compositional semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfpat sent lou a letter pat...
TRANSCRIPT
![Page 1: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/1.jpg)
Compositional Semantics
Jacob Andreas
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Problem 1
2
Each of the three girls has a platypus.
Each of the three girls climbed the mountain.
How many platypuses?
How many mountains?
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Problem 1
3
Each of the three girls has a platypus.
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Problem 1
4
Each of the three girls climbed the mountain.
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Problem 2
5
name type coastal
Columbia city no
Cooper river yes
Charleston city yes
There are 128 cities in South Carolina.
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Problem 3
6
Is Barack Obama from the United States?
Barack Obama was the 44th President of the United States. Obama was born on August 4 in Honolulu, Hawaii. In late August 1961, Obama's mother moved with him to the University of Washington in Seattle for a year…
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Compositional semantics
7
It’s not enough to have structured representations of syntax: We also need structured representations of meaning.
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Compositional semantics
8
It’s not enough to have structured representations of syntax: We also need structured representations of meaning.
Today: How do we get from language to meaning?
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PART IWhat is meaning?
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10
a + b = 17
Meaning in formal languages
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11
a + b = 17
Meaning in formal languages
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12
a + b = 17
a = ? b = ?
Meaning in formal languages
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13
{a=0, b=0}
{a=3, b=10}
{a=5, b=12}
{a=17, b=0}
{a=10, b=7}
{a=5, b=5}
a + b = 17
Meanings are sets of valid assignments
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{a=0, b=0}
{a=5, b=12}14
✘
✔
{a=3, b=10}
{a=17, b=0}
{a=10, b=7}
{a=5, b=5}
✔
✔✘
✘
a + b = 17
Meanings are sets of valid assignments
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{a=0, b=0}
{a=5, b=12}15
✘
✔
{a=3, b=10}
{a=17, b=0}
{a=10, b=7}
{a=5, b=5}
✔
✔✘
✘
a + 3 = 20 - b
Meanings are sets of valid assignments
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{a=5, b=12}16
✔
⟦a + b = 17⟧
Meanings are functions that judge validity
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17
⟦a + b = 17⟧
{a=3, b=10} ✘
Meanings are functions that judge validity
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Lessons from math
18
The meaning of a statement is the set of possible worlds consistent with that statement.
Here, a “possible world” is an assignment of values to variables.
⟦a + b = 17⟧
{a=3, b=10}
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19
Pat likes Sal.
Meaning in natural languages
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Representing possible worlds
20
Individuals
Properties
Relations
Pat Sal
whale
loves
sad
contains
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21
Pat
Sal
Sam
Lou
Example world
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worried
22
Pat
Sal
Sam
Lou
likes
likes
contains
loves
likes
happy
scared
shark
Example world
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23
Pat
Sal
Sam
Louloves
loves
lovessad
sad
sad
sad
Different example world
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Representing possible worlds
24
Individuals
Properties
Relations
Pat Sal
whale={Lou},sad={Pat,Sal}
likes={(Pat,Sal),(Sal,Sam)}
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25
Pat likes Sal.
worried Pat
Sal
Sam
Lou
likes
likes
loves
likes
happy
scared
shark
worried Pat
Sal
Sam
Lou
loves contains
loves
likes scared
shark
worried Pat
Sal
Sam
Lou
likes
likes
contains
likes
happy
scared
human
worried Pat
Sal
Sam
Lou
likes
likes
contains
loves
likes
happy
scared
dog
Interpretations of sentences
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26
Lou is a shark.
worried Pat
Sal
Sam
Lou
likes
likes
loves
likes
happy
scared
shark
worried Pat
Sal
Sam
Lou
loves contains
loves
likes scared
shark
worried Pat
Sal
Sam
Lou
likes
likes
contains
likes
happy
scared
human
worried Pat
Sal
Sam
Lou
likes
likes
contains
loves
likes
happy
scared
dog
Interpretations of sentences
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27
Sam is inside Lou, a shark.
worried Pat
Sal
Sam
Lou
likes
likes
loves
likes
happy
scared
shark
worried Pat
Sal
Sam
Lou
loves contains
loves
likes scared
shark
worried Pat
Sal
Sam
Lou
likes
likes
contains
likes
happy
scared
human
worried Pat
Sal
Sam
Lou
likes
likes
contains
loves
likes
happy
scared
dog
Interpretations of sentences
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KEY IDEAThe meaning of a sentence is the set
of possible worlds it picks out.
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PART IIHow is meaning constructed?
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30
Pat likes Sal.
worried Pat
Sal
Sam
Lou
likes
likes
loves
likes
happy
scared
shark
worried Pat
Sal
Sam
Lou
loves contains
loves
likes scared
shark
worried Pat
Sal
Sam
Lou
likes
likes
contains
likes
happy
scared
human
worried Pat
Sal
Sam
Lou
likes
likes
contains
loves
likes
happy
scared
dog
Explicit representation is too hard
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31
⟦Pat likes Sal⟧
worried Pat
Sal
Sam
Lou
likes
loves
likes
happy
scared
whale
✔
Meanings as functions
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32
⟦Pat likes Sal⟧
worried Pat
Sal
Sam
Lou
likes
likes
loves
likes
happy
scared
whale
✔
likes(Pat,Sal)
Meanings as logical statements
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33
Pat likes Sallikes(Pat,Sal)
Expressing functions with logic
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34
Lou is a sharkshark(Lou)
Meanings as logical statements
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35
Sam is inside Lou, a shark
Meanings as logical statements
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36
Sam is inside Lou, a sharkshark(Lou)∧contains(Lou,Sam)
Meanings as logical statements
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37
Nobody likes Lou
Meanings as logical statements
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38
Nobody likes Lou∀x.¬likes(x,Lou)
Meanings as logical statements
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39
Everyone who knows Sal is happy
Meanings as logical statements
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40
Everyone who knows Sal is happy
∀x.knows(x,Sal)→happy(x)
Meanings as logical statements
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KEY IDEACollections of possible worlds can be
compactly represented with logical forms.
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likes(Pat,Sal)
shark(Lou)
shark(Lou)∧contains(Lou,Sam)
∀x.¬likes(x,Lou)42
Pat likes Sal
Lou is a shark
Sam is inside Lou,a shark
Nobody likes Lou
Compositionality of meaning
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likes(Pat,Sal)
shark(Lou)
shark(Lou)∧contains(Lou,Sam)
∀x.¬likes(x,Lou)43
Pat likes Sal
Lou is a shark
Sam is inside Lou,a shark
Nobody likes Lou
Compositionality of meaning
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likes(Pat,Sal)
shark(Lou)
shark(Lou)∧contains(Lou,Sam)
∀x.¬likes(x,Lou)44
Pat likes Sal
Lou is a shark
Sam is inside Lou,a shark
Nobody likes Lou
Compositionality of meaning
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likes(Pat,Sal)
shark(Lou)
shark(Lou)∧contains(Lou,Sam)
∀x.¬likes(x,Lou)45
A Sal le gusta Pat
Lou es un tiburón
Sam está dentro deLou, un tiburón
A nadie le gusta Lou
Compositionality of meaning
![Page 46: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/46.jpg)
likes(Pat,Sal)
shark(Lou)
shark(Lou)∧contains(Lou,Sam)
∀x.¬likes(x,Lou)46
a12 b5 c67 a8
a12 b5 c0 a0
a12 b16 c12 c12
a53
Compositionality of meaning
![Page 47: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/47.jpg)
KEY IDEAPieces of logical forms
correspond to pieces of language
![Page 48: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/48.jpg)
48
Pat: Pat
Sal: Sal Sam: Sam
Lou: Lou
shark(Lou)∧contains(Lou,Sam)Sam is inside Lou, a shark
Building a lexicon
![Page 49: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/49.jpg)
49
Pat: Pat
Sal: Sal Sam: Sam
Lou: Lou
shark: λx.whale(x)
Sal: Sal Sam: Sam
Lou: Lou
shark(Lou)∧contains(Lou,Sam)Sam is inside Lou, a shark
Building a lexicon
![Page 50: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/50.jpg)
50
Pat: Pat
Sal: Sal Sam: Sam
Lou: Lou
shark: λx.shark(x)
Sal: Sal Sam: Sam
Lou: Lou
shark(Lou)∧contains(Lou,Sam)Sam is inside Lou, a shark
Building a lexicon
![Page 51: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/51.jpg)
51
Pat: Pat
Sal: Sal Sam: Sam
Lou: Lou
shark: λx.shark(x)
likes: λyx.likes(x,y) nobody: λf.∀x.¬f(x)
Lou: Lou...
shark(Lou)∧contains(Lou,Sam)Sam is inside Lou, a shark
Building a lexicon
![Page 52: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/52.jpg)
52
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
What do we do now?
![Page 53: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/53.jpg)
53
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
What do we do now?
![Page 54: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/54.jpg)
54
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
What do we do now?
Ax.letter(x)?
![Page 55: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/55.jpg)
55
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
What do we do now?
letter(λf.Ax.f(x))?
![Page 56: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/56.jpg)
56
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
What do we do now?
???
Ax.letter(x)?
![Page 57: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/57.jpg)
57
Pat sent Lou urgently .???λyzx.sent(x,y,z) LouPat
What do we do now?
?????
![Page 58: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/58.jpg)
58
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
ObjectBool
ObjectObject
Bool
{Obj,Obj,Obj}
Bool
Object
Bool
Semantic types
![Page 59: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/59.jpg)
59
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
NPS
NPNP
S
NP,NP,NP
S
NP
S
Semantic types & syntax
![Page 60: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/60.jpg)
60
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
NP NP S|NP((S|NP)|NP)|NP S|(S|NP)
Semantic types & syntax
![Page 61: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/61.jpg)
61
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
NP NP S/NPNP/(S/NP)((S\NP)/NP)/NP
Categorial grammar
![Page 62: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/62.jpg)
62
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
NP NP S/NPNP/(S/NP)((S\NP)/NP)/NP
NPAx.letter(x)
Parsing with a categorial grammar
![Page 63: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/63.jpg)
63
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
NP NP S/NPNP/(S/NP)
NP
((S\NP)/NP)/NP
Ax.letter(x)(S\NP)/NP
λzx.sent(x,Lou,z)
Parsing with a categorial grammar
![Page 64: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/64.jpg)
64
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
NP NP S/NPNP/(S/NP)
NP
((S\NP)/NP)/NP
Ax.letter(x)(S\NP)/NP
λzx.sent(x,Lou,z)
λx.sent(x,Lou,Ax.letter(x)) S\NP
Parsing with a categorial grammar
![Page 65: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/65.jpg)
65
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
NP NP S/NPNP/(S/NP)
NP
((S\NP)/NP)/NP
Ax.letter(x)(S\NP)/NP
λzx.sent(x,Lou,z)
λx.sent(x,Lou,Ax.letter(x)) S\NP
sent(Pat,Lou,Ax.letter(x)) S
Parsing with a categorial grammar
![Page 66: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/66.jpg)
66
Pat sent Lou a letter
Semantics → Synax!
![Page 67: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/67.jpg)
67
Pat sent Lou a letter
Semantics → Synax!
![Page 68: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/68.jpg)
KEY IDEATypes in logic correspond to
grammatical categories in language
![Page 69: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/69.jpg)
Problem 1
69
Each of the three girls has a platypus.
Each of the three girls climbed the mountain.
∀x.girl(x)→∃y.platypus(y)∧has(x,y)
∃y.mountain(y)∧∀x.girl(x)→climbed(x,y)
![Page 70: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/70.jpg)
Problem 2
70
name type coastal
Columbia city no
Cooper river yes
Charleston city yes
There are 128 cities in South Carolina
![Page 71: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/71.jpg)
Problem 2
71
name type coastal
Columbia city no
Cooper river yes
Charleston city yes
There are 128 cities in South Carolina
same(128,countx.city(x)∧in(x,SouthCarolina)∧
![Page 72: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/72.jpg)
Problem 3
72
Is Barack Obama from the United States?
Barack Obama was the 44th President of the United States. Obama was born on August 4 in Honolulu, Hawaii. In late August 1961, Obama's mother moved with him to the University of Washington in Seattle for a year…
![Page 73: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/73.jpg)
Problem 3
73
Is Barack Obama from the United States?
Barack Obama was the 44th President of the United States. Obama was born on August 4 in Honolulu, Hawaii. In late August 1961, Obama's mother moved with him to the University of Washington in Seattle for a year…
from(Obama,UnitedStates)
∧
born(Obama,Hawaii,August4)
∧
![Page 74: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/74.jpg)
Problem 3
74
Is Barack Obama from the United States?
Barack Obama was the 44th President of the United States. Obama was born on August 4 in Honolulu, Hawaii. In late August 1961, Obama's mother moved with him to the University of Washington in Seattle for a year…
born(Obama,Hawaii,August4)
∧
from(Obama,UnitedStates)
∧
born(x,y,z)→from(x,y)
from(x,y)∧in(y,z)→from(x,z)in(Hawaii,UnitedStates)∧
![Page 75: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/75.jpg)
KEY IDEAThe meaning of a sentence is the set
of possible worlds it picks out.
![Page 76: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/76.jpg)
KEY IDEACollections of possible worlds can be
compactly represented with logical forms.
![Page 77: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/77.jpg)
KEY IDEAPieces of logical forms
correspond to pieces of language
![Page 78: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/78.jpg)
KEY IDEATypes in logic correspond to
grammatical categories in language
![Page 79: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/79.jpg)
BONUS ROUNDWhat’s missing?
![Page 80: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/80.jpg)
80
Q: How do you like my cooking?
Saying what we mean
![Page 81: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/81.jpg)
81
Q: How do you like my cooking? A: It’s extremely interesting.
Saying what we mean
![Page 82: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/82.jpg)
82
Q: How do you like my cooking? A: It’s extremely interesting.
Q: Do you know what time it is?
Saying what we mean
![Page 83: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/83.jpg)
83
Q: How do you like my cooking? A: It’s extremely interesting.
Q: Do you know what time it is? A: Yes, I do.
Saying what we mean
![Page 84: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/84.jpg)
84
Sal might have seen a unicorn.
Pat thinks Sal saw a unicorn.
Pat wants to find a unicorn.
Belief & possibility
![Page 85: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/85.jpg)
KEY IDEANot all meaning is literal!
![Page 86: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/86.jpg)
BONUS ROUNDHistorical Notes
![Page 87: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/87.jpg)
Alfred Tarski Richard Montague
![Page 88: Compositional Semanticsweb.mit.edu/jda/www/slides/jda_info159.pdfPat sent Lou a letter Pat λyzx.sent(x,y,z) Lou λf.Ax.f(x) λx.letter(x) Object Bool Object Object Bool {Obj,Obj,Obj}](https://reader033.vdocuments.mx/reader033/viewer/2022060417/5f14eba04c38e86a7b39ef62/html5/thumbnails/88.jpg)
Learn more
88
ling121: “Logical Semantics”
Ted Briscoe’s lecture notes: https://www.cl.cam.ac.uk/teaching/1011/L107/semantics.pdf
Mark Steedman, “The Syntactic Process”