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Grammar as Choice 

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  1. Grammar as Choice Conflict, concord, & optimality

  2. Choice • Grammar involves Multi-criterion Decision Making • Similar problems arise in cognitive psychology (Gigerenzer, Kahneman, Tversky), economics (Arrow), neural networks (Smolensky), politics, operations research, and so on. • Many factors interact to determine the form of words, phrases, sentences,… • They need not be remotely in agreement about the best outcome or course of action.

  3. The Three Pillars of Decision • What are the alternatives? • from which one must choose. • What are the criteria? • which evaluate the alternatives. • How do the many criteria combine into a single decision? • given pervasive conflict among them.

  4. Alternatives • The generative stance: the alternatives are actions • They modify, structure, re-structure, or preserve an input • As a result, an output is defined. • The choice is among different (In,Out) pairings.

  5. An Example • The Regular Past Tense of English Spelled Pronounced Observed Suffix massed mæst -t nabbed næbd -d patted pætəd -əd

  6. An Example • The Regular Past Tense of English Spelled Pronounced Observed Suffix massed mæst -t nabbed næbd -d patted pætəd -əd

  7. An Example • The Regular Past Tense of English Spelled Pronounced Observed Suffix massed mæst -t nabbed næbd -d patted pætəd -əd  No overlap in distribution of suffix variants

  8. An Example • The Regular Past Tense of English Spelled Pronounced Observed Suffix massed mæst -t nabbed næbd -d patted pætəd -əd  No overlap in distribution of suffix variants  Suffix variants highly similar phonetically

  9. An Example • The Regular Past Tense of English Spelled Pronounced Observed Suffix massed mæst -t nabbed næbd -d patted pætəd -əd  No overlap in distribution of suffix variants  Suffix variants highly similar phonetically •  Choice of variant entirely predictable on general grounds

  10. Regular Past Tense Suffix

  11. Regular Past Tense Suffix d

  12. Regular Past Tense Suffix d Similarity ← Identity There is just one suffix: /d/

  13. Lexical Representation Lexical Representation • ‘massed’ mæs+d • ‘nabbed’ næb+d • ‘patted’ pæt+d • RelationsElementary Actions d  d nil d  t devoice d  -əd insert

  14. Dilemmas of Action • Reluctance  +voi  –voi doesn’t remove all b,d,g’s from the language • Ø  ə doesn’t spray schwas into every crevice • Compliance • Faithful reproduction of input not possible: • *mæsd, * pætd  Action is taken only to deal with such problems • Choices, choices – Insertion solves all problems. Yet we don’t always do it. *mæsəd is entirely possible (cf. ‘placid’)

  15. The Two Classes of Criteria Markedness. Judging the outcome.e.g. *Diff(voi). (Final) Obstruent clusters may not differ in voicing. *pd, *bt, *td, *ds, *zt,etc. *Gem. Adjacent consonants may not be identical. *tt, *dd, *bb,… [in pronunciation] This analysis follows Bakovic 2004. Faithfulness. Judging the action. Input=Output in a certain property Every elementary action is individually proscribed: e.g. NoDevoicing. NoInsertion. NoDeletion.

  16. The Two Classes of Criteria Markedness. Judging the outcome.e.g. *Diff(voi). (Final) Obstruent clusters may not differ in voicing. *pd, *bt, *td, *ds, *zt, etc. *Gem. Adjacent consonants may not be identical. *tt, *dd, *bb,… [in pronunciation] This analysis follows Bakovic 2004. Faithfulness. Judging the action. Input=Output in a certain property Every elementary action is individually proscribed: e.g. NoDevoicing. NoInsertion. NoDeletion.

  17. The Two Classes of Criteria Markedness. Judging the outcome. Demands compliance with output standards Faithfulness. Judging the action. Enforces reluctance to act

  18. Penalties • Constraints assess only penalties • no rewards for good behavior • Actions are reluctant because constraints on action always favor inaction — by penalizing change. • Actions happen because constraints on outcome force violation of constraints against action.

  19. Conflicts Abound • The faithfulness constraints disagree among themselves • And M:*Diff disagrees with F:NoDevoicing.

  20. Conflicts Abound • The faithfulness constraints disagree among themselves  W marks preference for desired winner;  L preference for desired loser

  21. Conflicts Abound • The faithfulness constraints disagree among themselves • And M:*Diff disagrees with F:NoDev.

  22. All Conflicts Resolved • Impose a strict priority order ‘>>’ on the set of constraints • Here: *Gem, *Diff >> NoIns >>NoDel • In any pairwise comparison of x vs. y x y ‘x is better than y’ iff the highest-ranked constraint distinguishing x from y prefers x. • Optimal. x is optimal iff x y for every y y violationwise distinct from x

  23. Lexicographic • Better Than, ‘’: lexicographic order on the alternatives. • Sort by the highest ranked constraint • If it does not decide, on to the next highest. • And so on. • Like sorting by first letter (able < baker) • and then the next, if that doesn’t decide: (aardvark<abacus) • and then the next (azimuth < azure), and so on. • Or ordering numerals by place 100 < 200 119 < 130 2235 < 2270

  24. Optimality Theory • Alternatives. • A set of (input,output) pairs. • A given input is matched with every possible output. • Criteria. • A set of constraints, of two species • Markedness: judging outcomes • Faithfulness: judging actions • Collective judgment. • Derives from a strict prioritization of the constraint set. • Imposes lexicographic order on alternatives. Take the best.

  25. Universality To make maximal use of theoretical resources and minimal commitment to extraneous devices, assume: • Fixed. • The set of alternatives is universal. • Fixed. • The set of constraints is universal. • Varying. • Languages differ freely in the ranking of the constraint set.

  26. Harmonic Ascent Getting better all the time

  27. 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

  28. 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

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

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

  31. 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.

  32. Markedness Rating by H|M M: *Diff(voi) >> M:*Voi pt, bd (0) pt (0) bd (2) bt, pd (1) bt, pd (1) Good Bad  Note lexicographic refinement of classes Constraints from Lombardi 1999

  33. Markedness-Admissible Mappings pt bd btpd Good Bad  Where you stop the ascent, and if you can, depends on H|F.

  34. Utterly Impossible Mappings pt bd btpd Good Bad

  35. Consequences of Harmonic Ascent • 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

  36. 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 • y → z • z → x • Such a cycle would give: x  x (contradiction!)

  37. Way Up ≠ Way Down z y x Good Bad

  38. Shift Data • Large numbers exist • Moreton & Smolensky collect 35 segmental cases • 3 doubtful, 4 inferred: 28 robustly evidenced. • Onepotential counterexample • Taiwanese/ Xiamen Tone Circle • See Yip 2002, Moreton 2002, and many others for discussion.

  39. Coastal Taiwanese Tone Shifts Diagram from Feng-fan Hsieh, http://www.ling.nthu.edu.tw/teal/TEAL_oral_FengFan_Hsieh.pdf

  40. 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.

  41. No Endless Shifts NO: x → y →z → … → ……

  42. No Endless Shifts NO: x → y →z → … → …… • E.g: “Add one syllable to input”

  43. 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.

  44. 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.

  45. Conclusions • Harmonic Ascent and its consequences nontrivial, since mod of theory can easily eliminate. E.g. ‘Antifaithfulness.’ • Design of the theory succeeds in taking property of atomic components (single M constraint) and propagating it to the aggregate judgment. • Requires: transitive, asymmetric order, commitment to penalization, strict limitation to M & F constraints.

  46. Concord Nonconflict in OT

  47. Constraints in conflict

  48. Constraints in conflict

  49. Constraints in conflict

  50. Constraints need not conflict