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Natural Language SemanticsLeonid Kof
kof@in.tum.de
Technische Universitat Munchen
Natural Language Semantics – p. 1
Outline
1. Motivation (→ Turing Test)
2. How is NL–Semantics defined?
3. Is NL–Semantics compositional?
4. How do different sentences interact? (→ DiscourseRepresentation Theory)
5. Non–compositional approachesVerb framesParsing & annotation
Natural Language Semantics – p. 2
Turing Test
Question
AnswerComputer?Human?
Natural Language Semantics – p. 3
Outline
1. Motivation (→ Turing Test)
2. How is NL–Semantics defined?
3. Is NL–Semantics compositional?
4. How do different sentences interact? (→ DiscourseRepresentation Theory)
5. Non–compositional approachesVerb framesParsing & annotation
Natural Language Semantics – p. 4
Semantics Definition
Verb = Main Predicate
Alice loves Bob = love(Alice, Bob)
Alice loves a man = ∃x.(man(x) ∧ love(Alice, x ))
Every woman loves Bob =∀x.(woman(x) → love(x , Bob))
Every woman loves a boxer =∃x.(boxer(x) ∧ (∀y.(woman(y) → love(y , x ))))
Every woman loves a boxer =∀y.(woman(y) → ∃x.(boxer(x) ∧ love(y , x )))
Natural Language Semantics – p. 5
Outline
1. Motivation (→ Turing Test)
2. How is NL–Semantics defined?
3. Is NL–Semantics compositional?
4. How do different sentences interact? (→ DiscourseRepresentation Theory)
5. Non–compositional approachesVerb framesParsing & annotation
Natural Language Semantics – p. 6
Compositionality Problem
Words are in the “wrong” order
Alice loves Bob = love(Alice, Bob) Ã
love, Alice, Bob
Alice loves a man = ∃x.(man(x) ∧ love(Alice, x )) Ã
a, man, love, Alice, . . .
. . .
Natural Language Semantics – p. 7
Sidestep:λ–Calculus
Function abstraction:λx.(function expression)
Function application:expression1 expression2
β–Reduction:(λx.(function expression)) argument =function expression[x/argument]
Natural Language Semantics – p. 8
Semantics withλ–Terms
Special λ–term for every word class
Proper names: Alice = λP.(P@Alice)
Common names: woman = λy.(woman(y))
Intransitive verbs: walks = λx.(walk(x ))
Transitive verbs: loves = λX.(λz.(X@(λx.love(z , x ))))
“every”: every = λP.(λQ.(∀x.((P@x) → (Q@x))))
“a”: a = λP.(λQ.(∃y.((P@y) ∧ (Q@y))))
Natural Language Semantics – p. 9
Does it really work?
Alice loves Bob =
(λP.(P@Alice))@((λX.(λz.(X@(λx.love(z , x )))))@(λP.P@Bob)) =(λP.(P@Alice))@(λz.((λP.P@Bob)@(λx.love(z , x )))) =(λP.(P@Alice))@(λz.(λx.love(z , x )@Bob)) =(λP.(P@Alice))@(λz.love(z , Bob)) =(λz.love(z , Bob))@Alice =love(Alice, Bob)
Natural Language Semantics – p. 10
Outline
1. Motivation (→ Turing Test)
2. How is NL–Semantics defined?
3. Is NL–Semantics compositional?
4. How do different sentences interact? (→ DiscourseRepresentation Theory)
5. Non–compositional approachesVerb framesParsing & annotation
Natural Language Semantics – p. 11
Sentence Interaction
Alice is a woman. She loves Bob.
What is a possible λ–term for “she”?
Natural Language Semantics – p. 12
Sentence Interaction
There is no λ–term for “she”!!!
Natural Language Semantics – p. 13
Discourse Representation Structures 1/4
x1, x2, x3
P1(x1, x2, x3)
P2(x1, x2, x3)
P3(x1, x2, x3)
Natural Language Semantics – p. 14
Discourse Representation Structures 2/4
Alice loves Bob
Alice, Bob
love(Alice, Bob)
Natural Language Semantics – p. 15
Discourse Representation Structures 3/4
Alice loves a man
Alice, x
man(x)
love(Alice, x)
Natural Language Semantics – p. 16
Discourse Representation Structures 4/4
Every women loves a boxer
x
woman(x)
y
boxer(y)love(x, y)
→
Natural Language Semantics – p. 17
Anaphora Resolution
A woman loves a boxer. She walks
x, y, z
woman(x), boxer(y)
loves(x, y)
z = x
walk(z)
Natural Language Semantics – p. 18
Outline
1. Motivation (→ Turing Test)
2. How is NL–Semantics defined?
3. Is NL–Semantics compositional?
4. How do different sentences interact? (→ DiscourseRepresentation Theory)
5. Non–compositional approachesVerb framesParsing & annotation
Natural Language Semantics – p. 19
Verb Frames
Verb frame = verb with its arguments
Component X sends message Y to component Z=
send (Component X, message Y, component Z)
Verb frame defines:
Verb type (predicate type)
Predicate argument structure
Natural Language Semantics – p. 20
Sidestep: Part–of–Speech Tagging
Each word is assigned a Part–of–Speech tag:
Coponent X sends message Y to component Z Ã
Component/NN X/NN sends/VBZ message/NN Y/NN to/TOcomponent/NN Z/NN
Natural Language Semantics – p. 21
Verb Frames as Templates
templatename=communicationframe
sender(POS=NN, syn=subject, sem=agent)comm-action(pos=VB, syn=verb-phrase,
default=’send’)message (...)prep (..., default=’to’)receiver (...)
end
Natural Language Semantics – p. 22
Semantics Computation with Frames
Finite number of possible frames
POS–tagging as preprocessing
Semantics computation is matching of actual sentenceswith predefined frames(Ã POS–Sequence matching)
Natural Language Semantics – p. 23
Frame example
Component/NN X/NN sends/VBZ message/NN Y/NN to/TOcomponent/NN Z/NN Ã
Component/NN X/NN sendersends/VBZ send
message/NN Y/NN messageto/TOcomponent/NN Z/NN receiver
à send (Coponent X, message Y, component Z)
Natural Language Semantics – p. 24
Outline
1. Motivation (→ Turing Test)
2. How is NL–Semantics defined?
3. Is NL–Semantics compositional?
4. How do different sentences interact? (→ DiscourseRepresentation Theory)
5. Non–compositional approachesVerb framesParsing & annotation
Natural Language Semantics – p. 25
Sidestep: NL Parsing
Oversimplified:
Chomsky–2 Grammar
Each rule is assigned a probability
The parser calculates the most probable parse tree
Probability distribution is calculated on the basis ofmanually crafted training data
Natural Language Semantics – p. 26
Training Data Example
Alice loves Bob =
NN/Alice
S/loves
NPB/Alice
VBZ/loves
VP/loves
NPB/Bob
NN/Bob
Natural Language Semantics – p. 27
Semantics Annotation in Training Data
Alice loves Bob =
NN/Alice
Actor/Alice VBZ/loves Patient/Bob
Predicate/loves
S/loves
NN/Bob
Natural Language Semantics – p. 28
Summary
Goal: Extract predicates (verbs) with their arguments
Firm and statistical approaches
None is really working
Natural Language Semantics – p. 29
That’s all, folks !!!
Natural Language Semantics – p. 30
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