Computational Semantics LING 571 Deep Processing for NLP October - - PowerPoint PPT Presentation

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Computational Semantics LING 571 Deep Processing for NLP October - - PowerPoint PPT Presentation

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Computational Semantics LING 571 Deep Processing for NLP October 28, 2019 1 Announcements HW5: your grammar should use rules and features that are linguistically motivated (e.g. number, gender, aspect, animacy, .) Consider

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Computational Semantics

LING 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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FOL Syntax Summary

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Formula → AtomicFormula Connective → ∧ | ∨ | ⇒ | Formula Connective Formula Quantifier → ∀ | ∃ | Quantifier Variable, … Formula Constant → VegetarianFood | Maharani | … | ¬ Formula Variable → x | y | … | (Formula) Predicate → Serves | Near | … AtomicFormula → Predicate(Term,…) Function → LocationOf | CuisineOf | … Term → Function(Term,…) | Constant | Variable

J&M p. 556 (3rd ed. 16.3)

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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 𝒠

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Objects Matthew, Franco, Katie, Caroline a,b,c,d Frasca, Med, Rio e,f,g Italian, Mexican, Eclectic h,i,j Properties Noisy Frasca, Med, and Rio are noisy Noisy={e,f,g} Relations Likes Matthew likes the Med Likes={〈a,f〉,〈c,f〉, 〈c,g〉, 〈b,e〉, 〈d,f〉, 〈d,g〉} Katie likes the Med and Rio Franco likes Frasca Caroline likes the Med and Rio Serves Med serves eclectic Serves={〈c,f〉, 〈f,i〉, 〈e,h〉} Rio serves Mexican Frasca serves Italian

via J&M, p. 554

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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 Bowie Bowie playing Tesla

The Prestige (2006) SpaceX Falcon Heavy Test Launch (2/6/2018)

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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 Space Teslas Teslas Things in Space

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

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

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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 Syntax

  • 1. 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 Syntax

  • 2. 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))
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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

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Attachments as SQL!

>>> nltk.data.show_cfg('grammars/book_grammars/sql0.fcfg') % start S S[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

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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?]

slide-28
SLIDE 28

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

slide-29
SLIDE 29

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?]

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SLIDE 30

Transitive Verbs

30

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SLIDE 31

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))

31

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SLIDE 32

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.

32

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SLIDE 33

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

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SLIDE 34

Transitive Verbs

  • Instead: λX y.X(λx.loves(x,y))

34

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SLIDE 35

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)

35

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

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SLIDE 36

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

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SLIDE 37

Quantifiers & Scope

37

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SLIDE 38
  • 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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SLIDE 39

“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

✘

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SLIDE 40

“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)

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SLIDE 41

“A flight arrived”

  • We just need one item for truth value
  • So, start with ∃x…
  • λP.λQ.∃x P(x)∧Q(x)

41

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SLIDE 42

“The flight arrived”

  • …yeah, this turns out to be tricky.
  • We’ll save it for Wednesday.
  • It’s not on the homework.

42

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SLIDE 43

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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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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‘John Booked A Flight’

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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.

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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

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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

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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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