Approaches
to
plural
reference
generation
emphasise
descriptive
brevity
,
but
often
lack
empirical
backing
.
This
paper
describes
a
corpus-based
study
of
plural
descriptions
,
and
proposes
a
psycholinguistically-motivated
algorithm
for
plural
reference
generation
.
The
descriptive
strategy
is
based
on
partitioning
and
incorporates
corpus-derived
heuristics
.
An
exhaustive
evaluation
shows
that
the
output
closely
matches
human
data
.
1
Introduction
Generation
of
Referring
Expressions
(
GRE
)
is
a
well-studied
sub-task
of
microplanning
in
Natural
Language
Generation
.
Most
algorithms
in
this
area
view
GRE
as
a
content
determination
problem
,
that
is
,
their
emphasis
is
on
the
construction
of
a
semantic
representation
which
is
eventually
mapped
to
a
linguistic
realisation
(
i.e.
a
noun
phrase
)
.
Content
Determination
for
GRE
starts
from
a
Knowledge
Base
(
KB
)
consisting
of
a
set
of
entities
U
and
a
set
of
properties
P
represented
as
attribute-value
pairs
,
and
searches
for
a
description
D
C
P
which
distinguishes
a
referent
r
G
U
from
its
distractors
.
Under
this
view
,
reference
is
mainly
about
identification
of
an
entitiy
in
a
given
context
(
represented
by
the
KB
)
,
a
well-studied
pragmatic
function
of
definite
noun
phrases
in
both
the
psycholinguistic
and
the
computational
literature
(
Olson
,
1970
)
.
For
example
,
the
KB
in
Table
1
represents
8
entities
in
a
2D
visual
domain
,
each
with
6
attributes
,
including
their
location
,
represented
as
a
combination
of
horizontal
(
X
)
and
vertical
(
Y
)
numerical
co
-
ordinates
.
To
refer
to
an
entity
an
algorithm
searches
through
values
of
the
different
attributes
.
GRE
has
been
dominated
by
Dale
and
Reiter
's
(
1995
)
Incremental
Algorithm
(
IA
)
,
one
version
of
which
,
generalised
to
deal
with
non-disjunctive
plural
references
,
is
shown
in
Algorithm
1
(
van
Deemter
,
2002
)
.
A
non-disjunctive
reference
to
a
set
R
is
possible
just
in
case
all
the
elements
of
R
can
be
distinguished
using
the
same
attribute-value
pairs
.
Such
a
description
is
equivalent
to
the
logical
conjunction
of
the
properties
in
question
.
This
algorithm
,
lApiur
,
initialises
a
description
D
and
a
set
of
distractors
C
[
1.1-1.2
]
,
and
traverses
an
ordered
list
of
properties
,
called
the
preference
order
(
PO
)
[
1.3
]
,
which
reflects
general
or
domain-specific
pref
-
return
D
end
if
end
if
Proceedings
of
the
2007
Joint
Conference
on
Empirical
Methods
in
Natural
Language
Processing
and
Computational
Natural
Language
Learning
,
pp.
102-111
,
Prague
,
June
2007
.
©
2007
Association
for
Computational
Linguistics
erences
for
attributes
.
For
instance
,
with
the
PO
in
the
top
row
of
the
Table
,
the
algorithm
first
considers
values
of
type
,
then
colour
,
and
so
on
,
adding
a
property
to
D
if
it
is
true
of
the
intended
referents
R
,
and
has
some
contrastive
value
,
that
is
,
excludes
some
distractors
[
1.4
]
.
The
description
and
the
dis-tractor
set
C
are
updated
accordingly
[
1.5-1.6
]
,
and
the
description
returned
if
it
is
distinguishing
[
1.7
]
.
Given
R
=
{
ei
,
e2
}
,
this
algorithm
would
return
the
following
description
:
This
description
is
overspecified
,
because
ORIENTATION
is
not
strictly
necessary
to
distinguish
the
referents
(
(
size
:
small
)
suffices
)
.
Moreover
,
the
description
does
not
include
TYPE
,
though
it
has
been
argued
that
this
is
always
required
,
as
it
maps
to
the
head
noun
of
an
NP
(
Dale
and
Reiter
,
1995
)
.
We
will
adopt
this
assumption
here
,
for
reasons
explained
below
.
Due
to
its
hillclimbing
nature
,
the
IA
avoids
combinatorial
search
,
unlike
some
predecessors
which
searched
exhaustively
for
the
briefest
possible
description
of
a
referent
(
Dale
,
1989
)
,
based
on
a
strict
interpretation
of
the
Gricean
Maxim
of
Quantity
(
Grice
,
1975
)
.
Given
that
,
under
the
view
proposed
by
Olson
(
1970
)
among
others
,
the
function
of
a
referential
NP
is
to
identify
,
a
strict
Gricean
interpretation
holds
that
it
should
contain
no
more
information
than
necessary
to
achieve
this
goal
.
The
Incremental
Algorithm
constitutes
a
departure
from
this
view
given
that
it
can
overspecify
through
its
use
of
a
PO
.
This
has
been
justified
on
psycholinguistic
grounds
.
Speakers
overspecify
their
descriptions
because
they
begin
their
formulation
of
a
reference
without
exhaustively
scanning
a
domain
(
Pechmann
,
1989
;
Belke
and
Meyer
,
2002
)
.
They
prioritise
the
basic-level
category
(
TYPE
)
of
an
object
,
and
salient
,
absolute
properties
like
COLOUR
(
Pechmann
,
1989
;
Eikmeyer
and
Ahlsen
,
1996
)
,
as
well
as
locative
properties
in
the
vertical
dimension
(
Arts
,
2004
)
.
Relative
attributes
like
SIZE
are
avoided
unless
absolutely
required
for
identification
(
Belke
and
Meyer
,
2002
)
.
This
evidence
suggests
that
speakers
conceptualise
referents
as
gestalts
(
Pechmann
,
1989
)
whose
core
is
their
basic-level
TYPE
(
Murphy
,
2002
)
and
some
other
salient
attributes
like
COLOUR
.
For
instance
,
according
to
Schriefers
and
Pechmann
(
1988
)
,
an
NP
such
as
the
large
black
triangle
reflects
a
conceptualisation
of
the
referent
as
a
black
triangle
,
of
which
the
SIZE
property
is
predicated
.
Thus
,
the
type+colour
combination
is
not
mentally
represented
as
two
separable
dimensions
.
In
what
follows
,
we
will
sometimes
refer
to
this
principle
as
the
Conceptual
Gestalts
Principle
.
Note
that
the
IA
does
not
fully
mirror
these
human
tendencies
,
since
it
only
includes
preferred
attributes
in
a
description
if
they
remove
some
distractors
given
the
current
state
of
the
algorithm
,
whereas
psycholin-guistic
research
suggests
that
people
include
them
irrespective
of
contrastiveness
(
but
cf.
van
der
Sluis
and
Krahmer
(
2005
)
)
.
More
recent
research
on
plural
GRE
has
de-emphasised
these
issues
,
especially
in
case
of
disjunctive
plural
reference
.
Disjunction
is
required
whenever
elements
of
a
set
of
referents
R
do
not
have
identical
distinguishing
properties
.
For
example
,
{
ei
,
e3
}
can
be
distinguished
by
the
following
Conjunctive
Normal
Form
(
CNF
)
description1
:
Such
a
description
would
be
returned
by
a
generalised
version
of
Algorithm
1
proposed
by
van
Deemter
(
2002
)
.
This
generalisation
,
IAboo1
(
so
called
because
it
handles
all
Boolean
operators
,
such
as
negation
and
disjunction
)
,
first
tries
to
find
a
non-disjunctive
description
using
Algorithm
1
.
Failing
this
,
it
searches
through
disjunctions
of
properties
of
increasing
length
,
conjoining
them
to
the
description
.
This
procedure
has
three
consequences
:
Efficiency
:
Searching
through
disjunctive
combinations
results
in
a
combinatorial
explosion
(
van
Deemter
,
2002
)
.
Gestalts
and
content
:
The
notion
of
a
'
preferred
attribute
'
is
obscured
,
since
it
is
difficult
to
apply
the
same
reasoning
that
motivated
the
P
O
in
the
IA
to
combinations
like
(
COLOUR
V
SIZE
)
.
1Note
that
logical
disjunction
is
usually
rendered
as
linguistic
coordination
using
and
.
Thus
,
the
table
and
the
desk
is
the
union
of
things
which
are
desks
or
tables
.
Form
:
Descriptions
can
become
logically
very
complex
(
Gardent
,
2002
;
Horacek
,
2004
)
.
Proposals
to
deal
with
(
3
)
include
Gardent
's
(
2002
)
non-incremental
,
constraint-based
algorithm
to
generate
the
briefest
available
description
of
a
set
,
an
approach
extended
in
Gardent
et
al.
(
2004
)
.
An
alternative
,
by
Horacek
(
2004
)
,
combines
best-first
search
with
optimisation
to
reduce
logical
complexity
.
Neither
approach
benefits
from
empirical
grounding
,
and
both
leave
open
the
question
of
whether
previous
psycholinguistic
research
on
singular
reference
is
applicable
to
plurals
.
This
paper
reports
a
corpus-based
analysis
of
plural
descriptions
elicited
in
well-defined
domains
,
of
which
Table
1
is
an
example
.
This
study
falls
within
a
recent
trend
in
which
empirical
issues
in
gre
have
begun
to
be
tackled
(
Gupta
and
Stent
,
2005
;
Jordan
and
Walker
,
2005
;
Viethen
and
Dale
,
2006
)
.
We
then
propose
an
efficient
algorithm
for
the
generation
of
references
to
arbitrary
sets
,
which
combines
corpus-derived
heuristics
and
a
partitioning-based
procedure
,
comparing
this
to
iaboo1
.
Unlike
van
Deemter
(
2002
)
,
we
only
focus
on
disjunction
,
leaving
negation
aside
.
Our
starting
point
is
the
assumption
that
plurals
,
like
singulars
,
evince
preferences
for
certain
attributes
as
predicted
by
the
Conceptual
Gestalts
Principle
.
Based
on
previous
work
in
Gestalt
perception
(
Wertheimer
,
1938
;
Rock
,
1983
)
,
we
propose
an
extension
of
this
to
sets
,
whereby
plural
descriptions
are
preferred
if
(
a
)
they
maximise
the
similarity
of
their
referents
,
using
the
same
attributes
to
describe
them
as
far
as
possible
;
(
b
)
prioritise
salient
(
'
preferred
'
)
attributes
which
are
central
to
the
conceptual
representation
of
an
object
.
We
address
(
3
)
above
by
investigating
the
logical
form
of
plurals
in
the
corpus
.
One
determinant
of
logical
form
is
the
basic-level
category
of
objects
.
For
example
,
to
refer
to
(
ei
,
e2
}
in
the
Table
,
an
author
has
at
least
the
following
options
:
(
b
)
the
small
red
desk
and
the
small
blue
sofa
(
c
)
the
small
desk
and
the
small
blue
sofa
(
d
)
the
small
objects
These
descriptions
exemplify
three
possible
sources
of
variation
:
Disjunctive
/
Non-disjunctive
:
The
last
description
,
(
3d
)
,
is
non-disjunctive
(
i.e.
it
is
logically
a
conjunction
of
properties
)
.
This
,
however
,
is
only
achievable
through
the
use
of
a
non-basic
level
value
for
the
type
of
the
entities
(
objects
)
.
Using
the
basic-level
would
require
the
disjunction
(
(
type
:
desk
)
V
(
type
:
sofa
)
)
,
which
is
the
case
in
(
3a-c
)
.
Given
that
basic-level
categories
are
preferred
on
independent
grounds
(
Rosch
et
al.
,
1976
)
,
we
would
expect
examples
like
(
3d
)
to
be
relatively
infrequent
.
Aggregation
:
If
a
description
is
disjunctive
,
it
may
be
aggregated
,
with
properties
common
to
all
objects
realised
as
wide-scope
modifiers
.
For
instance
,
in
(
3a
)
,
small
modifies
desk
and
sofa
.
By
contrast
,
(
3b
)
is
non-aggregated
:
small
occurs
twice
(
modifying
each
coordinate
in
the
np
)
.
Non-aggregated
,
disjunctive
descriptions
are
logically
equivalent
to
a
partition
of
a
set
.
For
instance
,
(
3c
)
partitions
the
set
R
=
{
ei
,
e2
}
into
{
{
ei
}
,
{
e2
}
}
,
describing
each
element
separately
.
Descriptions
like
(
3b
)
are
more
overspecified
than
their
aggregated
counterparts
due
to
the
repetition
of
information
.
Paralellism
/
Similarity
:
Non-aggregated
,
disjunctive
descriptions
(
partitions
)
may
exhibit
semantic
parallelism
:
In
(
3b
)
,
elements
of
the
partition
are
described
using
exactly
the
same
attributes
(
that
is
,
type
,
colour
,
and
size
)
.
This
is
not
the
case
in
(
3c
)
,
which
does
represent
a
partition
but
is
nonparallel
.
Parallel
structures
maximise
the
similarity
of
elements
of
a
partition
,
using
the
same
attributes
to
describe
both
.
The
likelihood
of
propagation
of
an
attribute
across
disjuncts
is
probably
dependent
on
its
degree
of
salience
or
preference
(
e.g.
colour
is
expected
to
be
more
likely
to
be
found
in
a
parallel
structure
than
size
)
.
The
data
for
our
study
is
a
subset
of
the
tuna
Corpus
(
Gatt
et
al.
,
2007
)
,
consisting
of
900
references
to
furniture
and
household
items
,
collected
via
a
controlled
experiment
involving
45
participants
.
In
addition
to
their
type
,
objects
in
the
domains
have
colour
,
orientation
and
size
(
see
Table
1
)
.
For
each
subset
of
these
three
attributes
,
there
was
an
equal
number
of
domains
in
which
the
minimally
distinguishing
description
(
md
)
consisted
of
values
of
that
subset
.
For
example
,
Table
1
represents
a
domain
in
which
the
intended
referents
,
{
ei
,
e2
}
,
can
&lt;
ATTRIBUTE
name
=
'
sizey
value
=
,
small
'
&gt;
small
&lt;
/
ATTRIBUTE
&gt;
&lt;
ATTRIBUTE
name
=
'
coloury
value
=
*
red
'
&gt;
red
&lt;
/
ATTRIBUTE
&gt;
&lt;
ATTRIBUTE
name
=
^type
'
value
=
Mesk
'
&gt;
desk
&lt;
/
ATTRIBUTE
&gt;
&lt;
/
DESCRIPTION
&gt;
and
&lt;
ATTRIBUTE
name
=
'
sizey
value
=
,
small
'
&gt;
small
&lt;
/
ATTRIBUTE
&gt;
&lt;
ATTRIBUTE
name
=
'
coloury
value
=
*
blue
'
&gt;
blue
&lt;
/
ATTRIBUTE
&gt;
&lt;
ATTRIBUTE
name
=
^type
'
value
=
*
sofa
'
&gt;
sofa
&lt;
/
ATTRIBUTE
&gt;
&lt;
/
DESCRIPTION
&gt;
&lt;
/
DESCRIPTION
&gt;
Figure
1
:
Corpus
annotation
examples
be
minimally
distinguished
using
only
size2
.
Thus
,
overspecified
usage
of
attributes
can
be
identified
in
authors
'
descriptions
.
Domain
objects
were
randomly
placed
in
a
3
(
row
)
x
5
(
column
)
grid
,
represented
by
x
and
y
in
Table
1
.
These
are
relevant
for
a
subset
of
descriptions
which
contain
locative
expressions
.
Corpus
descriptions
are
paired
with
an
explicit
xml
domain
representation
,
and
annotated
with
semantic
markup
which
makes
clear
which
attributes
a
description
contains
.
This
markup
abstracts
away
from
differences
in
lexicalisation
,
making
it
an
ideal
resource
to
evaluate
content
determination
algorithms
,
because
it
is
semantically
transparent
,
in
the
sense
of
this
term
used
by
van
Deemter
et
al.
(
2006
)
.
This
markup
scheme
also
enables
the
compositional
derivation
of
a
logical
form
from
a
natural
language
description
.
For
example
,
the
xml
representation
of
(
3b
)
is
shown
in
Figure
1
,
which
also
displays
the
lf
derived
from
it
.
Each
constituent
np
in
(
3b
)
is
annotated
as
a
set
of
attributes
enclosed
by
a
description
tag
,
which
is
marked
up
as
singular
(
sg
)
.
The
two
coordinates
are
further
enclosed
in
a
plural
description
;
correspondingly
,
the
lf
is
a
disjunction
of
(
the
lfs
of
)
the
two
internal
descriptions
.
Descriptions
in
the
corpus
were
elicited
in
7
domains
with
one
referent
,
and
13
domains
with
2
referents
.
Plural
domains
represented
levels
of
a
Value
Similarity
factor
.
In
7
Value-Similar
(
vs
)
domains
,
referents
were
identifiable
using
identical
values
of
the
minimally
distinguishing
attributes
.
In
the
remaining
6
Value-Dissimilar
(
vds
)
domains
,
the
minimally
distinguishing
values
were
different
.
Table
1
represents
a
vs
domain
,
where
[
e
\
,
e2
}
can
2type
was
not
included
in
the
calculation
of
md.
%
overall
Table
2
:
%
disjunctive
and
non-disjunctive
plurals
be
minimally
distinguished
using
the
same
value
of
size
(
small
)
.
In
terms
of
our
introductory
discussion
,
referents
in
Value-Similar
conditions
could
be
minimally
distinguished
using
a
conjunction
of
properties
,
while
Value-Dissimilar
referents
required
a
disjunction
since
,
if
two
referents
could
be
minimally
distinguished
by
different
values
v
and
v
'
of
an
attribute
a
,
then
md
had
the
form
(
a
:
v
)
V
(
a
:
v
'
)
.
However
,
even
in
the
vs
condition
,
referents
had
different
basic-level
types
.
Thus
,
an
author
faced
with
a
domain
like
Table
1
had
at
least
the
descriptive
options
in
(
3a-d
)
.
If
they
chose
to
refer
to
entities
using
basic-level
values
of
type
,
their
description
would
be
disjunctive
(
e.g.
3a
)
.
A
non-disjunctive
description
would
require
the
use
of
a
superordinate
value
,
as
in
(
3d
)
.
Our
analysis
will
focus
on
a
stratified
random
sample
of
180
plural
descriptions
,
referred
to
as
pli
,
generated
by
taking
4
descriptions
from
each
author
(
2
each
from
vs
and
vds
conditions
)
.
We
also
use
the
singular
data
(
sg
;
N
=
315
)
.
The
remaining
plural
descriptions
(
pl2
;
N
=
405
)
are
used
for
evaluation
.
3
The
logical
form
of
plurals
Descriptions
in
pl1
were
first
classified
according
to
whether
they
were
non-disjunctive
(
cf.
3d
)
or
disjunctive
(
3a-c
)
.
The
latter
were
further
classified
into
aggregated
(
3a
)
and
non-aggregated
(
3b
)
.
Table
2
displays
the
percentage
of
descriptions
in
each
of
the
four
categories
,
within
each
level
of
Value
Similarity
.
Disjunctive
descriptions
were
a
majority
in
either
condition
,
and
most
of
these
were
non-aggregated
.
As
noted
in
§
1
,
these
descriptions
correspond
to
partitions
of
the
set
of
referents
.
Since
referents
in
vs
had
identical
properties
except
for
type
values
,
the
most
likely
reason
for
the
majority
of
disjunctives
in
vs
is
that
people
's
descriptions
represented
a
partition
of
a
set
of
referents
induced
by
the
basic-level
category
of
the
ob
-
Non-Parallel
Parallel
overspec
.
underspec
.
well-spec
.
Table
3
:
Parallelism
:
%
per
description
type
jects
.
This
is
strengthened
by
the
finding
that
the
likelihood
of
a
description
being
disjunctive
or
non-disjunctive
did
not
differ
as
a
function
of
Value
Similarity
(
x2
=
2.56
,
p
&gt;
.
1
)
.
A
x2
test
on
overall
frequencies
of
aggregated
versus
non-aggregated
disjunctives
showed
that
the
non-aggregated
descriptions
(
'
true
'
partitions
)
were
a
significant
majority
(
x2
=
83.63
,
p
&lt;
.
However
,
the
greater
frequency
of
aggregation
in
vs
compared
to
vds
turned
out
to
be
significant
(
x2
=
15.498
,
p
&lt;
.
Note
that
the
predominance
of
non-aggregated
descriptions
in
vs
implies
that
properties
are
repeated
in
two
disjuncts
(
resp
.
coordinate
nps
)
,
suggesting
that
authors
are
likely
to
redundantly
propagate
properties
across
disjuncts
.
This
evidence
goes
against
some
recent
proposals
for
plural
reference
generation
which
emphasise
brevity
(
Gardent
,
2002
)
.
3.1
Conceptual
gestalts
and
similarity
Allowing
for
the
independent
motivation
for
set
partitioning
based
on
type
values
,
we
suggested
in
§
1
that
parallel
descriptions
such
as
(
3b
)
may
be
more
likely
than
non-parallel
ones
(
3c
)
,
since
the
latter
does
not
use
the
same
properties
to
describe
the
two
referents
.
Similarity
,
however
,
should
also
interact
with
attribute
preferences
.
For
this
part
of
the
analysis
,
we
focus
exclusively
on
the
disjunctive
descriptions
in
pl1
(
N
=
150
)
in
both
vs
and
vds.
The
descriptions
were
categorised
according
to
whether
they
had
parallel
or
nonparallel
semantic
structure
.
Evidence
for
Similarity
interacting
with
attribute
preferences
is
strongest
if
it
is
found
in
those
cases
where
an
attribute
is
over-speciied
(
i.e.
used
when
not
required
for
a
distinguishing
description
)
.
In
those
cases
where
corpus
descriptions
do
not
contain
locative
expressions
(
the
x
and
/
or
y
attributes
)
,
such
an
overspecified
usage
is
straightforwardly
identified
based
on
the
md
of
a
domain
.
This
is
less
straightforward
in
the
case
of
locatives
,
since
the
position
ofobjects
was
randomly
determined
in
each
domain
.
Therefore
,
we
divided
Predicted
ORIENTATION
X-DIMENSION
Y-DIMENSION
Table
4
:
Actual
and
predicted
usage
probabilities
descriptions
into
three
classes
,
whereby
a
description
is
considered
to
be
:
1
.
underspecified
if
it
does
not
include
a
locative
expression
and
omits
some
md
attributes
;
2
.
overspecified
if
either
(
a
)
it
does
not
omit
any
md
attributes
,
but
includes
locatives
and
/
or
non-required
visual
attributes
;
or
(
b
)
it
omits
some
md
attributes
,
but
includes
both
a
locative
expression
and
other
,
non-required
attributes
;
3
.
well-specified
otherwise
.
Proportions
of
Parallel
and
Non-Parallel
descriptions
for
each
of
the
three
classes
are
are
shown
in
Table
3
.
In
all
three
description
types
,
there
is
an
overwhelming
majority
of
Parallel
descriptions
,
conirmed
by
a
x2
analysis
.
The
difference
in
proportions
of
description
types
did
not
differ
between
vs
and
vds
(
x2
&lt;
1
,
p
&gt;
.
8
)
,
suggesting
that
the
tendency
to
redundantly
repeat
attributes
,
avoiding
aggregation
,
is
independent
of
whether
elements
of
a
set
can
be
minimally
distinguished
using
identical
values
.
Our
second
prediction
was
that
the
likelihood
with
which
an
attribute
is
used
in
a
parallel
structure
is
a
function
of
its
overall
'
preference
'
.
Thus
,
we
expect
attributes
such
as
colour
to
feature
more
than
once
(
perhaps
redundantly
)
in
a
parallel
description
to
a
greater
extent
than
size
.
To
test
this
,
we
used
the
sg
sample
,
estimating
the
overall
probability
of
occurrence
of
a
given
attribute
in
a
singular
description
(
denoted
p
(
a
,
sg
)
)
,
and
using
this
in
a
non-linear
regression
model
to
predict
the
likelihood
of
usage
of
an
attribute
in
a
plural
partitioned
description
with
parallel
semantic
structure
(
denoted
p
(
a
,
pps
)
)
.
The
data
was
fitted
to
a
regression
equation
of
the
form
p
(
a
,
pps
)
=
k
x
p
(
a
,
sg
)
s.
The
resulting
equation
,
shown
in
(
4
)
,
had
a
near-perfect
fit
to
the
data
(
R2
=
.
910
)
3
.
This
is
confirmed
by
comparing
actual
probability
of
occurrence
in
the
second
column
of
Table
4
,
to
the
predicted
probabilities
in
the
third
column
,
which
are
estimated
from
singular
probabilities
using
(
4
)
.
Note
that
the
probabilities
in
the
Table
con-irm
previous
psycholinguistic
indings
.
To
the
extent
that
probability
of
occurrence
reflects
salience
and
/
or
conceptual
importance
,
an
order
over
the
three
attributes
colour
,
size
and
orientation
can
be
deduced
(
c
&gt;&gt;
o
&gt;&gt;
s
)
,
which
is
compatible
with
the
findings
of
Pechmann
(
1989
)
,
Belke
and
Meyer
(
2002
)
and
others
.
The
locative
attributes
are
also
ordered
(
Y
&gt;&gt;
X
)
,
confirming
the
findings
of
Arts
(
2004
)
that
vertical
location
is
preferred
.
or-derings
deducible
from
the
SG
data
in
turn
are
excellent
predictors
of
the
likelihood
of
'
propagating
'
an
attribute
across
disjuncts
in
a
plural
description
,
something
which
is
likely
even
if
an
attribute
is
redundant
,
modulo
the
centrality
or
salience
of
the
attribute
in
the
mental
gestalt
corresponding
to
the
set
.
Together
with
the
earlier
indings
on
logical
form
,
the
data
evinces
a
dual
strategy
whereby
(
a
)
sets
are
partitioned
based
on
basic-level
conceptual
category
;
(
b
)
elements
of
the
partitions
are
described
using
the
same
attributes
if
they
are
easily
perceived
and
conceptualised
.
Thus
,
of
the
descriptions
in
(
3
)
above
,
it
is
(
3b
)
that
is
the
norm
among
authors
.
4
Content
determination
by
partitioning
In
this
section
we
describe
IApart
,
a
partitioning-based
content
determination
algorithm
.
Though
presented
as
a
version
of
the
IA
,
the
basic
strategy
is
generalisable
beyond
it
.
For
our
purposes
,
the
assumption
of
a
preference
order
will
be
maintained
.
lApart
is
distinguished
from
the
original
IA
and
lAbool
(
cf.
§
1
)
in
two
respects
.
First
,
it
induces
partitions
opportunistically
based
on
KB
information
,
and
this
is
is
reflected
in
the
way
descriptions
are
represented
.
Second
,
,
the
criteria
whereby
a
property
is
added
to
a
description
include
a
consideration
of
the
overall
salience
or
preference
of
an
attribute
,
and
its
contribution
to
the
conceptual
cohesiveness
3A
similar
analysis
using
linear
regression
gave
essentially
the
same
results
.
of
the
description
.
Throughout
the
following
discussion
,
we
maintain
a
running
example
from
Table
1
,
in
which
R
=
{
e1
,
e2
,
e5
}
.
4.1
Partitioned
descriptions
iApart
generates
a
partitioned
description
(
Dpart
)
of
a
set
R
,
corresponding
to
a
formula
in
Disjunctive
Normal
Form
.
Dpart
is
a
set
of
Description
Fragments
(
DFs
)
.
A
DFis
atriple
(
RDF
,
TDF
,
MDF
)
,
where
RDF
-
R
,
TDF
is
a
value
of
type
,
and
MDF
is
a
possibly
empty
set
of
other
properties
.
DFs
refer
to
disjoint
subsets
of
R.
As
the
representation
suggests
,
type
is
given
a
special
status
.
lApart
starts
by
selecting
the
basic-level
values
of
type
,
partitioning
R
and
creating
a
DF
for
each
element
of
the
partition
on
this
basis
.
In
our
example
,
the
selection
of
type
results
in
two
DFs
,
with
MDF
initialised
to
empty
:
Although
neither
DF
is
distinguishing
,
RDF
indicates
which
referents
a
fragment
is
intended
to
identify
.
In
this
way
,
the
algorithm
incorporates
a
'
divide-and-conquer
'
strategy
,
splitting
up
the
referential
intention
into
'
sub-intentions
'
to
refer
to
elements
of
a
partition
.
Following
the
initial
step
of
selecting
TYPE
,
the
algorithm
considers
other
properties
in
PO
.
Suppose
(
colour
:
blue
)
is
considered
first
.
This
property
is
true
of
e2
and
e5
.
Since
DF2
refers
to
e2
,
the
new
property
can
be
added
to
MDF2
.
Since
e5
is
not
the
sole
referent
of
DF1
,
the
property
induces
a
further
partitioning
of
this
fragment
,
resulting
in
a
new
DF
.
This
is
identical
to
DF1
except
that
it
refers
only
to
e5
and
contains
(
COLOUR
:
blue
)
.
DF1
itself
now
refers
only
to
e1
.
Once
(
COLOUR
:
red
)
is
considered
,
it
is
added
to
the
latter
,
yielding
(
6
)
.
RDF
-
R
'
[
2.4
]
.
This
corresponds
to
our
example
involving
(
COLOUR
:
blue
)
and
DF2
.
The
property
is
simply
added
to
MDF
[
2.5
]
and
R
'
is
updated
by
removing
the
elements
thus
accounted
for
[
2.6
]
.
Suppose
RDF
^
R
'
.
If
RDF
n
R
'
is
empty
,
then
(
a
:
v
)
is
not
useful
.
Suppose
on
the
other
hand
that
RDF
n
R
'
=
0
[
2.7
]
.
This
occurred
with
(
COLOUR
:
red
)
in
relation
to
DF1
.
The
procedure
initialises
Rnew
,
a
set
holding
those
referents
in
RDF
which
are
also
in
R
'
[
2.8
]
.
A
new
DF
(
DFnew
)
is
created
,
which
is
a
copy
of
the
old
DF
,
except
that
(
a
)
it
contains
the
new
property
;
and
(
b
)
its
intended
referents
are
Rnew
[
2.9
]
.
The
new
DF
is
included
in
the
description
[
2.10
]
,
while
the
old
DF
is
altered
by
removing
Rnew
from
RDF
[
2.11
]
.
This
ensures
that
DFs
denote
disjoint
subsets
of
R.
(
_L
)
and
the
property
is
included
in
M
[
2.18
]
4
.
Note
that
this
procedure
easily
generalises
to
the
singular
case
,
where
D
part
would
only
contain
one
DF
.
4.2
Property
selection
criteria
IApart
's
content
determination
strategy
maximises
the
similarity
of
a
set
by
generating
semantically
parallel
structures
.
Though
contrastiveness
plays
a
role
in
property
selection
,
the
'
preference
'
or
conceptual
salience
of
an
attribute
is
also
considered
in
the
decision
to
propagate
it
across
DFs
.
Candidate
properties
for
addition
need
only
be
true
of
at
least
one
element
of
R.
Because
of
the
partitioning
strategy
,
properties
are
not
equally
con-strastive
for
all
referents
.
For
instance
,
in
(
5
)
,
e2
needs
to
be
distinguished
from
the
other
sofas
in
Table
1
,
while
{
e1
;
e5
}
need
to
be
distinguished
from
the
desks
.
Therefore
,
distractors
are
held
in
an
associative
array
C
,
such
that
for
all
r
G
R
,
C
[
r
]
is
the
set
of
distractors
for
that
referent
at
a
given
stage
in
the
procedure
.
Contrastiveness
is
deined
via
the
following
Boolean
function
:
We
turn
next
to
salience
and
similarity
.
Let
A
(
Dpart
)
be
the
set
of
attributes
included
in
Dpart
.
A
property
is
salient
with
respect
to
D
part
if
it
satis-ies
the
following
:
that
is
,
the
attribute
is
already
included
in
the
description
,
and
the
predicted
probability
of
its
being
propagated
in
more
than
one
fragment
of
a
description
is
greater
than
chance
.
A
potential
problem
arises
here
.
Consider
the
description
in
(
5
)
once
more
.
At
this
stage
,
IApart
begins
to
consider
colour
.
The
value
red
is
true
of
e1
,
but
non-contrastive
(
all
the
desks
which
are
not
in
R
are
red
)
.
If
this
is
the
first
value
of
colour
considered
,
(
8
)
returns
false
because
the
attribute
has
not
been
used
in
any
part
of
the
description
.
On
later
considering
(
COLOUR
:
blue
)
,
the
algorithm
adds
it
to
4This
only
occurs
if
the
kb
is
incomplete
,
that
is
,
there
some
entities
have
no
type
,
so
that
R
is
not
fully
covered
by
the
intended
referents
of
the
dfs
when
type
is
initially
added
.
Dpart
,
since
it
is
contrastive
for
{
e2
,
e5
}
,
but
will
have
failed
to
propagate
colour
across
fragments
.
As
a
result
,
lApart
considers
values
of
an
attribute
in
order
of
discriminatory
power
(
Dale
,
1989
)
,
deined
in
the
present
context
as
follows
:
Discriminatory
power
depends
on
the
number
ofref-erents
a
property
includes
in
its
extension
,
and
the
number
of
distractors
(
U
—
R
)
it
removes
.
By
prioritising
discriminatory
values
,
the
algorithm
irst
considers
and
adds
(
colour
:
blue
)
,
and
subsequently
will
include
red
because
(
8
)
returns
true
.
To
continue
with
the
example
,
at
the
stage
represented
by
(
6
)
,
only
e5
has
been
distinguished
.
orientation
,
the
next
attribute
considered
,
is
not
contrastive
for
any
referent
.
On
considering
SIZE
,
small
is
found
to
be
contrastive
for
e1
and
e2
,
and
added
to
DF1
and
DF2
.
However
,
size
is
not
added
to
DF3
,
in
spite
of
being
present
in
two
other
fragments
.
This
is
because
the
probability
function
p
(
SLZE
,
PPS
)
returns
a
value
below
0.5
(
see
Table
4
,
reflecting
the
relatively
low
conceptual
salience
of
this
attribute
.
The
inal
description
is
the
blue
desk
,
the
small
red
desk
and
the
small
blue
sofa
.
This
example
illustrates
the
limits
set
on
semantic
parallelism
and
similarity
:
only
attributes
which
are
salient
enough
are
redundantly
propagated
across
DFs
.
An
estimate
of
the
complexity
of
IApart
must
account
for
the
way
properties
are
selected
(
§
4.2
)
and
the
way
descriptions
are
updated
(
Algorithm
2
)
.
Property
selection
involves
checking
properties
for
contrastive
value
and
salience
,
and
updating
the
ordering
of
values
of
each
attribute
based
on
discriminatory
power
(
9
)
.
Clearly
,
the
number
of
times
this
is
carried
out
is
bounded
by
the
number
of
properties
in
the
KB
,
which
we
denote
np.
Every
time
a
property
is
selected
,
the
discriminatory
power
ofval-ues
changes
(
since
the
number
of
remaining
distrac-tors
changes
)
.
Now
,
in
the
worst
case
,
all
np
properties
are
selected
by
the
algorithm
5
.
Each
time
,
the
algorithm
must
compare
the
remaining
properties
5Only
unique
properties
need
to
be
considered
,
as
each
property
is
selected
at
most
once
,
though
it
can
be
included
in
more
than
one
DF
.
Table
5
:
Edit
distance
scores
pairwise
for
discriminatory
power
,
a
quadratic
operation
with
complexity
O
(
n2
)
.
With
respect
to
the
procedure
update-Description
,
we
need
to
consider
the
number
of
iterations
in
the
for
loop
starting
at
line
[
2.1
]
.
This
is
bounded
by
nr
=
|
R
|
(
there
can
be
no
more
DFs
than
there
are
referents
)
.
Once
again
,
if
at
most
np
properties
are
selected
,
then
the
algorithm
makes
at
most
nr
iterations
np
times
,
yielding
complexity
O
(
npnr
)
.
Overall
,
then
,
lApart
has
a
worst-case
runtime
complexity
O
(
npnr
)
.
5
Evaluation
iApart
was
compared
to
van
Deemter
's
lAboo1
(
§
1
)
against
human
output
in
the
evaluation
sub-corpus
PL2
(
N
=
405
)
.
This
was
considered
an
adequate
comparison
,
since
IAboo1
shares
with
the
current
framework
a
genetic
relationship
with
the
IA
.
Other
approaches
,
such
as
Gardent
's
(
2002
)
brevity-oriented
algorithm
,
would
perform
poorly
on
our
data
.
As
shown
in
§
3
,
overspecification
is
extremely
common
in
plural
descriptions
,
suggesting
that
such
a
strategy
is
on
the
wrong
track
(
but
see
§
6
)
.
lApart
and
lAboo1
were
each
run
over
the
domain
representation
paired
with
each
corpus
description
.
The
output
logical
form
was
compared
to
the
LF
compiled
from
the
XML
representation
of
an
author
's
description
(
cf.
Figure
1
)
.
LFs
were
represented
as
and-or
trees
,
and
compared
using
the
tree
edit
distance
algorithm
of
Shasha
and
Zhang
(
1990
)
.
On
this
measure
,
a
value
of
0
indicates
identity
.
perfect
agreement
with
an
author
.
As
the
means
and
modes
indicate
,
lApart
outperformed
lAboo1
on
both
datasets
,
with
a
consistently
higher
PRP
(
this
coincides
with
the
modal
score
in
the
case
of
-
loc
)
.
Pairwise
t-tests
showed
that
the
trends
were
significant
in
both
+LOC
(
t
(
147
)
=
9.28
,
p
&lt;
.
001
)
and
-
LOC
(
t
(
256
)
=
10.039
,
p
&lt;
.
001
)
.
lAboo1
has
a
higher
(
worse
)
mean
on
-
LOC
,
but
a
better
PRP
than
on
+LOC
.
This
apparent
discrepancy
is
partly
due
to
variance
in
the
edit
distance
scores
.
For
instance
,
because
the
Y
attribute
was
highest
in
the
preference
order
for
+LOC
,
there
were
occasions
when
both
referents
could
be
identiied
using
the
same
value
of
Y
,
which
was
therefore
included
by
IAboo1
at
first
pass
,
before
considering
disjunctions
.
Since
Y
was
highly
preferred
by
authors
(
see
Table
4
)
,
there
was
higher
agreement
on
these
cases
,
compared
to
those
where
the
values
of
Y
were
different
for
the
two
referents
.
In
the
latter
case
,
Y
was
only
when
disjunctions
were
considered
,
if
at
all
.
The
worse
performance
of
lApart
on
+LOC
is
due
to
a
larger
choice
of
attributes
,
also
resulting
in
greater
variance
,
and
occasionally
incurring
higher
Edit
cost
when
the
algorithm
overspeciied
more
than
a
human
author
.
This
is
a
potential
shortcoming
of
the
partitioning
strategy
outlined
here
,
when
it
is
applied
to
more
complex
domains
.
Some
example
outputs
are
given
below
,
in
a
domain
where
COLOUR
sufficed
to
distinguish
the
referents
,
which
had
different
values
of
this
attribute
(
i.e.
an
instance
of
the
VDS
condition
)
.
The
formula
returned
by
lApart
(
10a
)
is
identical
to
the
(
LF
of
)
the
human-authored
description
(
with
Edit
score
of
0
)
.
The
output
of
IAboo1
is
shown
in
(
10b
)
.
As
a
result
of
IAboo1
's
requiring
a
property
or
disjunction
to
be
true
of
the
the
entire
set
of
referents
,
COLOUR
is
not
included
until
disjunctions
are
considered
,
while
values
of
size
and
orientation
are
included
at
first
pass
.
By
contrast
,
IApart
includes
COLOUR
before
any
other
attribute
apart
from
TYPE
.
Though
overspecification
is
common
in
our
data
,
iAboo1
overspecifies
with
the
'
wrong
'
attributes
(
those
which
are
relatively
dispreferred
)
.
The
rationale
in
IApart
is
to
overspecify
only
if
a
property
will
enhance
referent
similarity
,
and
is
suficiently
salient
.
As
for
logical
form
,
the
Conjunctive
Normal
Form
output
of
IAboo1
increases
the
Edit
score
,
given
the
larger
number
of
logical
operators
in
(
10b
)
compared
to
(
10a
)
.
6
Summary
and
conclusions
This
paper
presented
a
study
of
plural
reference
,
showing
that
people
(
a
)
partition
sets
based
on
the
basic
level
type
or
category
of
their
elements
and
(
b
)
redundantly
propagate
attributes
across
disjuncts
in
a
description
,
modulo
their
salience
.
Our
algorithm
partitions
a
set
opportunistically
,
and
incorporates
a
corpus-derived
heuristic
to
estimate
the
salience
of
a
property
.
Evaluation
results
showed
that
these
principles
are
on
the
right
track
,
with
sig-niicantly
better
performance
over
a
previous
model
(
van
Deemter
,
2002
)
.
The
partitioning
strategy
is
related
to
a
proposal
by
van
Deemter
and
Krah-mer
(
2007
)
,
which
performs
exhaustive
search
for
a
partition
of
a
set
whose
elements
can
be
described
non-disjunctively
.
Unlike
the
present
approach
,
this
algorithm
is
non-incremental
and
computationally
costly
.
lApart
initially
performs
partitioning
based
on
the
basic-level
type
of
objects
,
in
line
with
the
evidence
.
However
,
later
partitions
can
be
induced
by
other
properties
,
possible
yielding
partitions
even
with
same-TYPE
referents
(
e.g.
the
blue
chair
and
the
red
chair
)
.
Aggregation
(
the
blue
and
red
chairs
)
may
be
desirable
in
such
cases
,
but
limits
on
syntactic
complexity
of
NPs
are
bound
to
play
a
role
(
Ho-racek
,
2004
)
.
Another
possible
limitation
of
IApart
is
that
,
despite
strong
evidence
for
overspeciica-tion
,
complex
domains
could
yield
very
lengthy
outputs
.
Strategies
to
avoid
them
include
the
utilisation
of
other
boolean
operators
like
negation
(
the
desks
which
are
not
red
)
(
Horacek
,
2004
)
.
These
issues
are
open
to
future
empirical
research
.
7
Acknowledgements
Thanks
to
Ehud
Reiter
and
Ielka
van
der
Sluis
for
useful
comments
.
This
work
forms
part
of
the
TUNA
supported
by
epsrc
grant
GR
/
S13330
/
01
.
