On the Priority of Markedness

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On the Priority of Markedness

• Paul Smolensky
• Cognitive Science Department
• Johns Hopkins University

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Markedness Rules

• Markedness is prior to lexical frequency
• ? Developmentally
• Explanatorily
• ? Markedness determines possible inventories
  (e.g., of lexical items)
• Markedness determines relative frequency of
  structures
• Have few solid results mostly suggestive
  evidence, empirical and theoretical

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? Developmental Priority

• Look to see whether young infants are sensitive
  to markedness before theyve had sufficient
  relevant experience
• Before 6 months, infants have not shown
  sensitivity to language-particular phonotactics

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? Experimental Exploration of the Initial State
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Talk Outline

• Markedness is prior to lexical frequency
• ? Developmentally
• Explanatorily
• ? Markedness determines possible inventories
  (e.g., of lexical items)
• Markedness determines relative frequency of
  structures

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? Markedness and Inventories

• Insert SHarC Theorem
• Insert Lango

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? 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

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? Summary

• OT builds formal grammars directly from
  markedness MARK with FAITH
• Inventories consistent with markedness relations
  are formally the result of OT with local
  conjunction TLCF, 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

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Talk Outline

• Markedness is prior to lexical frequency
• ? Developmentally
• Explanatorily
• ? Markedness determines possible inventories
  (e.g., of lexical items)
• Markedness determines relative frequency of
  structures ???

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? Markedness ? Frequency

• How are markedness and frequency to be
  theoretically related?
• Markedness theory must predict frequency
  distributions
• Frequencies are the data to be explained

• The question is not
• why does John say X more frequently than Y?, but
• why does Johns speech community say X more
  frequently than Y?

• How, within generative grammar?
• Consider an extreme (but important) distribution
  in cross-linguistic typology

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? A Generativist Paradox

• UG must not generate unattested languages
• What counts as unattested?
• The overwhelming generalization is U the
  proposed UG0 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

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? 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

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? The Generativist Paradox?

• A proposed UG0 entails a universal U T ? K
• UG0 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 Xs inventory includes K but not T
• there are errors T ? K
• UG0-impossible!
• Is this evidence for or against UG0?
• Must UG0 be weakened to allow languages with K ?
  T ?

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? Approaches to the Paradox

• UG is not responsible for X not core
• Linguists judgment determines the core data
• Good approach

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? Approaches to the Paradox

• UG is not responsible for X not core

• UG generates X and is not responsible for its
  rarity
• Derives from extra-grammatical factors

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? Approaches to the Paradox

• UG is not responsible for X not core

• UG generates X and is not responsible for its
  rarity

• UG generates X and derives its rarity
• qualitatively or
• quantitatively

I have no idea Well, maybe three ideas
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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

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? Graded Generability in OT

• 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

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? Graded Generability in OT

• 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

• Can this work for cross-linguistic variation?
• I havent a clue
• Well, maybe three clues

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? Clue 1 CV Theory

• Encouraging or discouraging???

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? Clue 2 Constraint Sensitivity

• The probabilistic interpretation would provide
  additional empirical constraints on OT theories
• Markedness of low-front-round ?? (IPA )
• ? fr, lo, rd or
• ? fr, rd, lo, rd, fr, lo ?
• Faithfulness constraints
• Ffr, Frd, Flo
• Probability of ?? in the inventory
• ? 25
• ? 7
• Empirical probability informs constraint discovery

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? Clue 3 BO(WO)nW and D

• In Basic Inventory Theory with Local Conjunction,
  the proportion of rankings yielding a BO(WO)nW
  inventory is

• Even when many conjunctions are present, the
  likelihood that they matter becomes vanishingly
  small as n (the order of conjunction) increases

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? Graded Generability in OT

• Idea ?. Learnability
• Rarer grammars are less robustly learnable
• ? Grammar general learning theory
• ???

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? 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

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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
• Must we allow violations of dor cor ?
• Alternative approach via processing theory
• Crucial global vs. local optimization

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? OT ? prI?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

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? 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

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BrbrNet
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BrbrNets 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

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? 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
• ts output derives from UG
• ks output derives from performance error

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? 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???

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Markedness Rules

• Markedness is prior to lexical frequency
• ? Developmentally
• Explanatorily
• ? Markedness determines possible inventories
  (with local conjunction)
• Markedness determines relative frequency of
  structures --- ???