Constraint Conjunction and Strong Harmonic Completeness

1
Constraint Conjunction and Strong Harmonic
Completeness

• Paul Smolensky
• Cognitive Science Department
• Johns Hopkins University

2
Jakobsons Program

• A Grand Unified Theory for the cognitive science
  of language is enabled by Markedness
• Avoid a
• ? Structure
• Alternations eliminate a
• Typology Inventories lack a
• ? Acquisition
• a is acquired late
• ? Processing
• a is processed poorly
• ? Neural
• Brain damage most easily disrupts a

Formalize through OT?
3
Markedness Theory from OT

• ? Theoretical. OT (Prince Smolensky 91, 93)
  
• Construct formal grammars directly from
  markedness principles
• Strongly universalist inherent typology

• ? Theoretical. Local Conjunction
• OT must be extended in order to generate all
  markedness-governed inventories

• ? Empirical. OT with Local Conjunction
• Allows completely formal markedness-based
  explanation of highly complex data

4
? The Great Dialectic

• Phonological representations serve two masters

FAITHFULNESS
MARKEDNESS
Locked in conflict
5
OT from Markedness Theory

• MARKEDNESS constraints a No a
• But exactly when is a avoided?
• FAITHFULNESS constraints
• Fa demands that /input/ ? output leave a
  unchanged (McCarthy Prince 95)
• Fa controls when a is avoided (and how)
• Interaction of violable constraints Ranking
• a is avoided when a Fa
• a is tolerated when Fa a
• M1 M2 combines multiple markedness dimensions

6
OT from Markedness Theory

• MARKEDNESS constraints a
• FAITHFULNESS constraints Fa
• Interaction of violable constraints Ranking
• a is avoided when a Fa
• a is tolerated when Fa a
• M1 M2 combines multiple markedness dimensions
• Typology All cross-linguistic variation results
  from differences in ranking in how the
  dialectic is resolved (and in how multiple
  markedness dimensions are combined)

7
OT from Markedness Theory

• MARKEDNESS constraints
• FAITHFULNESS constraints
• Interaction of violable constraints Ranking
• Typology All cross-linguistic variation results
  from differences in ranking in resolution of
  the dialectic
• Harmony MARKEDNESS FAITHFULNESS
• A formally viable successor to Minimize
  Markedness is OTs Maximize Harmony (among
  competitors)

8
? Markedness Theory from OT

• Explanatory goals achieved by OT
• Individual grammars are literally and formally
  constructed directly from universal markedness
  principles
• Inherent Typology
• Within the analysis of phenomenon F in language
  L is inherent a typology of F across all languages

9
Markedness Theory from OT

• ? Theoretical. OT (Prince Smolensky 91, 93)
  
• Construct formal grammars directly from
  markedness principles
• Strongly universalist inherent typology

• ? Theoretical. Local Conjunction
• OT must be extended in order to generate all
  markedness-governed inventories

• ? Empirical. OT with Local Conjunction
• Allows completely formal markedness-based
  explanation of highly complex data

10
? Markedness and Inventories

• An inventory structured by markedness
• An inventory I is harmonically complete (HC) iff
• x ? I and y is (strictly) less marked than x
• implies
• y ? I
• A typology structured by markedness
• A typology T is strongly Harmonically complete
  (SHarC) iff
• L ? T if and only if L is harmonically complete
• (Prince Smolensky 93 Ch. 9)
• Are OT inventories harmonically complete?
• Are OT typologies SHarC?

11
Harmonic Completeness

• English obstruent inventory
• is HC w.r.t. Place/continuancy

Inventory Bans Only the Worst Of the Worst (BOWOW)
but is not generable by ranking velar,
cont FPlace, Fcont
12
Local Conjunction

• Crucial to distinguish
• taxi
• ?saki

x w.r.t segment inventory cont, velar
fatal in same segment

• cont, velar
• cont, velar

Local conjunction cont seg velar
violated when both violated in same segment
13
Basic Inventories/Typologies

• Formal analysis of HC/SHarC in OT Definitions
• Basic inventory I F of elements of type D,
  where F fk
• Candidates X ?f1, ?f2, ?f3, ?f4,
• Con MARK f1, ?f2,
• FAITH Ff1, Ff2,
• I F a ranking of Con
• Basic typology T F All rankings of Con
• Basic typology w/ Local Conjunction, T LCF All
  rankings of ConLC Con all conjunctions of
  constraints in MARK, local to D

14
SHarC Theorem

• SHarC Theorem
• T F
• each language is HC
• SHarC property does not hold
• TLCF
• each language is HC
• SHarC property holds

15
? Empirical Relevance

• Local conjunction has seen many empirical
  applications here, vowel harmony
• Lango (Nilotic, Uganda) ATR harmony
• Woock Noonan 79
• Archangeli Pulleyblank 91 et seq., esp. 94
• Markedness
• ATR, ?hi/fr
• ?ATR, hi/fr
• A/sclosed
• HD-LATR

Rather than imposing a parametric superstructure
on spreading rules (AP 94), we build the
grammar directly from these markedness constraints
16
Lango ATR Harmony

• Inventory of ATR domains D ATR ( tiers)
• Vowel harmony renders many possibilities
  ungrammatical yourSING/PLUR stew
• d?k Cí ? d? k k í ? dè kk í d? kk
  ? ATR ? ? 0
  ?0 ?
• d?kwú ? ?d?kwú dèkwú d?kw?
• critical difference ifr vs. u?fr ?fr
  worse source for ATR spread violates
  ATR, ?fr marked w.r.t. ATR
• Complex system interaction of 6 dimensions (26
  64 distinct environments)

17
(No Transcript)
18
d?k Cí ? dèkkí
19
d?kwú ? d?kwú
20
(No Transcript)
21
The Lango Challenge

• Need a grammatical framework able to handle this
  nightmarish descriptive complexity
• while staying strictly within the confines of
  rigidly universal (markedness) principles

22
Lango rules


a


ß







ATR
ATR





V C V


V
(C)C
V




a


b


c













ATR
ATR
ATR

• Archangeli Pulleyblank 94

V C V


V (C)C V


V (C)C V








hi



hi


hi



fr



x


-


ATR


V (C)C V



-

hi


-
fr



23
(No Transcript)
24
(No Transcript)
25
cont seg velar
A/sclosed DA ?hi,A/HDA No ?ATR
spread into a closed syllable from a ?hi
source
26
BOWOW ?hi, ?A HD-L?A No regressive ?ATR
spread from a ?hi source
27
X,Y,Z ?A 1,2,3 A AGREE FA
28
The Lango Challenge

• Need a grammatical framework able to handle this
  nightmarish descriptive complexity
• while staying strictly within the confines of
  rigidly universal (markedness) principles

? OT with conjunctive constraint interaction
29
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

30
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

31
Advertisement

• The complete story Chapter 14
• The harmonic mind From neural computation to
  optimality-theoretic grammar
• Smolensky Legendre
• Forthcoming (2003) Blackwell

32
Thank you for your attention