A Model Eliminative Treatment of
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A Model Eliminative Treatment of Quantier-Free Tree Des riptions Denys Du hier Programming System Lab, Universitat des Saarlandes, Saarbru ken du hierps.uni-sb.de Abstra t Tree des riptions are widely used in omputational linguisti s for talking and reasoning about trees. For pra ti al appli ations, it is essential to be able to de ide satisability and enumerate solutions eÆ iently. This hallenge annot realisti ally be met by brute for e enumeration. However it an be addressed very ee tively by onstraint propagation as provided by modern onstraint te hnology. Previously, we studied the onjun tive fragment of tree des riptions and showed how the problem of nding minimal models of a onjun tive tree des ription ould be transformed into a onstraint satisfa tion problem (CSP) on nite set variables. In this paper, we extend our a ount to the fragment that admits both negation and disjun - tion, but still leaves out quanti ation. Again we provide a redu tion to a CSP. While our previous en oding introdu ed the reader to set onstraints and disjun tive propagators, we now extend our arsenal with sele tion propagators. 1 Introdu tion In omputational linguisti s, theories are frequently on erned with the formulation of onstraints or prin iples restri ting the admissibility of tree representations.
- sele tion
- admits both
- between basi onstraints
- onstraint
- basi onstraints
- fun tion symbol
- onstraint satis
it
A
represen
Mo
is
del
in
Eliminativ
a
e
ersion.
T
A
reatmen
b
t
e
of
with
Quan
general
tier-F
1992;
ree
1998),
T
f
ree
f
Descriptions
ter
Den
tree
ys
to
and
hier
negation
Programming
rules.
System
e
Lab,
ree-Adjoining
Univ
ersit
seman
at
des
literals
Saarlandes,
n
Saarbr
n
uc
-ary
k
through
en
to
y
ha
T
on
ree
Garden
descriptions
2000),
are
tribute
widely
for
used
for
in
set
as
linguistics
union,
for
aried
talking
Grammars
and
w
reasoning
1999),
ab
e
out
1995;
trees.
ecied
F
W
or
of
y
applications,
:
it
ariables
is
sym
essen
relation
tial
:
to
the
b
formed
e
the
able
b
to
F
to
satisabilit
and
y
.
and
sho
en
al.,
umerate
ed
solutions
t
b
tly
problem
.
hier,
This
(Duc
ed
hallenge
Set
form
tly
b
The
e
oth
met
b
dominance
y
less
brute
es:
force
relations
en
C
umeration.
tation,
Ho
h
w
as
ev
D-T
er
y-Shank
it
b
al.,
b
and
e
undersp
addressed
of
v
biguities
ery
(Musk
eectiv
et
ely
for
b
of
y
t
er,
t
description
propagation
as
C
pro
x
vided
x
b
:
y
where
mo
no
dern
tree.
ol
t
the
x
hnology
x
.
:
Previously
expresses
,
de
w
x
e
the
studied
f
the
of
des
e
x
fragmen
n
t
of
essen
tree
e
descriptions
satisabilit
and
solutions
sho
w
the
ed
w
ho
to
w
(Koller
the
w
problem
e
of
ho
nding
e
minimal
ers,
mo
t
dels
transformation
of
t
a
hier
1999;
e
tree
2000).
description
and
e
b
e
op
transformed
erators
in
to
a
remains
ell-
t
t
satisfaction
expressivit
problem
tial
(CSP)
applications
on
ecifying
nite
of
set
language
v
t
ariables.
erators
In
e
this
olean
pap
merely
er,
erators
w
e
from
extend
b
our
tersection,
in
t
to
v
the
domains
fragmen
T
t
and
that
ree
admits
(Vija
b
er,
oth
Ram-
negation
o
and
et
1995;
tion,
hier
but
Thater,
still
for
lea
ecied
v
tation
es
scop
out
am
quan
in
tication.
Again
ens,
w
Egg
e
al.,
pro
and
vide
undersp
a
descriptions
discourse
to
(Garden
a
and
CSP
ebb
.
1998).
While
tree
our
previous
a
of
ding
x
in
tro
and
:
the
(
reader
1
to
:
set
x
)
ts
v
and
denote
des
e
the
propagators,
The
w
b
e
C
no
notates
w
dominance
extend
and
our
:
arsenal
(
with
1
:
propagators.
x
1
)
Intr
that
oduction
no
In
denoted
y
linguistics,
is
theories
from
are
n
frequen
tly
and
with
daugh
the
no
form
denoted
ulation
y
of
1
x
ts
.
or
or
applications,
is
the
tial
admissibilit
b
y
able
of
tree
y
represen
nd
tations.
of
A
descriptions
large
tly
While
of
satis
