Vagueness Facilitates Search

1. Vagueness Facilitates Search Kees van Deemter Computing Science University of Aberdeen Kees van Deemter (SSE, Jan '10)

2. Who I am: I ... • studied logic and philosophy of language • University of Amsterdam (PhD) • Stanford University (postdoc) • worked for Philips Electronics on HCI and Language Technology • have worked on Natural Language Generation since 1994 • University of Brighton (ITRI) • University of Aberdeen Kees van Deemter (SSE, Jan '10)

3. sources for this talk (KvD 2009a) “What Game Theory Can Do For NLG: the case of vague language”. In Proc. 12th Eur. Workshop on Natural Language Generation. (KvD2009b) “Utility and Language Generation: The Case of Vagueness”. J. Philosophical Logic38/6. (Kvd2009c) “Vagueness Facilitates Search”, in Proc. of the Amsterdam Colloquium, Dec. 2009 Kees van Deemter (SSE, Jan '10)

4. An expression is vague (V) iff it has borderline cases or degrees, e.g. • large, small, fast, slow, many, few , ... • Not just words, e.g., • “he came, he saw, he conquered” • generic statements Common in all human languages • 8 out of top 10 adjectives in BNC • Dominant among the first words we learn Kees van Deemter (SSE, Jan '10)

5. Two “big” problems with vagueness • The semantic problem: How to model the meaning of V expressions? • Classical models: 2-valued • Partial models: 3-valued • Degree models: many-valued (e.g. Fuzzy Logic, Probabilistic Logic) No agreement how to answer this question (e.g., Keefe & Smith 1997) Kees van Deemter (SSE, Jan '10)

6. The pragmatic problem: • Why is language vague? • Vague expressions seem a bit unclear • Is it ever a good idea to be V? • Suppose you built an electronic information provider; would you ever want it to offer you V information? Kees van Deemter (SSE, Jan '10)

7. Barton Lipman • chapter in A.Rubinstein, “Economics and Language” (2000) • working paper “Why is Language Vague” (2006) Lipman: Why have we tolerated an apparent “worldwide several-thousand year efficiency loss”? That’s today’s topic Kees van Deemter (SSE, Jan '10)

8. The scenario of Lipman (2000, 2006) Airport scenario: I describe Mr X to you, to pick up X from the airport. All I know is X’s height; heights are uniformly distributed across people on [0,1]. If you identify X right away, you get payoff1; if you don’t then you get payoff-1 Kees van Deemter (SSE, Jan '10)

9. What description would work best? • State X’s height “precisely” If each of us knows X’s exact height then the probability of confusion is close to 0. Kees van Deemter (SSE, Jan '10)

10. What description would work best? • State X’s height “precisely” If each of us knows X’s exact height then the probability of confusion is close to 0. If only one property is allowed: • Say “the tall person” if height(X) > 1/2, else say “the short person”. Kees van Deemter (SSE, Jan '10)

11. What description would work best? • State X’s height “precisely” If each of us knows X’s exact height then the probability of confusion is close to 0. If only one property is allowed: • Say “the tall person” if height(X) > 1/2, else say “the short person”. No boundary cases, so this is not vague! Theorem: under standard game-theory assumptions (Crawford/Sobel), vague communication can never be optimal Kees van Deemter (SSE, Jan '10)

12. One type of answer to Lipman: conflict between S and H • Aragones and Neeman (2000): ambiguity can add to speakers’ utility US (politician’s example) Kees van Deemter (SSE, Jan '10)

13. One type of answer to Lipman: conflict between S and H • Aragones and Neeman (2000): ambiguity can add to speakers’ utility US (politician’s example) • De Jaegher (2003) argued that Aragones & Neeman’s solution won’t work for vagueness • (KvD 2009a) adapted Aragones & Neeman for vagueness • But what if language is used “honestly”? (i.e., US =UH) • An illustrative application: Natural Language Generation Kees van Deemter (SSE, Jan '10)

14. Natural Language Generation (NLG) is an area of AI with many practical applications (e.g. Reiter and Dale 2000) • An NLG program “translates” input data to linguistic output • Essentially the problem of choosing the best linguistic Form for a given Content • What does this choice depend on? Kees van Deemter (SSE, Jan '10)

15. Example: Roadgritting (Turner et al. 2009) Kees van Deemter (SSE, Jan '10)

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17. Example: Roadgritting (e.g.,Turner et al. 2009) Compare • “Roads above 500m are icy” • “Roads in the Highlands are icy” Decision-theoretic perspective: 1. 100 false positives, 2 false negatives 2. 10 false positives, 10 false negatives Suppose each false positive has utility of -0.1 each false negative has utility of -2 Kees van Deemter (SSE, Jan '10)

18. Example: Roadgritting (e.g.,Turner et al. 2009) Suppose false positive has utility of -0.1 false negative has utility of -2 Then 1: 100 false pos, 2 false neg = -14 2: 10 false pos, 10 false neg = -21 So summary 1 is preferred over summary 2. Kees van Deemter (SSE, Jan '10)

19. Our question: “When (if ever) is vague communication more useful than crisp communication?” • The question is not: “Can vague communication be of some use?” • The question is: “When is vague communication more useful than crisp communication?” • Aside: Is vagueness useful at all? Kees van Deemter (SSE, Jan '10)

20. Gary Marcus: The haphazard construction of the human mind Kees van Deemter (SSE, Jan '10)

21. Two related questions • When/why should a person express information vaguely? • When/why should an NLG system express information vaguely? Kees van Deemter (SSE, Jan '10)

22. 1. Vicissitudes of measurement 11m 12m Kees van Deemter (SSE, Jan '10)

23. 1. Vicissitudes of measurement [a] • Example: One house of 11m height and one house of 12m height • “the house that’s 12m tall needs to be demolished” • “the tall house needs to be demolished” • Comparison is easier and more reliable than measurement  prefer utterance 2 • Measurable as likelihood of incorrect action Kees van Deemter (SSE, Jan '10)

24. 1. Vicissitudes of measurement [a] • Example: One house of 11m height and one house of 12m height • “the house that’s 12m tall needs to be demolished” • “the tall house needs to be demolished” • Comparison is easier and more reliable than measurement  prefer utterance 2 • [But arguably, this utterance is not vague Its vagueness is merely local] Kees van Deemter (SSE, Jan '10)

25. Apparent vagueness is frequent • ‘the tall house’ the tallest house • ‘Physical exercise is good for young and old’ regardless of age • ‘Bad for bacteria, good for gums’gums improve as a result of bacterial death • ‘Fast-flowing rivers are deep’the faster the deeper (positive correlation between variables) Kees van Deemter (SSE, Jan '10)

26. 1. Vicissitudes of measurement [b] • Numbers can suggest spurious precision • Weather prediction: “It will be 23.75 degrees Celcius” • Margin of error may be as much as 2 degrees • “It will be mild” does not have this problem • [But why not say: ”approx. 24 degrees” ?] Kees van Deemter (SSE, Jan '10)

27. 2. Production/interpretation Effort • Effort needs to be commensurate with utility. In many cases, more precision adds little benefit. • E.g., Feasibility of an outing does not depend on whether it’s 20C or 30C. • ‘Mild’ takes fewer syllables than ‘twenty three point seven five’. • Time pressure affects speakers’ choices (e.g. Horton & Keysar 1996) • Vague words tend to be short (Krifka 2002) • Context dependence adds to efficiency Kees van Deemter (SSE, Jan '10)

28. 3.Evaluation payoff • Example: The doctor says • Utterance 1: “Your blood pressure is 153/92.” • Utterance 2: “Your blood pressure is high.” • U2 offers less detail than U1 • But U2 also offers evaluation of your condition (cf. Veltman 2000) Kees van Deemter (SSE, Jan '10)

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30. Example: The doctor says • Utterance 1: “Your blood pressure is 153/92.” • Utterance 2: “Your blood pressure is high.” • U2 offers less detail than U1 • But U2 also offers evaluation of your condition (cf. Veltman 2000) • A link with actions (cut down on salt, etc.) • Especially useful if metric is “difficult” • Measurable as likelihood of incorrect action Kees van Deemter (SSE, Jan '10)

31. Empirical evidence • B.Zikmund-Fisher et al. (2007) • E.Peters et al. (2009) Experiments showing that evaluative categories (i.e., “labels”) affect readers’ decisions Kees van Deemter (SSE, Jan '10)

32. Empirical evidence E.Peters et al. (2009): Hospital ratings based on numerical factors: (1) survival percentages (!), (2) percentages of recommended treatment, and (3) patient satisfaction Evaluation judgment: “How attractive is this hospital to you?” Kees van Deemter (SSE, Jan '10)

33. E.Peters et al. (2009) • When numerical information was accompanied by labels (“fair”, “good”, “excellent”), a greater proportion of variance in evaluation judgments could be explained by the numeric factors • Without labels, the most important information (i.e., factor 1) was not used at all • Without labels, less numerate subjects were influenced by mood (“I feel good/bad/happy/upset”) Kees van Deemter (SSE, Jan '10)

34. Practical implications • People are bad at interpreting numbers • Mood etc. tend to take their place • Evaluative categories (i.e., labels like “good”) matter Kees van Deemter (SSE, Jan '10)

35. [But why should labels be vague?] [Why does English not have a (brief) expression that says “Your blood pressure is 150/90 and too high”?] Compare “You are obese” means “Your BMI is above 30 and this is dangerous”. Kees van Deemter (SSE, Jan '10)

36. 4. Future contingencies • Indecent Displays Control Act (1981) forbids public display of indecentmatter • “indecent” at the time  the law has been parameterised (Waismann 1968, Hart 1994, Lipman 2006) • Obama/Volcker: Not “too much risk” should be concentrated into one bank (Jan. 2010) • opening bid in a policy war Kees van Deemter (SSE, Jan '10)

37. 5. Lack of a good metric • Mathematics: How difficult is a proof? (“As the reader may easily verify”) • Multidimensional measurements: What’s the size of a house? • Esthaetics: How beautiful is a sunset? Kees van Deemter (SSE, Jan '10)

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39. End of survey ... • on previous answers to the question why language is vague Kees van Deemter (SSE, Jan '10)

40. Remainder of this talk • Explore tentative new answer: V can “oil the wheels” of communication • Starting point: it’s almost inconceivable that all speakers arrive at exactly the same concepts Kees van Deemter (SSE, Jan '10)

41. Causes of semantic mismatches • Perception varies per individual • Hilbert 1987 on colour terms: density of pigment on lens & retina; sensitivity of photo receptors • Cultural issues. • Reiter et al. 2005 on temporal expressions. Example: “evening”: Are the times of dinner and sunset relevant? • R.Parikh (1994) recognised that mismatches exist … Kees van Deemter (SSE, Jan '10)

42. Parikh proposed utility-oriented perspective on meaning • Utility as reduction in search effort • showed communication doesn’t always break down when words are understood (slightly) differently by different speakers • Consider the expression “blue book” Kees van Deemter (SSE, Jan '10)

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44. Blue books (Bob) 75 225 25 Blue books (Ann) 675 Ann: “Bring the blue book on topology” Bob: Search [[blue]]Bob, then, if necessary, all other books (only10% probability!) Kees van Deemter (SSE, Jan '10)

45. What Parikh did not do: show utility of V • Ann and Bob used crisp concepts! This talk: • “tall” instead of “blue”. 2-dimensional  [[tall1]]  [[tall2]] or [[tall2]]  [[tall1]] • Focus on V Kees van Deemter (SSE, Jan '10)

46. The story of the stolen diamond “A diamond has been stolen from the Emperor and (…) the thief must have been one of the Emperor’s 1000 eunuchs. A witness sees a suspicious character sneaking away. He tries to catch him but fails, getting fatally injured (...). The scoundrel escapes. (…) The witness reports “The thief is tall” , then gives up the ghost. How can the Emperor capitalize on these momentous last words?” (book, to appear) Kees van Deemter (SSE, Jan '10)

47. The problem with dichotomies • Suppose Emperor uses a dichotomy, e.g. Model A: [[tall]]Emperor = [[>180cm]] (e.g., 500 people) • What if [[tall]]Witness = [[>175cm]]?If thief [[tall]]Witness - [[tall]]Emperor then Predicted search effort: 500+ ½(500)=750 Without witness’ utterance: ½(1000)=500 • The witness’ utterance “misled” the Emperor A 180cm thief 175cm Kees van Deemter (SSE, Jan '10)

48. Model A uses a crisp dichotomy between [[tall]]A and [[tall]]A • Contrast this with a partial model B, which has a truth value gap [[?tall?]]B Kees van Deemter (SSE, Jan '10)

49. 2-valued 3-valued Model A Model B tallA tallB 180cm 180cm ?tall?B tallA 165cm tallB Kees van Deemter (SSE, Jan '10)

50. How does the Emperor classify the thief? s(X) =defexpected search time given model X Three types of situations Type 1: thief  [[tall]]A = [[tall]]B In this case, s(A)=s(B) Kees van Deemter (SSE, Jan '10)