. l i h P / . g . h g . g . n c n n y i i i L - - PDF document

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. l i h P / . g . h g . g . n c n n y i i i L L L s P D D D U M M M H U U U J d a i r k s r b e o t e l r n t H a e i d z P H u i n L l i m t f s f u i T P a e J u J

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SLIDE 1 T i m H u n t e r U M D L i n g . J u s t i n H a l b e r d a J H U P s y c h . J e f f L i d z U M D L i n g . P a u l P i e t r
  • s
k i U M D L i n g . / P h i l .
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SLIDE 2
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SLIDE 3
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SLIDE 4
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SLIDE 5
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SLIDE 6
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SLIDE 7

′ ∩ ′ ∩

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SLIDE 8
  • ∩
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SLIDE 9
  • ∩
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SLIDE 10
  • ∩
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SLIDE 11
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SLIDE 12
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SLIDE 13

∃ ′ ′ ′ ⊂

A B A′

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SLIDE 14 | D O T S

∩

Y E L L O W | > | D O T S – Y E L L O W | i f f

∃

A

′

[ O n e T
  • O
n e ( A

′

, ( D O T S – Y E L L O W ) ) a n d A

′ ⊂

( D O T S

∩

Y E L L O W ) ] D O T S

∩

Y E L L O W D O T S – Y E L L O W
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SLIDE 15 | D O T S

∩

Y E L L O W | > | D O T S – Y E L L O W | i f f

∃

A

′

[ O n e T
  • O
n e ( A

′

, ( D O T S – Y E L L O W ) ) a n d A

′ ⊂

( D O T S

∩

Y E L L O W ) ] i f f O n e T
  • O
n e P l u s ( D O T S

∩

Y E L L O W , D O T S – Y E L L O W ) w h e r e : O n e T
  • O
n e P l u s ( A , B )

≡ ∃

A

′

[ O n e T
  • O
n e ( A

′

, B ) a n d A

′ ⊂

A ]
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SLIDE 16
  • D
e h a e n e 1 9 9 7 F e i g e n s
  • n
, S p e l k e & D e h a e n e 2 4 W h a l e n , G a l l i s t e l & G e l m a n 1 9 9 9
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SLIDE 17
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SLIDE 18
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SLIDE 19
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SLIDE 20

× ×

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SLIDE 21
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SLIDE 22
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SLIDE 23
  • !
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SLIDE 24
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SLIDE 25
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SLIDE 26
  • !

"#

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SLIDE 27
  • !

"# !"#

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SLIDE 28
  • !

"# !"#

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SLIDE 29
  • !

"# !"#

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SLIDE 30
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SLIDE 31
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SLIDE 32

∩

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SLIDE 33 H a l b e r d a , S i r e s & F e i g e n s
  • n
2 7 T r i e s m a n & G
  • r
m i c a n 1 9 8 8 W
  • l
f e 1 9 9 8
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SLIDE 34
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SLIDE 35

× ×

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SLIDE 36
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SLIDE 37
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SLIDE 38
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SLIDE 39
  • |
D O T S

∩

Y E L L O W | > | D O T S – Y E L L O W |
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SLIDE 40 t i m h @ u m d . e d u h t t p : / / w w w . l i n g . u m d . e d u / ~ t i m h /
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SLIDE 41

‘most’ tmost pmost Cardinality OneToOne+ Approximate

count 1-to-1+ count 1-to-1+

Level 1 Computation

(truth conditions)

Level 1.5 Families of Algorithms

(understanding)

# ΨHP ΨHP

ANSb ANSa

a. ANS Gaussian numerosity identification b. ANS Gaussian GreaterThan operation via subtraction

Word Further Distinctions

(towards verification)

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SLIDE 42

Multiple Sets Enumerated In Parallel

Probe Before

Halberda, Sires & Feigenson 2006

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SLIDE 43

Multiple Sets Enumerated In Parallel

Probe After

Halberda, Sires & Feigenson 2006

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SLIDE 44
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SLIDE 45
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SLIDE 46
  • !

!"

#