On Being Vague and on Being Not Unhappy: Two Applications of Bidirectional Optimality Theory Manfred Krifka Manfred Krifka Humboldt University Berlin Center.

On Being Vague and on Being Not Unhappy:

Two Applications of Bidirectional Optimality Theory

Manfred Krifka

Manfred Krifka

Humboldt University Berlin

Center for General Linguistics (ZAS), Berlin

Copy of presentation at:

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

How much precision is enough?

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

Economy of language use:

George K. Zipf (1949), Principle of the least effort.

H. P. Grice (1967), Maxime of Manner: Be brief!

Atlas & Levinson (1981), Horn (1984), Levinson (2000):I-Principle,Produce the minimal linguistic informationsufficient to achieve your communicational ends.

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

First 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 (a) interpreted in a more precise way.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:

Average number of syllables: 2,73(b) ten, twenty, thirty, fourty, fivty, ... one hundred:

Average number of syllables: 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 102:... nine hundred, one thousand, one thousand one hundredone thousand and ten suggests precision level 101:... nine hundred ninety, one thousand, one thousand and ten ...one thousand and one suggests precision level 100:... 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 distance is 965 kmIf 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 PRECISEINT

one 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!

A preference for 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.

How Brevity and Vagueness interact

Interaction of BRIEFEXPRESSION and VAGUEINTERPRETATIONaccording to Bidirectional Optimality-Theory(Reinhard Blutner, Gerhard Jäger)

Classical OT: Input: a set of expressions, output: expression(s) that violate the constraints the least.

Bidirectional OT: Input is a set of pairs of objects, constraints are independently specified for the members of the pairs, the output are those pairs that violate the constraints the least.

The constraints are formulated in a modular fashion, for the members of the pairs.

But finding the optimal solution(s) requires optimization in both dimensions.

In semantic and pragmatic applications of Bidirectional OT, the pairs are pairs Exp, Int of an Expression and its Interpretation.

How Brevity and Vagueness interact

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

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

Generalization:• If Exp < Exp’, then Exp, Int < Exp’, Int • If Int < Int’, then Exp, Int < Exp, Int’ Exp, Int and Exp’, Int’ cannot be compared directly

if Exp Exp’ and Int Int’.

Strong Optimality

Finding the optimal pair: Strong Optimality

An expression-interpretation pair Exp, Int is optimal iffthere are no other pairs Exp’, Int or Exp, Int’ such that Exp’, Int < Exp, Int or Exp, Int’ < Exp, Int

Problem:Then only one thousand, vague is optimal, and nine hundred sixty-five, precise is not,as nine hundred sixty-five, vague and one thousand, preciseare to be preferred.

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

Non-optimal,even least optimal!

Weak Optimality Recapitulate:

Finding the optimal pair: Strong OptimalityAn expression-interpretation pair Exp, Int is optimal iffthere are no other pairs Exp’, Int or Exp, Int’ such that Exp’, Int < Exp, Int or Exp, Int’ < Exp, IntProblem:Then only one thousand, vague is optimal, and nine hundred sixty-five, precise is not,as nine hundred sixty-five, vague and one thousand, preciseare to be preferred.

But: These pairs are themselves not optimal!

Finding the optimal pair: Weak Optimality (Jäger 2000):

An expression-interpretation pair Exp, Int is optimal iffthere are no other optimal pairs Exp’, Int or Exp, Int’ such that Exp’, Int < Exp, Int or Exp, Int’ < Exp, Int

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.

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: The more attractive woman would leave the man, and the more attractive man would leave the woman.“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.

Is preference for vague interpretation really necessary?

Another take on the RN/RI phenomenon:• Vague and precise interpretation ranked equally (p = 0.5)• Under vague interpretation, round numbers are preferred (brevity)

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

range of vague interpretation

twenty

shortest expressionwithin the range of interpretation

Rule: Choose the least complex number expression within the range of interpretation!

If interpretation is precise, there is only one possible number expression.

precise interpretation

thirty-seven

Is preference for vague interpretation really necessary?

Another take on the RN/RI phenomenon:• Vague and precise interpretation ranked equally (p = 0.5)• Under vague interpretation, round numbers are preferred (brevity)• Assume that each value occurs with the same likelihood

(for 1 to 100: each number occurs with p = 0.01)• This boosts the probability of a vague interpretation

on hearing a round number.

20

vague interpretation: p = 0.5probability of value: p = 0.08

total probability: p = 0.04

twenty

20

precise interpretation: p = 0.5probability of value: p = 0.01total probability: p = 0.005

twenty

Speaker-Mode and Hearer-Mode Optimization

Hearer mode optimization:

If the expression happens to be a long number (say, twenty-three),then there is no special preference for a vague or precise interpretation,as both have the same probability (say, 0.05 * 0.01 = 0.005)

If the expression happens to be a short number (say, twenty), then there is a preference for the vague interpretation, as it captures more likely the observed value (say, 0.05 * 0.08 = 0.04)

In general: long, precise <> long, vague,short, precise < short, vague

Speaker mode optimization:

As before, preference for shorter expressions if the interpretation is the same.

In general: long, precise < short, precise,long, vague < short, vague

Optimal expression-interpretation pairs:Preference for Vagueness only for Short Expressions

short, precise

short, vague

long, vague

long, precise

Non-optimal Non-optimal

Optimal

Optimal, as the other

comparable pairis non-optimal.

hearer-optimal speaker-optimal

speaker-optimal

Optimization of Scales

Optimization of Scales if range of vague interpretation is centered around them:

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

ranges of vague interpretation

This leaves a problem with the numbers based on five, which can belong to either range of vague interpretation.

Optimal extension of this scale: New target numbers centered around five:

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

ranges of vague interpretation

Phonological simplifying of expressions (syllable structure, phonological complexity)-- English fifteen (*fiveteen), fifty (*fivety): diphthong monophthong-- Colloquial German fuffzehn (fünfzehn), fuffzig (fünfzig): unrounding ü > u, loss of n.

Generalization: M-Implicatures

Levinson (2000), Presumptive Meanings:

I-Principle (Information):

• 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 expressions that contrast with those that you would choose for normal, stereotypical situations.

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

The M-principle is invoked in cases where I-inferences to stereotypical situations are to be avoided.

Examples of M-Implicatures

Syntactic causatives:John killed the sheriff.John caused the sheriff to die. (McCawley 1978)

Word choice:Her house is on the corner.Her residence is on the corner.

Generic NPs:He went to school.He went to the school.

Meaning extension:A red wall.A reddish wall.

Positive use of comparatives (German):Ein alter Mann kam herein. ‘An old man came in.’Ein älterer Mann kam herein. ‘An older (elderly) man came in (= somewhat younger)’

Optimal expression-interpretation pairs:M-Implicature

kill, non-prototypical

kill, prototypical

cause to die, prototypical

cause to die, non-prototypical

Non-optimal Non-optimal

Optimal

Optimal, as the other

comparable pairsare non-optimal.

A difference with other M-Implicatures

John killed the sheriff.John caused the sheriff to die.

I-Implicature ofJohn killed the sheriff.prototypical killings.

M-Implicature ofJohn caused the sheriff to die.non-prototypical killings.

M-Implicatures according to Levinson:

A difference with other M-Implicatures

The distance is one thousand kilometers.Vague interpretation

The distance is nine hundred sixty-five kilometersVague interpretation

The distance is nine hundred sixty-five kilometers.Precise interpretation

Different configuration than with M-Implicatures;Bi-OT explanationis more general.

1000 km965 km

Weak Bi-OT on Being not Unhappy

Basic observation:

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

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

Grüne Harmonie. Glücklich (ganz links): Fraktionschefin Kerstin Müller. Glücklich (darunter): Fraktionschef Rezzo Schlauch.Glücklich (rechts daneben): Gesundheitsministerin Andrea Fischer. Glücklich (darüber): Schleswig-Holsteins Umwelt-minister Klaus Müller. Glücklich (verdeckt): Umweltminister Jürgen Trittin. Nicht unglücklich (vor Trittin): Außenminister Joschka Fischer. Überglücklich: die neue Parteichefin Renate Künast. (TAZ 26.6.2000,found by Reinhard Blutner)

What does Happy and Unhappy mean?

Standard account: happy and unhappy, good and bad etc. are contraries; they cannot be applied to emotional states in the middle range.

happy unhappy

The literal meaning of the negations not happy and not unhappyare then as follows:

happy unhappy

not unhappy not happy

Negated forms compete with shorter forms and are pragmatically restricted:

happy unhappy

not unhappy not happy

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

A Weak Bi-OT Theory about Happiness

Assume that antonyms are literally interpreted in an exhaustive way(cf. supervaluations-approach)

Initial situation: Antonym pairs and their negations.

not unhappy not happy

happy unhappy

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

not unhappy not happy

happy unhappy

not unhappy not happy

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.

A Reason for I-Implicature

With exhaustive interpretation of antonyms: It may be unclear where to draw the border.

happy unhappy

Saying that someone is happy or unhappy may not very informativeif the person’s state is in the border area;this is a motivation for restricting the use of happy/unhappy to the clear cases.

happy unhappy

unhappyhappy

happy unhappy