[PPT] - More -Calculus Lexical Semantics LING 571 Deep Processing PowerPoint Presentation

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More λ-Calculus  Lexical Semantics

LING 571 — Deep Processing Techniques for NLP October 30, 2019 Shane Steinert-Threlkeld

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Announcements

HW5:
readme: be detailed!
What problems you ran into (e.g. agreement), how you solved them, and

exhibit of the solution

HSPG-style subcategorization extra credit: yes, but with max 100 points
We will drop your lowest score when calculating final grades. But you still

need to do all the assignments!

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Ambiguity of the Week

Derivative of an alleged Groucho Marx-ism:
In the US, a woman gives birth every fifteen minutes.
We must find her and put a stop to it.
Thank you scope ambiguity! (Not the same as attachment ambiguity.)

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Roadmap

More Lambdas
Learning Semantic Parsers
Lexical Semantics
Motivation & Definitions
Word Senses
Tasks:
Word sense disambiguation
Word sense similarity
Distributional Similarity

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Creating Attachments

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Det → ‘Every’ { λP.λQ.∀x P(x) ⇒ Q(x) } Noun → ‘flight’ { λx.Flight(x) } Verb → ‘arrived’ {λy.∃eArrived(e) ∧ ArrivedThing(e, y)} VP → Verb { Verb.sem } Nom → Noun { Noun.sem } S → NP VP { NP.sem(VP.sem) } NP → Det Nom { Det.sem(Nom.sem) }

“Every flight arrived”

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NP → Det.sem(NP.sem) λP.λQ.∀xP(x) ⇒Q(x)(λy.Flight(y)) λQ.∀xλy.Flight(y)(x) ⇒Q(x) λQ.∀xFlight(x) ⇒Q(x)

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λQ.∀xFlight(x) ⇒Q(x)(λz.∃eArrived(e) ∧ ArrivedThing(e, z)) ∀xFlight(x) ⇒λz.∃eArrived(e) ∧ ArrivedThing(e, z)(x) ∀xFlight(x) ⇒∃eArrived(e) ∧ ArrivedThing(e, x)

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More λ-Calculus

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Target Representations

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Common Nouns

λx.Restaurant(x) → ‘restaurant’
Somewhat similar to the NNP construction
λ var.Predicate(var)
But common nouns represent relations, rather than constants
Meaning of the noun encoded in the predicate
Relate the concept of the noun to a particular instance of variable

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Negation

“No vegetarian restaurant serves meat.”
¬(∃xVegetarianRestaurant(x) ∧ Serves(x,Meat))
“All vegetarian restaurants do not serve meat.”
∀x VegetarianRestaurant(x)⇒¬Serves(x,Meat)
These are semantically equivalent!
¬[IF P, THEN Q] ⇔ P AND NOT Q
For NLTK, use the hyphen/minus character: ‘-‘

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‘John booked a flight’

Target representation:
∃x Flight(x) ∧ (∃eBooked(e) ∧ Booker(e, John) ∧ BookedThing(e, x))

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‘John booked a flight’

∃x Flight(x) ∧ (∃eBooked(e) ∧ Booker(e, John) ∧ BookedThing(e, x))

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S → NP VP {NP.sem(VP.sem)}

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‘John booked a flight’

∃x Flight(x) ∧ (∃eBooked(e) ∧ Booker(e, John) ∧ BookedThing(e, x))

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S → NP VP {NP.sem(VP.sem)}

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‘John booked a flight’

∃x Flight(x) ∧ (∃eBooked(e) ∧ Booker(e, John) ∧ BookedThing(e, x))

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S → NP VP {NP.sem(VP.sem)} NNP → ‘John’ {λX.X(John)} NP → NNP {NNP.sem} VP → Verb NP {Verb.sem(NP.sem)}

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‘John booked a flight’

∃x Flight(x) ∧ (∃eBooked(e) ∧ Booker(e, John) ∧ BookedThing(e, x))

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S → NP VP {NP.sem(VP.sem)} NNP → ‘John’ {λX.X(John)} NP → NNP {NNP.sem} VP → Verb NP {Verb.sem(NP.sem)}

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‘John booked a flight’

∃x Flight(x) ∧ (∃eBooked(e) ∧ Booker(e, John) ∧ BookedThing(e, x))

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S → NP VP {NP.sem(VP.sem)} NNP → ‘John’ {λX.X(John)} NP → NNP {NNP.sem} VP → Verb NP {Verb.sem(NP.sem)}

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‘John booked a flight’

∃x Flight(x) ∧ (∃eBooked(e) ∧ Booker(e, John) ∧ BookedThing(e, x))

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NP → Det NN {Det.sem(NN.sem)}

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‘John booked a flight’

∃x Flight(x) ∧ (∃eBooked(e) ∧ Booker(e, John) ∧ BookedThing(e, x))

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NP → Det NN {Det.sem(NN.sem)} NN → ‘flight’ {λx.Flight(x)}

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