Measure Expressionsand M-Implicatures

Manfred KrifkaHumboldt University, Berlin

Center for General Linguistics (ZAS), Berlin

Talk at Seoul National University,June 27, 2003

Krifka, Manfred. 2002. “Be brief and vague! And how Bidirectional Optimality Theory allows for verbosity and precision.”

In Sounds and systems: studies in the structure and change. A Festschrift for Theo Vennemann, eds. David Restle and Dietmar Zaefferer, 439-458. Berlin / New York: Mouton de Gruyter.

Dowloadable at: 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.

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 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.

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):

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:• 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’.

Finding the (super)optimal pair, cf. Jäger (2000):

An expression-interpretation pair Exp, Int is optimal iff

there 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.

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:-- English fifteen (*fiveteen), fifty (*fivety)-- Colloquial German fuffzehn (fünfzehn), fuffzig (fünfzig)

0 10 20 30 405

Scale 3

15 25 35

Generalization: M-Implicatures

Levinson (2000), Presumptive Meanings:

M-Principle: Marked expressions have marked meanings.

“Indicate an abnormal, nonstereotypical situation by using marked expressions that contrast with those you would use to describe the corresponding normal, stereotypical situations” (p. 136).

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.

Litotes:Mary is happy.Mary is not unhappy.

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 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

Krifka, Manfred. 2002. “Be brief and vague! And how Bidirectional Optimality Theory allows for verbosity and precision.”

In Sounds and systems: studies in the structure and change. A Festschrift for Theo Vennemann, eds. David Restle and Dietmar Zaefferer, 439-458. Berlin / New York: Mouton de Gruyter.

Dowloadable at: amor.rz.hu-berlin.de/~h2816i3x, “Articles”