Semantics and Computational Semantics

Seman&c
Analysis
in
Language
Technology

http://stp.lingﬁl.uu.se/~santinim/sais/2016/sais_2016.htm  
 
Semantics and  
Computational Semantics 

Marina
San(ni

san$nim@stp.lingﬁl.uu.se

Department
of
Linguis(cs
and
Philology

Uppsala
University,
Uppsala,
Sweden

Spring
2016

Lecture 2: Computational Semantics
1

Acknowledgements

The
content
of
these
slides
is
mostly
based
on
the
following
chapter:

•  Stone
M.
(In
Press)
Seman$cs
and
computa$onal
seman$cs
To
appear
in

Paul
Dekker
and
Maria
Aloni,
eds.,
Cambridge
Handbook
of
Formal

Seman(cs.
hJps://www.cs.rutgers.edu/~mdstone/pubs/compsem13.pdf

•  Blackburn
P.

and
Bos
J.
(2003)
Computa$onal
Seman$cs

hJp://www.let.rug.nl/bos/pubs/BlackburnBos2003Theoria.pdf

Some
slides
are
borrowed
from
/
inspired
by:

•  Manning
C.:
Computa(onal
Seman(cs,
CS224N
Stanford
University

hJp://web.stanford.edu/class/cs224n/handouts/Computa(onal
%20Seman(cs.pdf

•  Dragomir
Radev:
Introduc(on
to
NLP,
Coursera

2

Outline

•  Representa(on
and
Seman(cs

•  Computa(on
and
Composi(onal
Seman(cs

– Logic

– Uniﬁca(on

•  Conclusions

3

What
is
Seman(cs?

4

Generally
speaking…

seman(cs
is
the
study
of
meaning

that
is
used
for
understanding

human
expressions
through

language

•  Seman&cs
is
the
study
of
meaning:

accounts
for
links
between
words
and
the
world.

•  Seman(cs
is
the
study
of
how
meaning
is
conveyed
through
signs

and
language.

–  Denota(ons
are
the
literal
or
primary
meanings
of
words.

–  Connota(ons
are
ideas
or
feelings
that
a
word
invokes
for
a
person
in

addi(on
to
its
literal
or
primary
meaning.

•  Seman(cs
focuses
on
the
rela(on
between
signiﬁers
(like
words,

phrases,
signs,
and
symbols)
and
what
they
stand
for,
ie
their

denota(ons
(concepts)
and
connota(ons
(seman(c
analysis).

5

Comput(er)-‐a(onal
Seman(cs

•  Seman$cs
is
the
study
of
meaning
in
language.

•  Computer
science
is
the
study
of
precise

descrip(ons
of
ﬁnite
processes;

•  Thus,
computa(onal
seman(cs
embraces
any

project
that
approaches
the
phenomenon
of

meaning
by
way
of
tasks
that
can
be
performed
by

following
deﬁnite
sets
of
mechanical
instruc(ons.

6

We
can
start
by
saying
that…

”The
aim
of
computa(onal
seman(cs
is
to
ﬁnd

techniques
for
automa(cally
construc&ng

seman&c
representa&ons
for
expressions
of

human
language,
representa(ons
that
be
used

to
perform
inference.
”

Blackburn
and
Bos
(2003).

Inference
=
reasoning

7

Why
do
we
need
”meaning”
in

Language
Technology?

•  The
short
answer
is:
because
”intelligent”

applica(ons
must
”understand”
in
order
to

act.

8

Ex
1:
Google
-‐
What
is
the
capital
of

Sweden?

•  Answer:

9

Ex
2:
Siri
-‐
Which
countries
does
the

Danube
river
ﬂows
through?

10

Ex
3:
Facebook
Graph
Search

Facebook
Graph
Search
was
a
seman$c
search

engine
that
was
introduced
by
Facebook
in
March

2013.

It
was
designed
to
give
answers
to
user
natural

language
queries
rather
than
a
list
of
links.”

Examples:

"Friends
who
Like
Star
Wars
and
Harry
Po@er”

"photos
of
my
friends
taken
at
Na&onal
Parks"

hJps://en.wikipedia.org/wiki/Facebook_Graph_Search

11

Understanding
Meaning

If
an
agent
(eg.
a
robot)
hears
a
sentence
and

act
accordingly,
the
agent
is
said
to
understand

the
sentence:

Example:
Leave
the
book
on
the
table

Understanding
may
involve
inference:
Which

book?
Which
table?

So,
understanding
may
involve
some
kind
of

reasoning…

12

NLP/LT
and
Seman(cs

•  Not
all
LT-‐based
applica(ons
require
seman(cs.

– 
Ex:
taggers,
parsers,
etc.

•  Much
can
be
done
with
shallow
seman(cs.

–  Ex:
word
sense
disambigua(on,
etc.

•  For
more
complex
tasks
(more
”intelligent”

tasks”)
seman(c
reasoning
is
needed.

–  Ex:
QAnswering,
Info
Extrac(on,
Ontology
Crea(on,

etc.

13

Tradi(onally…

…reasoning
is
done
by
using
some
kind
of
logic…

A
tradi(onal
approach
is
to
use
FOL
(ﬁrst
order

logic)
to
”formalize”
meaning
(see
Formal

Seman(cs
Theories).

…
before
start
studying
how
seman(cs
is
used
in

Language
Technology-‐based
applica(ons,
let’s

summarise
how
seman(cs
has
been
brought
into

computer
science
and
ar(ﬁcial
intelligence.

14

REPRESENTATION
AND
SEMANTICS

15

Proper(es
of
Meaning
in
Logic

•  Veriﬁability

–  Can
a
statement
be
veriﬁed
against
a
knowledge
base
(KB)

–  Example:
does
my
cat
Mar(n
have
whiskers?

•  Unambiguousness

–  Give
me
the
book

–  Which
book?

•  Canonical
form
(standard/abstract
form
of
an
expression)

•  Expressiveness

–  Can
the
formalism
express
temporal
rela(ons,
beliefs,
…?

–  Is
it
domain-‐independent?

•  Inference

16

Represen(ng
Meaning

•  A
tradi(onal
approach
to
meaning
is
to

– 
use
proposi(onal
logic

– predicate/ﬁrst
order
logic
(FOL)

– use
theorem
proving
(inference)
to
determine

whether
a
statement
entails
another

17

Proposi(onal
Logic
:
proposi(ons
are

represented
by
leJers

•  In
proposi(onal
logic,
we
use
leJers
to

symbolize
en(re
proposi(ons.

•  Proposi(ons
are
statements
of
the
form
"x
is

y"
where
x
is
a
subject
and
y
is
a
predicate.

•  For
example,
"Socrates
is
a
Man"
is
a

proposi(on
and
might
be
represented
in

proposi(onal
logic
as
"S".

18

True
and
False

•  Proposi(onal
Logic
studies
proposi(ons,
whether
they
are
true
or
false.

•  A
sentence
might
contain
several
proposi(ons
that
are
linked
together
by

logical
connec(ves.

•  Logical
connec(ves
are
found
in
natural
languages.
In
English
for
example,

some
examples
are
"and"
(conjunc(on),
"or"
(disjunc(on),

"not”
(nega(on)
and
"if"
(but
only
when
used
to
denote
material

condi(onal).

•  Ex
(wikipedia):
simple
inference
within
the
scope
of
proposi(onal
logic:

•  Premise
1:
If
it's
raining
then
it's
cloudy.

•  Premise
2:
It's
raining.

•  Conclusion:
It's
cloudy.

Both
premises
and
the
conclusion
are
proposi(ons.
The
premises
are
taken

for
granted
and
then
with
the
applica(on
of
modus
ponens
(an
inference

rule)
the
conclusion
follows.

19

Syntax
of
Proposi(onal
Logic

•  The
simplest
type
of
logic

–
If
S
is
a
sentence,
¬S
is
a
sentence
(nega(on)

–
If
S1
and
S2
are
sentences,
S1
∧
S2
is
a
sentence

(conjunc(on)

–
If
S1
and
S2
are
sentences,
S1
∨
S2
is
a
sentence

(disjunc(on)

–
If
S1
and
S2
are
sentences,
S1
⇒
S2
is
a
sentence

(implica(on)

–
If
S1
and
S2
are
sentences,
S1
⇔
S2
is
a

sentence(bicondi(onal)

20

Proposi(onal
Logic
and
Natural
Language

Operator
Precedence

¬
(highest)
=
nega(on

∧
=
conjunc(on

∨
=
disjunc(on

⇒
=
implica(on

⇔
(lowest)
=
bicondi(onal*

*A
bicondi(onal
statement
is

deﬁned
to
be
true
whenever

both
parts
have
the
same
truth

value.

Logic
and
Language

A
=
Today
is
a
holiday.

B
=
We
are
going
to
the
park.

A
⇒
B

A
∧
¬
B

¬
A
⇒
B

¬
B
⇒
A

B
⇒
A

21

Truth
table

22

Proposi(onal
Logic
and
Seman(cs

Transla$ng
propos$ons
to
Eng
Seman$cs
of
Proposi$onal
Logic

23

Proposi(onal
logic
vs
FOL/Predicate
Logic

•  Proposi(onal
logic
(also
called
senten(al
logic)
is
logic
that
includes

sentence
leJers
(A,B,C
…
)
and
logical
connec(ves,
but
not

quan(fiers.
The
seman(cs
of
proposi(onal
logic
uses
truth

assignments
to
the
leJers
to
determine
whether
a
compound

proposi(onal
sentence
is
true.

•  Predicate
logic
is
usually
used
as
a
synonym
for
first-‐order
logic.

Syntac(cally,
first-‐order
logic
has
the
same
connec(ves
as

proposi(onal
logic,
but
it
also
has
variables
for
individual
objects,

quan(fiers,
symbols
for
func(ons,
and
symbols
for
rela(ons.

•  Its
seman(cs
includes
a
domain
of
discourse
for
the
variables
and

quan(fiers
to
range
over,
along
with
interpreta(ons
of
the
rela(on

and
func(on
symbols.

24

Predicate
Logic:
more
expressive
than

Proposi(onal
Logic

•  In
predicate
logic,
we
symbolize
subject
and
predicate

separately.

•  The
important
difference
is
that
you
can
use
predicate

logic
to
say
something
about
a
set
of
objects.

•  By
introducing
the
universal
quan(fier
("∀"),
the

existen(al
quan(fier
("∃")
and
variables
("x",
"y"
or

"z"),
we
can
use
predicate
logic
to
represent
thing
like:

–  "Everything
is
green"
as
"∀Gx”
”

–  Something
is
blue"
as
"∃Bx”

25

Used
to
represent

•  Objects
–
Mar(n
the
cat

•  Rela(ons
–
Mar(n
and
Moses
are
brothers

•  Func(ons
–
Mar(n’s
age

26

FOL
elements
(short
version)

•  Constant

•  Variables

•  Predicates

•  Boolean
connec(ves

•  Quan(ﬁers

•  Brackets
and
comma
to
group
the
symbols

together

•  Ex:
A
woman
crosses
Sunset
Boulevard

27

FOL
elements
(long
version)

Formula
→
AtomicFormula
or
Formula

Connec(ve
Formula
or
Quan(ﬁer
Variable

Formula
or
¬
Formula

(Formula):

28

FOL’s
most
important
feature:

quan(ﬁers
à
generaliza(on

29
To ace a test =
to get a very
high score on a
test

Proper(es
of
Predicate
Logic

•  Pros

– Composi(onal

– Declara(ve

•  Cons

– Limited
expressive
power

– Represents
facts

30

Lambda
calculus
à
Variable
subs(tu(on

Useful
for
expressing
computa(on
by
way
of
variable
binding
and
subs(tu(on.

Variables
are
just
names
that
are
bound
as
arguments.

Lambda
calculus
is
important
in
programming
language
theory.

Example

–
inc(x)
=
λx
x+1

–
then
inc(4)
=
(λx
x+1)(4)
=
5

Example

–
add(x,y)
=
λx,λy(x+y)

–
then
add(3,4)
=
(λx,λy(x+y))(3)(4)=
(λy
3+y)(4)
=3+4
=
12

31

Stages
of
Seman(c
Parsing

•  Input

– Sentence

• 
Syntac(c
Analysis

– 
Syntac(c
structure

•  Seman(c
Analysis

– Seman(c
representa(on

32

Composi(onal
Seman(cs

•  Add
seman(c
aJachments
to
syntac(c
rules

• 
Composi(onal
seman(cs

– Parse
the
sentence
syntac(cally

– Associate
some
seman(cs
to
each
word

– Combine
the
seman(cs
of
words
and
non

terminals
recursively

– Un(l
the
root
of
the
sentence

33

Example
•  Input

– Javier
likes
pizza

•  Output

– like(Javier,

pizza)

34
Associate a
semantic
expression
with each
node

Seman(c
Parsing

•  Conver(ng
natural
language
to
a
logical
form

– e.g.,
executable
code
for
a
speciﬁc
applica(on

– 
Example:

•  Airline
reserva(ons

•  Geographical
query
systems

35

What
about
”kick
the
bucket”?

•  What
happens
when
the
meaning
of
single

words
does
not
lead
to
the
meaning
of
the

whole?

36

COMPUTATION
AND

COMPOSITIONAL
SEMANTICS

37

Unifica(on
Grammar

•  Unifica(on
grammar
is
a
formalism
that
derives

seman(c
representa(ons
by
accumula(ng

constraints
in
tandem
with
a
syntac(c
deriva(on.

•  The
constraints
take
the
form
of
equa(ons

between
terms
which
may
contain
variables.

•  The
formalism
gets
its
name
from
the
process,

unifica$on,
which
determines
values
for

variables
to
solve
the
equa(ons.

38

Example:
”everybody
walks”

The
meaning
representa(on
of
∀x.walks(x)
is

assembled
as
the
solu(on
to
a
set
of
constraints

and
not
through
the
func(on–argument

maninupula(on
of
the
lambda
calculus.

39

More
flexibility

•  Lambda-‐calculus
techniques
expect
each
element
in
a
meaning

representa(on
to
be
specified
exactly
once.

•  Unifica(on:
we
model
sentence
meaning
as
the
solu(on
to
a
set
of

equa(ons
à
we
might

find
elements
of
meaning
that
are

simultaneously
determined
by
mul(ple
equa(ons,
and
elements
of

meaning
that
are
lev
unconstrained
and
must
be
resolved
by

context.

•  Constraint
techniques
offer
new
ways
to
analyze
idioms
and
mul(-‐
word
expressions.
Each
cons(tuent
can
not
only
specify
its
own

meaning
but
can
impose
a
constraint
on
the
meaning
of
the
whole.

40

Limita(ons

•  Composi(onal
seman(cs
(any
formalisms)

gives
us
representa(ons
that
capture
aspects

of
the
logical
structure
of
meaning.

•  But:
what
speciﬁc
en((es
and
concepts
does
a

sentence
describe,
and
what
speciﬁc
claim

does
it
make
about
them?

41

CONCLUSIONS

42

Basically…

•  We
need
to
(e
together:

– Grammar
(grammar
and
composi(onal
meaning
is

not
enough)

– Speaker’s
kowledge
about
the
wolrd

– PaBerns
of
use
à
unique
insights
given
by
large

corpora
of
linguis$c
evidence

43

In
this
course…

•  We
review
research
about
diﬀerent
aspects
of

word
meaning
that
are
needed
for
LT-‐based

applica(ons.

44

How
is
*meaning*
handled
in

Seman(c-‐Based
LT-‐Applica(ons

•  Seman(c
Role
Labelling/Predicate-‐Argument

Structure
(???)

•  Sen(ment
Analysis
(???)

•  Word
sense
disambigua(on
(???)

•  Informa(on
extrac(on
(???)

•  Ques(on
Answering
(???)

•  Ontologies
(???)

45

Reminder:
Glossary
Entries

•  Which
concepts
are
the
most
salient
in
this

lecture?

•  Start
crea(ng
your
Glossary
now…

46

The
End

47

Semantics and Computational Semantics

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