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Precision Levels and Rounded Numbers in Measurement Expressions

This talk by Manfred Krifka explores the relationship between precision levels and the use of rounded numbers in measurement expressions. It discusses the preference for short expressions and how brevity affects the interpretation of precision.

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Precision Levels and Rounded Numbers in Measurement Expressions

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  1. Measure Expressionsand M-ImplicaturesManfred KrifkaHumboldt University, BerlinCenter for General Linguistics (ZAS), BerlinTalk 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

  2. Street sign in Kloten, Switzerland. How much precision is enough? • From the land of bankers and watchmakers.

  3. 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.

  4. 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?

  5. 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 information sufficient 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.

  6. 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

  7. 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.

  8. 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.

  9. 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! • VAGUEINTERPRETATION:Vague interpretation of measure terms are preferred. • Assume, again, the distance is exactly 1000 km. • Expression BRIEFEXPR VAGUEINT • one thousand kilometers   • Hearer prefers vague interpretations nevertheless.

  10. 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.

  11. 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.

  12. 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, precise • one thousand, vague>BInine hundred sixty five, vague • nine 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

  13. Optimal expression-interpretation pairs Optimal one thousand, vague Non-optimal Non-optimal nine hundred sixty-five, vague one thousand, precise nine hundred sixty-five, precise Optimal, as the other comparable pairsare non-optimal.

  14. Scale 1 0 10 20 30 40 Scale 2 20 30 40 10 5 0 2 3 1 6 0 5 9 8 4 7 Scale 3 15 10 20 30 40 25 35 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. Average complexity of expressions is smaller in Scale 1 than in Scale 2 Development of intermediate scales with anchor 5 Phonological simplifying of expressions:-- English fifteen (*fiveteen), fifty (*fivety)-- Colloquial German fuffzehn (fünfzehn), fuffzig (fünfzig)

  15. 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.

  16. 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)’

  17. Optimal expression-interpretation pairs:M-Implicature Optimal kill, prototypical Non-optimal Non-optimal cause to die, prototypical kill, non-prototypical cause to die, non-prototypical Optimal, as the other comparable pairsare non-optimal.

  18. A difference with other M-Implicatures M-Implicatures according to Levinson: 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.

  19. 1000 km 965 km A difference with other M-Implicatures The distance is one thousand kilometers.Vague interpretation The distance is nine hundred sixty-five kilometersVague interpretation Different configuration than with M-Implicatures;Bi-OT explanationis more general! The distance is nine hundred sixty-five kilometers.Precise interpretation

  20. 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”

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