On the Priority
of Markedness
Paul Smolensky
Cognitive Science Department
Johns Hopkins University
January 24-25, 2003
1
Workshop on Markedness and the Lexicon
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
January 24-25, 2003
2
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
3
Workshop on Markedness and the Lexicon
 Experimental Exploration
of the Initial State
January 24-25, 2003
4
Workshop on Markedness and the Lexicon
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
January 24-25, 2003
5
Workshop on Markedness and the Lexicon
 Markedness and
Inventories
• Insert: SHarC Theorem
• Insert: Lango
January 24-25, 2003
6
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
7
Workshop on Markedness and the Lexicon
 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: TLC[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
January 24-25, 2003
8
Workshop on Markedness and the Lexicon
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 [???]
January 24-25, 2003
9
Workshop on Markedness and the Lexicon
 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,
The question
within generative
is not
grammar?
– why does an
Johnextreme
say X more
frequently
than Y?, but
• Consider
(but
important)
– why does John’s
speech community typology
say X more
distribution
in cross-linguistic
frequently than Y?
January 24-25, 2003
10
Workshop on Markedness and the Lexicon
 A Generativist Paradox
• UG must not generate unattested
languages
celebrates: X
not generated
• What counts as unattested?
• “The overwhelming generalization is U;
the proposed UG0 is right because all
systems it generates satisfy U” Inconsistent !
• “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”
celebrates: X is generated
January 24-25, 2003
11
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
12
Workshop on Markedness and the Lexicon
 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 X’s 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 ?
January 24-25, 2003
13
Workshop on Markedness and the Lexicon
 Approaches to the Paradox
• UG is not responsible for X; not core
– Linguists’ judgment determines the core data
– Good approach
January 24-25, 2003
14
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
15
Workshop on Markedness and the Lexicon
 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
How, within a generative
theory — OT?
I have no idea
Well, maybe three ideas …
January 24-25, 2003
16
Workshop on Markedness and the Lexicon
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
January 24-25, 2003
17
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
18
Workshop on Markedness and the Lexicon
 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 haven’t a clue
• Well, maybe three clues
January 24-25, 2003
19
Workshop on Markedness and the Lexicon
 Clue 1: CV Theory
Distribution of Basic Syllable Languages
(C)V(C), 13
CV(C), 20
CV, 47
(C)V, 20
• Encouraging or discouraging???
January 24-25, 2003
20
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
21
Workshop on Markedness and the Lexicon
 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
n
n 2
2
~  
n
 e 
(2  2n  1)!
 
2 n 1  n  1
 2
2
(2 n2  2 n  1)
2 n
• Even when many conjunctions are present, the
likelihood that they matter becomes vanishingly
small as n (the order of conjunction) increases
January 24-25, 2003
22
Workshop on Markedness and the Lexicon
 Graded Generability in OT
Idea . Learnability
Rarer grammars are less robustly learnable
 Grammar + general learning theory
???
January 24-25, 2003
23
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
24
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
25
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
January 24-25, 2003
26
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
January 24-25, 2003
27
Workshop on Markedness and the Lexicon
BrbrNet
σ
Ons
σ
Nuc
C
V
Ons
WONSET
C
Nuc
WONSET = 28
V
a
a
a
Wa
8
W8 = 28  1
i
i
i
Wi
7
W7 = 27  1
r
r
r
Wr
6
W6 = 26  1
n
n
n
Wn
5
W5 = 25  1
z
z
z
Wz
4
W4 = 24  1
s
s
s
Ws
3
W3 = 23  1
d
d
d
Wd
2
W2 = 22  1
t
t
t
Wt
1
W1 = 21  1
b
i
/ Januaryt 24-25, 2003
28
/
Workshop on Markedness and the Lexicon
a
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
January 24-25, 2003
29
Workshop on Markedness and the Lexicon
 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
January 24-25, 2003
30
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 I  O mapping
• Extensible to systematic exceptions in I  O
or to exceptional grammars???
January 24-25, 2003
31
Workshop on Markedness and the Lexicon
Markedness Rules
Markedness is prior to lexical frequency

Developmentally
Explanatorily
 Markedness determines possible
inventories (with local conjunction)
 Markedness determines relative frequency
of structures --- ???
January 24-25, 2003
32
Workshop on Markedness and the Lexicon