computational linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10....
TRANSCRIPT
![Page 1: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/1.jpg)
Computational LinguisticsCS579: Fall Semester 2020
School of ComputingKorea Advanced Institute of Science and Technology
Jong C. Park
© All rights reserved.
![Page 2: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/2.jpg)
First-Order Logic• First-Order Logic• Three Inference Tasks• A First-Order Model Checker• First-Order Logic and Natural Language
Lambda Calculus• Compositionality• Two Experiments• The Lambda Calculus• Implementing Lambda Calculus• Grammar Engineering
Fall 2020 KAIST CS579: Computational Linguistics 2
Review of Previous Lectures
![Page 3: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/3.jpg)
Lambda Calculus• We showed how to define a grammar that is
modular, extensible and reusable, in a framework of grammar engineering.
Fall 2020 KAIST CS579: Computational Linguistics 3
Review of the Last Lecture
![Page 4: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/4.jpg)
Scope Ambiguities Montague’s Approach Storage Methods Hole Semantics
Fall 2020 KAIST CS579: Computational Linguistics 4
Underspecified Representations
![Page 5: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/5.jpg)
Goals Today• We examine the nature of scope ambiguities.• We introduce Montague’s approach to scope
ambiguities.
Fall 2020 KAIST CS579: Computational Linguistics 5
Underspecified Representations
![Page 6: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/6.jpg)
Observation• Sentences with scope ambiguities are often
semantically ambiguous but fail to exhibit any syntactic ambiguity.
• They may have at least two non-equivalent first-order representations, but have only one syntactic analysis.
Problem• If there is no syntactic ambiguity, we will be able
to build only one of the possible representations.
Fall 2020 KAIST CS579: Computational Linguistics 6
Underspecified Representations
![Page 7: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/7.jpg)
We investigate four different approaches to scope ambiguities.• Montague’s original method• Two storage based methods• Cooper storage• Keller storage
• A modern underspecification based approach• Hole semantics
Fall 2020 KAIST CS579: Computational Linguistics 7
Underspecified Representations
![Page 8: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/8.jpg)
SCOPE AMBIGUITIES
CS579: Computational Linguistics 8Fall 2020 KAIST
![Page 9: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/9.jpg)
Scope ambiguity is a common semantic phenomenon and can arise from many sources.• quantifier, coordination, negation, adverbs, etc.
We will be concerned primarily with quantifier scope ambiguities. • They arise in sentences containing more than one
quantifying noun phrase.• Every boxer loves a woman.
Fall 2020 KAIST CS579: Computational Linguistics 9
Scope Ambiguities
![Page 10: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/10.jpg)
Deriving a representation for the sentence:
Fall 2020 KAIST CS579: Computational Linguistics 10
Every boxer loves a woman (S)∀x(boxer(x)→ ∃y(woman(y)∧love(x,y)))
Every boxer (NP)𝜆u. ∀x(boxer(x)→u@x)
loves a woman (VP)𝜆z. ∃y(woman(y)∧love(z,y))
loves (TV)𝜆v. 𝜆z. v@𝜆x.love(z,x))
a woman (NP)𝜆w. ∃y(woman(y) ∧ w@y
![Page 11: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/11.jpg)
The reading corresponding to the constructed first-order formula • x(boxer(x) y(woman(y) love(x,y)))• For each boxer there is a woman that he loves.• “every boxer” has scope over (or out-scopes) “a
woman”. • In other words, “every boxer” has wide scope
and “a woman” has narrow scope.
Fall 2020 KAIST CS579: Computational Linguistics 11
![Page 12: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/12.jpg)
There is another reading for the sentence.• y(woman(y) x(boxer(x) love(x,y)))• There is one woman who is loved by all boxers.• “a woman” has scope over (or out-scopes)
“every boxer”. • In other words, “a woman” has wide scope and
“every boxer” has narrow scope.
Is this a genuine reading, distinct from the previous reading?
Fall 2020 KAIST CS579: Computational Linguistics 12
∀x(boxer(x)→ ∃y(woman(y)∧love(x,y)))
![Page 13: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/13.jpg)
Question• Are scope ambiguities really such a problem?
For instance, we can argue • that the first reading is sufficient to cover both
readings, in that it is ‘weaker’, • that the weaker reading is the ‘real’
representation of the sentence, and • that the stronger reading is pragmatically
inferred from the weaker reading with the help of the contextual knowledge.
Fall 2020 KAIST CS579: Computational Linguistics 13
1. ∀x(boxer(x)→ ∃y(woman(y)∧love(x,y)))2. ∃y(woman(y)∧ ∀x(boxer(x)→ love(x,y)))
![Page 14: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/14.jpg)
Another sentence• Every owner of a hash bar gives every criminal
a big kahuna burger. • The sentence has 18 readings:
1. ∀x(∃y(hbar(y) ⋀ of(x,y) ⋀ owner(x)) → ∀z(crim(z) →∃u(bkb(u) ⋀ give(x,z,u))))
2. ∀x(crim(x) → ∀y((∃z(hbar(z) ⋀ of(y,z))⋀ owner(y)) → ∃u(bkb(u) ⋀ give(y,x,u))))
3. ∀x((∃y(hbar(y) ⋀ of(x,y) ⋀ owner(x)) →∃z(bkb(z) ⋀ ∀u(crim(u) → give(x,u,z))))
Fall 2020 KAIST CS579: Computational Linguistics 14
![Page 15: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/15.jpg)
4. ∀x(crim(x) → ∃y(bkb(y) ∧ ∀z(∃u(hbar(u) ⋀ of(z,u) ⋀owner(z)) → give(z,x,y))))
5. ∀x(crim(x) → ∃y(hbar(y) ∧ ∀z((of(z,y) ⋀ owner(z)) →∃u(bkb(u) ⋀ give(z,x,u)))))
6. ∀x(crim(x) → ∃y(hbar(y) ⋀ ∃z(bkb(z) ⋀ ∀u of u, y⋀ owner(u)) → give(u,x,z)))))
7. ∀x(crim(x) → ∃y(bkb(y) ⋀ ∃z(hbar(z) ⋀ ∀u of u, z⋀ owner(u)) → give(u,x,y)))))∃x bkb x ⋀ ∀y ∃z hbar z ⋀ of y,z ⋀ owner y → ∀u crim u → give y,u,x
9. ∃x bkb x ⋀ ∀y crim y → ∀z ∃u hbar u ⋀ of z,u ⋀ owner z → give z,y,x
Fall 2020 KAIST CS579: Computational Linguistics 15
Every owner of a hash bar gives every criminal a big kahuna burger.
![Page 16: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/16.jpg)
∃x hbar x ⋀ ∀y of y,x ⋀ owner y → ∀z crim z → ∃u bkb u → give y,z,u∃x hbar x ⋀ ∀y crim y → ∀z of z,x
⋀ owner z → ∃u bkb u ⋀ give z,y,u∃x hbar x ⋀ ∀y of y,x ⋀ owner y → ∃z bkb z ⋀ ∀u crim u → give y,u,z∃x hbar x ⋀ ∃y bkb y ⋀ ∀z of z,x ⋀ owner z →∀u crim u → give z,u,y∃x bkb x ⋀ ∃y hbar y ⋀ ∀z of z,y ⋀ owner z →∀u crim u → give z,u,x∃x hbar x ⋀ ∀y crim y → ∃z bkb z ⋀ ∀u of u,x ⋀ owner u → give u,y,z
Fall 2020 KAIST CS579: Computational Linguistics 16
Every owner of a hash bar gives every criminal a big kahuna burger.
![Page 17: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/17.jpg)
∃x hbar x ⋀ ∃y bkb y ⋀ ∀z crim z → ∀u of u,x ⋀ owner u → give u,z,y∃x bkb x ⋀ ∃y hbar y ⋀ ∀z crim z → ∀u of u,y ⋀ owner u → give u,z,x∃x bkb x ⋀ ∀y crim y → ∃z hbar z ⋀ ∀u of u,z ⋀ owner u → give u,y,x
Fall 2020 KAIST CS579: Computational Linguistics 17
Every owner of a hash bar gives every criminal a big kahuna burger.
![Page 18: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/18.jpg)
The logical equivalence of the readings leads to 11 distinct readings.• {1,2}, {8,9}, {6,7}, {10,11}, {13,14,16,17}• {3}, {4}, {5}, {12}, {15}, {18}
Fall 2020 KAIST CS579: Computational Linguistics 18
![Page 19: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/19.jpg)
The following diagram shows the logical relationships among the readings:
Fall 2020 KAIST CS579: Computational Linguistics 19
13/14/16/17
12 15 18
10/11 6/7
5
8/9
4 3
1/2
![Page 20: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/20.jpg)
Note that each group has a strongest reading ({13,14,16,17} and {8,9}) and a weakest reading ({5} and {1,2}), but there is no single weakest reading that covers all the possibilities.
In particular, it is hard to see how a pragmatic approach could account for this example.
Fall 2020 KAIST CS579: Computational Linguistics 20
![Page 21: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/21.jpg)
In addition, the idea of computing the weakest reading and relying on pragmatics for the rest faces difficulties even when the weakest reading exists.• Example• A boxer is loved by every woman.
• ∃y(boxer(y)∧ ∀x(woman(x)→ love(x,y)))• ∀x(woman(x)→ ∃y(boxer(y)∧love(x,y)))
• The stronger reading is what is generated by the direct approach to semantic construction.
Fall 2020 KAIST CS579: Computational Linguistics 21
![Page 22: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/22.jpg)
MONTAGUE’S APPROACH
CS579: Computational Linguistics 22Fall 2020 KAIST
![Page 23: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/23.jpg)
Scope ambiguities are a genuine problem. Montague introduced a rule of quantification
(called quantifier raising):• Instead of directly combining syntactic entities
with the quantifying noun phrase we are interested in, we are permitted to choose an ‘indexed pronoun’ and to combine the syntactic entity with the indexed pronoun instead.
• These indexed pronouns are ‘placeholders’ for the quantifying noun phrase.
Fall 2020 KAIST CS579: Computational Linguistics 23
Montague’s Approach
![Page 24: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/24.jpg)
• When this placeholder has moved high enough in the tree to give us the scoping we are interested in, we are permitted to replace it by the quantifying NP of interest.
Fall 2020 KAIST CS579: Computational Linguistics 24
![Page 25: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/25.jpg)
Example: the first stage• Every boxer loves a woman.
Fall 2020 KAIST CS579: Computational Linguistics 25
Every boxer loves her-3 (S)∀x(boxer(x)→ love(x,𝑧 ))
Every boxer (NP)𝜆u. ∀x(boxer(x)→u@x)
loves her-3 (VP)𝜆y. love(y,𝑧 )
loves (TV)𝜆v. 𝜆y. v@𝜆x.love(y,x))
her-3 (NP)𝜆w. w@𝑧
![Page 26: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/26.jpg)
Example: the second stage of substituting the quantifying NP
Fall 2020 KAIST CS579: Computational Linguistics 26
Every boxer loves a woman (S)
a woman (NP)𝜆u. ∃y(woman(y) ∧ u@y
Every boxer loves her-3 (S,3)∀x(boxer(x)→ love(x,𝑧 ))
![Page 27: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/27.jpg)
Lambda abstracting with respect to and -converting:
Fall 2020 KAIST CS579: Computational Linguistics 27
Every boxer loves a woman (S)
a woman (NP)𝜆u. ∃y(woman(y) ∧ u@y
Every boxer loves her-3 (S,3)𝜆𝑧 .∀x(boxer(x)→ love(x,𝑧 )))
∃y(woman(y)∧ ∀x(boxer(x)→ love(x,y)))
![Page 28: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/28.jpg)
Montague’s approach makes use of syntactic and semantic placeholders so that we can place quantifying NPs in parse trees at exactly the level required to obtain the desired scope relations.
A neat piece of ‘lambda programming’ ensures that the semantic information recorded by the placeholder is re-introduced into the semantic representation correctly.
Fall 2020 KAIST CS579: Computational Linguistics 28
![Page 29: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/29.jpg)
SUMMARY
CS579: Computational Linguistics 29Fall 2020 KAIST
![Page 30: Computational Linguisticsnlpcl.kaist.ac.kr/~cs579_2020/slides/579-fall-2020-12.pdf · 2020. 10. 13. · •∀x(woman(x)→∃y(boxer(y)∧love(x,y))) •The stronger reading is what](https://reader033.vdocuments.us/reader033/viewer/2022060814/60930b3951caea5e621087d6/html5/thumbnails/30.jpg)
Scope ambiguities• A sentence with multiple quantifiers may have
genuine scope ambiguities. • We need a solution to generate multiple
readings.
Montague’s approach• Multiple readings can be derived by the use of
placeholders and ‘lambda programming’.
Fall 2020 KAIST CS579: Computational Linguistics 30
Summary