formalized as a fsmthat is unambiguous on the input side

• Select marked structure X and perceptibilitythreshold θ, prune unfaithful arcs above θ



P-map fragment

0

V:V / 0

1C:C / 0

C:- / .25

2C:C / 0

C:- / .5

C:C / 0C:- / .25

C:C / 0

C:- / .5

V:V / 0



X = C, θ = .3

0

V:V / 0

1C:C / 0

C:- / .25

2C:C / 0

C:- / .5

C:C / 0C:- / .25

C:C / 0

C:- / .5

V:V / 0



X = C, θ = .3

0

V:V / 01

C:C / 0

C:- / .25

2C:C / 0

C:C / 0C:- / .25

C:C / 0

V:V / 0



X = C, θ = .3

0

V:V / 01

C:C / -1

C:- / +1

2C:C / 0

C:C / -1C:- / +1

C:C / 0

V:V / 0



• P-map fragment needed to project±SPREAD-R(+nasal) would reflectperseveratory nasal coarticulation

• In general, need internal domination (Prince2001) to prefer higher-similarity repairsamong those that fall below threshold θ


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Colin Wilson UCLA Current Perspectives on Phonology ...Colin Wilson UCLA Current Perspectives on Phonology Bloomington, Indiana June 23 Unbounded spreading is myopic – p.1/?? Unbounded