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CS 4705: Semantic Analysis: Syntax-Driven Semantics

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McDonalds gave customers a bonus. Predicate(Agent, Patient, ... V.sem Applied to McDonalds serves burgers. application binds x to value of NP.sem (burgers) ... – PowerPoint PPT presentation

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Title: CS 4705: Semantic Analysis: Syntax-Driven Semantics


1
CS 4705 Semantic Analysis Syntax-Driven
Semantics
Slides adapted from Julia Hirschberg
2
Today
  • Reading Ch 17.2-17.4, 18.1-18.7 (cover material
    through today) Ch 17.1-17.5 (next time)
  • First Order Predicate Calculus as a
    representation
  • Semantic Analysis translation from syntax to FOPC

3
First Order Predicate Calculus
  • Not ideal as a meaning representation and doesn't
    do everything we want -- but better than many
  • Supports the determination of truth
  • Supports compositionality of meaning
  • Supports question-answering (via variables)
  • Supports inference

4
NL Mapping to FOPC
  • Terms constants, functions, variables
  • Constants objects in the world, e.g. Huey
  • Functions concepts, e.g. sisterof(Huey)
  • Variables x, e.g. sisterof(x)
  • Predicates symbols that refer to relations that
    hold among objects in some domain or properties
    that hold of some object in a domain
  • likes(Kathy, pasta)
  • female(Kathy) person(Kathy)

5
  • Logical connectives permit compositionality of
    meaning
  • pasta(x) ? likes(Kathy,x) Kathy likes pasta
  • cat(Vera) odd(Vera) Vera is an odd cat
  • sleeping(Huey) v eating(Huey) Huey either is
    sleeping or eating
  • Sentences in FOPC can be assigned truth values
  • Atomic formulae are T or F based on their
    presence or absence in a DB (Closed World
    Assumption?)
  • Composed meanings are inferred from DB and
    meaning of logical connectives

6
  • cat(Huey)
  • sibling(Huey,Vera)
  • cat(Huey) sibling(Huey,Vera) ? cat(Vera)
  • Limitations
  • Do and and or in natural language really mean
    and v?
  • Mary got married and had a baby. And then
  • Your money or your life!
  • Does ? mean if?
  • If you go, Ill meet you there.
  • How do we represent other connectives?
  • She was happy but ignorant.

7
Compositional Semantics
  • Assumption The meaning of the whole is comprised
    of the meaning of its parts
  • George cooks. Dan eats. Dan is sick.
  • cook(George) eat(Dan) sick(Dan)
  • George cooks and Dan eats
  • cook(George) eat(Dan)
  • George cooks or Dan is sick.
  • cook(George) v sick(Dan)
  • If George cooks, Dan is sick
  • cook(George) ? sick(Dan) or
  • cook(George) v sick(Dan)

8
  • If George cooks and Dan eats, Dan will get sick.
  • (cook(George) eat(Dan)) ? sick(Dan)
  • sick(Dan) ? cook(George) eat(Dan) ??
  • Dan only gets sick when George cooks.
  • You can have apple juice or orange juice.
  • Stuart sits in front and Boris sits in the
    middle.
  • George cooks but Dan eats.
  • George cooks and eats Dan.

9
  • Quantifiers
  • Existential quantification There is a unicorn in
    my garden. Some unicorn is in my garden.
  • Universal quantification The unicorn is a
    mythical beast. Unicorns are mythical beasts.
  • Many? A few? Several? A couple?
  • Some examples
  • Someone at Columbia is smart.
  • Everyone is loved by someone.
  • Mary showed every boy an apple.
  • Then she told them they could eat them.
  • Then she placed it on the stand in front of the
    room and told them they could start painting
    their still life.

10
Temporal Representations
  • How do we represent time and temporal
    relationships between events?
  • It seems only yesterday that Martha Stewart was
    in prison but now she has a popular TV show.
    There is no justice.
  • Where do we get temporal information?
  • Verb tense
  • Temporal expressions
  • Sequence of presentation
  • Linear representations Reichenbach 47

11
  • Utterance time (U) when the utterance occurs
  • Reference time (R) the temporal point-of-view of
    the utterance
  • Event time (E) when events described in the
    utterance occur
  • George is eating a sandwich.
  • -- E,R,U ?
  • George had eaten a sandwich (when he realized)
  • E R U ?
  • George will eat a sandwich.
  • --U,R E ?
  • While George was eating a sandwich, his mother
    arrived.

12
Verbs and Event Types Aspect
  • Statives states or properties of objects at a
    particular point in time
  • I am hungry.
  • Activities events with no clear endpoint
  • I am eating.
  • Accomplishments events with durations and
    endpoints that result in some change of state
  • I ate dinner.
  • Achievements events that change state but have
    no particular duration they occur in an instant
  • I got the bill.

13
Beliefs, Desires and Intentions
  • Very hard to represent internal speaker states
    like believing, knowing, wanting, assuming,
    imagining
  • Not well modeled by a simple DB lookup approach
    so..
  • Truth in the world vs. truth in some possible
    world
  • George imagined that he could dance.
  • George believed that he could dance.
  • Augment FOPC with special modal operators that
    take logical formulae as arguments, e.g. believe,
    know

14
  • Believes(George, dance(George))
  • Knows(Bill,Believes(George,dance(George)))
  • Mutual belief I believe you believe I believe.
  • Practical importance modeling belief in dialogue
  • Clarks grounding

15
Semantic Analysis
16
Meaning derives from
  • The entities and actions/states represented
    (predicates and arguments, or, nouns and verbs)
  • The way they are ordered and related
  • The syntax of the representation may correspond
    to the syntax of the sentence
  • Can we develop a mapping between syntactic
    representations and formal representations of
    meaning?

17
Syntax-Driven Semantics
  • S
  • NP VP
    eat(Dan)
  • Nom V
  • N
  • Dan eats
  • Goal Link syntactic structures to corresponding
    semantic representation to produce representation
    of the meaning of a sentence while parsing it

18
Specific vs. General-Purpose Rules
  • Dont want to have to specify for every possible
    parse tree what semantic representation it maps
    to
  • Do want to identify general mappings from parse
    trees to semantic representations
  • One way
  • Augment lexicon and grammar
  • Devise mapping between rules of grammar and rules
    of semantic representation
  • Rule-to-Rule Hypothesis such a mapping exists

19
Semantic Attachment
  • Extend every grammar rule with instructions on
    how to map components of rule to a semantic
    representation, e.g.
  • S ? NP VP VP.sem(NP.sem)
  • Each semantic function defined in terms of
    semantic representation of choice
  • Problem how to define semantic functions and how
    to specify their composition so we always get the
    right meaning representation from the grammar

20
Example McDonalds serves burgers.
  • Associating constants with constituents
  • ProperNoun ? McDonalds McDonalds
  • PluralNoun ? burgers burgers
  • Defining functions to produce these from input
  • NP ? ProperNoun ProperNoun.sem
  • NP ? PluralNoun PluralNoun.sem
  • Assumption meaning representations of children
    are passed up to parents when non-branching (e.g.
    ProperNoun.sem(X) X)
  • Butverbs are where the action is

21
  • V ? serves ?(e,x,y) (Isa(e,Serving)
    Agent(e,x) Patient (e,y)) where e event, x
    agent, y patient
  • Will every verb needs its own distinct
    representation?
  • McDonalds hires students.
  • Predicate(Agent, Patient)
  • McDonalds gave customers a bonus.
  • Predicate(Agent, Patient, Beneficiary)

22
Composing Semantic Constituents
  • Once we have the semantics for each constituent,
    how do we combine them?
  • E.g. VP ? V NP V.sem(NP.sem)
  • If goal for VP semantics of serve is the
    representation (? e,x) (Isa(e,Serving)
    Agent(e,x) Patient(e,Meat)) then
  • VP.sem must tell us
  • Which variables to be replaced by which
    arguments?
  • How is replacement accomplished?

23
First Lambda Notation
  • Extension to First Order Predicate Calculus
  • ? x P(x) ? variable(s) FOPC expression in
    those variables
  • Lambda reduction
  • Apply lambda-expression to logical terms to bind
    lambda-expressions parameters to terms
  • ?xP(x)
  • ?xP(x)(car)
  • P(car)

24
For NLP Semantics
  • Parameter list (e.g. x in ?x) in lambda
    expression makes variables (x) in logical
    expression (P(x)) available for binding to
    external arguments (car) provided by semantics of
    other constituents
  • P(x) loves(Mary,x)
  • ?xP(x)car loves(Mary,car)

25
Defining VP Semantics
  • Recall we have VP ? V NP V.sem(NP.sem)
  • Target semantic representation is
  • ?(e,x,y) (Isa(e,Serving) Agent(e,y)
    Patient(e,x))
  • Define V.sem as
  • ?x ?(e,y) (Isa(e,Serving) Agent(e,y)
    Patient(e,x))
  • Now x will be available for binding when V.sem
    applied to NP.sem of direct object

26
V.sem Applied to McDonalds serves burgers
  • ? application binds x to value of NP.sem
    (burgers)
  • ?x ?(e,y) (Isa(e,Serving) Agent(e,y)
    Patient(e,x)) (burgers)
  • ?-reduction replaces x within ?-expression with
    burgers
  • Value of V.sem(NP.sem) is now ?(e,y)
    (Isa(e,Serving) Agent(e,y) Patient(e,burgers))

27
But were not done yet.
  • Need to define semantics for
  • S? NP VP VP.sem(NP.sem)
  • Where is the subject?
  • ?(e,y) (Isa(e,Serving) Agent(e,y)
    Patient(e,burgers))
  • Need another ?-expression in V.sem so the subject
    NP can be bound later in VP.sem
  • V.sem, version 2
  • ?x ?y ?(e) (Isa(e,Serving) Agent(e,y)
    Patient(e,x))

28
  • VP ? V NP V.sem(NP.sem)
  • ?x ?y ?(e) (Isa(e,Serving) Agent(e,y)
    Patient(e,x))(burgers)
  • ?y ?(e) (Isa(e,Serving) Agent(e,y)
    Patient(e,burgers))
  • S ? NP VP VP.sem(NP.sem)
  • ?y ?(e) Isa(e,Serving) Agent(e,y)
    Patient(e,burgers)(McDonalds)
  • ?(e) Isa(e,Serving) Agent(e,McDonalds)
    Patient(e,burgers)

29
What is our grammar now?
  • S ? NP VP VP.sem(NP.sem)
  • VP ? V NP V.sem(NP.sem)
  • V ? serves ?x ?y E(e) (Isa(e,Serving)
    Agent(e,y) Patient(e,x))
  • NP ? Propernoun Propernoun.sem
  • NP ? Pluralnow Pluralnoun.sem
  • Propernoun ? McDonalds
  • Pluralnoun ? burgers

30
But this is just the tip of the iceberg.
  • Terms can be complex
  • A restaurant serves burgers.
  • a restaurant ? x Isa(x,restaurant)
  • ? e Isa(e,Serving) Agent(e,lt ? x
    Isa(x,restaurant)gt) Patient(e,burgers)
  • Allows quantified expressions to appear where
    terms can by providing rules to turn them into
    well-formed FOPC expressions
  • Issues of quantifier scope
  • Every restaurant serves a burger.

31
How represent other constituents?
  • Adjective phrases
  • Happy people, cheap food, purple socks
  • Intersective semantics works for some
  • Nom ? Adj Nom ?x (Nom.sem(x) Isa(x,Adj.sem))
  • Adj ? cheap Cheap
  • ?x Isa(x, Food) Isa(x,Cheap)
  • But.fake gun? Local restaurant? Former friend?
    Would-be singer?
  • Ex Isa(x, Gun) Isa(x,Fake)

32
Doing Compositional Semantics
  • To incorporate semantics into grammar we must
  • Determine right representation for each basic
    constituent
  • Determine right representation constituents
    that take these basic constituents as arguments
  • Incorporate semantic attachments into each rule
    of our CFG

33
Parsing with Semantic Attachments
  • Modify parser to include operations on semantic
    attachments as well as syntactic constituents
  • E.g., change an Early-style parser so when
    constituents are completed, their attached
    semantic function is applied and a meaning
    representation created and stored with state
  • Or let parser run to completion and then walk
    through resulting tree, applying semantic
    attachments from bottom-up

34
Option 1 (Integrated Semantic Analysis)
  • S ? NP VP VP.sem(NP.sem)
  • VP.sem has been stored in state representing VP
  • NP.sem stored with the state for NP
  • When rule completed, retrieve value of VP.sem and
    of NP.sem, and apply VP.sem to NP.sem
  • Store result in S.sem.
  • As fragments of input parsed, semantic
    fragments created
  • Can be used to block ambiguous representations

35
Drawback
  • You also perform semantic analysis on orphaned
    constituents that play no role in final parse
  • Case for pipelined approach Do semantics after
    syntactic parse

36
Non-Compositional Language
  • Some meaning isnt compositional
  • Non-compositional modifiers fake, former, local,
    so-called, putative, apparent,
  • Metaphor
  • Youre the cream in my coffee. Shes the cream in
    Georges coffee.
  • The break-in was just the tip of the iceberg.
    This was only the tip of Shirleys iceberg.
  • Idiom
  • The old man finally kicked the bucket. The old
    man finally kicked the proverbial bucket.
  • Deferred reference The ham sandwich wants his
    check.
  • Solution special rules? Treat idiom as a unit?

37
Summing Up
  • Hypothesis Principle of Compositionality
  • Semantics of NL sentences and phrases can be
    composed from the semantics of their subparts
  • Rules can be derived which map syntactic analysis
    to semantic representation (Rule-to-Rule
    Hypothesis)
  • Lambda notation provides a way to extend FOPC to
    this end
  • But coming up with rule to rule mappings is hard
  • Idioms, metaphors and other non-compositional
    aspects of language makes things tricky (e.g.
    fake gun)

38
Next
  • Read Ch 19 1-5
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