Embedding DRT in a Situation Theoretic Frmnework
Alan W Black
Dept of Artificial Intelligence, University of Edinburgh,
80 South Bridge, Edinburgh EII1 tHN, UK.
awb@ed, ac, uk
S T a n d Computation
Abstract
This paper proposes the use of situation theory as a
basic semantic formalism for defining general semantic theories. ASTL, a computational situation theoretic
language, is described which goes some way to offering
such a system. After a general description of Discourse
Representation Theory an encoding of DRT in ASTL is
given. Advantages and disadvantages of this method
are then discussed.
Topie: computational formalisms in semantics and discourse
Introduction
T b e pnrpose of this paper is to show how a computational language based on situation theory can be
used as a basic formalism ill which genera] semantic
theories can be implemented. T h e r e are m a n y different semantic theories which, because of their different notations, are difficult to compare. A general
language which allows those theories to be implemented within it would offer an envirolnnent where
similar semantic theories could be more easily evaluated.
Situation T h e o r y (ST) has been developed over
the last ten years [2]. Much work has been done in
both tlle formal aspects of situation theory and its
use in natural language semantics (situation semantics), however so far little work has been dram ill its
c o m p u t a t i o n a l aspects. It is the eventual goal of
tile work presented here to show how situation theory can be used c o m p u t a t i o n a l l y and how a computational situation theoretic language call provide
an e n v i r o m n e n t ill which different semantic theories
call I)e easily compared.
Because there are so m a n y variants of ST we
must define our own here. T h e language ASTL [3]
has been defined. Althongb it uses surprisingly
few features of situation theory, it seems powerful enough to act as a basic language for semantics. It has been considered that somc extension
to "classical" feature structures be m a d e and use
those to encode semantic forms. Features systems
a u g m e n t e d with set vahms, eyclicity and other extensions m a y be powerful enough but the m e t h o d
described here takes an existing semantic theory
and refines it rather than building a new one.
This paper is ba.sically split into two sections.
Tlw first discusses how ST can be used in a computational system, and introduces the language ASTL.
T h e second half of this paper discusses Discourse
Representation T h e o r y ( D R T ) as a theory in itself
and shows how it can be encoded with ASTL.
AcrEs DECOLING-92, NANTES,23-28 Ao~r 1992
1 l 16
T h e view according to situation theory is t h a t parts
of the "world" can be described as situations. Situations support facts. Facts can be true, false, or
undefined in some situation. A fact's truth value
m a y be different in different situations. Situations
are tirst class objects in the theory, and hence they
can be used as a r g u m e n t s to facts so that relations can be defined between situations. Situations
are useful in translations for naked infinitives (e.g.
"see") Situations make ST different from more
conventional logical theories although there have
been proposals to add situation-like objects to more
classical theories like Montagne g r a m m a r [8].
As well as situations and partiality, situation
theory offers m a n y other iutensional objects, including abstractions, types, and p a r a m e t e r s (partially determined objects). These form a rich forrealism for describing semantic phenomena. However these features alone do not constitute a computational system, with tile addition of constraints
and rules of inference we call have the basis for
a c o m p u t a t i m l a l system. T h e idea of a c o m p u t a tional situation theoretic language has been considercd elsewhere. Most notable is the language
PRosv[' [9] which offers a Prolog-like language
based on situation theory rather t h a n first order
logic. Other systems (e.g. [5]) allow the representation of situations etc. within s o m e other formalism
(e.g. feature structures) but do not use situation
theory itself as the basis for the language.
ASTL
ASTL is a language based on situation theory. It
takes a very conscrvative view of situation theory,
a d m i t t i n g only some basic parts. Although ASTL
m a y need to be extended later, it already can be
used to describe simple versions of s e m a u t i c theories (such ms situation semantics and D R T ) . Rather
than use, or extend, PROSlT it was decided to develop a new language. ASTL includes stone builtill support for natural language parsing based on
tile ideas of Situation Theoretic G r a m m a r [4] while
PRoslrr is designed more for knowledge representation than direct language processing.
ASTL allows the following basic terms:
I n d i v i d u a l s : e.g. a, b, c.
P a r a m e t e r s : e.g. X, Y, Z.
V a r i a b l e s : e.g. *X, *g, *Z.
R e l a t i o n s : e.g. s e e / 2 . Relation n a m e and arity.
i - t e r m s : consisting of a relation, a r g u m e n t s and
a polarity (0 or 1), e.g. < < s i n g , h , 1>>.
PROC. OF COLING-92, NANTES,AUG. 23-28, 1992
tylms
: consisting of an abstractioll ow!r proposi
tions. For e x a m p l e
~m3
"}Immko"-=~ |
/
[S ! S !~ < < a i n g , h , l > >
S !~ < < a o e , h , S , l > > ]
T h a t is tile type of s i t u a t i o n which s u p p o r t s
the fact t h a t h sings and h sees t h a t situation.
S i t n a t i r m s : written ,as n a m e s optionally followed
by a type. e.g.
SI::[T
$2::[S
! T !- <<rua,t,l>>].
! S !~ < < u e e , i i , S l , l > > ] .
tn addition to t e r m s there are the following sentc~tccs:
Propositions
: consisting of a situation and a
t y p e e.g.
Sitl:[S
Constraints
: are detlncd betweell i)ropositions,
d m y coasist of a proposition following by <=
lbllowed by a l i s t ofl)ropositioas. For examph~
Sltl:[S
! s !~ < < h a p p y , h , l > > ]
<~ Sitl:[S ! S !~ <<smile,it, l>>].
T h e selnantics of ASTI, (delin,~d fully ill [3]) are de
lined in t e r m s of a model consisting of individuals,
relalions, p a r a m e t e r s , s i t u a t i o n s s l i d a set coasisting of pairs of situations and facts, lnfflrmally, a
proposition is true if the denotation of the situation
s u p p o r t s all of the facts in the type. A constraint is
true if when all the propositions in the right hand
side of the constraint are true, the left han(l p r o p ( .
sition is true also. As it is currently defined ASTL
has no bailt-in delinition with respect to coherence.
t h a t is there is no built-in m e c h a n i s m that stops a
situation SUl)l)orting b a t h a fact and its dual (the
fact with the opposite p o l a r i t y )
C o a s t r a i n t s can be generalised using variabh,s.
An e x a m p l e will help to illustrate this. If we define
the folh)wing basic situation and constraint:
S i t l : [ S ) S !: <<smile,t,l>>].
* S : [ S ! S != <<happy,*Y,l>>]
*S:[S
! S )= <<smile,*Y,l>>],
hfforlnally the constrainl s t a t e s that in ally situ
ati(m where s o m e t h i n g smiles it. is also Imppy (m
tlmt s a n w situation). From the above bmsi(: a x i o m s
we can derive t h a t tile following is true:
Sitl:[S
cat(gIT123,ProperNotm)
use.of (SIT 123 ,"llartako")
T h a t is, the use of the phrase "llanako" gives rise
to a situation t h a t s u p p o r t s the facts t h a t it (the
situation) is a P r o p e r N o u n and it is a use of the
word "Hanako". We call these utterance situaiions.
As an u t t e r a n c e h a p p e n s at a particular t i m e and
location this fact should also be recorded in the
situation. In ASTL this t e m p o r a l aspect is builtin to the language. A special f o r m of constraint,
grammar rules, can Ire used to constrain u t t e r a n c e
situations~ (-;eneral constraints apply to any f o r m
of situation (utterance or otherwise) while g r a m m a r rules only apply to u t t e r a n c e situations. A
grallilllar rllle betweea !ltLel-allce s i t u a t i o n s such a.,4
! s !~ < < ~ o e , h , S , l > >
S !~ <<dance,h,l>>]
<=
j
! s !~ < < h a p p y , t , l > >
S != < < s m i l e , t , l > > ]
l l a t h e r t h a n j u s t use the linear forlns for displaying ASTL objects, an extension has been added for
OUtlmt. Based on EKN [l] ASTL objects can be
displayed a.s boxes, m a k i n g comple× objects nmch
easier to view. In this notation we write s i t u a t i o n s
its boxes with their n a m e s m a top left inset with
facts written (in a more conventional predicate arg m n e n t f o r m ) inside the box.
Using the work of C o o p e r [d] we can process
l a n g u a g e in a situation theoretic way. Situation
T h e o r e t i c G r a m m a r takes the view t h a t utterances
can be represented by situations. For e x a m p l e
AL'DASDE COLING-92, NAI~'H~S,23-28 aot~r 1992
1I 17
* S : [ S ! S !~ < < c a t , S , ~ o n t o n c e , t > > ]
<- * N P : [ S ! S !~ < < c a t , S , N o u n P h r a 8 e , l > > ] ,
*VP:[S ! S !~ < < c a t , S , V o r b P h r a s e , l > > ] .
t;tkes into accollllt t h a t the two u t t e r a n c e s i t u a t i o n s
occm next to each o t h e r It is possible to model all
of this within the s t a n d a r d constraint s y s t e m by
a d d i n g facts a l m u t s t a r t and end l)oints of utterances (in a mmihu, way t h a t l)C(_~s arc interpreted
in l'roh)g) but as one of the m a i n uses of ASTL is lang u a g e processing it w~s felt m o r e elllcient to buiht
utterance situations (and constraints on t h e m ) drr e d l y into the language.
A basic i m p i e n m n t a t i o n has been m a d e within
C o m m o n I,isp which takes ASTL dcscriplions (deftnitions, basic s i t u a t i o n s and constraints) and allows
queries to be m a d e a b o u t their sets of constraints
and I)itsic situations.
Discourse
representation
theory
Given a simple language like ASTL there is now the
question a b o u t }low it can be used in rel)resenting
other s e m a n t i c theories. D R T [7] ota~rs a representat, ion lot discourses. A discourse rcprcsenlalion
structure ( I ) R S ) is dctined at each s t a g e in a discourse describing the cllrrellt state of the analys/8.
A I)RS consists of two parts; a set of domain markrr.s, whicll can be bound to objects introduced into
the current discourse, and a set of conditions on
these markers. I)ltSs are typically written as boxes
with the m a r k e r s in the top part and conditions below. For e x a m p l e a I)RS for the u t t e r a n c e "a m a n
81liftS" iS
X
=an ( X)
l_='72 ]
T h e following description of I ) R T in ASTL is based
on lhe I ) H T definition in [6]. First we need a syntactic backbone to be able to discuss the constructi(m of a I ) R S for a discourse. As seen (briefly)
above AS'I'I, oilers a basic g r a m m a r f o r m a l i s m . T h a t
is, g r a m m a r rules are Sl)ecilled as e o a s t r a i n t s betwet'n iltterance siluatiollS,
I'ROC. OF COLING-92, NANrFs, AUG. 23-28, 1992
Given such a backbone we need to define an
aSTL representation for DRSs.
DRSs have two
parts. Discourse m a r k e r s c0.n be represenled as parallleters ill ASTI.. Ill situation theor3 p a r a m e t e r s
denote partially d e t e r m i n e d objects. P a r a m e t e r s
can be anchored to other objects as i n f o r m a t i o n
about tt~eir denotation is found. D R S conditions
arc represented by i-terms. A D R S itself is represented as a p a r a m e t r i c s i t u a t i o n - - a situation whose
type contains p a r a m e t e r s . Discourse m a r k e r s are
not explicitly listed in the 1)ITS representation. An
ASTI. representation of the I)RS for % man stags"
is
Sit34S::[S
! S != <<man,X,1>>
S != <<sing,X,l>>]
W]lerl' X is a paraoleter.
T h i s allows a siml)le s e m a n t i c s close to thai of
a conven(.ional I)RS. T h a t is an ASTL I)RS will be
truc Ior s o m e situation (i.e. a model) if there exists
an anchoring for the p a r a m e t e r s in it which m a k e
it a lype of the model-situation. A special definition will be needed for tile condition e v e r y (and
possil)ly others if extensions to basic D I ( I ' are inehMed). It m a y be better to think of the situation
nellie also as a p a r a m e t e r which gets anchored Io
the model-sitnation. Hut as the s e m a n t i c s of ASTL
relates situations n a m e s to situations (i.e. two sitm~t.ion nanles can denote the s a m e situation) flmre
is still a level of indirection.
DHSs arc objects which are related to utter
anee situations. T h e y are not themselves representations of the utterances but representations of
whal tile utterances describe.
Threading
An iml>ortant aspect of I ) R T is how a I)RS is constructed from a discourse. Here (and in [6]) we use
tile technique of threading. Tile general idea is t h a t
a DH.S gets passed through a discoarse being added
to as the discourse l)rogresses.
hi this description, a discourse consists of a
set of u t t e r a n c e situations which call In' viewed
t i m ) u g h a n u m b e r of different structural relations,
T h e tirsl is through tile relation d a u g h t e r which
defines tile syntactic s t r u c t u r e of lhe discourse as
defined by the g r a m m a r rules ( i m m e d i a t e doininance and linear precedence). Secondly the t h r e a d
rdal.ion defines an ordering of tile ntlerance situaliens used in the generation of the l)RSs. I,aslly
there are two relations, r a n g e a n d body lined ill
defining the logical structure of the discourse.
T h e t h r e a d i n g relation is a binary relation between utterance situations. We will say the first
a r g u m e n t is threaded to tile second. Each utterance
situation appears exactly once a,S t h e second argum e n t in tile t h r e a d relation (i.e. il. has exactly one
i n c o m i n g thread). T h e r e is one exeeplion, a special
situation called D S t a r t which does not have an inc o m i n g thread (it is used to represent the null context at the start of a discourse), b m does a p p e a r
as all incoming thread for one or more u t t e r a n c e
ACRES DE COLING-92, NANTES. 23-28 AOm 1992
1118
situations. T h e r e are no cycles m t h r e a d h l g but
as we shall see there m a y be more than one linked
thread of utterances within a discourse. T h e actual
construction of the t h r e a d i n g relations is discussed
later.
Each utterance situation is related to two DRSs,
through tim relations DRSIn and DRSOut. A DRSIn
D R S is tim DRSOut D R S of the i n c o m i n g thread.
Tiffs constraint can be written in ASTL o~'-;
*S:[S ! S !-<<DRSIn,S,*DRS,I>>]
<=
T S : [ T S ! TS != < < t h r e a d , * S l , * $ , l > > ] ,
* S I : [S1 ! S1 != < < D R S B u t , S I , * D R S , I > > ] .
T h e relation between the two D R S s related to an
utterance is also constrained, T h i s is a core part
of D R T . Basically the o u t g o i n g D R S contains the
s a m e i n f o r m a t i o n as the m c n m i n g D R S plus any
r e f o r m a t i o n the u t t e r a n c e adds to the discourse. In
the cruse of a proper noun u t t e r a n c e situation we can
capture this relation with the following constraint:
*S:[S
! S != < < D R S o u t , S , * D R S o u t : :
*DRSlnType k
[D ! D !~ <<name,*X,*N,l>>],l>>]
<=
*S: [S ! S != <<cat,S,ProperNotm,l>>
S !~ <<uBe of,S,*N,l>>
S != <<aem,S,*X,l>>
S != <<DRSTn,S,*DRSin: :*DRSInType,l>>]
h f f o r m a t i o n is monotonically increasing m l ) R S s as
we traverse along a thread. We are not destructively m o d i f y i n g a D R S as the discourse progresses
but constructing a new D R S which s u p p o r t s the
s a m e conditions as the i n c o m i n g DRS. T h e cons t r a i n t above f o r m s the o u t g o i n g I)RS from the
type (*DRSInType) of tile i n c o m i n g one, which will
contain all the conditions of the i n c o m i n g D R S ,
plus a new condition introducing the p a r a m e t e r for
the I)roper noun and a condition on its n a m e .
We also have tile constraint t h a t any a r g u m e n t
or relation that a p p e a r s in the conditions of a D R S
m u s t be related to s o m e u t t e r a n c e situation by the
relation sere previously ill t h a t thread. T h i s condition m e a n s t h a t a r g n m e n t s are threaded before
predicates. For e x a m p l e both the subject N P and
object N P of a s i m p l e sentence will be threaded l)efore the VP. In eontrmst in [6] tile V P c o m e s before
a object N P which m e a n s a I ) R S is created with
an a r g m n e n t in a condition which is not yet determ i n e d (i.e. a free variable).
T h e other structural relations are r a n g e and
b o d y Each d e t e r m i n e r u t t e r a n c e situation a p p e a r s
in exactly one r a n g e - r e l a t i o n and exactly one b o d y r e l a t i o n . Tile second a r g u m e n t to these relations
are utterance s i t u a t i o n s t h a t do not a p p e a r as first
a r g u m e n t s in any t h r e a d i n g relation (i.c. they are
ends of threads). Tile DRS0ut of a d e t e r m i n e r utterance situation is a flmction of the DRSIn I)I?~S
plus i n f o r m a t i o n from the r a n g e a n d b o d y related
threads, hi the e v e r y d e t e r m i n e r case tile DRSOut,
constraint is
*S:[S
! S != <<DRSBut,S,*DRSOut::
*DRSInType It
[DS ! DS != <<every,*RangeDRS,
*BodyDRS, l>>] , 1>>]
PROC. OF COL1NG-92, NANrrES, AUG. 23-28, 1992
<~
*S: [S ! S != < < c a t , S , D o t e r l a i n e r , l > >
S != < < D R S I n , S , * D R S I n :
:*DRSInTyfm,I>>
S !~ <<aem,S,every,l>>],
TS : ITS !
TS
IS
TS
IS
!=
!
}=
!
<<body,*S,*Body: :
S != <<DRSOut,S,*BodyDRS,I>>] , i > >
<<range,*S,*Range: :
S != < < D R S D u t , S , * R a n g e D R S , I > > ] , I > > ]
relation body, llence th(~ o u t p u t D R S f r o m the sentence (from the d e t e r m i n e r "a"
by the constraints
given shove) is built from tile i n c o m i n g l)tkq p l u s
lhe o u t g o i n g l)}lSs from NP1 and S (which are related to I) v i a the r a n g e and body relations).
Pronouns
and
Accessibility
While for the indrtlnite d e t e r m i n e r the DRS0ut sitsply contains all the conditions from thr DRSin,
r a n g e a n d b o d y related utterances.
Unlike other utterance sitmttions, pronouns do not
just add new i n f o r m a t i o n to a I)RS. T h e y a l s o require existence of sonre referent already introduced
in the context, q b put it s i m p l y there m u s t be a
suitable object m the i n c o m i n g I)RS t h a t the pro-
*s:[s
IIOIIn C;MI II/~LLch. A ( : o i l ( l i t i o n c a n |re w r i t t e n
! s != < < D R S U o t , S , * D R S 0 u t : :
*DRSlnType • *DRSRType •
*DRSBType, 1>>]
<=
*S: [S
;L~
S !" < < D R S o u t , S , * D R S o u t : :
*DII.SInType •
*S:[S
! S
[DS ! DS != < < i s ) * X , * Y , I > > J , I > > ]
!-<<cat,S,neter~iner,l>>
S !~ < < D R S I n , S , * D R S l n : :*DRSInType,I>>
S != < < ~ e m , S , s o m e , l > > ] ,
*S:(S
T,q: [TS !
S != < < c a t , S , P r o n o u n , l > >
S
S
S
S
TS != < < b o d y , * S , * B o d y : :
[IS ! S != <<DRSihlt,S,
*[]odyDRS : : * D R S B T y p e , i>>] , I>>
TS != <<range,*S,*Ilange: :
[S ! S != <<DRSIIut,S,
*ltangeDRS : : *DRSRType, 1>>] , 1>>] .
!=
!=
!~
!~
<<type,S,*TYPE,t>>
<<sem,S,*X,l>>
<<DRSIn, S, *DRSIn: : *DIISInType, 1>>
<<acceBsible,S,*h: :
[A ! A !~ < < * T Y P E , a Y , I > ~ ] , t ) > ] .
~Vhero *TYPE will Ire o u r o f m a l e , f e m a l e or
llow(~vcr, it. is not su/licient to sinlply
check the conditions in the i n c o m i n g l)lLq lbr s o m e
tnarkvt of the right type.
T h e a c c e s s ± b ] . e relation is also dctined over the
three(ling relations. Each u t t e r a n c e s i t u a t i o n is re}ah!d to ;t situation t h a t s u p p o r t s the facts a b o u t
which m a r k e r s are accessible at t h a t point m the
discotn'se. T h e accessible m a r k e r s for an u t t e r a n c e
situati0n U are defined (inlormally) m~ follows:
rteutex
lhH }low is t h r e a d i n g huilt? T h r g r a n H n a r rule~
sl)ecit 3' I,h(~ I)asic s y n t a c t i r st, ructurc (via Ih(,
daughl~er relations). At, the same tim(' the thread
ilig inforlllatioll can be COllStrllCLl!d. Each ilttl!rallc(!
s i t u a t i o n is related to I,wo others I)y (lie relations
n e e d mid o u t . Th(! n e e d r(!Iation id('ntities tJ.' ut
teranc( situation (either itself or on( of its daughters) which requires an i n t e r n i n g tin'end while o u t
identifies which situation is to be threaded on to the
next part of the discourse. A I I h o u g h th( n e e d and
o u t relations are d e t e r m i n e d al the tillle a grall/ill~tr rule is realised the :-tetllaI t : h r e a d , r a n g e and
b o d y relations Inay not be d e t r r m i n e d locally. T h e
u t t e r a n c e to be threaded to the n e e d of an N P can
not Ire realised until t h r NI ) is p u t in c o n t e x t tn
contrast with [6) inslea(I of i)assing up the utter
a n t e t h a t needs a I h r r a d , they i)ass down the "hi
t.erance" that is to be tlu'('a(led in. lh're w(' giv('
a }>ottolll tip definition r a t h e r 1111111 ~1.¢; ill [(i] a l o p
( [ o w n OIle.
As seen ill the (Ollstraillts above Ill(' strtlctural
[a('ts whose relations are t h r e a d , r a n g e and b o d y
ar(~ colhx:t,ed in a siUiation called T S tlelow is an
(!xanlp[(! sent, eiicc s h o w a ;is a sylll,ax tree willl the
thread relation dr~twn as arrows to show the flow
of information through the disconrs(~
These couditiolis can e~Lsily be represented by ASTL
D
,*
,nan
like,~
¢ O l l s t , r a i n Ls
ll.),.ko
in adclition, D S t a r t is threaded to D, N and NP2.
T h e m a i n discourse thread will go throngh D. T h e r e
are two other threads ending at NP1 and S. D will be
related to NP1 by the relation r a n g e and to S by the
AcrEs Dv.'COLING-92, NAbrrlis, 23-28 AO/n' 1992
If U is a noun (or propernoun) the accessible
m a r k e r s are from t h a t noun plus the accessil)le m a r k e r s li'on, the i n c o m i n g thread.
if U is the s t a r t of a t h r e a d whose end is related
to a d e t e r m i n e r by tile relation body then the
acc(,ssihl[~ m a r k e r s are those from the end of
t h a i d e t e r m i n e r ' s r a n g e thread.
if U is the' start, of a r m x g e thread, the accessible
m a r k e r s are those froln tlw i n c o m i n g thread
of (he relatrd determiner.
if U is an ind('lini).(~ d('.terminer tim accessible
nlarkers are thos(~ of the end of the b o d y
thread
if ( is an e v e r y d e t e r m i n e r I,he accessible m a r k
ers are those from its i n c o m i n g thread (i.e.
does . o r inclmh: Oar m a r k e r s introduced in
Lhe r a n g e and body threads).
otherwise the accessible m a r k e r s are those of the
incoming thread
11 19
C~iven the abow! descriptions: a syntactic backb o n e a I)RS represent, aLien, t h r e a d i n g and definition for accessibility) we can refill I)RSs for s i m p l e
(liscourses. T h e coverage is t h a t of [6]. T h i s still
allows an e x a m p l e of donkey a n a p h o r a ;is ill " e v e r y
m a n w i t h a d o ) l k e y l i k e s i t " T h e DRS0ut for the
discourse utterance situation is.
PROC. OF C(11,1NG-92, NANTES, AUG. 23-28, 1992
every(
~ith(NA1,DA1)
donkey(DA1)
mnn(MAl)
like (NA1,PN1)
is (PNI ,DA1)
)
Discussion
Although translation of DRT into ASTI, is possible
there are some important consequences. Tile semantics of an ASTL DRS, briefly described above,
requires that it is possible to tell the properties of
every object in the situation. As situations are partial it may not be defined for everything whether it
is a man or not, thus it is not possible to define "all
men." (Note, lack of information does not imply
falsity.) This is perhaps unfair to consider this as
a problem as m the standard definitions of DR?I' it
is required that the model be complete (all propertics are defined on all objects) - so it seems no
worse to require this of the situation in which we
are finding tile trnth conditions of a 1)RS. llowever
we could include further definitions for the e v e r y
relation and require that there be some resource
situation that identifies actual objects that fall in
its scope. This technique has been used by [4].
There is the question of compositionality. It
could be said that the threading relations are only
partially determined eompositionally. But this
seems exactly what the theory states and the intuition behind it. We cannot define a I)RS for a
noun phrase nnless we know what context tile NP
is ill. All that can be determined is partial definition with conditions on the context.
An important aspect of DRT is that there is a
left to right dependency on DRSs. This does not
necessarily mean that parsing must be left to right,
though normally it will be. A definition of I)RT
should inelnde this dependency and not rely on how
a implementation happens to order processing. Tile
ASTL definition does include a left to right dependency, without specifying a processing order on the
inference mechanisn].
Summary
This paper has introduced tile notion of using situation theory a.s a basic formalism in which other
semantic theories might be defined. A computational situation theoretic language called ASTL is
discussed. Sitnatlon theory is suitable as basis for a
metatheory because a representation of situations
allows the representation of higher order objects
necessary for describing other semantic theories. A
Ac-r~ DECOLING-92, NANTES,23-28 AOt3T 1992
1 120
possible translation of I)I~T in ASTL is given. The
coverage is that of [6].
This translation is interesting because first it
shows that situation theory is not some opposing
semantic theory but that it can be used ill discussing other theories, tIowever perhaps it is not
surprising that a language such as ASTL is powerful enough to give this translation. A feature system, with sets (or some definition), cycles and constraints is close to what ASTL is, but it is interesting
that these properties can be found as the basis ill a
current semantic theory without introducing a new
theory. Finally a situation theoretic description of
DRT allows extensions of DRT to use the properties of situation theory. Situations which are useful ill describing various natural language semantic
phenomena (e.g. naked infinitives) are now readily
available to be included in exteusious of DRT.
Acknowledgements: This work w~s supported by an
SEltC studentship award number 89313458. I would
also like to thank Robin Cooper, Inn Lewin and Graeme
Ritchie for comments anti guidance on this work.
References
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Theory and its graphical representation. In
Partial and Dynamic Semantics HI, DYANA
R2.I.C, Cognitive Science, University of Edinburgh, 1991.
[2] J. Barwise and J. Perry. Situations and Attitudes. MIT Press, 1983.
[3] A. Black. A situation theoretic approach to
computation semantics, forthcoming PhD thesis, 1)ept of AI, University of Ediuburgh, 1992.
[4] R. Cooper. Information and grammar. Technical Report t/.17 No. 438, Dept of AI, University
of Edinburgh, 1989.
[5] J. l"enstad, P-K. tlalvorsen, T. Langhohn, and
d. van Bcntham. Situations, Language, and
Logic. Reidel, l)ordrecht, 1987.
[6] M. Johnson and E. Klein. Discourse, anaphora
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[7] H. Kamp. A theory of truth and semantic
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[8] R. Muskens. Meaning and Partiality. PhD timsis, University of Amsterdam, 1989.
[9] 11. Nakashima, H. Suzuki, P-K. Halvorsen, and
S. Peters. Towards a computational interpretation of situation theory. In FGCS, ICOT, 1988.
PROC. OF COLING-92, NAI~rEs,AUG.23-28, 1992