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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
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Graded Generability in OT • Problem identified by Matt Goldrick • Aphasic errors predominantly kt but also tk occurs, rarely • Exceptional behavior w.r.t. markedness • How is this possible if *dor ≫ *cor in UG? Under no possible ranking can tk • Must we allow violations of *dor ≫ *cor ? • Alternative approach via processing theory • Crucial: global vs. local optimization Workshop on Markedness and the Lexicon
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: prT(a) ∝eH(a)/T • During search, T 0 Workshop on Markedness and the Lexicon
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 Workshop on Markedness and the Lexicon
BrbrNet Workshop on Markedness and the Lexicon
BrbrNet’s Global Harmony Maxima • Contrasts with Goldsmith’s Dynamic Linear Models (Goldsmith & Larson ’90; Prince ’93) For a given input string, a state of BrbrNet is a global Harmony maximum if and only if it realizes the syllabification produced by the serial Dell-Elmedlaoui algorithm • (assuming no sonority plateaux) Workshop on Markedness and the Lexicon
BrbrNet’s Search Dynamics Greedy local optimization at each moment, make a small change of state so as to maximally increase Harmony (“gradient ascent”) Workshop on Markedness and the Lexicon
t x z n t /txznt/ tx́.zńt ‘yousing stored’ H Workshop on Markedness and the Lexicon
The Hardest Case: 12378/t́.bś.yá* * hypothetical, but compare tbx́.lákkw‘she even behaved as a miser’ Workshop on Markedness and the Lexicon
Parsing sonority profile 8 1 2 1 3 4 5 7 87 á.tb́.kf.́zń.yáy 8 1 2 1 3 4 5 7 8 7 Workshop on Markedness and the Lexicon
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 Workshop on Markedness and the Lexicon
Competence, Performance • So how can tk ? • 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 kt • an imperfect Search Dynamics allowstk • The huge ‘general case/exception’ contrast • t’s output derives from UG • k’s output derives from performance error Workshop on Markedness and the Lexicon
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 IO mapping • Extensible to systematic exceptions in IO or to exceptional grammars??? Workshop on Markedness and the Lexicon
