Harmonic Ascent

Getting better all the time

Timestamp: Jul 25, 2005

2

Endowing CON with Structure

• Thus far, we have examined properties that inhere in any OT grammar, regardless of what constraints there are.

• This addresses the question ‘How do you DO it’ at the most basic level.

• To reach a minimal theory of generative phonology, to make OT into a linguistic theory, the first step was to impose the distinction between Markedness & Faithfulness. (Prince & Smolensky 1991 et seq.)

3

MF / OT

• Let the constraints in CON, the universal shared set, fall exhaustively into two disjoint classes.

• A candidate relates an Input to an Output.

• A Markedness constraint only evaluates the Output, regardless of the Input.

• A Faithfulness constraint evaluate the Input-Output relation along some dimension of structure– demanding that In = Out along this dimension.

4

Beyond Faithful Replication

• Faithful mapping: In=Out‘nabbed’ næb+d næbd

• What does it take to beat the faithful candidate?– Moreton 2002, 2004 asks and answers this question.

• Fully Faithful xx satisfies every F constraint.– Nothing can do better than that on the F’s.

• Nonfaithful xy beats faithful xx iff– The highest ranked constraint distinguishing them

prefers xy

5

Beyond Replication

• Faithful mapping: In=Out‘nabbed’ næb+d næbd

• What does it take to beat the faithful candidate?– Moreton 2002, 2004 asks and answers this question.

• Fully Faithful xx satisfies every F constraint.– Nothing can do better than that on the F’s.

• Nonfaithful xy beats faithful xx iff– The highest ranked constraint distinguishing them

prefers xy

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Triumph of Markedness

That decisive constraint must be a Markedness constraint.– Since every F is happy with the faithful candidate.

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Triumph of Markedness

That decisive constraint must be a Markedness constraint.– Since every F is happy with the faithful candidate.

M:*Gem M:*Diff F:NoIns NoDev Action

W: pæd+d pædəd 0 0 1 0 Ins

L: pædd 1 W 0 0 L 0 faithful

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Harmonic Ascent = Markedness Descent

• For a constraint hierarchy H, let H|M be the subhierarchy of Markedness constraints within it.

• If H:α φ, for φ fully faithful, then H|M: α φ– If things do not stay the same, they must get better.

• Analysis and results due to Moreton 2002, 2004.

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Markedness Rating by H|M

M: *Diff(voi) >> M:*Voi

pt, bd (0) pt (0)

bd (2)

bt, pd (1) bt, pd (1)

• Let us consider the situation given this M subhierarchy

Good

Bad

Constraints from Lombardi 1999

Note lexicographic refinement of classes

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Markedness-Admissible Mappings

pt

bd

bt pd

• NB: we assume M:*Diff >> M:*Voi

Good

Bad

Where you stop the ascent, and if you can, depends on H|F.

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Utterly Impossible Mappings

pt

bd

bt pd

• In any grammar with the assumed M subhierarchy

Good

Bad

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Two Consequences of Harmonic Ascent

[1] No Circular Shifts in MF/OT

Shifts that happen– Western Basque (Kirchner 1995)

a → e alaba+a → alabea

e → i seme+e → semie

– Catalan (Mascaró 1978, Wheeler 1979)

nt → n kuntent → kunten

n → Ø plan → pla

Analyzed recently in Moreton & Smolensky 2002

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[1] No Circular Shifts

• Harmonic Ascent – Any such shift must result in betterment vis-à-vis H|M.– The goodness order imposed on alternatives is

• Asymmetric: NOT[ a b & b a]• Transitive: [a b & b c] a b

• Can’t have • x → y or even ▪ x → y• y → z ▪ y → x• z → x

• Any such cycle would give: x x (contradiction!)

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Way Up ≠ Way Down

z

y

x

Good

Bad

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Shift Data

• Large numbers of noncircular shifts exist– Moreton & Smolensky collect 35 segmental cases

• 3 doubtful, 4 inferred: 28 robustly evidenced.

• A potential counterexample– Taiwanese/ Xiamen Tone Circle– See Yip 2002, Moreton 2002, and many others for discussion.

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Coastal Taiwanese Tone Shifts

Diagram from Feng-fan Hsieh, http://www.ling.nthu.edu.tw/teal/TEAL_oral_FengFan_Hsieh.pdf

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Not the True Article?

• No basis in justifiable Markedness for shifts (Yip).

• “Paradigm Replacement” ?– Moreton 2002. Yip 1980, 2002. Chen 2002. Mortensen 2004.

Hsieh 2004. Chen 2000.

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[2] No Endless Shifts

NO: x → y →z → … → ……

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[2] No Endless Shifts

NO: x → y →z → … → ……

• E.g: “Add one syllable to input”

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[2] No Endless Shifts

NO: x → y →z → … → ……

• E.g: “Add one syllable to input”

• Because constraints only penalize,

there is an end to getting better.

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[2] No Endless Shifts

NO: x → y →z → … → ……

• E.g: “Add one syllable to input”

• Because constraints only penalize,

there is an end to getting better.

This is certainly a correct result.— we can add one syllable to hit a fixed target (e.g. 2 sylls.)

not merely to expand regardless of shape of outcome.

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From Abstract Theory to Research Challenge

• The Harmonic Ascent property of MF/OT determines absolutely the structure of certain analyses.

• A chain shift like H|M • a b b a• b c c b, therefore c a.

can only be obtained via Fac = F(*ac)

• No M constraint can stop the headlong rush ac.– Because we can’t have a c on H|M.

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What are these F of which we speak?

• Ergo, MF/OT + [reality of chain shifts] in data means:

• We must be able to define F that treat not just * nt n Ø *ae

* n Ø *e i

• But also, and distinctly, the composed fell swoops*nt Ø *a i

The anti-Fell-Swoop constraints are unviolated; while the step-wise F constraints are violated.

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Some Thoughts on the Topic

• See such analysts as – Moreton & Smolensky 2002, ROA-525– Gnanadesikan 1997, ROA-195– Kirchner 1996. ROA-66– Mortensen 2004, ROA-667– Lubowicz 2002. ROA-554– and undoubtedly others as well

• For a variety of inventive approaches.

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Conclusions

• Local to Global. Design of the theory succeeds in taking property of atomic components (single M constraint) and propagating it to the aggregate judgment.

• Moreton’s abstract question about basic design leads directly to basic empirical predictions of the theory.

• And to a truly central research challenge, tied to realizing its basic predictions in empirical reality.