compositional semanticsjda/slides/jda_info159.pdf · 2020-02-18 · compositional semantics 8...
TRANSCRIPT
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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
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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
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KEY IDEAPieces of logical forms
correspond to pieces of language
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48
Pat: Pat
Sal: Sal Sam: Sam
Lou: Lou
shark(Lou)∧contains(Lou,Sam)Sam is inside Lou, a shark
Building a lexicon
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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
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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
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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
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52
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
What do we do now?
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53
Pat sent Lou a letterλx.letter(x)λf.Ax.f(x)λyzx.sent(x,y,z) LouPat
What do we do now?
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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)?
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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))?
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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)?
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57
Pat sent Lou urgently .???λyzx.sent(x,y,z) LouPat
What do we do now?
?????
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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
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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
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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
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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
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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
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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
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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
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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
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66
Pat sent Lou a letter
Semantics → Synax!
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67
Pat sent Lou a letter
Semantics → Synax!
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KEY IDEATypes in logic correspond to
grammatical categories in language
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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)
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Problem 2
70
name type coastal
Columbia city no
Cooper river yes
Charleston city yes
There are 128 cities in South Carolina
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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)∧
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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…
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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)
∧
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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)∧
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KEY IDEAThe meaning of a sentence is the set
of possible worlds it picks out.
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KEY IDEACollections of possible worlds can be
compactly represented with logical forms.
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KEY IDEAPieces of logical forms
correspond to pieces of language
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KEY IDEATypes in logic correspond to
grammatical categories in language
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BONUS ROUNDWhat’s missing?
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80
Q: How do you like my cooking?
Saying what we mean
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81
Q: How do you like my cooking? A: It’s extremely interesting.
Saying what we mean
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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
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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
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84
Sal might have seen a unicorn.
Pat thinks Sal saw a unicorn.
Pat wants to find a unicorn.
Belief & possibility
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KEY IDEANot all meaning is literal!
![Page 86: Compositional Semanticsjda/slides/jda_info159.pdf · 2020-02-18 · Compositional semantics 8 It’s not enough to have structured representations of syntax: We also need structured](https://reader034.vdocuments.us/reader034/viewer/2022042919/5f634956e4d44d11aa27b45e/html5/thumbnails/86.jpg)
BONUS ROUNDHistorical Notes
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Alfred Tarski Richard Montague
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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”