Transcript Document 7491510

Constraint Conjunction, Ties, Opacity
Plan of this unit.
Discussion of Optionality
Introduction of Ties
Technicalities
Cumulative Effects
Introduction of Constraint
Conjunctions
The Limits of the Approach
Constraint Conjunction, Ties, Opacity
We saw yesterday that the relation
between input and output is not
always one-to-one but that some
inputs lead to ineffability.
Today we will see more cases of
more complex relations between
inputs, outputs and candidates.
.
Optionality
The reverse of ineffability is a case
where several outputs emerge as
optimal, not just one. This is a case of
optionality or free variation.
A phenomenon like optionality or free
variation implies that the grammar
must be flexible enough to allow
competing expressions to emerge.
.
Multiple outputs:optionality
Different ways to express ‘Who did you
see?’ in French:
Tu as vu qui?
Qui as-tu vu?
Qui est-ce que tu as vu?
C’est qui que tu as vu?
Multiple outputs:optionality
Expletive Insertion vs. Movement
there was a moose shot
a moose was shot
Dative Shift
I gave a book to Mary
I gave Mary a book
Multiple outputs:optionality
Complementizer Deletion
I think (that) she is intelligent
Extraposition / HNPS / Particle Shift
a man from India arrived
a man arrived from India
she looked up the interesting answer
she looked the interesting answer up
Multiple outputs:optionality
Scrambling
dass niemand das Buch gelesen hatte
that nobody the book read had
dass das Buch niemand gelesen hatte
Topicalization
das Buch hatte niemand gelesen
gelesen hatte das Buch niemand
niemand hatte das Buch gelesen
Multiple outputs:optionality
Free variation in the phonology of German
a. Segmental alternation
[taç] and [ta:k] for Tag ‘day’
[g´reo:n] and [ge:reo:n] for Gereon ‘a name’
b. Alternation in stress position
Télefon vs. Telefón
Multiple outputs:optionality
Free variation in the phonology of French
a. Choice of an alternant
ancien ‘old’: [ãsj´n] and [ãsj´~n] in the
masculine liaison case (un ancien ami)
b. Glide formation
ouest [w´st] ~ [u.´st] ‘west’, nuage
[nu.aΩ] ~ [n¥aΩ] ‘cloud’, piano [pja.no] ~
[pi.a.no]
Solutions
1.
2.
3.
4.
Optionality is only apparent
Identity of profiles
Co-Phonologies (Co-syntaxes)
Tied Constraints
1. Apparent Optionality
First, optionality may be only
apparent.
There IS a meaning difference
between
der Pfarrer kommt
‘the priest comes’
and
es kommt der Pfarrer
1. Apparent Optionality
The same would seem to hold for
a moose was shot
there was a moose shot
Scrambling
Different Topicalizations
One can encode such differences in
terms of semantic/pragmatic features.
1. Apparent Optionality
If these are in the input, than
structures do not really compete with
each other in instances of apparent
optionality.
Likewise, dative shift may involve a
difference in lexical composition.
2. Identical violation profiles
Second, EVAL will not always be able
to differentiate between the options
...
Suppose e.g. that complementizers
do not induce a violation of Full
Interpretation ...
2. Identical violation profiles
Then
I think he will come
I think that he will come
can be derived from the same input, and they
have identical constraint violation profiles
(Grimshaw)
--> both can be grammatical
(Dative Shift)
Solution 3 : cophonologies
Within phonology, quite a different solution has
been proposed:
Co-phonologies are parallel phonologies for
different parts of the phonology.
(Co-phonologies as a way to account for free
variation is usually dismissed because too
permissive. Most cases which have been explained
with co-phonologies can be explained otherwise.)
Cophonologies
Typical cases imply the co-existence of two
systems of stress patterns in a language
(Turkish is a standard example, and
German, too).
We saw that in multi-stratal approaches, each
stratum defines its own phonology.
Remember class, classy, classic and levels.
Cophonologies
The most relevant case for OT is stratification of the
lexicon.
Different parts of the vocabulary can define different
strata: some segments, stress patterns,
phonotactic generalizations and the like can be
specific to some strata and absent in others.
In German, final full vowels are typical for nonnative
words: Auto, Menü, Biologie…
Cophonologies
A widely accepted view is that the lexicon is
organized concentrically (see Ito & Mester for
Japanese, Féry for German).
In the center there are the native words, obeying a
strict phonology. A great deal of markedness
constraints are active there. Going away from the
center, words are less and less assimilated nonnative words. The less assimilated words are, the
less markedness constraints they fulfill and the more
faithful they are to their source language.
Cophonologies
1. Native vocabulary
2. Assimilated foreign
3. Unassimilated foreign
1
2
3
Cophonologies
Each stratum formed by some part of the vocabulary
(Germanic, Latinate, Sino-Chinese,
unassimilated…) is a co-phonology.
It must been observed that ideally the markedness
constraints are organized in just one hierarchy.
Words fulfill the constraints up to a certain point, a
different one for each stratum.
Thus cophonologies are just partial.
3. Cophonologies
Free variation as cophonologies implies that one
word can be in one stratum for one speaker and in
another stratum for another speaker (genre in
English, city in German…)
Example in Japanese
Citybank (a Japanese bank) is pronounced [∫it∫i],
[∫iti] or [siti] bank
3. Cosyntax
Syntax shows related phenomena, though they are
typically ignored.
Consider e.g. the Germanic co-syntax of English
Restricted V/2:
In the garden stands a fountain
„I am sick“ said the ugly stranger
Rules of English proper must not follow Engliman
*Does in the garden stand a fountain?
4. Ties
Ties are two (or more) constraints of the same rank.
In case it is these constraints which decide on the
optimality of candidates, the result of a tie is two
or more different optimal outputs.
This solution differs from the identity of profiles
solution since the optional candidates have
different profiles.
4. Ties
Ties can be interpreted differently. In the first
interpretation, two hierarchies define simultaneous
grammars from a certain point up (this is a case of
cophonology and cosyntax).
The result is two or more different optimal outputs.
First interpretation of ties
C2a >> C2b >> C3 …
/
…C1 >>
\
C2b >> C2a >> C3 …
or
C1 >> C2a >> C2b >> C3 …
C1 >> C2b >> C2a >> C3 …
First interpretation of ties
Given the hierarchy
A .... B C1/C2 D ... E
If C1 and C2 are tied by hierarchy, then
S is grammatical iff
S is optimal with respect to
A ...B C1D ...E
or
A ...B C2D ...E
Multiple outputs: optionality
(11) Free variation in ‘nuage’
/nuage/
NOHIATUS
NOCOMPLEXONSET
.nuag e.
*
.nu.ag e.
*
A Tie between Constraints in Syntax
Pesetsky-style treatment of complemetizers:
A different solution for
I think (that) he will come
LE(CP):
A CP must begin with a
complementizer
(Align (CP, COMP, left)
TEL:
Do no pronounce
function words
Complementizers in embedded clauses
(1)
(2)
I think that he is a fool
I think he is a fool
TEL LECP
(1) *
(2)
*
Relative Clauses
(1)
(2)
(3)
(4)
a
a
a
a
man who that I like
man who I like
man that I like
man I like
Candidate (4) is eliminated because it violates both
Tel and LECP.
The other candidates violate either Tel or LCPC and
are thus all optimal.
Mixed case of identity of profiles and ties.
Relative Clauses
(1)
TEL
LECP
*(!)
*(!)
(2)
(3)
(4)
*
*
*
Possible drawback
Since the candidates differ in their profiles it can be
the case that a lower ranking constraint decide to
eliminate one of the candidate which was chosen as
optimal by the tie.
Second interpretation of ties
The tie is defined in the same way as before, but the
remaining of the hierarchy is identical.
The drawback identified above is eliminated.
Second interpretation of tie
C2a >> C2b
/
\
C1 >>
>> C3 …
\
/
C2b >> C2a
or
C1 >> C2a >> C2b >> C3 …
C1 >> C2b >> C2a >> C3 …
Relative Clauses
(1)
TEL
LECP
NOSTRUC
*(!)
*(!)
**
*
*
(2)
(3)
(4)
*
*
*
Third interpretation of ties
In this concept of a tie, the number of violations of
the tied constraints taken together is relevant for
evaluation
C1 >> C2a + C2b >> C3 …
Such a definition is needed when more than two
candidates emerge as optimal.
Ties between Constraints
Given the hierarchy
A .... B C1/C2 D ... E
If C1 and C2 are tied cumulatively, then
S is grammatical iff
S is optimal with respect to
A ...B F D ...E
where F is the sum of violations of C1 and
C2
Pesetsky’s Concept of a Tie
Wh-expletive insertion in German
seems to be another case in point:
any combination of Stay and FI
violations yields a grammatical result
A Tie between Constraints
1. Wen denkst du t dass sie meint t
dass Fritz liebt
who think you that she believes that
Fritz loves
2. was denkst du wen sie meint t
dass Fritz liebt
3. was denkst du was sie meint wen
Fritz liebt
4. was denkst du t dass sie meint
wen Fritz liebt
A Tie between Constraints
FI
1.
2.
3.
4.
Wen … t … t …
was … wen … t …
was … was … wen …
was … t … wen …
Stay
**
*
**
*
*
*
A Tie between Constraints
In interpretation 1 and 2, only the first and
third candidates can emerge as optimal.
The Need for a further concept
Ich denke / I think
1. dass der Fritz nicht geschlafen hat
that the Fritz not slept has
2. der Fritz hat nicht geschlafen
1.
2.
FI
Stay (Comp) and Stay (prefield)
A Pesetsky-style tie would favor 1.!
GENERATE TWO HIERARCHIES
Another case in point
Scrambling as an instance of multiple
hierarchies (Uszkoreit)
1. nom > acc/dat
2. animate > inanimate
3. definite > indefinite
NOM
ANIM
DEF
A sentence is grammatical if it satisfies at
least one constraint
Ties between Constraints
Dass der Mann ein Buch liest
that the man a book reads
NOM, DEF, ANIM
*dass ein Buch der Mann liest
*NOM, *DEF, *ANIM
dass ein Mann das Buch liest
that a man the book reads
NOM, ANIM,*DEF
dass das Buch ein Mann liest
*NOM, *ANIM, DEF
Ties between Constraints
Dass ein Buch der Frau hilft
that a book the woman helps
NOM, *DEF, *ANIM
dass der Frau ein Buch hilft
*NOM, DEF, ANIM
dass das Buch einer Frau hilft
NOM, DEF,*ANIM
dass einer Frau das Buch hilft
*NOM, *DEF, ANIM
Ties between Constraints
A Pesetsky style concept of a tie would
incorrectly predict that structures with n
violations are blocked by structures with nk violations.
What we need for such examples is a
concept of ties in which complete
hierarchies are tied ...
Lexicographic Conflict Resolution
Recall that conflict resolution in OT is
lexicographic:
there is a hierarchy H of constraints,
and C is better than D relative to H
iff D violates the highest constraint
on which C and D differ more often
than C
Lexicographic Conflict Resolution
A number of proposals have been
made which imply that conflict
resolution is not always lexicographic
Constraint conjunction
Two cases of constraint conjunction: selfconjunction of one constraint and
conjunction of different constraints.
Universal ranking schema:
C1 & C1 >> C1
(self-conjunction)
C1 & C2 >> C1 , C2 (conjunction of different
constraints)
Constraint conjunction
1. Self-conjunction of constraints: it is worse
to violate the same constraints n times than
to violate it n-1 times.
2. Conjunction of different constraints: we will
see that some typical derivational effects
have been accounted for with the help of
constraint conjunction.
When do we need local constraint
conjunction?
Constraint conjunction
Chain shift A -> B, B –> C but not: A –> C
In Western Basque (Etxarri dialect), mid vowels raise to high,
and high to raised (Kirchner 1996)
Indef
e –> i
seme bat
o –> uasto bat
i –> ij
erri bet
u –> uw
buru bet
Def
semi-e‘son’
astu-e ‘donkey’
errij-e ‘village’
buruw -e
‘head’
Constraint conjunction
Raised {ij, uw}: [-low, +high, +raised]
High {i, u}: [-low, +high, –raised]
Mid {e,o}: [-low, –high, –raised]
Low {a}: [+low, –high, –raised]
In a serial approach, this is not a problem: raising from high
to raised is ordered before raising from mid to high
But in standard OT this is difficult to express.
Constraint conjunction
HIATUS-RAISING: In V1V2, maximize height of V1.
This constraint is gradient: a is 3 violations, mid vowels 2,
high 1 and raised none.
Faithfulness:
IDENT-IO(high): If an input segment id [ahigh], then its
output correspondent is [ahigh]
IDENT-IO(raised): If an input segment id [araised], then its
output correspondent is [araised]
Wrong results
HIAT-RAIS IDENT(high) IDENT (rais)
a.i
e –> e*!*
a.ii
e –> i
a.iii e –> ij
b.i
b.ii
i –> i
i –> ij
*
*
*
*
*!
*
Right results with constraint conjunction
[ID(high) & HIAT-RAIS ID(high)
ID(raised)]
e –> e
*!
e –> i
*
e –> ij *!
*
*
i –> i
*!
i –> ij
ID(rais)
*
Constraint conjunction
Another nice example:
Rendaku in Japanese :
/ore-kami/ –> [ore-gami]: voicing of the first
obstruent in the second part of a compound
The application of Rendaku is limited by
Lyman’s Law:
‘Only one voiced obstruent per morpheme’
/kami-kaze/ –> [kami-kaze] *kami-gaze.
Constraint conjunction
/ore-kami/ *voicObstr2
ore-gami
ore-kami
/kami-kaze/
kami-kaze
kami-gaze
Rendaku
*
*!
*
*!
*voicObstr
*
**
Constraint conjunction
2. Conjunction of different constraints: only
markedness, only faithfuness, both kinds
(Lubowicz, Ito & Mester)?
To imitate the effect of the strict alternant condition
(only segments subject to allophony can be
subject to a rule (or the effect of a markedness
constraint), it seems that faithfulness and
markedness must be conjoined.
Chomsky on Barriers in „Barriers“
In his 1986 book „barriers“, Chomsky
proposed that we measure the
distance between a phrase and its
trace in terms of the numnber of
barriers that have been crossed.
Chomsky on Barriers in „Barriers“
O barriers
what do you fix
1 barrier
what do you wonder how to fix
2 barriers
??what do you wonder how one
should fix
Chomsky on Barriers in „Barriers“
If it is true that languages/
construction types may differ as to
how many barriers may be crossed,
then we need to be able to rank e.g.
the PARSE constraint between
k barriers crossed > PARSE > k-1
barriers crossed
CERTAINLY: k barriers crossed should
not be an atomic constraint
Self conjunction of constraints
Recall for self-conjunction of
constraints:
We say that CONk is violated if CON
is violated at least k times ...
It seems necessary to assume that
CONk >> PRIN >> CONk-1
Locality of self conjunction
It seems more adequate to say that
CONk is violated if CON is violated at
least k times by the same element/in
the same domain!
2 violations by SAME element
*?What do you wonder who bought
2 violations by DIFFERENT elements
what he wonders how to fix has an
influence on what I wonder when to
fix
Conjunction of different constraints
What do you wonder how to fix t
*how do you wonder what to fix t
Adjuncts have to fulfill stricter locality
requirements than arguments ...
REF: a chain is not headed by an
adjunct
Conjunction of different constraints
how do you think that she did it
*how do you wonder when to
fix the car
what do you wonder when to fix
BAR1 & REF > ParseScope >
BAR1
An obvious problem
By allowing constraint
conjunction, the weighting
(compensatory) type of conflict
resolution can be represented in
OT -->>
OT gets less restrictive
An obvious problem
A is more important than B, and
A is more important than C, but
B and C together outrank A
B&C>A>B>C
Compensatory Effects in NL?
Q-Scope in German
Pafel proposes the following
principles
PREF: a quantifier in the prefield
takes wide scope
NOM: A nominative quantifier takes
wide scope
DIST: Inherently distributive
quantifiers take wide scope
Compensatory Effects in NL?
Jeder Pianist hat eine Fuge gespielt
every pianist has a fugue played

by pref, nom & dist
Jede Fuge hat ein Pianist gespielt

nom alone does not win over
pref
Ein Pianist hat jede Fuge gespielt

dist alone does not win over
pref
Compensatory Effects in NL?
Eine Fuge hat jeder Pianist gespielt
 and 
dist and nom win over pref
A factual problem
jeden Studenten hatte ein Pianist aus
Polen empfangen
each-acc student had a pianist from
Polen received
Grammaticality vs. Parsing Ease?