Grammar as Choice

1
Grammar as Choice?

• Conflict, concord, optimality

2
Choice

• Grammar involves Multi-criterion Decision Making
• Similar problems arise in cognitive psychology
  (Gigerenzer, Kahneman, Tversky), economics
  (Arrow), neural networks (Smolensky), politics,
  operations research, and so on.
• Many factors interact to determine the form of
  words, phrases, sentences,
• They need not be remotely in agreement about the
  best outcome or course of action.

3
The Three Pillars of Decision

• What are the alternatives?
• from which one must choose.
• What are the criteria?
• which evaluate the alternatives.
• How do the many criteria combine into a single
  decision?
• given pervasive conflict among them.

4
Alternatives

• The generative stance the alternatives are
  actions
• They modify, structure, re-structure, or preserve
  an input
• As a result, an output is defined.
• The choice is among different (In,Out) pairings.

5
An Example

• The Regular Past Tense of English
• Spelled Pronounced Observed Suffix
• massed mæst -t
• nabbed næbd -d
• patted pæt?d -?d

6
An Example

• The Regular Past Tense of English
• Spelled Pronounced Observed Suffix
• massed mæst -t
• nabbed næbd -d
• patted pæt?d -?d

7
An Example

• The Regular Past Tense of English
• Spelled Pronounced Observed Suffix
• massed mæst -t
• nabbed næbd -d
• patted pæt?d -?d

• ? No overlap in distribution of suffix variants

8
An Example

• The Regular Past Tense of English
• Spelled Pronounced Observed Suffix
• massed mæst -t
• nabbed næbd -d
• patted pæt?d -?d

• ? No overlap in distribution of suffix variants
• ? Suffix variants highly similar phonetically

9
An Example

• The Regular Past Tense of English
• Spelled Pronounced Observed Suffix
• massed mæst -t
• nabbed næbd -d
• patted pæt?d -?d

• ? No overlap in distribution of suffix variants
• ? Suffix variants highly similar phonetically
• ? Choice of variant entirely predictable on
  general grounds

10
Regular Past Tense Suffix
11
Regular Past Tense Suffix
d
12
Regular Past Tense Suffix
d
Similarity ? Identity There is just
one suffix /d/
13
Lexical Representation

• Lexical Representation
• massed mæsd
• nabbed næbd
• patted pætd
• Relations Elementary Actions
• d ? d nil
• d ? t devoice
• d ? -?d insert

14
Dilemmas of Action

• Reluctance
• ? voi ? voi doesnt remove all b,d,gs from
  the language
• Ø ? ? doesnt spray schwas into every
  crevice
• Compliance
• Faithful reproduction of input not possible
• mæsd, pætd
• ? Action is taken only to deal with such problems
• Choices, choices
• Insertion solves all problems. Yet we dont
  always do it.
• mæs?d is entirely possible (cf. placid)

15
The Two Classes of Criteria

• Markedness. Judging the outcome. e.g.
• Diff(voi). (Final) Obstruent clusters may not
  differ in voicing.
• pd, bt, td, ds, zt, etc.
• Gem. Adjacent consonants may not be identical.
• tt, dd, bb, in pronunciation
• ?This analysis follows Bakovic 2004.
• Faithfulness. Judging the action.
• InputOutput in a certain property
• Every elementary action is individually
  proscribed e.g.
• NoDevoicing.
• NoInsertion.
• NoDeletion.

16
The Two Classes of Criteria

• Markedness. Judging the outcome. e.g.
• Diff(voi). (Final) Obstruent clusters may not
  differ in voicing.
• pd, bt, td, ds, zt, etc.
• Gem. Adjacent consonants may not be identical.
• tt, dd, bb, in pronunciation
• ?This analysis follows Bakovic 2004.
• Faithfulness. Judging the action.
• InputOutput in a certain property
• Every elementary action is individually
  proscribed e.g.
• NoDevoicing.
• NoInsertion.
• NoDeletion.

17
The Two Classes of Criteria

• Markedness. Judging the outcome.
• Demands compliance with output standards
• Faithfulness. Judging the action.
• Enforces reluctance to act

18
Penalties

• Constraints assess only penalties
• no rewards for good behavior
• Actions are reluctant because constraints on
  action always favor inaction by penalizing
  change.
• Actions happen because constraints on outcome
  force violation of constraints against action.

19
Conflicts Abound

• The faithfulness constraints disagree among
  themselves
• And MDiff disagrees with FNoDevoicing.

20
Conflicts Abound

• The faithfulness constraints disagree among
  themselves

? W marks preference for desired winner ? L
preference for desired loser
21
Conflicts Abound

• The faithfulness constraints disagree among
  themselves
• And MDiff disagrees with FNoDev.

22
All Conflicts Resolved

• Impose a strict priority order gtgt on the set of
  constraints
• Here Gem, Diff gtgt NoIns gtgtNoDel
• In any pairwise comparison of x vs. y
• x ? y x is better than y
• iff the highest-ranked constraint
  distinguishing x from y
• prefers x.
• Optimal. x is optimal iff x ? y for every y
• y violationwise distinct from x

23
Lexicographic

• Better Than, ? lexicographic order on the
  alternatives.
• Sort by the highest ranked constraint
• If it does not decide, on to the next highest.
• And so on.
• Like sorting by first letter (able lt baker)
• and then the next, if that doesnt decide
  (aardvarkltabacus)
• and then the next (azimuth lt azure), and so on.
• Or ordering numerals by place
• 100 lt 200 119 lt 130 2235 lt 2270

24
Optimality Theory

• Alternatives.
• A set of (input,output) pairs.
• A given input is matched with every possible
  output.
• Criteria.
• A set of constraints, of two species
• Markedness judging outcomes
• Faithfulness judging actions
• Collective judgment.
• Derives from a strict prioritization of the
  constraint set.
• Imposes lexicographic order on alternatives. Take
  the best.

25
Universality

• To make maximal use of theoretical resources
• and minimal commitment to extraneous devices,
  assume
• Fixed.
• The set of alternatives is universal.
• Fixed.
• The set of constraints is universal.
• Varying.
• Languages differ freely in the ranking of the
  constraint set.

26
Harmonic Ascent?

• Getting better all the time

27
Beyond Replication

• Faithful mapping InOut
• nabbed næbd ? næbd
• What does it take to beat the faithful candidate?
• Moreton 2002, 2004 asks and answers this
  question.
• Fully Faithful ?x?x? satisfies every F
  constraint.
• Nothing can do better than that on the Fs.
• Nonfaithful ?x?y? beats faithful ?x?x? iff
• The highest ranked constraint distinguishing them
• prefers ?x?y?

28
Beyond Replication

• Faithful mapping InOut
• nabbed næbd ? næbd
• What does it take to beat the faithful candidate?
• Moreton 2002, 2004 asks and answers this
  question.
• Fully Faithful ?x?x? satisfies every F
  constraint.
• Nothing can do better than that on the Fs.
• Nonfaithful ?x?y? beats faithful ?x?x? iff
• The highest ranked constraint distinguishing them
• prefers ?x?y?

29
Triumph of Markedness

• That decisive constraint must be a Markedness
  constraint.
• Since every F is happy with the faithful
  candidate.

30
Triumph of Markedness

• That decisive constraint must be a Markedness
  constraint.
• Since every F is happy with the faithful
  candidate.

31
Harmonic Ascent Markedness Descent

• For a constraint hierarchy H, let HM be the
  subhierarchy of Markedness constraints within it.
• If Ha ? f, for f fully faithful, then HM a ? f
• If things do not stay the same, they must get
  better.
• Analysis and results due to Moreton 2002, 2004.

32
Markedness Rating by HM

• M Diff(voi) gtgt MVoi
• pt, bd (0) pt (0)
• bd (2)
• bt, pd (1) bt, pd (1)

Good
Bad
? Note lexicographic refinement of classes
Constraints from Lombardi 1999
33
Markedness-Admissible Mappings

• pt
• bd
• bt pd

Good
Bad

? Where you stop the ascent, and if you can,
depends on HF.
34
Utterly Impossible Mappings

• pt
• bd
• bt pd

Good
Bad

35
Consequences of Harmonic Ascent

• No Circular Shifts in MF/OT
• Shifts that happen
• Western Basque (Kirchner 1995)
• a ? e alabaa ? alabea
• e ? i semee ? semie
• Catalan (Mascaró 1978, Wheeler 1979)
• nt ? n kuntent ? kunten
• n ? Ø plan ? pla
• ? Analyzed recently in Moreton Smolensky 2002

36
? No Circular Shifts

• Harmonic Ascent
• Any such shift must result in betterment
  vis-à-vis HM.
• The goodness order imposed on alternatives is
• Asymmetric NOT a ?b b ?a
• Transitive a ?b b ?c ? a ?b
• Cant have
• x ? y
• y ? z
• z ? x
• Such a cycle would give x ? x (contradiction!)

37
Way Up ? Way Down

• z
• y
• x

Good
Bad

38
Shift Data

• Large numbers exist
• Moreton Smolensky collect 35 segmental cases
• 3 doubtful, 4 inferred 28 robustly evidenced.
• One potential counterexample
• Taiwanese/ Xiamen Tone Circle
• See Yip 2002, Moreton 2002, and many others for
  discussion.

39
Coastal Taiwanese Tone Shifts
Diagram from Feng-fan Hsieh, http//www.ling.nthu
.edu.tw/teal/TEAL_oral_FengFan_Hsieh.pdf
40
Not the True Article?

• No basis in justifiable Markedness for shifts
  (Yip).
• Paradigm Replacement
• Moreton 2002. Yip 1980, 2002. Chen 2002.
  Mortensen 2004. Hsieh 2004. Chen 2000.

41
? No Endless Shifts

• NO x ? y ?z ? ?

42
? No Endless Shifts

• NO x ? y ?z ? ?
• E.g Add one syllable to input

43
? No Endless Shifts

• NO x ? y ?z ? ?
• E.g Add one syllable to input
• Because constraints only penalize,
• there is an end to getting better.

44
? No Endless Shifts

• NO x ? y ?z ? ?
• E.g Add one syllable to input
• Because constraints only penalize,
• there is an end to getting better.
• This is certainly a correct result.
• we can add one syllable to hit a fixed target
  (e.g. 2 sylls.)
• not merely to expand regardless of shape of
  outcome.

45
Conclusions

• Harmonic Ascent and its consequences nontrivial,
  since mod of theory can easily eliminate. E.g.
  Antifaithfulness.
• Design of the theory succeeds in taking property
  of atomic components (single M constraint) and
  propagating it to the aggregate judgment.
• Requires transitive, asymmetric order,
  commitment to penalization, strict limitation to
  M F constraints.

46
Concord?

• Nonconflict in OT

47
Constraints in conflict
48
Constraints in conflict
49
Constraints in conflict
50
Constraints need not conflict
51
Constraints need not conflict
52
Constraints need not conflict
53
Constraints need not conflict
54
Constraints need not conflict
55
Constraints need not conflict
56
Constraints need not conflict
57
Constraints need not conflict
58
Constraints need not conflict
59
Constraints and Scales

• Imagine a goodness scale a ? b ? c ? d

60
Abstract Scale
better
61
Constraints and Scales

• a ? b ? c ? d
• Consider every bifurcation good ? bad
• abc ? d B1 d
• ab ? cd B2 c,d
• a ? bcd B3 (b,c,d

62
B1
better
63
B2
better
64
B3
better
65
Binary Constraints in Stringency Relation
66
Generating Conflations

• From B1, B2, B3 any respectful coarsening of the
  scale
• may be generated
• B1 B2 ab ? c ? d
• i.e., abc ?d ab?cd
• B2 B3 a ? b ? cd
• i.e., ab?cd a ?bcd
• B1 B2 B3 a ? b ? c ? d and so on

67
Generating Conflations

• From B1, B2, B3 any respectful coarsening of the
  scale
• may be generated
• B1 B2 ab ? c ? d
• i.e., abc ?d ab?cd
• B2 B3 a ? b ? cd
• i.e., ab?cd a ?bcd
• B1 B2 B3 a ? b ? c ? d and so on

68
Generating Conflations

• From B1, B2, B3 any respectful coarsening of the
  scale
• may be generated
• B1 B2 ab ? c ? d
• i.e., abc ?d ab?cd
• B2 B3 a ? b ? cd
• i.e., ab?cd a?bcd
• B1 B2 B3 a ? b ? c ? d and so on

69
Generating Conflations

• From B1, B2, B3 any respectful coarsening of the
  scale
• may be generated
• B1 B2 ab ? c ? d
• i.e., abc ?d ab?cd
• B2 B3 a ? b ? cd
• i.e., ab?cd a ?bcd
• B1 B2 B3 a ? b ? c ? d and so on

70
B1 B2
better
71
Full DNC on 4 candidates

?These Do Not Conflict ?
72
Full DNC on 4 candidates

73
Full DNC on 4 candidates

? B1 B2 T12
74
B1 B2
better
75
Ecological Examples Abound

• Positional Faithfulness vs. general Faithfulness
• Id/Ovoi vs. Idvoi
• be faithful to voicing in Onset vs. be
  faithful to voicing
• Contextual Markedness vs. Less so
• VoicedGemObstruent vs. VoicedObstruent
• (s? vs. ?
• Natural featural subset/superset relations
• hi vs. -low i,u vs. i,u,e,o
• Relations arising between between constraints
  mid-hierarchy as conflict-inducing candidates
  drop out.

76
Special / General as Stringency

• S/G. Such examples show nonconflicting
  constraints tracking the special case/ general
  case relationship.
• Stringency. We study only the extensional impact
  of the relationship, as embodied in violation
  profiles.
• i.e. in ordinal classes imposed by viol.
  profiles.
• We dont care about the exact violation
  quantities
• Constraints form a hierarchy of increasing
  stringency, as more and more is rejected.

77
Linguistic Scales

• Particularly informative is the relation between
  scales of relative sonority and placement of
  stress.
• This allows us to probe the varying behavior of
  similar scales across languages.

78
Intrinsic Sonority of vowels
79
Sonority-Sensitive Stress

• Main-stress falls in a certain position
• say, 2nd to last syllable xXx
• Except when adjacent vowel has greater sonority
• then the stronger vowel attracts the stress Xxx
• This perturbation evidences the fine structure of
  the scale.

80
Sonority-Sensitive Stress

• Chukchi (Kenstowicz 1994, Spencer 1999)
• Typically base-final when suffixed xXx
• jará-?a migcirét-?k
• reqokál-g?n wirí?-?k
• welól-g?n ekwét-?k
• pi?é-pi? nuté-nut
• But one syll. back when stronger available Xxx
• céri-cer cerí-cer egti
• kéli-kel
• wéni-wen

81
Sonority-Sensitive Stress

• Schwa yields to any other vowel
• ?tlá
• ??ló
• ?nré
• ??nín
• ??nún
• ? a,o, e, i, u gt ?

• But behaves normally with itself
• ?tl?q
• ?tt?m
• k?t??t
• c?m??
• ? ? ?

NB. stress typically avoids the last syllable of
the word.
82
Chukchi Scale

• These considerations motivate a scale like this
• aeogt iu gt ?
• In terms of goodness of fit wrt stress
• áéó ? íú ? ?

83
Intrinsic Sonority of vowels
84
Flattened Chukchi Scale
better
85
B1 B2
86
Achieving Chukchi

• How does this relate to the full scale that
  registers every level of distinction?
• To coarsen the scale in the Chukchi fashion,
• we must disable B3 and activate both B1 and B2.
• Ranking will yield this.

87
Ranking?

• How can the Bis be ranked? They dont conflict!

88
Ranking?

• How can the Bis be ranked? They dont conflict!
• Transitivity. Find a constraint C with which they
  conflict.

89
Ranking?

• How can the Bis be ranked? They dont conflict!
• Transitivity. Find a constraint C with which they
  conflict.
• B1, B2 gtgt C

90
Ranking?

• How can the Bis be ranked? They dont conflict!
• Transitivity. Find a constraint C with which they
  conflict.
• B1, B2 gtgt C gtgt B3

91
Ranking?

• How can the Bis be ranked? They dont conflict!
• Transitivity. Find a constraint C with which they
  conflict.
• B1, B2 gtgt C gtgt B3

92
Ranking?

• How can the Bis be ranked? They dont conflict!
• Transitivity. Find a constraint C with which they
  conflict.
• B1, B2 gtgt C gtgt B3
• ? Here C demands stress in a certain position

93
The Hierarchy

• B1, B2 gtgt POS gtgt B3

94
The Hierarchy

• B1, B2 gtgt POS gtgt B3
• Stress flees from ? to iueoa (B1)

95
The Hierarchy

• B1, B2 gtgt POS gtgt B3
• Stress flees from ? to iueoa (B1)
• Stress flees from ?iu to eoa (B2)

96
The Hierarchy

• B1, B2 gtgt POS gtgt B3
• Stress flees from ? to iueoa (B1)
• Stress flees from ?iu to eoa (B2)
• The distinction eo/a is ignored (B3)

97
The Hierarchy

• B1, B2 gtgt POS gtgt B3
• Stress flees from ? to iueoa (B1)
• Stress flees from ?iu to eoa (B2)
• The distinction eo/a is ignored.
• Conjunctivity.
• Because B1 and B2 do not conflict, their demands
  are both met.
• see Samek-Lodovici Prince 1999, 21 Favoring
  Intersection Lemma

98
The Optima

• B1,B2 gtgt POS gtgt B3

99
The Optima

• B1,B2 gtgt POS gtgt B3

100
The Optima

• B1,B2 gtgt POS gtgt B3

101
The Optima

• B1,B2 gtgt POS gtgt B3

102
The Optima

• B1,B2 gtgt POS gtgt B3

103
The Optima

• B1,B2 gtgt POS gtgt B3

104
The Ranking

• B1,B2 gtgt POS gtgt B3

105
Known Conflations

• Kobon (Kenstowicz 1994). a gt e,o gt
  i,u gt ö,?
• In a final 2 s window, stress the most sonorous,
  else initial in window.
• Chukchi (K 94) a, e, o gt i,u gt
  ?
• In base-final words, penult stress unless
  antepenult is greater on scale.
• Nganasan (de Lacy 2002) a, e, o gt
  i, ü, u, ?, ?
• Penult, except antepenult when a.p. stronger
  precedes weaker pen.
• Mari (K 94) a, ä, e, o, i, u gt ?
• Rightmost nonfinal full V, else leftmost V.

106
Currently Known Conflations
Adapted from de Lacy 2002
107
Conclusion

• All types currently attested except B2B3
• Assumptions
• Simplest binary interpretation of scale in
  constraints
• Free ranking of all constraints, as usual
• Result
• All respectful collapses are generated
• Nonconflict automatically provides a theory of
  scales in OT

108
Optimality?

• Harmonic bounding

109
Here Comes Everybody

• Alternatives. Come in multitudes.
• But many rankings produce the same optima.
• Not all constraints conflict
• Extreme formal symmetry to produce all possible
  optima
• Not often encountered ecologically

110
Completeness Symmetry

• Perfect System on 3 constraints.

111
Completeness Symmetry

• Perfect System on 3 constraints.

112
Completeness Symmetry

• Perfect System on 3 constraints.

113
Completeness Symmetry

• Perfect System on 3 constraints.

114
Optima and Alternatives

• Limited range of possible optima
• Much, much less than n! for n constraint system
• But there are Alternatives Without Limit.
• Augmenting actions (insertion, adjunction, etc.)
  increase size and number of alternatives, no end
  in sight.
• Where is everybody?

115
Harmonic Bounding

• Many candidates almost all can never be
  optimal

116
Harmonic Bounding

• Many candidates almost all can never be
  optimal
• Example Profuse insertion

117
Harmonic Bounding

• Many candidates almost all can never be
  optimal
• Example Profuse insertion

Candidate (b) has nothing going for it.
?It is equal to (a) or worse than it on every
constraint
118
Harmonic Bounding

• Attempt the overinserted candidate as desired
  optimum
• It cant win this competition
• no constraint prefers it,
• and one prefers its competitor !

119
Harmonic Bounding

• Generically
• If there is no constraint on which a ? ß, for a
  ? ß violationwise,
• no W in the row and at least one L
• then a can never be optimal.
• ß is always better, so a cant be the best
• Even if ß itself is not optimal, or not possibly
  optimal !
• e.g. 19 is not the smallest positive number
  because 18lt19.

120
Harmonic Bounding

• Harmonic Bounding is a powerful effect
• E.g. Almost all insertional candidates are
  bounded
• This gives us a highly predictive theory of
  insertion

121
Harmonic Bounding

• Harmonic Bounding is a powerful effect
• E.g. Almost all insertional candidates are
  bounded
• This gives us a highly predictive theory of
  insertion
• Even though there are restrictions on insertions
  at all in defining the set of possible
  alternatives!

122
Harmonic Bounding

• Harmonic Bounding is a powerful effect
• E.g. Almost all insertional candidates are
  bounded
• This gives us a highly predictive theory of
  insertion
• Even though there are restrictions on insertion
  at all in defining the set of possible
  alternatives!
• But were not done.
• Simple Harmonic Bounding works without ranking
• Any positively weighted combination of violation
  scores will show the effect.

123
Collective Harmonic Bounding

• A ranking will not exist unless all competitions
• can be won simultaneously
• Neither C1 nor C2 may be ranked above the other
• If C1gtgtC2, then d ? a
• If C2 gtgtC1 then ß ? a
• ß and d cooperate to stifle a

124
Collective Harmonic Bounding

• An example from Basic Syllable Theory

125
Collective Harmonic Bounding

• An example from Basic Syllable Theory

126
Collective Harmonic Bounding

• The middle way is no way.

127
General Harmonic Bounding

• Def. Candidate a is harmonically bounded
• by a nonempty set of candidates B, x?B, over a
  constraint set S iff for every x?B, and for
  every C?S,
• if C a?x, then there is a y?B such that
  C y?a.
• If any member of B is beaten by a on a constraint
  C, another member of B comes to the rescue,
  beating a.
• If any ax earns W, then some ay earns L.
• If B has only one member, then a can never beat
  it.
• No harmonically bounded candidate can be optimal.

128
General Harmonic Bounding

• Def. Candidate a is harmonically bounded
• by a nonempty set of candidates B, x?B, over a
  constraint set S iff for every x?B, and for
  every C?S,
• if C a?x, then there is a y?B such that
  C y?a.
• If any member of B is beaten by a on a constraint
  C, another member of B comes to the rescue,
  beating a.
• If any ax earns W, then some ay earns L.
• If B has only one member, then a can never beat
  it.
• No harmonically bounded candidate can be optimal.

129
General Harmonic Bounding

• Def. Candidate a is harmonically bounded
• by a nonempty set of candidates B, x?B, over a
  constraint set S iff for every x?B, and for
  every C?S,
• if C a?x, then there is a y?B such that
  C y?a.
• If any member of B is beaten by a on a constraint
  C, another member of B comes to the rescue,
  beating a.
• If any ax earns W, then some ay earns L.
• If B has only one member, then a can never beat
  it.
• No harmonically bounded candidate can be optimal.

130
Some Stats

• Tesar 1999 studies a system of 10 prosodic
  constraints.
• with a large number of prosodic systems generated
• Among the 4 syllable alternatives
• ca. 75 are bounded on average
• ca. 16 are collectively bounded (approx. 1/5 of
  bounding cases)
• Among the 5 syllable alternatives
• ca. 62 are bounded
• ca. 20 are collectively bounded (approx. 1/3 of
  bounding cases)
• ? Calculated in Samek-Lodovici
  Prince 1999

131
Some Stats

• Tesar 1999 studies a system of 10 prosodic
  constraints.
• with a large number of prosodic systems generated
• Among the 4 syllable alternatives
• ca. 75 are bounded on average
• ca. 16 are collectively bounded (approx. 1/5 of
  bounding cases)
• Among the 5 syllable alternatives
• ca. 62 are bounded
• ca. 20 are collectively bounded (approx. 1/3 of
  bounding cases)
• ? Calculated in Samek-Lodovici
  Prince 1999

132
Bounding in the Large

• Simple Harmonic Bounding is Pareto optimality
• An assignment of goods is Pareto optimal or
  efficient if theres no way of increasing one
  individuals holdings without decreasing somebody
  elses.
• Likewise, it is non-efficient if someones
  holdings can be increased without decreasing
  anybody elses.
• A simply bounded alternative is
  non-Pareto-optimal. We can better its performance
  on some constraint(s) without worsening it on any
  constraint.
• Collective Harmonic Bounding is the creature of
  freely permutable lexicographic order.
• See Samek-Lodovici Prince 1999 for discussion.

133
Intuitive Force of Bounding

• Simple Bounding relates to the need for
  individual constraints to be minimally violated.
• If we can get (0,0,1,0) we dont care about
  (0,0,2,0).

134
Intuitive Force of Bounding

• Collective Bounding reflects the taste of
  lexicographic ordering for extreme solutions.
• If a constraint is dominated, it will accept any
  number of violations to improve the performance
  of a dominator.
• There is no compensation for a high-ranking
  violation
• If (1,1) meets (0,k), the value of k is
  irrelevant.

135
Explanation from Bounding

• Bounded alternatives are linguistically
  impossible.
• Yet their impossibility is not due to a direct
  restriction on linguistic structure.
• Impossibility follows from the interaction of
  constraints under ranking.
• Explanation emerges from the architecture of the
  theory.

136
Grammar as Choice?

• Conclusion, retrospect, overview

137
Among the Cognitive Sciences

• Perspectives on cognitive theory tend to
  bifurcate

?See esp. Smolenskys work for analysis
138
Among the Cognitive Sciences

• OT sits on the left side of every opposition
• But in every case there is currently an active
  technical interchange between advocates and
  critics leading to new understanding of the
  relations between apparent dichotomies.
• In psychology of reasoning, e.g., Gigerenzer and
  colleagues argue for the use of criteria under
  lexicographic order.

139
Gigerenzer Goldstein 1996
140
Fast and Frugal

• For Gigerenzer et al. the main contrast is with
  Bayesian probabilistic calculation over
  alternatives.
• Lexicographic choice is one reason decision
  making
• i.e. at the level of deciding between 2
  alternatives
• Therefore, fast and frugal.
• OT aims for neither speed nor frugality, but
  deploys the same mechanism of lexicographic
  decision-making

141
Looking Both Ways

• OT seeks to explain the basic properties of human
  language through a formal theory of the
  linguistic faculty.
• OT, as a lexicographic theory of ordinal
  preference, points toward new kinds of
  connections with the cognitive apparatus that
  acquires and uses grammatical knowledge.
• ?

142
Thanks

• Thanks to Vieri Samek-Lodovici, Paul Smolensky,
  John McCarthy, Jane Grimshaw, Paul de Lacy,
  Alison Prince, Adrian Brasoveanu, Naz Merchant,
  Bruce Tesar, Moira Yip.

143
Where to learn more about OT

• http//roa.rutgers.edu
• Many researchers have made their work freely
  available at the Rutgers Optimality Archive.
• Thanks to the Faculty of Arts Sciences, Rutgers
  University for support.

144
References

• ROA http//roa.rutgers.edu
• Alderete, J. 1999. Morphologically governed
  accent in Optimality Theory. ROA-393.
• Arrow, K. 1951. Social choice and Individual
  Values. Yale.
• Bakovic, E. 2004. Partial Identity Avoidance as
  Cooperative Interaction. ROA-698.
• Chen, M. 2000. Tone Sandhi. CUP.
• de Lacy, Paul. 2002. The Formal Expression of
  Markedness. ROA-542.
• Gigerenzer, G., P. Todd, and the ABC Research
  Group. Simple Heuristics that Make us Smart. OUP.
• Gigerenzer, G. and D. Goldstein. 1996. Reasoning
  the fast and frugal way Models of bounded
  rationality. Psych. Rev. 103, 650-669.
• Hsieh, Feng-fan. 2004. Tonal Chain-shifts as
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  Colloquium. http//web.mit.edu/ffhsieh/www/ANTS.pd
  f
• Kager, R. Optimality Theory. Textbook. CUP.
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• Kirchner, Robert. 1996. Synchronic chain shifts
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• Lombardi, L. 1999. Positional Faithfulness and
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  17, 267-302.
• Lubowicz, A. 2002. Contrast Preservation in
  Phonological Mappings. ROA-554
• Mascaró, J. 1978. Catalan Phonology and the
  Phonological Cycle. Ph. D.
• dissertation, MIT. Distributed by Indiana
  University Linguistics Club.

145
References

• McCarthy, J. 2002. A Thematic Guide to Optimality
  Theory. CUP.
• McCarthy, J., ed. 2004. Optimality Theory in
  Phonology. Blackwell.
• Moreton, E. 2002, 2004. Non-Computable Functions
  in Optimality Theory. ROA-364. Revised, in
  McCarthy 2004, pp.141-163.
• Moreton, E. and P. Smolensky. 2002. Typological
  consequences of local constraint conjunction.
  ROA-525.
• Mortensen, D. 2004. Abstract Scales in Phonology.
  ROA-667.
• Prince, A. 1997ff. Paninian Relations.
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• Prince, A.2002. Entailed Ranking Arguments.
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• Prince, A. 2002. Arguing Optimality. ROA-562.
• Prince, A. and P. Smolensky, 1993/2004.
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• Samek-Lodovici, V. and A. Prince. 1999. Optima.
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• Samek-Lodovici, V. and A. Prince. Fundamental
  Properties of Harmonic Bounding. RuCCS-TR-71.
  http//ruccs.rutgers.edu/tech_rpt/harmonicbounding
  .pdf
• Smolensky, P and G. Legendre. To appear 2005. The
  Harmonic Mind. MIT.
• Spencer, A. 1999. Chukchee. http//privatewww.es
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• Wheeler, Max. 1979. Phonology of Catalan.
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• Yip, M. 2002. Tone. CUP.

146
Grammar as Choice?

• Conflict, concord, optimality