Optimality Theory and Pragmatics Lecture series in three parts held at the V. Mathesius Center,...

Optimality Theory and Pragmatics

Lecture series in three partsheld at the V. Mathesius Center, Prague, March 2004

Part 2: M-Implicatures and Weak Optimality

Manfred Krifka

Humboldt University Berlin

Center for General Linguistics (ZAS), Berlin

Copy of presentation at:

http://amor.rz.hu-berlin.de/~h2816i3x



Things to Do:

1. The Classic Theory of Implicatures: Grice2. Optimality Theory3. An OT Account of Scalar Implicatures4. The Theory of I/R Implicatures: Horn, Levinson5. Strong Bidirectional Optimality Theory Accounts of blocking, pronoun interpretation, freezing of word order

6. The Theory of M Implicatures: Levinson7. Weak Bidirectional OT Account of Partial Blocking8. Weak Bi-OT Account of Measure Term Interpretation

9. An OT account of Scale Alignment10. Functional motivation for linguistic scales11. Stochastic OT12. Bidirectional OT account of Learning13. Bidirectional OT account of Language Change: 14. Differential Case Marking

Recapitulation: Q-Implicature / I-Implicature

Q-Principle: Say as much as you can.

Explains implicatures that restrict what is said to the literal meaning.

Example: Scalar implicatures.John has three children.restricted to: John doesn’t have more than three children.

I-Principle: Say (only) as much as you must.

Explains implicatures that enrich the literal meaning of what is said.

Example: Bridging..Bill unpacked the picknick. The beer was warm.enriched to: The beer that was part of the picknick was warm.

The M Principle

Levinson (2000) assumes a third principle beyond Q and I: Q-Principle:

Speaker: Choose the maximally informative expression alternative (that still is true). Addressee: Assume that speaker has chosen the maximally informative expression alternative (that still is true)

I-Principle:Speaker: Produce only as much linguistic information as necessary to satisfy the communicative purpose. Addressee: Enrich the given linguistic information, identify the most specific information relative to the communicative purpose.

M-Principle (Modality / Manner / Markedness)• Speaker:

Communicate non-normal, non-stereotypical situations by expressionsthat contrast with those that you would choose for normal, stereotypical situations.

• Adressee: If something is communicated by expressions that contrast with thosethat would be used for normal, stereotypical meanings,then assume that the speaker wants to communicate a non-normal, non-stereotypical meaning.

M-Implicatures and I-Implicatures

If the speaker utters an expression A[M], which contains a marked expression M with meaning B,

Literal meaning of M / U

Restriction by I-Implicatureif U is used.

Restriction by M-Implicatureif M is used.

and if there is an unmarked expression U with similar meaning M, and the speaker could have said A[U],

where A[U] would have triggered an I-Implicature, that U should be understood with the specialized meaning b

then the speaker implicates with A[M]that M is to be understood as the complement b in B.

M-Implicatures: To Kill and to Cause to Die

Generative Semantics:Syntactic treatment of lexical semantics:[kill] = [cause [to die]][die] = [become [not [alive]]][opentransitive] = [cause [to openintransitive]]

But McCawley (1978): Different interpretations of

Black Bart killed the sheriff. Direct killing.Black Bart caused the sheriff to die. Indirect killing.

Mary opened the door. Normal, stereotypical opening.Mary caused the door to open. Non-normal, atypical opening.

Explanation by M-Implicature:literal meaning of kill / cause to die

Restriction by I-Implicaturefor unmarked kill to direct killing.

Restriction by M-Implicaturefor marked cause to dieto indirect killing.

M-Implicature: Of Old Men and Elderly Men

(1) John is an old man.

(2) John is an elderly man.

English speakers understand (1) as indicating a higher age than (2),cf. the dictionary definition: elderly: being past middle age and approaching old; rather old.

Assume: • old (for people) and elderly literally mean the same: Older than average

(general principle of interpretation fo gradable adjectives in positive form)• but elderly is marked, which leads to an M-Implicature.

Age

old / elderly: literal meaning

old: I-Implicature

elderly: M-Implicature

Other Examples of M-Implicatures

Miss X sang “Home Sweet Home”.I-Implicature: Miss X sang “Home Sweet Home” in a normal way.

Miss X created a series of sounds that corresponded quite closely to the notes of “Home Sweet Home” M-Implicature: Miss X sang “Home Sweet Home” in a non-normal way.

Karen smiled.I-Implicature: Karen smiled in a regular way..

Karen lifted the corners of her lips.M-Implikature: Karen produced an aritificial smile.

Linda went to the library and copied an article.I-Implicature: She first went to the library and then copied an article.

Linda went to the library, and she also copied an article. M-Implikature: No claim about the order in which this happened.

M-Implicatures: The Meaning of Reduplications

Reduplications increase the complexity of expressionsand can trigger M-Implicatures.

He went to bed and slept.I-Implicature: prototypical sleeping.

He went to bed and slept and slept.M-Implikatur: Non-prototypical, long sleeping;iconic marking: repetition of expression - repetition / lengthening of event.

Often, reduplication means higher length or intensity,but not always:

• In Africans, reduplication can mean to do try to do something’ skop ‘kick’, skop-skop ‘try to kick’, ‘kick in an experimental way’

• In Western Desert, Australia, similar meaning for nouns:wati ‘men, wati-wati ‘boys that claim to be men’

• In Mayan languages (e.g. Tzeltal):Simple color terms: focal colorsReduplicated color words: non-focal color, like red - reddish

In general: reduplicated forms are more complexand denote non-typical situations or entities compared to simplex forms.

M-Principle and Bidirectional OT

Levinson assumes that the M-Principle is a separate principle.But it is tightly connected to other principles.Black Bart killed the sheriff.

Literal interpretation: brought it about that the sheriff diedEnrichment by I-Implicature: in a direct way

Black Bart caused the sheriff to dieLiteral interpretation: brought it about that the sheriff diedNo enrichment by I-Implicature, presumably because killed the sheriff shows this enrichment.Restriction to brought it about that the sheriff died,presumably because of contrast with I-Implicature to killed the sheriff.

To explain:• Why does only killed the sheriff show I-Implicature?• Why does interpretation of caused the sheriff to die

contrast with I-Implicature of killed the sheriff ?

Recapitulation: Strong Bidirectional OT

Evaluation algorithm for strongly optimal form-meaning pair:

F, M is strongly optimal iffa. F, M GEN, that is, F, M is generated.b. there is no F’, M GEN such that F’, M > F, Mc. there is no F, M’ GEN such that F, M’ > F, Mwhere P1 > P2 means: P1 is preferred over P2.

cheaper

more cheap

cheap

cheaper, cheap > more cheap, cheap, simplicity of expression

Mary wrote the novel

on a computer.

‘Mary wrote the novelby means of a computer’

‘Mary wrote the novelwhile she was on a computer’

Mary wrote..., by means > Mary wrote..., while on,stereotypicality of meaning

Strong Bi-OT and Kill / Cause to Die

kill

cause to die

cause deathin direct way

cause deathin indirect way

Speaker optimization:select simpler expression

Hearer optimization:select stereotypical meaning

kill

cause to die



combined Speaker + Hearer optimization

kill, cause death in direct way is the only strongly optimal pair;it is better than

kill, cause death in indirect way, cause to die, cause death in direct way, cause to die, cause death in indirect way

No way to express marked meaning (“ineffability”), complex epressions are always blocked (“uninterpretabiity”)

Weak Bidirectional OT

Recall strong optimality:F, M is strongly optimal iffa. F, M GEN, that is, F, M is generated.b. there is no F’, M GEN such that F’, M > F, Mc. there is no F, M’ GEN such that F, M’ > F, M

Alternative notion of weak optimality (Blutner 2000, Jäger 2002):F, M is weakly optimal iffa. F, M GEN, that is, F, M is generated.b. there is no weakly optimal F’, M GEN such that F’, M > F, Mc. there is no weakly optimal F, M’ GEN such that F, M’ > F, M

Infelicitous definition because definiens occurs in definiendum?This is only apparent!

Weak Bi-OT and Kill / Cause to Die

Generated alternatives GEN to consider:{kill, cause death in direct way, cause to die, cause death in direct way kill, cause death in indirect way, cause to die, cause death in indirect way}

First step: kill, cause death in direct way is weakly optimalbecause there is no weakly optimal (in fact, no) F’, cause death in direct way GENand no weakly optimal (in fact, no) kill, M’ GEN that is preferred over kill, cause death in direct way

Second step:kill, cause death in indirect way is not weakly optimal,as kill, cause death in direct way is weakly optimal and preferred.

Third step: cause to die, cause death in direct way is not weakly optimal,as kill, cause death in direct way is weakly optimal and preferred.

Fourth step: cause to die, cause death in indirect way is weakly optimal (!)because there is no weakly optimal F’, cause death in indirect way GEN and there is no weakly optimal kill, M’ GEN that is preferred over cause to die, cause death in indirect way


kill, cause death in direct way

cause to die, kill, cause death in direct way cause death in indirect way,

cause to die, cause death in indirect way

Notice: Partial blocking; the marked form is not blocked under the marked interpretation - the “emergence of the marked”


kill

cause to die



Speaker optimization:select simpler expression

Hearer optimization:select stereotypical meaning

kill

cause to die



combined Speaker + Hearer optimization:optimal (and weakly optimal)solution

kill

cause to die



combined Speaker + Hearer optimization:additional weakly optimal solution,prevents ineffabilityand uninterpretability

Weak Bi-OT on Being Elderly

old man, prototypically old

elderly man, old man, prototypically old non-prototypically old,

elderly man, non-prototypically old

A Kafkaesque Account of Strong and Weak Bidirectional OT

In his early prose piece Die Abweisung (“Turned Down”) Franz Kafka imagines a dialogue between himself and a young woman: "Du bist kein Herzog mit fliegendem Namen, kein breiter Amerikaner mit indianischem Wuchs, mit wagrecht ruhenden Augen, mit einer von der Luft der Rasenplätze und der sie durchströmenden Flüsse massierten Haut. Du hast keine Reisen gemacht zu den großen Seen und auf ihnen, die ich weiß nicht wo zu finden sind. Also ich bitte, warum soll ich, ein schönes Mädchen, mit Dir gehn?”

In short: Woman says to man: You are not the most attractive man. "Du vergißt, Dich trägt kein Automobil in langen Stössen schaukelnd durch die Gasse, ich sehe nicht die in ihre Kleider gepressten Herren Deines Gefolges, die Segensprüche für Dich murmelnd in genauem Halbkreis hinter Dir gehn; Deine Brüste sind im Mieder gut geordnet, aber Deine Schenkel und Hüften entschädigen sich für jene Enthaltsamkeit; Du trägst ein Taffetkleid mit plissierten Falten, wie es im vorigen Herbste uns durchaus allen Freude machte, und doch lächelst Du - diese Lebensgefahr auf dem Leibe - bisweilen.”

In short: Man says to woman: You are not the most attractive woman.Kafka’s ending is an example of Strong Optimality: Woman and man go home alone.

"Ja, wir haben beide recht und, um uns dessen nicht unwiderleglich bewusst zu werden, wollen wir, nicht wahr, lieber jeder allem nach Hause gehn.”

Krifka’s variant, an example of Weak Optimality: Woman and man go home together because other pairings would not be stable.“Ja, wir haben beide recht. Doch wenn Du Deine Prinzessin finden würdest, wärest Du nie sicher, wie lang sie bei Dir bleiben würde. Und wenn mir mein Held erschiene, würde er mich auch nur eines Blickes würdigen? So lass uns zusammen nach Hause gehen.

Weak Bi-OT on Being not Unhappy

Larry Horn (1991), Duplex negatio affirmat: The economy of double negation.

Mary is not unhappy implicates: Mary is not really happy.

Initial situation: Contrary (antonymic) pairs of expressions and their negations.

not unhappy not happy

happy unhappy

I-Implicatures: Restriction of simpler expressions to prototypical uses.


happy unhappy


happy unhappyM-Implicatures: Restriction of complex expressions to non-prototypical uses.

Weak Bi-OT on Being not Unhappy

happy,

not unhappy, happy,

not unhappy, unhappy,

not happy, unhappy,

not happy,

Cf. also:This is good.This is bad.This is not bad.This is not good.

An Alternative Theory about Happiness?

Speakers generally have the impression that the literal meaningsof happy and unhappy are different:

happy unhappy

Problem with this view:Unclear how to derive the different uses of not happy and not unhappy

happy unhappy

not unhappy not happyStrengthening by M-Implicature:

happy unhappy


Unclear how different interpretation of not happy an d not unhappy comes about,prediction: not unhappy should be totally blocked because it is longer than not happy!

A New Type of Blocking: Saussure on Plural and Dual

A type of blocking not considered so far:“The value of a German or Latin plural is not the value of a Sanskrit plural. But the meaning, if you like, is the same. In Sanskrit, there is the dual. Anyone who assigns the same value to the Sanskrit plural as to the Latin plural is mistaken because I cannot use the Sanskrit plural in all the cases where I use the Latin plural.” (Saussure, Notes taken by student, July 4, 1911)

1 2 3 4 ...

PluralLatin

Dual PluralSanskrit

Idea: Plural in Sanskrit has the same “meaning” as plural in Latin, but it is blocked when applied to the number 2 by the Dual,

hence their “values” are different.

Bi-OT on Dual and Plural

Consider form-meaning pairs like the following: Dual, 2 Plural, 2 Plural, 3 Plural, 4

Which constraints should we assume here?Form constraints?

Dual may be more complex than plural and hence dispreferred, but meaning 2 doesn’t appear to be a marked meaning, and hence dual may be blocked in general!

Also, a consideration of speaker vs. hearer perspective doesn’t help:

Dual

Plural

2

3

4

Hearer perspective

Dual

Plural

2

3

4

Speaker perspective

Dual

Plural

2

3

4

Common perspective

Bi-OT on Dual and Plural

But notice that the pair Dual, 2 is special, as a dual form cannot denote any other numbe;: it is unambiguous.

Proposal: Give preference to pairs F, M with forms Fthat cannot express any other meaning,

that is, for which there is no F, M’ GEN with M’ M.

Avoid ambigous forms (AAF): F, M > F’, M if F is unambigous.

It follows that Dual, 2 > Plural, 2, hence Plural, 2 is excluded by optimality priciples.

Notice: AAF is not a principle that can be reduced to forms (like: prefer simple expressions) or that can be reduced to meanings (like: prefer stereotypical meanings)

Dual

Plural

2

3

4

Avoid Ambiguity.

Avoid Ambiguous Forms and Weak Bi-OT

There is a connection between AAF and Weak Bi-OT;AAF is a simplified evalution algorithm.

Recall definition of weak optimality:F, M is weakly optimal iffa. F, M GENb. there is no weakly optimal F’, M GEN such that F’, M > F, Mc. there is no weakly optimal F, M’ GEN such that F, M’ > F, M

With partial blocking of plural by dual, alternative form/meaning pairs are not comparable: Dual, 2 < > Plural, 2, if dual and plural are equally complex.

Asymmetric optimality:

F, M is asymmetrically optimal iffa. F, M GEN,b. (does not apply)b. there is no F, M’ GEN different from F, M.

We have that Dual, 2 is asymmetrically optimal, as there is no Dual, n, n 2;

but Plural, 2 is not asymmetrically optimal, as we have, e.g. Plural, 3.

Bi-OT and other numbers

Similar reasoning applies to singular and plural in English.

General meaning of plural includes single cases:

Do you have children?Yes, I have one. / *No, I have (only) one.

Do you have more than one child?No, I have only one. / *Yes, I have one.

But in competition with singular, plural is blocked if meaning 1 is encoded.

Singular

Plural

1

2

3

Application to Paucal / Plural systems, e.g. Arabic:Paucal is used for small numbers, e.g. under 4, Plural is used elsewhere.

Avoid Ambiguity, generalized:F, M > F’, M if F is less ambiguous than F’.

Bi-OT and Measure Expressions

From the land of bankers and watchmakers.

Street sign in Kloten, Switzerland.

Pedantic and helpful answers.

A: The distance between Amsterdam and Vienna is one thousand kilometers.B: #No, you’re wrong, it’s nine hundred sixty-five kilometers.

A: The distance between A and V is nine hundred seventy-two kilometers.B: No, you’re wrong, it’s nine hundred sixty-five kilometers.

A: The distance between A and V is one thousand point zero kilometers.B: No, you’re wrong, it’s nine hundred sixty-five kilometers.

A: Her phone number is sixty-five one thousand.B: No, her phone number is sixty-five one-thousand and one.

The distance between A and V is roughly one thousand kilometers.The distance between A and V is exactly one thousand kilometers.

The distance between A and V is exactly nine hundred sixty-five kilometers.#The distance between A and V is roughly nine hundred sixty-five kilometers.

Precision level and rounded numbers

Precision Level Choice:When expressing a measurement of an entity, choose a precision level that is adequate for the purpose at hand.

Oddness explained: Change in precision level.A: The distance between Amsterdam and Vienna is one thousand kilometers.B: #No, you’re wrong, it’s nine hundred sixty-five kilometers.

Round Numbers / Round Interpretations (RN/RI)Short, simple, round numbers suggest low precision levels.Long, complex numbers suggest high precision levels.

The distance between Amsterdam and Vienna is one thousand kilometers.Low precision level, vague interpretation.

The distance between Amsterdam and Vienna is nine hundred sixty-five kilometers.High precision level, precise interpretation.

Question:How to explain RN/RI by more general pragmatic principles?

A Preference for Short Expressions

BRIEFEXPRESSION (first formulation):Brief, short expressions are preferred over longer, complex ones.

Informal explanation of RN/RI:(a) The distance between A and V is one thousand kilometers.(b) The distance between A and V is nine hundred sixty-five kilometers.

Speaker prefers (a) over (b) because it is shorter, even though it has to be interpreted in a vague way.

A closer look at brevity

A problem for brevity:(a) The distance between A and V is one thousand and one kilometers.

(b) The distance between A and V is one thousand and one hundred kilometers.

Note: (a) is shorter, but interpreted more precisely, than (b).(c) The train will arrive in five / fifteen / fourty-five minutes.

(d) The train will arrive in four / sixteen / fourty-six minutes.

Note: (c), (d) equally short, but (d) interpreted more precisely.

Solution:We cannot just look at the expression used, we also have to take its alternatives into account.

(a) ... nine hundred ninety nine, one thousand, one thousand and one, ...

(b) ... nine hundred, one thousand, one thousand one hundred, ...

Expressions in (a) are shorter/less complex on average than in (b), e.g. by morphological complexity or number of syllables.

Example:(a) one, two, three, four, five, ...., one hundred: Syllable average: 2,73

(b) ten, twenty, thirty, fourty, fivty, ... one hundred: Syllable average: 2,1

A closer look at brevity

BRIEFEXPRESSION (refined):Precision levels with smaller average expression sizeare preferred over precision levels with longer average expression size.

Suggested precision level:The use of a number words in measure expressionssuggests the precision level with the smallest average expression size.

For example, one thousand suggests precision level... nine hundred, one thousand, one thousand one hundred,

...one thousand and one suggests precision level

... nine hundred ninity-nine, one thousand, one thousand and one, ...

Informal explanation of RN/RI (refined):(a) The distance between A and V is one thousand kilometers.(b) The distance between A and V is nine hundred sixty-five kilometers.

Speaker prefers (a) over (b) because it indicate a precision level choicewith smaller average precision level, even though it has to be interpreted in a vague way.

A preference for precise interpretations?

Notice: Use of even though suggests that precise interpretations are preferred.

PRECISEINTERPRETATION:Precise interpretations of measure expressions are preferred.

This explains why (a) is interpreted precisely.(a) The distance between A and V is nine hundred sixty-five kilometers.

Why no precise interpretation with (b)? Because of BRIEFEXPRESSION.(b) The distance between A and V is one thousand kilometers.

If distance is 965 km, then we have the following constraint interaction:

Expression BRIEFEXPR PRECISEINT

(a) nine hundred sixty-five kilometers * (b) one thousand kilometers *

If constraints are unranked, both (a) and (b) are possible.If BRIEFEXPR > PRECISEINT, then (b) is preferred.

A preference for precise interpretations?

A problem with this reasoning:Assume the distance is exactly 1000 km,

then speaker doesn’t violate any constraint:

Expression BRIEFEXPR PRECISEINTone thousand kilometers

So, on hearing one thousand kilometers, the hearer should assume that the distance is exactly 1000 km,as in this case there is no violation at all.

But this is clearly not the case.So, the hearer should prefer vague interpretations!VAGUEINTERPRETATION:

Vague interpretation of measure terms are preferred.Assume, again, the distance is exactly 1000 km.

Expression BRIEFEXPR VAGUEINTone thousand kilometers

Hearer prefers vague interpretations nevertheless.

Preference for Vague Interpretations

Why should vagueness be preferred?Grice, Maxime of quantity, second submaxime:

Give not more information than required.Ochs Keenan (1976) (rural Madagascar): Vague interpretations help save face.P. Duhem (1904), cited after Pinkal (1995):

“There is a balance between precision and certainty.One cannot be increased except to the detriment of the other.”

Reduction of cognitive load?

Problem: Assume distance is 965 kilometers.Expression BRIEFEXPR VAGUEINT

(a) one thousand kilometers (b) nine hundred sixty-five kilometers * *

(b) would always be strongly dispreferred.We have to capture the interaction between the two principles:

Basic idea: We can violate one principle if we also violate the other.

Weak OT on Brevity and Vagueness

Ranking of pairs by B(rief)E(xpression) and V(ague)I(nterpretation):

one thousand, precise >BE nine hundred sixty five, precise,one thousand, vague) >VI one thousand, preciseone thousand, vague >BI nine hundred sixty five, vaguenine hundred sixty five, vague >VI nine hundred sixty five, precise

Generalization:

Finding the weakly optimal pair:

An expression-interpretation pair F, M is weakly optimal iff

there are no other weakly optimal pairs F, M’ or F’, M such that F, M’ > F, M or F’, M > F, M

Optimal expression-interpretation pairs

one thousand, precise

one thousand, vague

nine hundred sixty-five, vague

nine hundred sixty-five, precise

Non-optimal Non-optimal

Optimal

Optimal, as the other

comparable pairsare non-optimal.

Construction of Scalesand Complexity of Expressions

Requirement for vagueness / brevity interaction:Construction / historical development of appropriate scales (alternatives)optimally with equidistant representations.

Example: Decimal system of counting, different scales of granularity.

0 10 20 30 40

Scale 1

Average complexity of expressions is smaller in Scale 1 than in Scale 2

Development of intermediate scales with anchor 5

0 10 20 30 401 2 3 4 5 6 7 8 9

Scale 2

Phonological simplifying of expressions of coarse-grained scales:-- English fifteen (*fiveteen), fifty (*fivety)-- Colloquial German fuffzehn (fünfzehn), fuffzig (fünfzig)

0 10 20 30 405

Scale 3

15 25 35

Things Accomplished:

1. The Classic Theory of Implicatures: Grice

2. Optimality Theory

3. An OT Account of Scalar Implicatures

4. The Theory of I/R Implicatures: Horn, Levinson

5. Strong Bidirectional Optimality Theory Accounts of blocking, pronoun interpretation, freezing of word order

6. The Theory of M Implicatures: Levinson

7. Weak Bidirectional OT Account of Partial Blocking

8. Weak Bi-OT Account of Measure Term Interpretation

9. An OT account of Scale Alignment

10. Functional motivation for linguistic scales

11. Stochastic OT

12. Bidirectional OT account of Learning

13. Bidirectional OT account of Language Change: 14. Differential Case Marking

Optimality Theory and Pragmatics Lecture series in three parts held at the V. Mathesius Center,...

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