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  x  x  satisfies every F constraint. –Nothing can do better than that on the F’s. Nonfaithful  x  y  beats faithful  x  x  iff –The highest ranked constraint distinguishing them prefers  x  y 

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  x  x  satisfies every F constraint. –Nothing can do better than that on the F’s. Nonfaithful  x  y  beats faithful  x  x  iff –The highest ranked constraint distinguishing them prefers  x  y 

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

7 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 Ins L: pædd 1 W 0 0 L 0 faithful

8 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.

9 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

10 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.

11 Utterly Impossible Mappings pt bd bt pd In any grammar with the assumed M subhierarchy Good Bad

12 Two Consequences of Harmonic Ascent [1] No Circular Shifts in MF/OT Shifts that happen –Western Basque (Kirchner 1995) a → ealaba+a → alabea e → iseme+e → semie –Catalan(Mascaró 1978, Wheeler 1979) nt → nkuntent → kunten n → Ø plan→ pla  Analyzed recently in Moreton & Smolensky 2002

13  [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!)

14 Way Up ≠ Way Down z y x Good Bad

15 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.

16 Coastal Taiwanese Tone Shifts Diagram from Feng-fan Hsieh,

17 Not the True Article? No basis in justifiable Markedness for shifts (Yip). “Paradigm Replacement” ? –Moreton Yip 1980, Chen Mortensen Hsieh Chen 2000.

18  [2] No Endless Shifts NO: x → y →z → … → ……

19  [2] No Endless Shifts NO: x → y →z → … → …… E.g: “Add one syllable to input”

20  [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.

21  [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.

22 From Abstract Theory to Research Challenge The Harmonic Ascent property of MF/OT determines absolutely the structure of certain analyses. A chain shift likeH|M a  bb  a b  cc  b, therefore c  a. can only be obtained via Fac = F( * a  c) No M constraint can stop the headlong rush a  c. –Because we can’t have a  c on H|M.

23 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 * a  e * 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.

24 Some Thoughts on the Topic See such analysts as –Moreton & Smolensky 2002, ROA-525 –Gnanadesikan 1997, ROA-195 –Kirchner ROA-66 –Mortensen 2004, ROA-667 –Lubowicz ROA-554 –and undoubtedly others as well For a variety of inventive approaches.

25 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.