Transcript Slides

Meaning Representations
Computational Semantics
08/10/2001
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Grammar Coverage

Coverage is never
complete


Add more rules…
All grammars leak

More specific rules
 Add more features
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General NLP System Architecture
Grammar
User Modeling
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Dialogue Management
3
Big Transition




First we did words (morphology)
Then we looked at syntax
Now we’re moving on to meaning. Where some would
say we should have started to begin with.
Now we look at meaning representations –
representations that link linguistic forms to knowledge of
the world.
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Semantics

Syntax
Mr. Smith is expressive
how signs are related to each other

Semantics
how signs are related to things

Pragmatics
how signs are related to people
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Compositional Semantics

Compositional Semantics =
The abstract meaning of a sentence
(built from the meaning of its parts)

Situational Semantics =
Adds context-dependent information
”Forget about it”
World knowledge = knowledge about the
world shared between groups of people
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Computational Semantics?
Automating the processes of

mapping natural language to semantic
representations

using logical representation to draw inferences
Patrick Blackburn & Johan Bos (Saarbrücken, 1999)
Representation and Inference for Natural Language:
A First Course in Computational Semantics
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Linguistic Meaning
Translation from linguistic form to some “language of
thought”
(linguistic form = grammatical / syntactic form)
Fodor:
 mental states with propositional content are
“computational”
 the mind “computes” a conclusion from the premises
(beliefs, desires, etc.) on the basis of their structural
characteristics
Thus: beliefs, etc., must have a representational structure
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Logical Forms should be


Disambiguated:
alternative readings  different logical forms
John sees Bob
Representing literal “meanings”
(truth conditions)

Vehicle for reasoning

Basis for generation:
one logical form  several readings
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see(John,Bob)
He sees Bob
He sees him
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Semantic Processing

Touchstone application is always question answering

Can I answer questions involving the meaning of some
text or discourse?
 What kind of representations do I need to mechanize that
process?
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Sample Meaning Representations
I have a car.

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First-Order Predicate Calculus
Semantic Networks
Conceptual Dependency
Frame-based representation
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Common Meaning Representations

FOPC:
x, yHaving ( x)  Haver ( S , x)  HadThing ( y, x)  Car ( y )

Semantic Net:
having
haver
speaker
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had-thing
car
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
Conceptual Dependency Diagram:
Car
 Poss-By
Speaker

Frame
Having
Haver: S
HadThing: Car
All represent ‘linguistic meaning’ of I have a car
and state of affairs in some world
 All consist of structures, composed of symbols
representing objects and relations among them

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What requirements must meaning
representations fulfill?

Verifiability: The system should allow us to compare
representations to facts in a Knowledge Base (KB)


Ambiguity: The system should allow us to represent
meanings unambiguously


Cat(Huey)
German teachers has 2 representations
Vagueness: The system should allow us to represent
vagueness

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He lives somewhere in the south of France.
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Initial Simplifying Assumptions

Focus on literal meaning

Conventional meanings of words
 Ignore context
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Canonical Form

Inputs that mean the same thing have the same
representation.

Huey eats kibble.
 Kibble, Huey will eat.
 What Huey eats is kibble.
 It’s kibble that Huey eats.

Alternatives

Four different semantic representations
 Store all possible meaning representations in KB
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Canonical Form: Pros and Cons
Advantages
 Simplifies reasoning tasks
 Compactness of representations: don’t need to write
inference rules for all different “paraphrases” of the same
meaning
Disadvantages
 Complicates task of semantic analysis
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Inference

Draw valid conclusions based on the meaning
representation of inputs and its store of background
knowledge.
Does Huey eat kibble?
thing(kibble)
Eat(Huey,x) ^ thing(x)
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Expressiveness

Must accommodate wide variety of meanings
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First-Order Languages

Non-logical = all symbols in the vocabulary

Variables = x, y, z, w, … (infinitely many)

Boolean operators:





Quantifiers:



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negation
implication
disjunction
conjunction
universal
existential
(, ) and ,
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Beliefs

Acquiring a new belief:
linguistic form  mental representation

Aristotle:
Deduction and inference are based on formal relations

Circumstantial problem:
Accessing the language of thought via the language of speech

Fundamental problem:
Falls short of explaining what language really means
(We're just shifting the problem to another language.)
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What is Missing?

When we speak or think, we speak or think about something.

We speak about things in the world.

Utterances concerning the actual world may be true or false.

The truth or falsity of an utterance depends on
the meaning of the expression uttered
2. the factual constitution of its subject matter.
1.
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First-Order Models
A model is a pair (D,F)

D = domain:
the set of entities

F = interpretation function:
map symbols in the vocabulary to entities
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Model-Theoretic Semantics (Montague)

Separate meaning of expressions from factual
constitutions

The subject matter is represented by a model
Model = abstract structure encoding factual
information pertaining to truth values of sentences


1.
2.
State for each sentence S
in which possible models uttering S  truth
in which possible models uttering S  falsehood
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The Meaning of Sentences (Frege)

Giving an account of linguistic meaning =
describing the meanings of complete sentences

Explaining the meaning of a sentence S =
explaining under which conditions S is true

Explaining the meanings of other units = describe
how they contribute to S’s meaning
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Semantic Construction

Given a sentence of a language,
is there a systematic way of constructing its
semantic representation?

Can we translate a syntactic structure into an
abstract representation of its actual meaning?
(e.g. first-order logic)
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Compositionality, Frege’s Principle

Meaning ultimately flows from the lexicon

Meanings are combined by syntactic
information

The meaning of the whole is a function of the
meaning of its parts
(’parts’ = the substructure given by syntax)
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Syntactic Structure
Vincent loves Mia
S LOVES(VINCENT,MIA)
VP LOVES(?,MIA)
NP
V
NP
VINCENT likes
LOVES(?,?)
Mia
Vincent
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MIA
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Three Tasks
We Need to Specify:

a syntax for the language fragment

semantic representations for the lexical items

the translation compositionally
(= specify the translation of all expressions in terms of the
translation of their parts)
All in a way that is naturally implemented
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Task 1: A Context-Free Grammar
s  np, vp.
pname  [vincent].
pname  [mia].
vp  iv.
vp  tv, np.
n  [robber].
n  [woman].
np  pname.
np  det, n.
det  [a].
det  [every].
iv  [snores].
tv  [loves].
Montague: “I fail to see any great interest in syntax except as a
preliminary to semantics.”
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Incomplete / Quasi-Logical Forms
VP
LOVES(?,MIA)
To build representations we need to
1.
2.
work with ‘incomplete’ formulas
indicate where the information they lack must
go
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Task 2: Semantic Lexicon
pname(sem=vincent)  [vincent].
pname(sem=mia)  [mia].
n(sem=(X,robber(X)))  [robber].
n(sem=(X,woman(X)))  [woman].
iv(sem=(X,snore(X)))  [snores].
tv(sem=(X,Y,love(X,Y)))  [loves].
Associating missing information with an explicit
variable
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Quantifiers / Determiners

Every robber snores
x(ROBBER(x)  SNORE(x))
forall(X, robber(X) => snore(X))

A robber snores
x(ROBBER(x))& SNORE(x))
exists(X, robber(X) & snore(X))
det(X, N, VP, forall (X, N => VP)) [every].
det(X, N, VP, exists (X, N & VP)) [a].


Noun contribution = restriction
VP contribution = nuclear scope
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Task 3: Production Rules
s(sem=N)  np(sem=(X,VP,N)), vp(sem=(X,VP)).
vp(sem=(X,V))  iv(sem=(X,V)).
vp(sem=(X,N))  tv(sem=(X,Y,V)), np(sem=(Y,V,N)).
np(sem=(Name,X,X))  pname(sem=Name).
np(sem=(X,VP,Det)) det(sem=(X,N,VP,Det)), n(sem=(X,N)).
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How did we do?
+
It works!
+ The underlying intuition is pretty clear.
-
Much of the work is done by the rules.
- Hard to treat the grammar in a modular way.
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Lambda Calculus (Church)

Notational extension of first order logic

Variable binding by an operator  (“lambda”)
x.MAN(x)

Variables bound by  are ‘placeholders’
(for missing information)

“lambda reduction” performs the substitutions
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Functional Application & Lambda Reduction
Concatenation indicates ‘functional application’
(= that we wish to perform a substitution)
(x.MAN(x)) VINCENT
x.MAN(x)= functor
VINCENT = argument
lambda reduction = perform the substitution
MAN(VINCENT)
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Marking more complex kinds of information
Representation of “a man”
Q.x(MAN(x)  Q)
The variable Q indicates that:
 some information is missing
 where this information has to be plugged in
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“Every robber snores”
Step 1:
assign -expressions to the syntactic categories
robber:
x.ROBBER(x)
snores:
x.SNORES(x)
every:
N.VP.x(N(x)  VP(x))
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“Every robber snores”, cont.
Step 2:
associate the NP with the application that has the DET
as functor and the NOUN as argument
every robber (NP)
(N.VP.x(N(x)  VP(x))) (y.ROBBER(y))
every (DET)
N.VP.x(N(x)  VP(x))
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robber (N)
y.ROBBER(y)
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Lambda Reduction
Step 3:
Perform the
demanded
substitutions
every
robber
every
robber
(NP)(NP)
VP.x((y.ROBBER(y))(x)
VP.x(ROBBER(x)
VP(x))
 VP(x))
(N.VP.x(N(x)
 VP(x)))
(y.ROBBER(y))
every (DET)
N.VP.x(N(x)  VP(x))
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robber (N)
y.ROBBER(y)
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“Every robber snores”, final
representation
Step 4:
Add the VP
every
every
robber
robber
snores
snores
(S)
(S) (S)
every
robber
snores
(VP.x(ROBBER(x)
x(ROBBER(x)
(z.SNORES(z))(x))
VP(x)))(z.SNORES(z))
x(ROBBER(x)
SNORES(x))
every robber (NP)
VP.x(ROBBER(x) VP(x))
every (DET)
N.VP.x(N(x)  VP(x))
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snores (V)
z.SNORES(z)
robber (N)
y.ROBBER(y)
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Transitive Verbs
loves:
NP.z.(NP(x.LOVE(z,x))

TV semantic representations take their object NP’s
semantic representation as argument

Subject NP semantic representations take the VP
semantic representation as argument
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Quantifying Noun Phrases: “Every woman
loves a man”
every woman loves a man (S)
w(WOMAN(w)(x.(m(MAN(m)&
w(WOMAN(w)
x(MAN(m)& LOVE(w,m)))
LOVE(x,m)))(w)))
(VP.w(WOMAN(w)VP(w)))(x.(m(MAN(m)&
LOVE(x,m)))
every woman (NP)
VP.w(WOMAN(w)VP(w))
loves a man (VP)
(NP.x.(NP(y.LOVE(x,y)))
x.(VP.m(MAN(m)&VP(m))(y.LOVE(x,y)))
x.(m(MAN(m)&
x.(m(MAN(m)&(y.LOVE(x,y))(m)))
(VP.m(MAN(m)&
LOVE(x,m))) VP(m)))
loves (V)
NP.x.(NP(y.LOVE(x,y))
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a man (NP)
VP.m(MAN(m)& VP(m))
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Scope Ambiguities
Every woman loves a man
w(WOMAN(w) x(MAN(m)& LOVE(w,m)))
“for each woman there is a man that she loves”
Second reading:
x(MAN(m)& w(WOMAN(w) LOVE(w,m)))
“there is one man who is loved by all women”
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Construction of Semantic Representations
Three basic principles:

Lexicalization:
try to keep semantic information lexicalized

Compositionality:
pass information up compositionally from terminals

Underspecification:
Don’t make a choice unless you have to
(the interpretation of ambiguous parts is left unresolved)
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Underspecification

A meaning  of a formalism L is underspecified =
represents an ambiguous sentence in a more compact manner
than by a disjunction of all readings

L is complete = L’s disambiguation device produces all possible
refinements of any 
Example:
 consider a sentence with 3 quantified NPs
(with underspecifed scoping relations)

L must be able to represent all 23! = 64 refinements
(partial and complete disambiguations) of the sentence.
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Phenomena for Underspecification

local ambiguities
e.g., lexical ambiguities, anaphoric or deictic use of PRO

global ambiguities
e.g., scopal ambiguities, collective-distributive readings

ambiguous or incoherent non-semantic information
e.g., PP-attachment, number disagreement
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Predicate-Argument Structure

Represents concepts and relationships among them

Nouns as concepts or arguments (red(ball))
 Adjectives, adverbs, verbs as predicates (red(ball))

Subcategorization (or, argument) frames specify
number, position, and syntactic category of
arguments

NP likes NP
 NP likes Inf-VP
 NP likes NP Inf-VP
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Fillmore’s Theory about Universal Cases

Fillmore – there are a small number of semantic roles
that an NP in a sentence may play with respect to the
verb.

A major task of semantic analysis is to provide an
appropriate mapping between the syntactic constituents
of a parsed clause and the semantic roles (cases)
associated with the verb.
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Major Cases Include






Agent – doer of the action, entails intentionality
Experiencer – doer when no intentionality
Theme – thing being acted upon or undergoing change
Instrument – tool used to do the action
Beneficiary – person/thing for whom the event is
performed
To/At/From Loc/Poss/Time – location or possession or
time representations
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Some Sentences and their cases







John opened the door with a key.
The door was opened by John.
The door was opened with a key.
A key opened the door.
The door opened.
John gave Mary the book.
John gave the book to Mary.
Let’s identify the cases in these sentences – notice any
syntactic regularities in the case assignment.
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Some Sentences and their cases







John opened the door with a key.
The door was opened by John.
The door was opened with a key.
A key opened the door.
The door opened.
John gave Mary the book.
John gave the book to Mary.

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Agent – doer of action, attributes intention
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Some Sentences and their cases







John opened the door with a key.
The door was opened by John.
The door was opened with a key.
A key opened the door.
The door opened.
John gave Mary the book.
John gave the book to Mary.
Agent – doer of action, attributes intention
 Theme – thing being acted upon or undergoing change

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Some Sentences and their cases







John opened the door with a key.
The door was opened by John.
The door was opened with a key.
A key opened the door.
The door opened.
John gave Mary the book.
John gave the book to Mary.
Agent – doer of action, attributes intention
 Theme – thing being acted upon or undergoing change
 Instrument – tool used to do the action

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Some Sentences and their cases







John opened the door with a key.
The door was opened by John.
The door was opened with a key.
A key opened the door.
The door opened.
John gave Mary the book.
John gave the book to Mary.
Agent – doer of action, attributes intention
 Theme – thing being acted upon or undergoing change
 Instrument – tool used to do the action
 To-Poss –

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Some Sentences and their cases







John opened the door with a key.
The door was opened by John.
The door was opened with a key.
A key opened the door.
The door opened.
John gave Mary the book.
John gave the book to Mary.
Intuition – syntactic choices are largely a reflection of
underlying semantic relationships.
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Semantic Analysis

A major task of semantic analysis is to provide an
appropriate mapping between the syntactic constituents
of a parsed clause and the semantic roles associated
with the verb.
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Factors to Complicate

Ability of syntactic constituents to indicate several
different semantic roles

E.g., Subject position; agent versus instrument versus
theme




John broke the window.
The rock broke the window.
The window broke.
Large number of choices available for syntactic
expression of any particular syntactic role

E.g., agent and theme in different configurations


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
John broke the window.
It was the window that John broke.
The window was broken by John.
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Factors to Complicate (cont)

Prepositional ambiguities – it is the case that a
particular preposition does not always introduce the
same role

E.g., proposition “by” may indicate either agent or
instrument



The door was opened by John.
The door was opened by a key.
Optionality of a given role in a sentence




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
John opened the door with a key.
The door was opened by John.
The door was opened with a key.
A key opened the door.
The door opened.
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How bad is it?

It seems that semantic roles are playing “musical chairs”
with the syntactic constituents. That is, they seem to “sit
down” in any old syntactic constituent and one or more
of them seem to be left out at times!

Actually, it isn’t as bad as it may seem!

There is a great deal of regularity – consider the
following set of rules….
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Some Rules
If  Agent it becomes Subject
Else If  Instrument it becomes Subject
Else If  Theme it becomes Subject
Agent preposition is BY
Instrument preposition is BY if no agent, else WITH
Some Rules:
 Some verbs may have exceptions
 No case can appear twice in the same clause
 Only NP’s of same case can be conjoined
 Each syntactic constituent can fill only 1 case
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What’s missing???
If  Agent it becomes Subject
Else If  Instrument it becomes Subject
Else If  Theme it becomes Subject
How do I know whether or not an agent exists? How about an
instrument?
Selectional Restrictions – restrict the types of certain roles to be a
certain semantic entity
 Agents must be animate
 Instruments are not animate
 Theme? – type may be dependent on the verb itself.
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Selectional Restrictions
Selectional Restrictions: constraints on the types
of arguments verbs take
George assassinated the senator.
*The spider assassinated the fly.
assassinate: intentional (political?) killing
NOTE: dependence on the particular verb being used!
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So? What about Case in General?




You may or may not see particular cases used in
semantic analysis.
In the book, they have NOT used the specific cases.
But, note, the “roles” they use are derived from the
general cases identified in Fillmore’s work – they make
them verb-specific.
Semantic analysis is going to take advantage of the
syntactic regularities and selectional restrictions to
identify the role being played by each constituent in a
sentence!
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Representational Schemes

Let’s go back to the question – what kind of semantic
representation should we derive for a given
sentence?

We’re going to make use of First Order Predicate
Calculus (FOPC) as our representational framework

Not because we think its perfect
 All the alternatives turn out to be either too limiting or
 They turn out to be notational variants
 Essentially the important parts are the same no matter
which variant you choose!
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FOPC

Allows for…

The analysis of truth conditions


Supports the use of variables


Allows us to answer yes/no questions
Allows us to answer questions through the use of variable
binding
Supports inference

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Allows us to answer questions that go beyond what we know
explicitly
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FOPC



This choice isn’t completely arbitrary or driven by the
needs of practical applications
FOPC reflects the semantics of natural languages
because it was designed that way by human beings
In particular…
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Meaning Structure of Language

The semantics of human languages…

Display a basic predicate-argument structure
 Make use of variables (e.g., indefinites)
 Make use of quantifiers (e.g., every, some)
 Use a partially compositional semantics (sort of)
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Predicate-Argument Structure

Events, actions and relationships can be captured
with representations that consist of predicates and
arguments.

Languages display a division of labor where some
words and constituents function as predicates and
some as arguments.

E.g., predicates represent the verb, and the
arguments (in the right order) represent the cases of
the verb.
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Predicate-Argument Structure

Predicates

Primarily Verbs, VPs, PPs, adjectives, Sentences
 Sometimes Nouns and NPs

Arguments

Primarily Nouns, Nominals, NPs
 But also everything else; as we’ll see it depends on the
context
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Example



John gave a book to Mary
Giving(John, Mary, Book)
More precisely

Gave conveys a three-argument predicate
 The first argument is the giver (agent)
 The second is the recipient (to-poss), which is conveyed
by the NP in the PP
 The third argument is the thing given (theme), conveyed
by the direct object
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More Examples
What about situation of missing/additional cases?
 John gave Mary a book for Susan.
Giving(John, Mary, Book, Susan)

John gave Mary a book for Susan on Wednesday.
Giving(John, Mary, Book, Susan, Wednesday)

John gave Mary a book for Susan on Wednesday in
class.
Giving(John, Mary, Book, Susan, Wednesday, InClass)
Problem: Remember each of these predicates would be
different because of the different number of
arguments! Except for the suggestive names of
predicates and arguments, there is nothing that
indicates the obvious logical relations among them. 78
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Meaning Representation Problems
Assumes that the predicate representing the meaning of
a verb has the same number of arguments as are
present in the verb’s syntactic categorization frame.
This makes it hard to
 Determine the correct number of roles for any given
event
 Represent facts about the roles associated with the
event
 Insure that all and only the correct inferences can be
derived from the representation of an event

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Better

Turns out this representation isn’t quite as useful as it
could be.
 Giving(John,

Mary, Book)
Better would be one where the “roles” or “cases” are
separated out. E.g., consider:
 x, y Giving ( x)^ Giver ( John , x)^ Given( y, x)
^ Givee( Mary, x)^ Isa( y, Book )

Note: essentially Giver=Agent,
Given=Theme, Givee=To-Poss
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Predicates

The notion of a predicate just got more complicated…

In this example, think of the verb/VP providing a template like
the following
 w, x, y, zGiving ( x)^ Giver( w, x)^ Given( y, x)^ Givee( z , x)

The semantics of the NPs and the PPs in the sentence plug into
the slots provided in the template (we’ll worry about how in a
bit!)
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Advantages




Can have variable number of arguments associated
with an event: events have many roles and fillers can
be glued on as appear in the input.
Specifies categories (e.g., book) so that we can make
assertions about categories themselves as well as
their instances. E.g., Isa(MobyDick, Novel),
AKO(Novel, Book).
Reifies events so that they can be quantified and
related to other events and objects via sets of defined
relations.
Can see logical connections between closely related
examples without the need for meaning postulates.
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Additional Material

The following are some aspects covered in the book that
will likely not be covered in lecture!
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FOPC Syntax

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(Huey, kibble)
cat(Huey)
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
Logical connectives permit compositionality of
meaning
kibble(x)  likes(Huey,x)
cat(Vera) ^ weird(Vera)
sleeping(Huey) v eating(Huey)

Sentences in FOPC can be assigned truth values, T
or F, based on whether the propositions they
represent are T or F in the world

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
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
cat(Huey)
 sibling(Huey,Vera)
 sibling(x,y) ^ cat(x)  cat(y)
 cat(Vera)??

Limitations:

Do ‘and’ and ‘or’ in natural language really mean ‘^’
and ‘v’?
Mary got married and had a baby.
Your money or your life!
She was happy but ignorant.

Does ‘’ mean ‘if’?
I’ll go if you promise to wear a tutu.
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
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.

Inference:

Modus ponens:
rich(Harry)

x rich(x)  happy(x)
happy(Harry)

Production systems:

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Forward and backward chaining
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Temporal Representations

How do we represent time and temporal relationships
between events?
Last year Martha Stewart was happy but soon she will be
sad.

Where do we get temporal information?

Verb tense
 Temporal expressions
 Sequence of presentation

Linear representations: Reichenbach ‘47
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
Utterance time: when the utterance occurs
 Reference time: the temporal point-of-view of the
utterance
 Event time: when events described in the utterance
occur
George had intended to eat a sandwich.
E–R–U
George is eating a sandwich.
-- E,R,U 
George had better eat a sandwich soon.
--R,U – E 
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Verbs and Event Types: Aspect
Statives:
states or properties of objects
at a particular point in time
Mary needs sleep.
*Mary is needing sleep. *Need sleep. *Mary
needs sleep in a week.
Activities:
events with no clear
endpoint
Harry drives a Porsche. *Harry drives a Porsche
in a week.
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
Accomplishments: events with durations and
endpoints that result in some change of state
Marlon filled out the form. Marlon stopped filling out the
form (Marlon did not fill out the form) vs. Harry stopped
driving a Porsche (Harry still drove a Porsche …for a
while)

Achievements: events that change state but
have no particular duration
Larry reached the top. *Larry stopped reaching the top.
*Larry reached the top for a few minutes.
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Beliefs, Desires and Intentions

How do we represent internal speaker states like
believing, knowing, wanting, assuming, imagining..?

Not well modeled by a simple DB lookup approach
 Truth in the world vs. truth in some possible world
George imagined that he could dance.
Geroge believed that he could dance.

Augment FOPC with special modal operators that take
logical formulae as arguments, e.g. believe, know
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