Constraint Conjunction, Ties, Opacity

Plan of this unit.

Discussion of OptionalityIntroduction of TiesTechnicalitiesCumulative Effects Introduction of Constraint ConjunctionsThe 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.

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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.

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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. Movementthere was a moose shota moose was shot

Dative ShiftI gave a book to MaryI gave Mary a book

Multiple outputs:optionality

Complementizer DeletionI think (that) she is intelligent

Extraposition / HNPS / Particle Shifta man from India arriveda man arrived from Indiashe looked up the interesting answershe looked the interesting answer up

Multiple outputs:optionality

Scramblingdass niemand das Buch gelesen hattethat nobody the book read haddass das Buch niemand gelesen hatteTopicalizationdas Buch hatte niemand gelesengelesen hatte das Buch niemandniemand 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 positionTélefon vs. Telefón

Multiple outputs:optionality

Free variation in the phonology of Frencha. 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. Optionality is only apparent2. Identity of profiles3. Co-Phonologies (Co-syntaxes)4. Tied Constraints

1. Apparent Optionality

First, optionality may be only apparent.

There IS a meaning difference betweender Pfarrer kommt‘the priest comes’andes kommt der Pfarrer

1. Apparent Optionality

The same would seem to hold fora moose was shotthere was a moose shotScramblingDifferent 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 comeI think that he will comecan 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 non-native 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

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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 JapaneseCitybank (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 strangerRules 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 …

C1 >> C2a >> C2b >> C3 …

or C1 >> C2b >> C2a >> C3 …

First interpretation of ties

Given the hierarchyA .... B C1/C2 D ... EIf C1 and C2 are tied by hierarchy, thenS is grammatical iffS is optimal with respect toA ...B C1D ...EorA ...B C2D ...E

Multiple outputs: optionality

(11) Free variation in ‘nuage’/nuage/ NOHIATUS NOCOMPLEXONSET.nuage. *.nu.age. *

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) I think that he is a fool(2) I think he is a fool

TEL LECP

(1) *

(2) *

Relative Clauses

(1) a man who that I like(2) a man who I like(3) a man that I like(4) a 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

TEL LECP

(1) *(!) *(!)

(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

C1 >> C2a >> C2b >> C3 …

or C1 >> C2b >> C2a >> C3 …

Relative Clauses

TEL LECP NOSTRUC

(1) *(!) *(!) **

(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 hierarchyA .... B C1/C2 D ... EIf C1 and C2 are tied cumulatively, thenS is grammatical iffS is optimal with respect toA ...B F D ...Ewhere 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 liebtwho think you that she believes that Fritz loves2. was denkst du wen sie meint t dass Fritz liebt3. was denkst du was sie meint wen Fritz liebt4. was denkst du t dass sie meint wen Fritz liebt

A Tie between Constraints

FI Stay

1. Wen … t … t … **2. was … wen … t … * *3. was … was … wen … **4. was … t … wen … * *

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 think1. dass der Fritz nicht geschlafen hatthat the Fritz not slept has

2. der Fritz hat nicht geschlafen

1. FI2. 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 NOM2. animate > inanimateANIM3. definite > indefinite DEF

A sentence is grammatical if it satisfies at least one constraint

Ties between Constraints

Dass der Mann ein Buch liestthat the man a book readsNOM, DEF, ANIM*dass ein Buch der Mann liest*NOM, *DEF, *ANIMdass ein Mann das Buch liestthat a man the book readsNOM, ANIM,*DEFdass das Buch ein Mann liest*NOM, *ANIM, DEF

Ties between Constraints

Dass ein Buch der Frau hilftthat a book the woman helps NOM, *DEF, *ANIMdass der Frau ein Buch hilft*NOM, DEF, ANIMdass das Buch einer Frau hilftNOM, DEF,*ANIMdass 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 n-k 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: self-conjunction 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 Defe –> i seme bat semi-e ‘son’o –> u asto bat astu-e ‘donkey’i –> ij erri bet errij-e ‘village’

u –> uw buru bet 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 [high], then its output correspondent is [high]IDENT-IO(raised): If an input segment id [raised], then its output correspondent is [raised]

Wrong results

HIAT-RAIS IDENT(high) IDENT (rais)

a.i e –> e *!*a.ii e –> i * *a.iii e –> ij * *

b.i i –> i *!b.ii i –> ij *

Right results with constraint conjunction

[ID(high) & HIAT-RAIS ID(high) ID(rais) ID(raised)]e –> e *!e –> i *e –> ij *! * *i –> i *!i –> ij *

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 Rendaku *voicObstrore-gami *ore-kami *!

/kami-kaze/kami-kaze * *kami-gaze *! **

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 barrierswhat do you fix 1 barrierwhat do you wonder how to fix2 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 crossedCERTAINLY: 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 thatCONk >> 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 bought2 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 carwhat 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 GermanPafel proposes the following principlesPREF: a quantifier in the prefield takes wide scopeNOM: A nominative quantifier takes wide scopeDIST: Inherently distributive quantifiers take wide scope

Compensatory Effects in NL?

Jeder Pianist hat eine Fuge gespieltevery pianist has a fugue played

by pref, nom & distJede Fuge hat ein Pianist gespielt

nom alone does not win over prefEin 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 problemjeden Studenten hatte ein Pianist aus Polen empfangeneach-acc student had a pianist from Polen receivedGrammaticality vs. Parsing Ease?