1. January 24-25, 2003Workshop on Markedness and the Lexicon1 On the Priority of Markedness Paul Smolensky Cognitive Science Department Johns Hopkins University

2. January 24-25, 2003Workshop on Markedness and the Lexicon2 Markedness Rules Markedness is prior to lexical frequency  Developmentally Explanatorily  Markedness determines possible inventories (e.g., of lexical items) ÌMarkedness determines relative frequency of structures Have few solid results; mostly suggestive evidence, empirical and theoretical

3. January 24-25, 2003Workshop on Markedness and the Lexicon3  Developmental Priority Look to see whether young infants are sensitive to markedness before they’ve had sufficient relevant experience Before 6 months, infants have not shown sensitivity to language-particular phonotactics

4. January 24-25, 2003Workshop on Markedness and the Lexicon4  Experimental Exploration of the Initial State

5. January 24-25, 2003Workshop on Markedness and the Lexicon5 Talk Outline Markedness is prior to lexical frequency  Developmentally Explanatorily  Markedness determines possible inventories (e.g., of lexical items) ÌMarkedness determines relative frequency of structures

6. January 24-25, 2003Workshop on Markedness and the Lexicon6  Markedness and Inventories Insert: SHarC Theorem Insert: Lango

7. January 24-25, 2003Workshop on Markedness and the Lexicon7  Inherent Typology Method applicable to related African languages, where the same markedness constraints govern the inventory (Archangeli & Pulleyblank ’94), but with different interactions: different rankings and active conjunctions Part of a larger typology including a range of vowel harmony systems

8. January 24-25, 2003Workshop on Markedness and the Lexicon8  Summary OT builds formal grammars directly from markedness: M ARK … with F AITH Inventories consistent with markedness relations are formally the result of OT … with local conjunction: T LC [Φ], SHarC theorem Even highly complex patterns can be explained purely with simple markedness constraints: all complexity is in constraints’ interaction through ranking and conjunction: Lango ATR harmony

9. January 24-25, 2003Workshop on Markedness and the Lexicon9 Talk Outline Markedness is prior to lexical frequency  Developmentally Explanatorily  Markedness determines possible inventories (e.g., of lexical items) ÌMarkedness determines relative frequency of structures [???]

10. January 24-25, 2003Workshop on Markedness and the Lexicon10 The question is not – why does John say X more frequently than Y?, but – why does John’s speech community say X more frequently than Y?  Markedness  Frequency How are markedness and frequency to be theoretically related? Markedness theory must predict frequency distributions –Frequencies are the data to be explained How, within generative grammar? Consider an extreme (but important) distribution in cross-linguistic typology

11. January 24-25, 2003Workshop on Markedness and the Lexicon11  A Generativist Paradox UG must not generate unattested languages What counts as unattested? “The overwhelming generalization is U ; the proposed UG 0 is right because all systems it generates satisfy U ” “This UG generates the somewhat odd system X (violates U ) … but this is actually a triumph because it so happens that the actual (but obscure) language L is odd like X ” Inconsistent ! celebrates: X not generated celebrates: X is generated

12. January 24-25, 2003Workshop on Markedness and the Lexicon12  The Generativist Paradox That is, how to explain generalizations of the form “Overwhelmingly across languages, U is true, but in rare cases it is violated: (an ‘exception’) X ” Generative grammar has only two options: –Generate only U -systems: strictly prohibits X or –Generate both U and not-U systems: allows X Neither explains the generalization

13. January 24-25, 2003Workshop on Markedness and the Lexicon13  The Generativist Paradox A proposed UG 0 entails a universal U: T ≻ K UG 0 thus predicts –if a language allows T it must also allow K –errors must be directed K  T Suppose this is overwhelmingly true, but rarely: –a language X ’s inventory includes K but not T –there are errors T  K UG 0 -impossible! –Is this evidence for or against UG 0 ? –Must UG 0 be weakened to allow languages with K ≻ T ?

14. January 24-25, 2003Workshop on Markedness and the Lexicon14 UG is not responsible for X ; not core –Linguists’ judgment determines the core data –Good approach  Approaches to the Paradox

15. January 24-25, 2003Workshop on Markedness and the Lexicon15 UG is not responsible for X ; not core UG generates X and is not responsible for its rarity –Derives from extra-grammatical factors  Approaches to the Paradox

16. January 24-25, 2003Workshop on Markedness and the Lexicon16 UG is not responsible for X ; not core UG generates X and is not responsible for its rarity  Approaches to the Paradox UG generates X and derives its rarity –qualitatively or –quantitatively I have no idea Well, maybe three ideas … How, within a generative theory — OT?

17. January 24-25, 2003Workshop on Markedness and the Lexicon17 Graded Generability in OT Idea  :Ranking Restrictiveness Rare systems are those produced by only a highly restricted set of rankings Parallel to within-language variation in OT  Grammar + Ø

18. January 24-25, 2003Workshop on Markedness and the Lexicon18 Consider first within-language variation –a language has a range of rankings –for a given input, the probability of an output is the combined probability of all the rankings for which it is optimal Rankings: equal probability (Anttila) Rankings: “Gaussian probability” (Boersma) – works surprisingly well  Graded Generability in OT

19. January 24-25, 2003Workshop on Markedness and the Lexicon19 Consider first within-language variation –a language has a range of rankings –for a given input, the probability of an output is the combined probability of all the rankings for which it is optimal  Graded Generability in OT Can this work for cross-linguistic variation? – I haven’t a clue Well, maybe three clues

20. January 24-25, 2003Workshop on Markedness and the Lexicon20 Encouraging or discouraging???  Clue 1: CV Theory

21. January 24-25, 2003Workshop on Markedness and the Lexicon21  Clue 2: Constraint Sensitivity The probabilistic interpretation would provide additional empirical constraints on OT theories: ¿Markedness of low-front-round  (IPA Œ ): ① *[+fr, +lo, +rd] or ② *[+fr, +rd], *[+lo, +rd], [+fr, +lo] ? Faithfulness constraints F[fr], F[rd], F[lo] Probability of  in the inventory ① 25% ② 7% Empirical probability informs constraint discovery

22. January 24-25, 2003Workshop on Markedness and the Lexicon22  Clue 3: BO(WO) n W and & D In Basic Inventory Theory with Local Conjunction, the proportion of rankings yielding a BO(WO) n W inventory is Even when many conjunctions are present, the likelihood that they matter becomes vanishingly small as n (the order of conjunction) increases

23. January 24-25, 2003Workshop on Markedness and the Lexicon23  Graded Generability in OT Idea . Learnability Rarer grammars are less robustly learnable  Grammar + general learning theory ???

24. January 24-25, 2003Workshop on Markedness and the Lexicon24  Graded Generability in OT As with Ranking Restrictiveness, start with language-internal variation Idea  Connectionist substrate Given an input I, a rare output O is one that is rarely found by the search process  Grammar + general processing theory

25. January 24-25, 2003Workshop on Markedness and the Lexicon25  Graded Generability in OT Problem identified by Matt Goldrick Aphasic errors predominantly k  t but also t  k occurs, rarely Exceptional behavior w.r.t. markedness How is this possible if *dor ≫ *cor in UG? Under no possible ranking can t  k Must we allow violations of *dor ≫ *cor ? Alternative approach via processing theory Crucial: global vs. local optimization

26. January 24-25, 2003Workshop on Markedness and the Lexicon26  OT ⇒ pr[I → O] via Connectionism Candidate A : realized as an activation pattern a (distributed; or local to a unit) Harmony of A : H ( a ), numerical measure of consistency between a and the connection weights W Grammar: W Discrete symbolic candidate space embedded in a continuous state space Search: Probability of A : pr T ( a ) ∝ e H ( a )/ T –During search, T  0

27. January 24-25, 2003Workshop on Markedness and the Lexicon27  Harmony Maxima Patterns realizing optimal symbolic structures are global Harmony maxima Patterns realizing suboptimal symbolic structures are local Harmony maxima Search should find the global optimum Search will find a local optimum Example: Simple local network for doing ITBerber syllabification

28. January 24-25, 2003Workshop on Markedness and the Lexicon28 BrbrNet

29. January 24-25, 2003Workshop on Markedness and the Lexicon29 BrbrNet’s Local Harmony Maxima An output pattern in BrbrNet is a local Harmony maximum if and only if it realizes a sequence of legal Berber syllables (i.e., an output of Gen ) That is, every activation value is 0 or 1, and the sequence of values is that realizing a sequence of substrings taken from the inventory {CV, CVC, #V, #VC}, where C denotes 0, V denotes 1 and # denotes a word edge

30. January 24-25, 2003Workshop on Markedness and the Lexicon30  Competence, Performance So how can t  k ? – t a global max, k a local max –now we can get k when should get t Distinguish Search Dynamics (‘performance’) from Harmony Landscape (‘competence’) –the universals in the Harmony Landscape require that, absent performance errors, we must have k  t –an imperfect Search Dynamics allows t  k The huge ‘general case/exception’ contrast – t ’s output derives from UG – k ’s output derives from performance error

31. January 24-25, 2003Workshop on Markedness and the Lexicon31  Summary Exceptions to markedness universals may potentially be modeled as performance errors: the unmarked (optimal) elements are global Harmony maxima, but local search can end up with marked elements which are local maxima Applicable potentially to sporadic, unsystematic exceptions in I  O mapping Extensible to systematic exceptions in I  O or to exceptional grammars???

32. January 24-25, 2003Workshop on Markedness and the Lexicon32 Markedness Rules Markedness is prior to lexical frequency  Developmentally Explanatorily  Markedness determines possible inventories (with local conjunction) ÌMarkedness determines relative frequency of structures --- ???