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Introduction Use Acquisition Selection Conclusion . Modeling the dynamics of use and acquisition in language change . Christopher Ahern University of Pennsylvania March 2, 2015 Ahern (UPENN) Use, Acquisition, and Change March 2, 2015

  1. Introduction Use Acquisition Selection Conclusion Acquisition Grammar n Grammar n + 1 . . . . Data n Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 7 / 62

  2. Introduction Use Acquisition Selection Conclusion Acquisition Grammar n Grammar n + 1 . . . . Data n Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 7 / 62

  3. Introduction Use Acquisition Selection Conclusion Acquisition Grammar n Grammar n + 1 . . . . Data n Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 7 / 62

  4. Introduction Use Acquisition Selection Conclusion Acquisition Grammar n Grammar n + 1 . . . . Data n Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 7 / 62

  5. Introduction Use Acquisition Selection Conclusion Language Change . . . . . . . Grammar n Grammar n + 1 Acquisition Data n Data n + 1 Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 8 / 62

  6. Introduction Use Acquisition Selection Conclusion Use Grammar n Grammar n . . . . Data n Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 9 / 62

  7. Introduction Use Acquisition Selection Conclusion Use Grammar n Grammar n . . . . Data n Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 9 / 62

  8. Introduction Use Acquisition Selection Conclusion Use Grammar n Grammar n . . . . Data n Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 9 / 62

  9. Introduction Use Acquisition Selection Conclusion Language Change . . . . . . . . Grammar n Grammar n + 1 Acquisition U s e Data n Data n + 1 Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 10 / 62

  10. Introduction Use Acquisition Selection Conclusion Language Change Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 11 / 62

  11. Introduction Use Acquisition Selection Conclusion 1.00 0.75 Proportion 0.50 0.25 0.00 1200 1300 1400 1500 Year NEG V → NEG V NEG → V NEG ( USE ) ( ACQUISITION ) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 12 / 62

  12. Introduction Use Acquisition Selection Conclusion 1.00 0.75 Proportion 0.50 0.25 0.00 1200 1300 1400 1500 Year NEG V → NEG V NEG → V NEG ( ACQUISITION ) ( USE ) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 13 / 62

  13. Introduction Use Acquisition Selection Conclusion NEG V → NEG V NEG . . Pragmatic conditions 1 . . Experimental evidence 2 . . Information transmission 3 Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 14 / 62

  14. Introduction Use Acquisition Selection Conclusion Information Structure . ...the post-verbal negative element is heavily regulated by information-structural factors , and specifically by the discourse-old status of the denied proposition. . (Schwenter 2006) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 15 / 62

  15. Introduction Use Acquisition Selection Conclusion Discourse Status DISCOURSE NEW DISCOURSE OLD NEG V NEG V NEG Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 16 / 62

  16. Introduction Use Acquisition Selection Conclusion Discourse Status DISCOURSE NEW DISCOURSE OLD NEG V ✓ NEG V NEG # Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 16 / 62

  17. Introduction Use Acquisition Selection Conclusion Discourse Status DISCOURSE NEW DISCOURSE OLD NEG V ✓ ✓ NEG V NEG # ✓ Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 16 / 62

  18. Introduction Use Acquisition Selection Conclusion Discourse New Husband and wife expected the plumber to come fix their leaky faucet while they were at work during the day. Husband arrives home before his wife to find a still leaky faucet. Wife arrives home shortly and husband says: . (1) O bombeiro V EIO . NÃO The plumber neg came “The plumber didn’t come." (2) #O bombeiro V EIO NÃO . NÃO The plumber neg came neg “The plumber didn’t come." . Brazilian Portuguese (Schwenter 2006) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 17 / 62

  19. Introduction Use Acquisition Selection Conclusion Discourse Old ...Wife arrives home shortly and asks husband: . (3) O bombeiro veio hoje? The plumber came today “Did the plumber come today?" (4) a. O bombeiro NÃO V EIO . . b. O bombeiro NÃO V EIO NÃO . Brazilian Portuguese (Schwenter 2006) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 18 / 62

  20. Introduction Use Acquisition Selection Conclusion Inferrable ...Wife arrives home and points quizzically at sink: . (5) a. O bombeiro NÃO V EIO . b. O bombeiro NÃO V EIO NÃO . . Brazilian Portuguese (Schwenter 2006) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 19 / 62

  21. Introduction Use Acquisition Selection Conclusion Synchronic DISCOURSE NEW DISCOURSE OLD NEG V ✓ ✓ NEG V NEG # ✓ Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 20 / 62

  22. Introduction Use Acquisition Selection Conclusion Communication Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 21 / 62

  23. Introduction Use Acquisition Selection Conclusion Communication Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 22 / 62

  24. Introduction Use Acquisition Selection Conclusion What have you been up to... . . (Savitsky et al. 2011) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 23 / 62

  25. Introduction Use Acquisition Selection Conclusion What have you been up to... . Two pairs of friends (or spouses) sat back to back . (Savitsky et al. 2011) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 23 / 62

  26. Introduction Use Acquisition Selection Conclusion What have you been up to... . Two pairs of friends (or spouses) sat back to back Read 10 four-way ambiguous sentences out loud . (Savitsky et al. 2011) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 23 / 62

  27. Introduction Use Acquisition Selection Conclusion What have you been up to... . Two pairs of friends (or spouses) sat back to back Read 10 four-way ambiguous sentences out loud Speakers have one of four intended meanings ( � , � ,...) . (Savitsky et al. 2011) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 23 / 62

  28. Introduction Use Acquisition Selection Conclusion What have you been up to... . Two pairs of friends (or spouses) sat back to back Read 10 four-way ambiguous sentences out loud Speakers have one of four intended meanings ( � , � ,...) Hearers guess intended meaning from four ( � , � ,...) . (Savitsky et al. 2011) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 23 / 62

  29. Introduction Use Acquisition Selection Conclusion What have you been up to... . Two pairs of friends (or spouses) sat back to back Read 10 four-way ambiguous sentences out loud Speakers have one of four intended meanings ( � , � ,...) Hearers guess intended meaning from four ( � , � ,...) Speakers estimate how many sentences hearers got right . (Savitsky et al. 2011) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 23 / 62

  30. Introduction Use Acquisition Selection Conclusion What have you been up to... (Savitsky et al. 2011) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 24 / 62

  31. Introduction Use Acquisition Selection Conclusion Don’t talk about pink elephants! (Wardlow Lane, Groisman, and Ferreira 2006) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 25 / 62

  32. Introduction Use Acquisition Selection Conclusion Don’t talk about pink elephants! (Wardlow Lane, Groisman, and Ferreira 2006) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 26 / 62

  33. Introduction Use Acquisition Selection Conclusion Communication Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 27 / 62

  34. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  35. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  36. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  37. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  38. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  39. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  40. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  41. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  42. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  43. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  44. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  45. Introduction Use Acquisition Selection Conclusion Discourse Game t 0 : DISCOURSE NEW t 1 : DISCOURSE OLD a 0 : DISCOURSE NEW a 1 : DISCOURSE OLD t ∈ T a ∈ A . . . . . . . . . . O bombeiro O bombeiro r : M → A s : P ( T ) → M NÃO VEIO NÃO NÃO VEIO p : The plumber came. (Ahern and Clark Under Revision) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 28 / 62

  46. Introduction Use Acquisition Selection Conclusion . . . . . NEG V DISCOURSE NEW NEG V NEG DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 29 / 62

  47. Introduction Use Acquisition Selection Conclusion b t + b t . . . . . . DISCOURSE NEW DISCOURSE OLD p : The plumber came. Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 30 / 62

  48. Introduction Use Acquisition Selection Conclusion b t + b t . . . . . . DISCOURSE NEW DISCOURSE OLD p : The plumber came. Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 30 / 62

  49. Introduction Use Acquisition Selection Conclusion b t + b t . . . . . . DISCOURSE NEW DISCOURSE OLD p : The plumber came. Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 30 / 62

  50. Introduction Use Acquisition Selection Conclusion b t + b t . . . . . . DISCOURSE NEW DISCOURSE OLD p : The plumber came. Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 30 / 62

  51. Introduction Use Acquisition Selection Conclusion Information Transmission . U S ( t , a ) = − ( a − t − ( 1 − t ) b ) 2 b (1) U R U S U R ( t , a ) = − ( a − t ) 2 . Utility 0.0 0.5 1.0 Action taken by Receiver (Crawford and Sobel 1982) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 31 / 62

  52. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  53. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  54. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  55. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  56. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  57. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  58. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  59. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  60. Introduction Use Acquisition Selection Conclusion b b b b b NEG V NEG V NEG V NEG V NEG V NEG V NEG NEG V NEG NEG V NEG NEG V NEG NEG V NEG a NEG V a NEG V a NEG V a NEG V a NEG V a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG a NEG V NEG . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCOURSE NEW DISCOURSE OLD Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 32 / 62

  61. Introduction Use Acquisition Selection Conclusion 1.0 b > 1 0.8 4 p neg V neg 0.6 0.4 0.2 0.0 2 4 6 8 10 Time (Discrete-time replicator dynamics, Taylor and Jonker 1978) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 33 / 62

  62. Introduction Use Acquisition Selection Conclusion 1.00 0.75 Proportion 0.50 0.25 0.00 1200 1300 1400 1500 Year NEG V → NEG V NEG → V NEG ( USE ) ( ACQUISITION ) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 34 / 62

  63. Introduction Use Acquisition Selection Conclusion NEG V → NEG V NEG . . Pragmatic conditions: NEG V NEG is sensitive to discourse status 1 . . Experimental evidence: speakers over-estimate discourse status 2 . . Information transmission: bias leads to increase in NEG V NEG 3 Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 35 / 62

  64. Introduction Use Acquisition Selection Conclusion 1.00 0.75 Proportion 0.50 0.25 0.00 1200 1300 1400 1500 Year NEG V → NEG V NEG → V NEG ( ACQUISITION ) ( USE ) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 36 / 62

  65. Introduction Use Acquisition Selection Conclusion 1.00 0.75 Proportion 0.50 0.25 0.00 1200 1300 1400 1500 Year NEG V → NEG V NEG → V NEG ( USE ) ( ACQUISITION ) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 37 / 62

  66. Introduction Use Acquisition Selection Conclusion NEG V NEG → V NEG . . Variational learning 1 . . Negative evidence 2 . . Phonetic weight 3 Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 38 / 62

  67. Introduction Use Acquisition Selection Conclusion Variational Learning . Given input from environment E , learner chooses grammar G i with probability p i : { p ′ i = p i + γ ( 1 − p i ) If G i → s then (2) p ′ j = ( 1 − γ ) p j ∀ j ̸ = i { p ′ i = ( 1 − γ ) p i If G i ↛ s then (3) γ p ′ N − 1 +( 1 − γ ) p j j = ∀ j ̸ = i . (Yang 2000) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 39 / 62

  68. Introduction Use Acquisition Selection Conclusion Negation G ne G not . . . . . . . α β NEG V V NEG NEG V NEG (Rowlett 1998; Wallage 2008) Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 40 / 62

  69. Introduction Use Acquisition Selection Conclusion Negative evidence p ne p not 1 − α α G ne G ne G ne G not G not G not p ne NEG V NEG V NEG G ne G ne . . . . . . . . . . . . . . . . . . . . . . p not G not p not β lim t → ∞ p not = ⇑ p ne ⇓ p not ⇓ p ne ⇑ p not ⇑ p ne ⇓ p not p ne α + p not β Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 41 / 62

  70. Introduction Use Acquisition Selection Conclusion Negative evidence p ne p not 1 − α α G ne G ne G ne G not G not G not p ne NEG V NEG V NEG G ne G ne . . . . . . . . . . . . . . . . . . . . . . p not G not p not β lim t → ∞ p not = ⇑ p ne ⇓ p not ⇓ p ne ⇑ p not ⇑ p ne ⇓ p not p ne α + p not β Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 41 / 62

  71. Introduction Use Acquisition Selection Conclusion Negative evidence p ne p not 1 − α α G ne G ne G ne G not G not G not p ne NEG V NEG V NEG G ne G ne . . . . . . . . . . . . . . . . . . . . . . p not G not p not β lim t → ∞ p not = ⇑ p ne ⇓ p not ⇓ p ne ⇑ p not ⇑ p ne ⇓ p not p ne α + p not β Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 41 / 62

  72. Introduction Use Acquisition Selection Conclusion Negative evidence p ne p not 1 − α α G ne G ne G ne G not G not G not p ne NEG V NEG V NEG G ne G ne . . . . . . . . . . . . . . . . . . . . . . p not G not p not β lim t → ∞ p not = ⇑ p ne ⇓ p not ⇓ p ne ⇑ p not ⇑ p ne ⇓ p not p ne α + p not β Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 41 / 62

  73. Introduction Use Acquisition Selection Conclusion Negative evidence p ne p not 1 − α α G ne G ne G ne G not G not G not p ne NEG V NEG V NEG G ne G ne . . . . . . . . . . . . . . . . . . . . . . p not G not p not β lim t → ∞ p not = ⇑ p ne ⇓ p not ⇓ p ne ⇑ p not ⇑ p ne ⇓ p not p ne α + p not β Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 41 / 62

  74. Introduction Use Acquisition Selection Conclusion Negative evidence p ne p not 1 − α α G ne G ne G ne G not G not G not p ne NEG V NEG V NEG G ne G ne . . . . . . . . . . . . . . . . . . . . . . p not G not p not β lim t → ∞ p not = ⇑ p ne ⇓ p not ⇓ p ne ⇑ p not ⇑ p ne ⇓ p not p ne α + p not β Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 41 / 62

  75. Introduction Use Acquisition Selection Conclusion Negative evidence p ne p not 1 − α α G ne G ne G ne G not G not G not p ne NEG V NEG V NEG G ne G ne . . . . . . . . . . . . . . . . . . . . . . p not G not p not β lim t → ∞ p not = ⇑ p ne ⇓ p not ⇓ p ne ⇑ p not ⇑ p ne ⇓ p not p ne α + p not β Ahern (UPENN) Use, Acquisition, and Change March 2, 2015 41 / 62

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