Nonmonotonic Inheritance and Generic Reflexives David S. Touretzky

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From: AAAI-88 Proceedings. Copyright ©1988, AAAI (www.aaai.org). All rights reserved.
Nonmonotonic
Inheritance
and Generic
Reflexives
Richmond H. Thomason
Intelligent Systems Program
University of Pittsburgh
Pittsburgh,
PA 15260
David S. Touretzky
Computer Science Department
Carnegie Mellon University
Pittsburgh,
PA 15213
Generic reflexive statements
such as Elephants
have traditionally
been formalized
using
dove themselves
purposes
some variant
coreferentiality.
of predicate
logic, with variables
to mark
We present a radically different semantics
is presented
here.
The need for alternative
for reflexives,
based
limited
Abstract.
extension
system
on nonmonotonic
to Touretzky’s
can derive
as statements
predicate
about
logic-based
use variables;
human
inferential
new generic
this
ordering.
And unlike
our formalism
Our
as well
of a non-classical
for analyzing
commonsense
are common
in the world’s lanlinguistic
theories subsume reflex-
but
no independent
meaning,
other expressions,
thereby
are meaningful.
The leading
current
tics of reflexives’
no human
linguistic
language
in some way to
to larger units that
theories
to interpret
uses variables
marking
“logical
at surface
forms”
This
be
Though
are introduced,
they
that contain them.
however,
genforms like the
morphology,
to say whether
is a deep
linguistic
our only
having
one semantic
a logical
theory
that
mathematical
Sentences
be formalized
(Many
z)(Politiciun
as in En-
notations
discovery
theory
was originally
rather
between
languages
the
encode
or an artifact
of
of reflexivizationdesigned
than natural
to explain
language.
For
difficulties
have
Bowever,
Many
relatively
quantifier
call
natural
power.
like Most
politicians
using forms such as
z --f honest
CC)
led to a theory
of generalized
conservative
are totally
extensions
inadequate
pbzlrul, and so can’t
generic
to logical
such
for handling
deal
as a
what
with
sen-
can’t be used as they
formalisms
in interpreting
language because they are so limited in expressive
This paper doesn’t offer a solution
to the general
problem,
but we do show that we can account
for systematic interactions
between generics and reflexives,
using
techniques
from nonmonotonic
inheritance
theory.
This
suggests an alternative
representation
according
to which
reflexives-though
bound
still
to a relation
anaphoric
because
by appearing
they
in a path
must
be
containing
a
single relational
symbol R-seem
to resemble
individual
nodes in many ways, and to have a greater
measure
of
semantic
independence
than the variables of logical representations.
2
Structure
Figures
1 and
appear
in the
nodes,
of the Paper
2 contain
paper.
[Fahlman
representing
all the
network
Our graphical
19791. There
individuals
primitives
that
notation
is a variare several kinds of
(Clyde),
classes
(elephant),
instances
of the term “self” (denoted by o), and instances
of “other” (denoted
by 0).
There are also several kinds
of links.
IS-A
and
information,
and Clyde
is not a herbivore.
links (3
links
IS-NOT-A
taxonomic
tional
‘See [Thomason 19761 and [Th omason 19831 for the Montague
Grammar approach, and [May 19851 for the Government-Binding
approach.
by the
quantifiers2
ant of NETL
the discrepancy
form and the way in which human
reflexives
level-
watch is self-winding.
It is hard
logical
or in the verb
so-
must
a sentence.
Human languages
that mark reflexive,
erally do so either with special pronominal
themselves,
of the semanreflexives,
“co-referentiality”
in the course of parsing
differ on how these variables
theories
agree in producing
(along
have
are bound
contributing
use variables
or indices
these constructions
as expressions
that
introduced
glish
is intensified
logic to cope with the phenom-
language.
stand as an alternative
ivization under anaphoru, treating
with expressions
like each other)
English
such
to have alter-
One such alternative
theories
of first-order
can’t
be useful
of reflexive.
tences like Elephants
are gruy.3
Nonmonotonic
semantic networks
Reflexive
constructions
guages.
Contemporary
variables
and
linguists
Motivation
since
ability
are honest
it would
theories
ena of natural
knowlreasoning
phenomena.
1
of comparison,
semantic
the leading
does not
to ac tual
in structure
of this work for AI is
it closer
significance
of the benefits
its demonstration
and an
statements
approaches,
brings
edge representation
distance
reflexive
individuals.
The
languages.
inheritance
native
and $)
such
(-t
as that
Positive
represent
binary
and
#+) express
elephants
are gray
and negative
relations
rela-
between
2For example, the work of Altham [1971], and van Benthem &
ter Meulen [1985].
3See [Carlson 19821 for detailed arguments.
Touretzky
and Thomason
433
classes
The
or individuals,
asertion
themselves
2 indicates
celebrities
royal
by a $;
like gray things.
elephants
link
from
to a 0 (read “self”) node.
as a dashed line in network
an “other”
term
1 that
is expressed
phant node
link, drawn
nects
such as Herbivores
in Figure
node to its referent.
that
opera
stars
other
than
themselves.)
celebrities”
is written
“other
do not like
the royal
For example,
admire
other
ele-
A fifth type of
notation,
conFigure
celebrities
In path
notation
(i.e.,
the
@ : c.
3
Notation
Let
+
and
links.
Let
denote
nonmonotonic
and F
denote
nodes to their
Taxonomic
paths
are
such
as ~1 +
composed
purely
y-
over
individual
then z +
P
9
taxonomic
Elephant
paths,
or,
and
bind
IS-A and/or
of abutting
links,
of
“other”
x4.
Positive
while
negative
link at the end.
Taxonomic
and class nodes; they contain
no instances
of 0 or 0.
Lowercase
Greek letters
Gray Thing
Herbivore
that
~2 ---f x3 f,
of IS-A
paths include
an IS-NOT-A
paths contain only individual
IS-NOT-A
positive
I’ is a collection
plus the links
referents.
paths are sequences
links,
and
IS-A
nonmonotonic
A network
negative
relational
links.
these four types of links,
IS-NOT-A
Likes
ft
2
such
as a and
r will
range
in the
degenerate
case,
single
or class nodes, or the null path.
If Q is null
u -+ y should be read as x ---f y, and x ---f c j+ y
should be read as z f, y.
The notation ~1 3 . . . -+ xn refers to a path of length
whose ith element is zi. Other occurrences
variables
do not imply a continuous
chain
Likes
P
Royal
Elephant
ample,
-0
case
\
9
P
Figure
don’t
1: Herbivores
like themselves.
like gray things,
that
elephants
They
------->
... +
Celebrity
and
paths
taxonomic
paths,
Figure
paths
written
the
any
nodes
of form
yl,
where
5
... t
yi
respectively,
d -% 5 or 0
form
th e 3
$
as ~1 -+
link may
be
u and T must be positive
ym (or x,
the
8
relational
ym) must
path
E
+
be
T +
e + T t
C, which says that Ernie is
royal elephants
are elephants,
elephants
herbivores
gray, royal elephants
like gray things,
are elephants
(again),
royal elephant,
so Ernie likes Clyde.
The definition
of inheritability
governs
Movie
Star
in common
notations,
in expanded
... t
and x,
e 3 h 3
g +
a royal elephant,
Rock
Star
a path
. . . ----f ym and ? = ym +
1 generates
are herbivores,
first
backward
Tl le components
by $;.
whose
it is not necessarily
u has
are
often
R
Xn ----f ym +
in I’.
denotes
~~-1.
r = yr +
are
replaced
x,
subsequence
Relational
‘i.
CT+
are x1 and z,;
to be the forward
for the same path.
... +
0
the
We define
but royal
x1 3
elements
with 22 +
@
Ernie
Clyde
the path
and last
n
of subscripted
of xi’s; for ex-
elephants
are
and Clyde
is a
the way paths
may be extended
to form new paths.
A set of paths @ is
perfect iff every one of its elements is inheritable
in @ and
no path
Beverly
sions
ofr.
Frank
not in @ is inheritable
of a network
Finally,
Figure
don’t
2:
Opera
admire
The
next
stars
admire
other
celebrities,
but
they
rock stars.
few sections
introduce
a notation
for inheri-
tance paths and extensions
(nonmonotonic
theories),
followed by axioms for nonmonotonic
multiple
inheritance
with relations.
reflexive
with
and irreflexive
an evaluation
reflexives,
434
We will then extend
statements.
of the
The
inheritance-based
and some linguistic
Knowledge
this system
Representation
observations.
paper
to handle
concludes
approach
to
if K: is a path,
first link removed,
removed.
4
in a.
then
We now present
a nonmonotonic
and
to that
[Touretzky
of [Touretzky,
with
is K with
is K with
multiple
individuals.
et ad. 19871,
ward reasoner,
supersets
the
the last link
Inheritance
tem
lar
the ezten-
perfect
ButFirst
and ButLast
Taxonomic
for classes
We define
I’ to be the minimal
19861.
the system
coupled
The
inheritance
definition
In the
terminology
is a credulous,
extensions.
sys-
is simi-
But
of
down-
it uses
OE
which Sandewall
on Touretzky’s
path preemption,
an improvement
state
only
the axioms
the
negative
path
appropriate
Basis
for inheritability
axioms
substitution
step:
x +
Induction:
The
[1986]
original
can
of positive
be derived
from
and “ft”
links.
of “+”
y is inheritable
path
has proposed as
definition.
We
paths;
these
by
in @ iff x -+ y E @.
K = x1 --+ . . . +
ButFirst
E ip.
T2.
ButLast
E a.
T3.
There
is no path x1 +
T4.
There
is no w such
notions
of the
tradiction
both
that
E (a. (Contradiction)
xl
classic
of contradiction
nonmonotonic
keeps
being
paths
present
lows subclasses
+
r1 ---f w --f r2 +
and preemption
Con-
conflicting
conclusions
from
extension,
example.
as in Reiter’s
Preemption
the properties
from superclasses,
even in the presence
links.
See [Touretzky
et al. 19871 and [Horty
If Fred
crook,
there
dislike
Dick.
time
then
return
that
cept
for the use of off-path
Ethering-
ton,
who with
Reiter
preemption.
David
was the first
logic
to translate
[Etherington
recently produced a version of this system
as well [Etherington
1987131.
Basis
step:
x -% y is inheritable
ButFirst
E @.
R2.
ButLast
E @.
R3.
There
is no path
x1 ---f u $
in default
... +
5; t
tax1987a],
in Cp iff x 5
Induction
step: The path K: = x1 +
. . . + yr is inheritable
in @ iff:
Rl.
logic
y E a.
Z, -% ym t
There
are no w, w’ such that
X~ E ip, yr
W F
+
ri
--f
x:1 ---f rl +
20’ +
~1 or xn,
respectively,
w +
that
and similarly
71 or 74
(Preemption)
Fred
will like
of contradictory
relational
but Fred dislikes gray things.
elephants
because
directly,
hand,
double
such
are derived
back
like gray
and
elephants,
the
section,
in greater
as John
and
detail.
is a philoso-
ordinary
we can
Elephants
relational
For example,
are herbivores
things
hence
from
on themselves.
they’re
yr = xi for some
6.1
plicit
The
following
which
in
and are gray, from
derive
Elephants
like
The
like themselves.
lat-
i, 1 < i 5 n.
eflexive
rule
creates
can be inherited
Paths
a new implicit
reflexive
path
by lower nodes:
Let K be a relational
path of form xl --, . . . + x, 3
ym + . . . + yl where x1 = yi . Then the implicit reflexive
path
K t
SRl.
ButFirst
E a.
SR2.
ButLast
E a.
SR3.
There is no path
diction)
zr -+ u fi
5 t
yl E @.
SR4.
There is no path
diction)
x1 ----f Q $
7
0
0
Notice
present
an
is inheritable
paths
is:
Fred
that
“other”
green
the
in Qi. The
in Q iff:
things,
infer
can still
rule
Amazon
parrots
Amazon
infer
does
reason
statement.
and Amazon
can’t
An example
Readdefini-
section
to the discussion
the definitions
1, since elephants
72 +
may be null and w’ may equal yi or ym, respectively.
likes animals
statements.
with the preceding
These paths
confuse themselves.
R
. . . ---f x, ---f 0. Implicit
reflexive paths,
xi +
Herbivores
74 --) ym E a’, and
w’ E @‘, where 71 or r2 may be null and w may
equal
reflexive
(Contra-
y1 E <p. (Contra-
diction)
R4.
proceed
“self”
other
means
into default
an elected
ter conclusion
would be written
e ---+ h 3 g t e t 0.
Implicit
reflexive paths take the general form zr + . . . +
R
xn --) ym + . . . t
y1 + 0, where the doubling
back
relations.
19861, ex-
Ray
and Dick
and in it Fred does not
to skim this and the following
here to study
are of form
on the
Figure
Inheritance
inheritance
citizen
and philosophers
in-
We next present inheritance
axioms for binary
Again, this definition
is similar to [Touretzky,
onomic
of a relational
path is Citicitizens don’t dislike elected
Statements
through,
mention
pher,
would
et al. 19871
two
extension
There will be two kinds of reflexive paths in our system. Explicit
reflexive paths are derived from statements
paths
of redundant
These
each other.
is a gullible
tions are advised
first
gray.
in the same
is only one extension,
Reflexive
al-
and examples.
Relational
they contradict
they’re
appear
An example of preemption
zens dislike crooks, but gullible
is what
they
herit
5
are the
definition.
with
to override
for more details
because
never
ers who are not yet comfortable
inheritance
in the same
Nixon/pacifist
can
We are now ready to introduce
r f+ x,
(Preemption)
The
like them
paths
because
6
x+1
E Q, and w f, x, E a, where 71 or 72 may
be null, and zu may equal x1 or ~~-1, respectively.
heart
he won’t
reasoning
crooks.
xn is inheritable
in @ ifX
Tl.
other
Amazon
not
is that
For
parrots
parrots
E de. (Contra-
require
K itself
to be
K can be preempted
example,
given
are parrots
don’t like other
parrots
t
and
Amazon
like Amazon
by
Parrots
like
are green,
parrots,
parrots,
but
we
we
like themselves,
In one extension
animals;
in the
Tour&&y
and Tbomason
435
6.2
Inheritance
Let K be a reflexive
R
-
xn
ym
explicit
+
of Reflexive
path,
... +
reflexive
i.e.
y1 +
path;
Paths
a path
otherwise
of reflexive
To allow a reflexive
to be preempted
relational
link,
preempting
d -+ x,
we require
relational
E a.
Induction
is reflected
x 3
yr t
direct
link x,
path.
below.
by an ordinary
and tail nodes
in clause
x1 +
S5 below.
in <P iff x 3
K = x1 +
m possibly
-% 0;
path
See
Irreflexive
Let
2 JJi @ : y mean
y must
struct
otherwise,
. . . -+ x,
3
ym t
is a
with x1 # yr) is inheritable
stars
E ip.
... t
s2.
ButLast
E a.
gray things,
ate implicit
s3.
There
is no x1 ---) CT$
s4.
There
is no w such that
@,
---) 71 -
and w $;
statement.)
s5.
There
72 -
0
are no ~1,202
w2 +
73 -
’+
73
6.3
ordinary
Statements
72 +
by explicit
such
that
E a,
x1 +
7; -
In order to make the individual
2,
by more
about
R
-
If a *
Q -+ r +- @ E @, then
inheritable
in @.
In Figure
1 > this axiom derives
Clyde from the inherited
path Clyde
6.4
Modification
R
-
a ---f (T 4
r t
Clyde does not like
does not like himself.
Relations
of a conlike gray
things but Royal elephants
we should
relations
by adding
do not like themselves,
like royal elephants.
To achieve
the rule for inheriting
ordinary
an additional
are still free to infer the slightly
Royal elephants
Knowledge
like other
restriction,
more restricted
royal elephants.
Representation
R5.
path
back
... -
x,
p > 0.
is of
5
@ : c),
star
Beverly
admires
is generated
on itself.
In Figure
Bev-
(hence
a
Frank
when an ordi-
Implicit
... t
zp t
and elephants
paths for both
love other
(o 5
is a movie
that
paths
take
%1 ‘@:ym
1, since
+
herbivores
love
are gray herbivores,
we generElephants
love themselves
and
The
elephants.
K be a path
Irreflexive
of form
xi
+
~1 + y, where y = x1 and
individual.
Then the implicit
xn 3
zp +
... t
~1 t
ORl.
ButFirst
E Q,.
OR2.
ButLast
E a.
OR3.
There
latter
path
is written
Paths
... +
x,
-% zp t
... t
y is a class rather than an
irreflexive
path ~1 --f . . . -
@ : y is inheritable
in Q, ifE
But
we
is no path
x1 +
c $;
?- t
y E @. (Contradic-
tion)
OR4.
There
is no path
x1 -+ (T $
71 t
@ : i-2 t
y E Q.
(Contradiction)
As was the case with implicit
require
to Ordinary
conclude
Implicit
Let
a is
A reflexive
statement
should block inheritance
tradictory
ordinary
relation.
Thus, if Herbivores
not infer Royal elephants
this behavior
we modify
7.1
“self”
agree with its statements
about a, we add the following
axiom. Note that it is an implication,
not an equivalence:
SI.
con-
path
wr $
Individuals
a’s statements
irreflexive
E
0),
7-i --j
and either
y’s”
for this
[email protected]:e.
w1 -+
Wl -
wr E <p. (Preemption
relation.)
About
Elephants
reflexive
x1 ---f 71 +
ym E Q, (or m = 0),
w2 E @ or w2 +
specific
x,
w +
ym E @ (or m =
(P reemption
E a.
202 -
x1 ---f 71 +
w ---f 74 +
R to other
celebrities,
and Frank
doubles
yr , with
xn E
Forexample,
star,
11 +
72 -
statement.)
an individual,
explicit
other
irreflexive
relation
ButFirst
Xl
not
An
admire
([email protected]:ctmtF).
An implicit
nary
(Contradiction)
reflexive
“x’s are in relation
sense.
we may
Sl.
@ E a.
w +
formxl+...+x,[email protected]:y,t...tyr.
the form
7 t
71 -
ym E @, and w $; @ E @.
Statements
be a class,
to make
celebrity),
in @ ifE
436
7
Node
x1 -
7; +
w -
by explicit
erly is an opera
@ E a.
0, in which case there
7; -
(Preemption
if opera
The path
0 (with
of the
for an explanation
forthcoming]
@ is inheritable
step:
... t
implicit
is no w such that
@, Xl -
K is an
appears
link to be on the same
This
step:
paths
the head
[Touretzky
& Thomason,
of why this is necessary.
Basis
0 then
it is an
The rule for inheritability
path
There
of form x1 ---r . . . ---f
If m =
0.
R5.
7.2
K to be present
in a;
Inheritance
reflexive
it could
paths,
we do not
be preempted.
of Irreflexive
Paths
The 0 node never stands
nected to a node indicating
alone; it always appears
conthe referent of the word “other.”
To simplify
below,
ture
the definition
0 : y as a single
[email protected]:y)
x,
we will treat
In particular,
the struc-
ButLast(a
2
isaZF.
Let K be a path
21 +
node.
O:ym
-% @:ym.)
+
of form x1 ---f . . . +
.. . +
The
path
statement,
01.
ButFirst
E <p.
02.
ButLast
E a.
y1.
x,
(If p = 0 there
K: is inheritable
-% zp
t
is a direct
in @ iE
... t
link
03.
There is no path
diction)
~1 +
There
x1 +
u 8
5 t
y1 E a.
constructibility
(Contra-
fident
04.
is no path
0 $
71 t
@ : 72 t
yr E @.
(Contradiction)
There
05.
are no w, w’ such that
x1 +
~1 +
w +
72 -
7-i zp E Q (or, if
E a, y1 --) 71 --f w’ =
0,
then
y1
-+
7;
+
w’
---f
ri
+
ym E a), and
P
$ 8 : w’ E G’, where 7-r or 72 may be null and
w may equal x1 or x,, respectively,
and similarly
r[
or 7; may be null and w’ may equal yr or zp (or
W
ym ifp = O>, respectively.
irreflexive
statement.)
There
(Preemption
are no w, w’ such that
x1 +
by explicit
71 +
W &
w’ E a, where 71 or r2 may be null and w
and similarly
ri or
may equal x1 or xn, respectively,
r2/ may be null and w’ may equal yr or zp (or yna if
respectively.
by more
specific
then
x1 #
yr.
does
opera
due to 06.
cause
do not
Mick;
this
admire
We do no derive
Modification
Irreflexive
statements
tradictory
ordinary
like gray things,
(Non-
Beverly
admires
relations.
For example,
Wild elephants
do not like other
the inference
that
There
xn
We may
are no w, w’ such that x1 + rr + w --, 72 +
r; w’ --, 7-2’---+ ym E 4p, and
0:w’
E a.
generics
in classical
admit
first
exceptions,
order
logic.
they cannot
We therefore
a
statements
such as Elephants
are gray. We
the system by adding axioms for reflexive
tleties
in the phrasing
system
Although
there
of the new axioms
us to go into, the general
should
allowed
with
resent generic
then extended
not permit
that
started
inheritance
statements.
system
be expressed
nonmonotonic
and irreflexive
us to rep-
are some
which space does
nature
of the extended
tance
the problem
with
default
definition
1987b].
logic for-
which replaced
rules,
to filter
This
did indeed
still
relied
on
the set of exten-
was necessary
override
dis-
to reflexive
default
inheritance,
of our new system
to ensure
superclasses.
into default
A similogic would
to be straightforward.
Another
advantage
it does not
of our
require
path-based
logic-based
ive pronouns
map
of reflexives.
and the phrase
paths
by extracting
Elephants
Reflex-
“other
may be translated
the first
The
like themselves.
is
to constrain
mapping between inwhich does not exist
treatments
to @ nodes,
Inheritance
sentences
formulation
the use of variables
There is a natural
and surface structure
for predicate
node,
interior
y’s”
to En-
the relation,
g
t
e t
of the path
@ as
serves
as an argument
or justification
for the statement.
In conclusion,
there is no a priori reason why the rich
structure
of human language should
predicate
logic-based
representation.
developed
to describe mathematics.
power of classical
modal operators,
map conveniently
to a
Logic was originally
One can increase the
logic by adding nonstandard
and extra truth values, but
other formalisms
may in some
We find path-based
formalisms
cases prove more natural.
convenient
for inheritance
reasoning,
of reflexives
than
9
and their
logic- based
Some
treatment
more
natural
formalisms.
Linguistic
There
are two possible
other
word “other.”
of extensions.
Etherington’s
notation
[Etherington
the inferential
of preemption)
relational
distance
subclasses
glish
of extending
statements.
of ordinary
formalisms.
for them as well, since we
(the determiner
and irreflexive
that
semantic
will be valuable
ordering
stars detest
be clear.
the existence)
of
Observations
sub-
pretation
One thing we have not yet done is prove the constructibility (or at least
have solved
expressive
quantifiers,
Discussion
Since
than current
and the last node, as when we read e ---f h 2
E a’, y1 -
W p+
8
ele-
Wild elephants
are no instances
network
power
maps to @:y.
if Herbivores
This is accomplished
by R6 below.
like elephants.
still infer Wild elephants like themselves.
R6.
of con-
even if there
pressive
co-referentiality.
heritance
paths
can also block the inheritance
but
be-
Beverly
about classes
systems
based
This difference
becomes
more
are added to the language,
be-
like themselves,
Our formulation
appear
07.
relations
reflexive
statements.
From Herbivores
like gray
for example,
we can derive the generic conclusion
lar translation
Beverly
of preemption
constraint,
irreflexive
to operate
within a
logic has greater ex-
sions
to Ordinary
we want to block
phants,
stars,
is an instance
of the non-coreferentiality
7.3
rock
and
ordi-
We are con-
elephants
in the network.
Some researchers
may still prefer
default logic framework,
since default
that
stars
not admire
explicit
things,
our inferential
coreferentiality.)
Since
of reflexive
only
19861.
cause relational
paths that double back on themselves
can
generate
reflexive paths even when a network contains
no
our path-based
yr are individuals
containing
to constructibility.
on default
logic cannot.
apparent
when reflexives
mulation
relation.)
If x1 and
07.
(Preemption
addition
no obstacle
Elephants
w + 72 +
xn E a, y1 71 w’ r; zp E @ (or, if
p = 0, then yr --f ri + w’ + r.$ --) yrra E a), and
P = 0),
ordinary
that
presents
for networks
was given in [Touretzky,
Our system can derive new statements
as well as about individuals.
Inheritance
xn
06.
proof
nary relations
However,
a
of the sentence
depending
other
which
than
is that
himself
each
rock star
or herself.
Touretzky
Rock
on the scope of the
We have so far been using the narrow
of “other,”
all celebrities
interpretations
celebrities,
This
and Thomason
interdetests
is imple-
437
mented
by clause
07
in the definition
of inheritability
for
irreflexive
paths.
The
alternate,
broad
interpretation
Rock stars
detest
other
celebrities
is that
rock stars
detest
celebrities
other than rock stars. We will not formalize this
second interpretation
here, but it appears straightforward
to handle.
mixed
The
two
uses
by introducing
of “other”
a new node
can
type
even
be inter-
to denote
broadly
scoped “other .” Note that the distinction
between narrow
and broad scope disappears
when the origin of the relational
link is an individual,
can only mean
musicians
while
e.g.,
Trombone
Hurry
“musicians
players
is jealous
other
are jealous
of other
than
of other
himself,”
is
musicians
ambiguous.
Similarly,
for relational
ence the same
sense,
e.g.,
elephants
class,
e 2
other
In English
links whose head and tail refer-
only the narrow
@ :e could
than
one can substitute
compare
that
Elephants
the expression
of a relational
love other
of the use of “other”
part of the formal
system
requires
membership.
a subset
path
@ : c means
For
“politicians
intimidate
the
that
true
any politicians
English
networks
Finally,
actually
semantics
to require
accompanied
is not
Politicians
that
crooks
by imposing
any
link
of form
by a link x ---f y, unless
we acknowledge
that
We can get
a restriction
x 5
on
0 : y be
x = y.
our account
of “other”
is
far from complete.
For example,
“other” has an existential
interpretation
as well as the universal one we have been using.
A sentence
means
like Roger
some women
who is not his wife.
sense is appropriate,
For some speakers,
other
fools
than
Semantics
around
with other
women
his wife, not every
woman
mainly
determines
which
but there may also be syntactic
cues.
Elephants
love other elephants is pref-
erentially
understood
as an existential
because they expect
the universal interpretation
to be expressed
Elephants love
each other.
Acknowledgements
This research
dation under
to Jeff Horty
was supported
grant number
for helpful
by the National Science FounIRI-8700705.
We are grateful
discussions,
whose NETL
system
provided
investigation
of reflexives.
and to Scott
the original
Fahlman,
impetus
[Carlson 19821
sentences.”
Carlson,
Journal
for our
[Etherington
Knowledge
Representation
terms
of Philosophical
1987a]
Etherington,
nonmonotonic
reasoning
gence 31, pp. 41-85.
[Etherington
itance
and
D.
and
generic
Logic 11,
(1982),
1987b]
Etherington,
with
inferential
W.
systems.”
hierarchies
D. W.
“More
exceptions:
distance.”
Proc.
“Formalizing
Artificial
Intelli-
on inher-
default
theories
Seattle,
AAAI-87,
352-357.
19791
Fahlman,
E.,
S.
NETL:
a System
for
MIT
Using Real- World Knowledge.
Massachusetts,
1979.
R. H., and
[Horty et al. 19871 Horty, J. F., Thomason,
Touretzky,
D. S. “A skeptical
theory of inheritance
in nonmonotonic
87, pp. 358-363.
May.,
semantic
R.,
networks.”
Logical
MIT
Derivation.
Press,
Form:
Its
Cambridge,
Proc.
AAAI-
Structure
and
Massachusetts,
1985.
[Sandewall
19861 Sandewall,
ence rules for multiple
Proc.
[Thomason
19761
Montague
E. “Non-monotonic
inherinheritance
with exceptions.”
vol. 74, pp. 1345-1353.
IEEE
Thomason,
grammar.”
tee, ed., Academic
R.,
“Some
In Montague
Press,
extensions
Grammar,
New York,
1976,
of
B. Par-
pp. 77-117.
[Thomason
19831 Thomason,
R., “On the semantic
interpretation
of the Thomason
1972 fragment.”
Indiana
University
Linguistics
Club,
1979.
[Touretzky,
19861 Touretzky,
D. S. The Mathematics
Inheritance
Systems.
Morgan-Kauffman,
1986.
of
[Touretzky
et al. 19871 Touretzky,
D. S., Thomason,
R.
H., and Horty, J. F. “A clash of intuitions:
the current
state of nonmonotonic
multiple inheritance
systems.”
Proc. IJCAI-87,
Milan, pp. 476-482.
[Touretzky
& Thomason,
forthcoming]
Touretzky,
and Thomason,
R. II. “An inheritance-based
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Forthcoming
technical
Carnegie
Mellon
D. S.,
theory
report,
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& ter Meulen 19851 van Benthem,
A. ter Meulen, eds., Generalized
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ral Language.
438
1985.
“Generic
G.,
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of Anaphora.
pp. 145-182.
[May 19851
in general,
an individual
politihimself.”
It doesn’t
are crooks.
J., A Grammar
[Aoun 19851 Aoun.,
Press, Cambridge,
Massachusetts,
Representing
and
Press, Cambridge,
it usually
example,
[Altham 19711 Altham,
J. E. J. The Logic of Plurality.
Methuen
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Ltd., London, 1971.
[Fahlman
@:m)
substituthat
here is that
but do not conclude
from this that
cian who is also a crook intimidates
imply
This
in English
presented
are iden-
(e 5
cannot be true unless Politicians
our current set of axioms, the link
intimidate
other crooks
are crooks is true. With
p 3
love
“each other”
mammals
with Elephants
love each other (e -% 8 : e).
tion is mandatory
for some speakers.
One aspect
makes
elephants
themselves.
when the first and last nodes
tical:
interpretation
only mean
References
of
Foris
Publications,
Dordrecht.
J. and
in Natu-
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