computational semantics - shane · computational semantics ling 571 — deep processing for nlp...

Computational SemanticsLING 571 — Deep Processing for NLP

October 28, 2019

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Announcements● HW5: your grammar should use rules and features that are linguistically

motivated (e.g. number, gender, aspect, animacy, ….)

● Consider grammars for the following suite of examples:● This sentence is grammatical.● *This grammatical sentence is.

● The following is not an acceptable grammar (you would lose some points):● S[+grammatical] -> ‘This sentence is grammatical.’● S[-grammatical] -> ‘This grammatical sentence is.’

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Roadmap● First-order Logic: Syntax and Semantics

● Inference + Events

● Rule-to-rule Model● More lambda calculus

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FOL Syntax + Semantics

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Example Meaning Representation● A non-stop flight that serves Pittsburgh:

∃x Flight(x) ∧ Serves(x, Pittsburgh) ∧ Non-stop(x)

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Model-Theoretic Semantics● A “model” represents a particular state of the world

● Our language has logical and non-logical elements.

● Logical: Symbols, operators, quantifiers, etc

● Non-Logical: Names, properties, relations, etc

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Denotation● Every non-logical element points to a fixed part of the model

● Objects — elements in the domain, denoted by terms● John, Farah, fire engine, dog, stop sign

● Properties — sets of elements● red: {fire hydrant, apple,…}

● Relations — sets of tuples of elements● CapitalCity: {(Washington, Olympia), (Yamoussokro, Cote d’Ivoire),

(Ulaanbaatar, Mongolia),…}

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Sample Domain 𝒟

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ObjectsMatthew, Franco, Katie, Caroline a,b,c,dFrasca, Med, Rio e,f,gItalian, Mexican, Eclectic h,i,j

PropertiesNoisy Frasca, Med, and Rio are noisy Noisy={e,f,g}

RelationsLikes Matthew likes the Med Likes={〈a,f〉,〈c,f〉, 〈c,g〉, 〈b,e〉, 〈d,f〉,

〈d,g〉}Katie likes the Med and RioFranco likes FrascaCaroline likes the Med and Rio

Serves Med serves eclectic Serves={〈c,f〉, 〈f,i〉, 〈e,h〉}Rio serves MexicanFrasca serves Italian

via J&M, p. 554

Inference + Events(last Wednesday’s slides)

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Rule-to-Rule Model

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Recap● Meaning Representation ● Can represent meaning in natural language in many ways● We are focusing on First-Order Logic (FOL)

● Principle of compositionality ● The meaning of a complex expression is a function of the meaning of its parts

● Lambda Calculus● λ-expressions denote functions● Can be nested● Reduction = function application

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Semantics Reflects Syntax

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Chiasmus:Syntax affects Semantics!

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Tesla playing BowieBowie playing TeslaThe Prestige (2006) SpaceX Falcon Heavy Test Launch (2/6/2018)

Chiasmus:Syntax affects Semantics!

● “Never let a fool kiss you or a kiss fool you” (Grothe, 2002)

● “Then you should say what you mean,” the March Hare went on.

“I do,” Alice hastily replied; “at least—at least I mean what I say—that’s the same thing, you know.”

“Not the same thing a bit!” said the Hatter. “Why, you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!”

“You might just as well say,” added the March Hare, “that ‘I like what I get’ is the same thing as ‘I get what I like’!”

“You might just as well say,” added the Dormouse, which seemed to be talking in his sleep, “that ‘I breathe when I sleep’ is the same thing as ‘I sleep when I breathe’!”

—Alice in Wonderland, Lewis Carrol

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Ambiguity & Models● “Every Tesla is powered by a battery.” — Ambiguous!● ∀x.Tesla(x) ⇒ (∃(y).Battery(y) ∧ Powers(y, x))

● ∃(y).Battery(y) ∧ (∀x.Tesla(x) ⇒ Powers(y, x))

● Every Tesla is not hurtling toward Mars.● ∀x.Tesla(x) ⇒ ¬(HurtlingTowardMars(x))

● ¬∀x.(Tesla(x) ⇒(HurtlingTowardMars(x)))

● [∃(x).(Tesla(x) ∧ ¬HurtlingTowardsMars(x))]

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Things in SpaceTeslasTeslas Things in

Space

∃(x).(Tesla(x) ∧ HurtlingTowardsMars(x))

State of known Universe: 02/05/2018State of known Universe: 02/06/2018

Scope Ambiguity● Potentially O(n!) scope interpretations (“scopings”)● Where n=number of scope-taking operators.● (every, a, all, no, modals, negations, conditionals, …)

● Different interpretations correspond to different syntactic parses!

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Integrating Semantics into Syntax1. Pipeline System● Feed parse tree and sentence to semantic analyzer● How do we know which pieces of the semantics link to which part of the

analysis?● Need detailed information about sentence, parse tree● Infinitely many sentences & parse trees● Semantic mapping function per parse tree → intractable

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Integrating Semantics into Syntax2. Integrate Directly into Grammar● This is the “rule-to-rule” approach we’ve been implicitly examining and will now

make more explicit● Tie semantics to finite components of grammar (rules & lexicon)● Augment grammar rules with semantic info● a.k.a. “attachments” — specify how RHS elements compose to LHS

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Simple Example● United serves Houston

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∃e(Serving(e) ∧ Server(e, United) ∧ Served(e, Houston))

Rule-to-rule Model● Lambda Calculus and the Rule-to-Rule Hypothesis● λ-expressions can be attached to grammar rules● used to compute meaning representations from syntactic trees based on the

principle of compositionality● Go up the tree, using reduction (function application) to compute meanings at

non-terminal nodes

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Semantic Attachments● Basic Structure: A→a1, …, an {f(aj.sem, … ak.sem)}

● In NLTK syntax (more later): A → a1 … an[SEM=<f(?aj.sem …)>]

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Semantic Function

Attachments as SQL!>>> nltk.data.show_cfg('grammars/book_grammars/sql0.fcfg')% start SS[SEM=(?np + WHERE + ?vp)] -> NP[SEM=?np] VP[SEM=?vp]VP[SEM=(?v + ?pp)] -> IV[SEM=?v] PP[SEM=?pp]VP[SEM=(?v + ?ap)] -> IV[SEM=?v] AP[SEM=?ap]NP[SEM=(?det + ?n)] -> Det[SEM=?det] N[SEM=?n]PP[SEM=(?p + ?np)] -> P[SEM=?p] NP[SEM=?np]AP[SEM=?pp] -> A[SEM=?a] PP[SEM=?pp]NP[SEM='Country="greece"'] -> 'Greece'NP[SEM='Country="china"'] -> 'China'Det[SEM='SELECT'] -> 'Which' | 'What'N[SEM='City FROM city_table'] -> 'cities'IV[SEM=''] -> 'are'A[SEM=''] -> 'located'P[SEM=''] -> 'in'

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'What cities are located in China’

parses[0]: SELECT City FROM city_table WHERE Country="china"

NLTK book, ch. 10

https://www.nltk.org/book/ch10.html

Semantic Attachments: Options● Why not use SQL? Python?● Arbitrary power but hard to map to logical form● No obvious relation between syntactic, semantic elements

● Why Lambda Calculus?

● First Order Predicate Calculus (FOPC) + function application is highly expressive, integrates well with syntax

● Can extend our existing feature-based model, using unification● Can ‘translate’ FOL to target / task / downstream language (e.g. SQL)

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Semantic Analysis Approach● Semantic attachments:● Each CFG production gets semantic attachment

● Semantics of a phrase is function of combining the children

● Complex functions need to have parameters

● Verb → ‘arrived’ ● Intransitive verb, so has one argument: subject

● …but we don’t have this available at the preterminal level of the tree!

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Defining Representations● Proper Nouns

● Intransitive Verbs

● Transitive Verbs

● Quantifiers

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● Our instinct for names is to just use the constant:● NNP[SEM=<Khalil>] → ‘Khalil’

● However, we want to apply our λ-closures left-to-right consistently.

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Proper Nouns & Intransitive Verbs

27

ERROR: Constant “Khalil” is not a function!

S[SEM=np?(vp?)] → NP[SEM=np?] VP[SEM=vp?]

Proper Nouns & Intransitive Verbs● Instead, we use a dummy predicate:● λQ.Q(Khalil)

● “Generalizing to the worst case” (cf. Montague; Partee on type-shifting)

28

Proper Nouns & Intransitive Verbs● With the dummy predicate:● NNP[SEM=<\P.P(Khalil)>] → ‘Khalil’

29

S[SEM=np?(vp?)] → NP[SEM=np?] VP[SEM=vp?]

7

24

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:4

-:ॱ7)1 ᅶ\�VYRW�\ ॲVYRW

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7ॱ7)1 ᅶ4�4�/LEPMP �ᅶ\�VYRW�\ ॲ24


:4


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7ॱ7)1 ᅶ\�VYRW�\ �/LEPMP ॲ24


:4


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7ॱ7)1 VYRW�/LEPMP ॲ24


:4


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Transitive Verbs

30

Transitive Verbs● So, if we want to say “Alex loves Jim” we would want λy.λx.loves(x,y)

● …but going in linear order, we have one arg to the left and one to the right.

● So, instead:● λX y.X(λx.loves(x,y))

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Transitive Verbs● So, if we want to say “Alex loves Jim” we would want λy.λx.loves(x,y)

● …but going in linear order, we have one arg to the left and one to the right.

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7

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Transitive Verbs● TV(NP):● λy.λx.loves(x,y) (λQ.Q(Alex))

● λx.loves(x,λQ.Q(Alex))● ➜ Error! We can’t reduce Alex.

33

Transitive Verbs● Instead: λX y.X(λx.loves(x,y))

34

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Transitive Verbs● TV(NP):● λX y.X(λx.loves(x,y)) (λQ.Q(Jim))

● λy.(λQ.Q(Jim)(λx.loves(x,y))

● λy.(λx.loves(x,y)(Jim))

● λy.(loves(Jim,y))

● NP(VP):● λP.P(Alex)(λy.(loves(Jim,y))

● λy.(loves(Jim,y)(Alex)

● loves(Jim,Alex)

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λX takes (λQ.Q(Jim))λQ takes (λx.loves(x,y))λx takes (Jim)

λP takes (λy.(loves(Jim,y))λy takes (Alex)

Converting to an Event● “y loves x,” Originally:● λX y.X(λx.loves(x,y))

● as a Neo-Davidsonian event:● λX y.X(λx.∃e love(e) ∧ lover(e,y) ∧ loved(e,x))

36

Quantifiers & Scope

37

● Basic model● Neo-Davidsonian event-style model● Complex quantification

● Example: Every flight arrived

∀x Flight(x) ⇒ ∃e Arrived(e) ∧ ArrivedThing(e,x )

Semantic Analysis Example

38

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“Every flight arrived”● First intuitive approach:● Every flight = ∀x Flight(x)● “Everything is a flight”

● Instead, we want:● ∀x Flight(x) ⇒ Q(x) ● “if a thing is a flight, then Q”● Since Q isn’t available yet… Dummy predicate!● λQ.∀x Flight(x) ⇒ Q(x)

39

✘

“Every flight arrived”● “Every flight” is:● λQ.∀x Flight(x) ⇒ Q(x)

● …so what is the representation for “every”?● λP.λQ.∀x P(x) ⇒ Q(x)

40

“A flight arrived”● We just need one item for truth value● So, start with ∃x…

● λP.λQ.∃x P(x)∧Q(x)

41

“The flight arrived”● …yeah, this turns out to be tricky.

● We’ll save it for Wednesday.

● It’s not on the homework.

42

Creating Attachments

43

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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:4


45

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)

7|ষ /্)ঽ ষ /্*~24|ফ/্)ষ /্*~



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46

7|ষ /্)ঽ ষ /্*~24|ౠস/ѭভ ৌৈυ)* ш স)*~



:4|ౠ/Ѱন)* Ҕ ন υৎৈ)- *~:|ౠ/Ѱন)* Ҕ ন υৎৈ)- *~

EVVMZIH

47

7|ষ /্)ঽ ষ /্*~24|ౠস/ѭভ ৌৈυ)* ш স)*~




EVVMZIH

7|ѭভ ৌৈυ)* ш Ѱন)* Ҕ ন υৎৈ)- *~24|ౠস/ѭভ ৌৈυ)* ш স)*~




EVVMZIH

48

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)

7|ষ /্)ঽ ষ /্*~24|ౠস/ѭভ ৌৈυ)* ш স)*~




EVVMZIH

49

7|ѭভ ৌৈυ)* ш Ѱন)* Ҕ ন υৎৈ)- *~24|ౠস/ѭভ ৌৈυ)* ш স)*~




EVVMZIH

‘John Booked A Flight’

50

Det → ‘a’ { λP.λQ.∃x P(x) ∧ Q(x) }Det → ‘every’ { λP.λQ.∀x P(x) ⇒ Q(x) }NN → ‘flight’ {λx.Flight(x)}

NNP → ‘John’ {λX.X(John)}NP → NNP {NNP.sem}S → NP VP {NP.sem(VP.sem)}VP → Verb NP {Verb.sem(NP.sem)}Verb → ‘booked’ {λW.λz.W(∃eBooked(e) ∧ Booker(e,z) ∧ BookedThing(e,y))}

…we’ll step through this on Wednesday.

Strategy for Semantic Attachments● General approach:● Create complex lambda expressions with lexical items● Introduce quantifiers, predicates, terms● Percolate up semantics from child if non-branching● Apply semantics of one child to other through lambda● Combine elements, don’t introduce new ones

51

Semantics Learning● Zettlemoyer & Collins (2005, 2007, etc); Kate & Mooney (2007)

● Given semantic representation and corpus of parsed sentences● Learn mapping from sentences to logical form

● Similar approaches to:● Learning instructions from computer manuals● Game play via walkthrough descriptions● Robocup/Soccer play from commentary

52

https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0ahUKEwjA8Yz29ZTZAhVD44MKHXunA70QFggnMAA&url=https://homes.cs.washington.edu/~lsz/papers/zc-uai05.pdf&usg=AOvVaw2v7WVohPp5v7xnYOaXnBi1

https://homes.cs.washington.edu/~lsz/papers/zc-emnlp07.pdf

https://www.aaai.org/Papers/AAAI/2007/AAAI07-142.pdf

Parsing with Semantics● Implement semantic analysis in parallel with syntactic parsing● Enabled by this rule-to-rule compositional approach

● Required modifications● Augment grammar rules with semantics field● Augment chart states with meaning expression● Incrementally compute semantics

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Sidenote: Idioms● Not purely compositional● kick the bucket → die● tip of the iceberg → small part of the entirety

● Handling● Mix lexical items with constituents● Create idiom-specific construct for productivity● Allow non-compositional semantic attachments

● Extremely complex, e.g. metaphor

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computational semantics - shane · computational semantics ling 571 — deep processing for nlp...

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