Harmonic Ascent 

1. 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.

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  Note lexicographic refinement of classes Constraints from Lombardi 1999

10. Markedness-Admissible Mappings pt bd btpd • 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 btpd • 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 →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

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. • Apotential 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, http://www.ling.nthu.edu.tw/teal/TEAL_oral_FengFan_Hsieh.pdf

17. 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.

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 like H|M • a b b  a • b  c c  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 1996. ROA-66 • Mortensen 2004, ROA-667 • Lubowicz 2002. 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.