Embedding DRT in a Situation Theoretic Framework

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Embedding DRT in a Situation Theoretic Frmnework

Alan W Black

Dept of Artificial Intelligence, University of Edinburgh, 80 South Bridge, Edinburgh EII1 tHN, UK.

a w b @ e d , a c , u k

A b s t r a c t

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 dis- c o u r s e

Introduction

T b e pnrpose of this p a p e r is to show how a c o m p u - tational l a n g u a g e based on situation theory can be used as a basic f o r m a l i s m ill which genera] s e m a n t i c theories can be i m p l e m e n t e d . T h e r e are m a n y different s e m a n t i c theories which, because of their different notations, are difficult to c o m p a r e . A general l a n g u a g e which allows those theories to be imple- m e n t e d within it would offer an envirolnnent where similar semantic theories could be m o r e easily eval- uated.

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 l a n g u a g e s e m a n t i c s (situation s e m a n - tics), 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 com- p u t a t i o n a l situation theoretic language call provide an e n v i r o m n e n t ill which different s e m a n t i c theories call I)e easily c o m p a r e d .

Because there are so m a n y variants of ST we m u s t define our own here. T h e language ASTL [3] has been defined. A l t h o n g b it uses surprisingly few features of situation theory, it seems powerful enough to act as a basic language for s e m a n - tics. It has been considered t h a t s o m c extension to "classical" feature structures be m a d e and use those to encode s e m a n t i c 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 s e m a n t i c theory and refines it rather t h a n building a new one.

T h i s paper is ba.sically split into two sections. T l w first discusses how S T can be used in a c o m p u - tational s y s t e m , and introduces the language ASTL. T h e second half of this p a p e r 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.

S T a n d

Computation

T h e view according to situation theory is t h a t parts of the "world" can be described as situations. Sit- uations s u p p o r t facts. Facts can be true, false, or undefined in s o m e situation. A f a c t ' s t r u t h 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 t h a t relations can be defined between situations. Situations are useful in translations for naked infinitives (e.g.

"see") Situations m a k e S T different f r o m m o r e conventional logical theories a l t h o u g h there have been proposals to add situation-like objects to m o r e classical theories like M o n t a g n e g r a m m a r [8].

As well as situations and partiality, situation theory offers m a n y o t h e r iutensional objects, in- cluding abstractions, types, and p a r a m e t e r s (partially d e t e r m i n e d objects). T h e s e f o r m a rich for- realism for describing s e m a n t i c p h e n o m e n a . How- ever these features alone do not constitute a com- p u t a t i o n a l s y s t e m , with tile a d d i t i o n of constraints and rules of inference we call h a v e 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 l a n g u a g e has been con- sidercd elsewhere. Most notable is the l a n g u a g e PRosv[' [9] which offers a Prolog-like language based on situation theory r a t h e r t h a n first order logic. O t h e r s y s t e m s (e.g. [5]) allow the representation of situations etc. within s o m e o t h e r f o r m a l i s m (e.g. feature structures) but do not use situation theory itself as the basis for the l a n g u a g e .

ASTL

ASTL is a l a n g u a g e based on situation theory. It takes a very conscrvative view of situation theory, a d m i t t i n g only s o m e basic parts. A l t h o u g h ASTL m a y need to be extended later, it a l r e a d y can be used to describe simple versions of s e m a u t i c theories (such ms situation s e m a n t i c s and D R T ) . R a t h e r t h a n use, or extend, PROSlT it was decided to de- velop a new language. ASTL includes stone built- ill s u p p o r t for n a t u r a l l a n g u a g e parsing based on tile ideas of Situation T h e o r e t i c G r a m m a r [4] while PRoslrr is designed m o r e for knowledge representation t h a n direct l a n g u a g e 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>>.

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t y l m s : c o n s i s t i n g of an abstractioll ow!r proposi tions. For e x a m p l e

[S ! S !~ < < a i n g , h , l > > S !~ < < a o e , h , S , l > > ]

T h a t is tile t y p e 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 s i t u a t i o n . S i t n a t i r m s : w r i t t e n ,as n a m e s optionally followed

by a type. e.g.

S I : : [ T ! T ! - < < r u a , t , l > > ] . $ 2 : : [ S ! S !~ < < u e e , i i , S l , l > > ] .

tn a d d i t i o n to t e r m s there are the following sen- tc~tccs:

P r o p o s i t i o n s : consisting of a s i t u a t i o n and a t y p e e.g.

S i t l : [ S ! s !~ < < ~ o e , h , S , l > > S !~ < < d a n c e , h , l > > ]

C o n s t r a i n t s : are detlncd betweell i)ropositions, d m y coasist of a proposition following by <= lbllowed by a l i s t o f l ) r o p o s i t i o a s . For examph~

S l t l : [ S ! s !~ < < h a p p y , h , l > > ] <~ Sitl:[S ! S !~ <<smile,it, l>>].

T h e s e l n a n t i c s of ASTI, (delin,~d fully ill [3]) are de lined in t e r m s of a m o d e l c o n s i s t i n g of i n d i v i d u a l s , 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 coasist- ing of pairs of s i t u a t i o n s and facts, lnfflrmally, a p r o p o s i t i o n is true if the d e n o t a t i o n of the s i t u a t i o n s u p p o r t s all of the facts in t h e type. A c o n s t r a i n t is true if when all the p r o p o s i t i o n s in t h e right hand side of t h e c o n s t r a i n t are true, the left han(l p r o p ( . sition is true also. As it is c u r r e n t l y defined ASTL has no bailt-in delinition w i t h respect to coherence. t h a t is there is no built-in m e c h a n i s m t h a t stops a s i t u a t i o n SUl)l)orting b a t h a fact a n d its dual (the fact with the o p p o s i t e 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 s i t u a t i o n and c o n s t r a i n t :

S i t l : [ S ) S ! : < < s m i l e , t , l > > ] .

* S : [ S ! S != <<happy,*Y,l>>] <= * S : [ S ! S )= < < s m i l e , * Y , l > > ] ,

hfforlnally the c o n s t r a i n l s t a t e s that in ally situ ati(m where s o m e t h i n g s m i l e s it. is also Imppy (m tlmt s a n w s i t u a t i o n ) . F r o m t h e above bmsi(: a x i o m s we can derive t h a t tile following is true:

S i t l : [ S ! 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 display- ing ASTL objects, an e x t e n s i o n has been added for OUtlmt. Based on EKN [l] ASTL o b j e c t s can be displayed a.s boxes, m a k i n g c o m p l e × objects n m c h easier to view. In this n o t a t i o n we w r i t e s i t u a t i o n s its boxes w i t h their n a m e s m a top left inset with facts w r i t t e n (in a m o r e conventional predicate ar- g m n e n t f o r m ) inside the box.

Using t h e work of C o o p e r [d] we can process l a n g u a g e in a s i t u a t i o n theoretic way. S i t u a t i o n T h e o r e t i c G r a m m a r takes the view t h a t u t t e r a n c e s can be represented by s i t u a t i o n s . For e x a m p l e

~ m 3

j

"}Immko"-=~ | cat(gIT123,ProperNotm) / u s e . o f (SIT 123 ,"llartako")

T h a t is, the use of t h e p h r a s e "llanako" gives rise to a s i t u a t i o n t h a t s u p p o r t s the facts t h a t it (the s i t u a t i o n ) is a P r o p e r N o u n and it is a use of t h e 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 p a r t i c u l a r t i m e and location this fact should also be recorded in t h e s i t u a t i o n . In ASTL this t e m p o r a l a s p e c t is built- in to the l a n g u a g e . A special f o r m of c o n s t r a i n t , g r a m m a r rules, can Ire used to constrain u t t e r a n c e situations~ (-;eneral c o n s t r a i n t s apply to a n y f o r m of s i t u a t i o n ( u t t e r a n c e 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 b e t w e e a !ltLel-allce s i t u a t i o n s such a.,4

* 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 > > ] ,

* V P : [ 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 o c c m next to each o t h e r It is possible to m o d e l all of this within the s t a n d a r d c o n s t r a i n t s y s t e m by a d d i n g facts a l m u t s t a r t a n d end l)oints of u t t e r - ances (in a mmihu, way t h a t l)C(_~s arc i n t e r p r e t e d in l'roh)g) but as one of the m a i n uses of ASTL is lan- g u a g e processing it w~s felt m o r e elllcient to buiht u t t e r a n c e s i t u a t i o n s ( a n d c o n s t r a i n t s on t h e m ) dr- r e d l y into the l a n g u a g e .

A basic i m p i e n m n t a t i o n has been m a d e w i t h i n C o m m o n I,isp which takes ASTL dcscriplions (deft- nitions, basic s i t u a t i o n s a n d c o n s t r a i n t s ) a n d allows queries to be m a d e a b o u t their sets of c o n s t r a i n t s and I)itsic s i t u a t i o n s .

D i s c o u r s e r e p r e s e n t a t i o n t h e o r y

Given a s i m p l e l a n g u a g e like ASTL there is now t h e 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 represen- tat, 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 s t a t e of the analys/8. A I ) R S consists of two p a r t s ; a set of domain mark- rr.s, whicll can be b o u n d to o b j e c t s i n t r o d u c e d into the current discourse, and a set of conditions on these m a r k e r s . I ) l t S s are typically w r i t t e n as boxes with the m a r k e r s in the top part and c o n d i t i o n s be- low. For e x a m p l e a I ) R S 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 syn- tactic backbone to be able to discuss the construc- ti(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 be- twet'n iltterance siluatiollS,

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G i v e n such a b a c k b o n e we need to define an aSTL representation for DRSs. D R S s have two parts. Discourse m a r k e r s c0.n be represenled as pa- rallleters ill ASTI.. Ill s i t u a t i o n 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 d e n o t a t i o n 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 s i t u a t i o n whose type c o n t a i n s 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 ) R S for % man stags" is

S i t 3 4 S : : [ 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 ) R S will be truc Ior s o m e s i t u a t i o n (i.e. a m o d e l ) if there exists an a n c h o r i n g for the p a r a m e t e r s in it which m a k e it a l y p e of the m o d e l - s i t u a t i o n . A special definition will be needed for tile condition e v e r y (and possil)ly o t h e r s if e x t e n s i o n s to basic D I ( I ' are in- ehMed). It m a y be b e t t e r to think of the s i t u a t i o n nellie also as a p a r a m e t e r which gets anchored Io the m o d e l - s i t n a t i o n . Hut as the s e m a n t i c s of ASTL relates s i t u a t i o n s n a m e s to s i t u a t i o n s (i.e. two sit- m~t.ion nanles can denote t h e s a m e s i t u a t i o n ) flmre is still a level of indirection.

D H S s arc objects which are related to utter anee s i t u a t i o n s . T h e y are not t h e m s e l v e s repre- s e n t a t i o n s of the u t t e r a n c e s b u t r e p r e s e n t a t i o n s of whal tile u t t e r a n c e s describe.

T h r e a d i n g

An iml>ortant aspect of I ) R T is how a I ) R S is con- s t r u c t e d f r o m 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 t h r o u g h 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 s i t u a t i o n s which call In' viewed t i m ) u g h a n u m b e r of different s t r u c t u r a l relations, T h e tirsl is t h r o u g h tile relation d a u g h t e r which defines tile s y n t a c t i c 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 doini- nance and linear precedence). Secondly the t h r e a d rdal.ion defines an o r d e r i n g of tile n t l e r a n c e situ- a l i e n s used in the g e n e r a t i o n of the l)RSs. I,aslly there are two relations, r a n g e a n d body lined ill defining the logical s t r u c t u r e of the discourse.

T h e t h r e a d i n g relation is a b i n a r y relation between u t t e r a n c e situations. We will say t h e first a r g u m e n t is threaded to tile second. Each u t t e r a n c e s i t u a t i o n a p p e a r s e x a c t l y once a,S t h e second argu- m e n t in tile t h r e a d relation (i.e. il. h a s exactly one i n c o m i n g thread). T h e r e is one exeeplion, a special s i t u a t i o n called D S t a r t which does not have an in- c o m i n g t h r e a d (it is used to represent the null context at the s t a r t of a discourse), b m does a p p e a r as all i n c o m i n g t h r e a d for one or more u t t e r a n c e

situations. T h e r e are no cycles m t h r e a d h l g b u t as we shall see there m a y be m o r e t h a n one linked t h r e a d of u t t e r a n c e s w i t h i n a discourse. T h e actual construction of the t h r e a d i n g relations is discussed later.

Each u t t e r a n c e s i t u a t i o n is related to two D R S s , t h r o u g h 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 c o n s t r a i n t can be w r i t t e n in ASTL o~'-;

* S : [ S ! S ! - < < D R S I n , S , * D R S , 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 t h e two D R S s related to an u t t e r a n c e is also constrained, T h i s is a core p a r t of D R T . Basically the o u t g o i n g D R S c o n t a i n s 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 a n y r e f o r m a t i o n the u t t e r a n c e a d d s to the discourse. In the cruse of a proper noun u t t e r a n c e s i t u a t i o n we can c a p t u r e this relation with the following c o n s t r a i n t :

* 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 m o n o t o n i c a l l y increasing m l ) R S s as we traverse along a t h r e a d . We are not destruc- tively m o d i f y i n g a D R S as the discourse progresses but c o n s t r u c t i n g a new D R S which s u p p o r t s the s a m e conditions as t h e i n c o m i n g D R S . T h e con- s t r a i n t above f o r m s the o u t g o i n g I ) R S f r o m t h e type (*DRSInType) of tile i n c o m i n g one, which will contain all the c o n d i t i o n s of the i n c o m i n g D R S , plus a new condition i n t r o d u c i n g 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 c o n s t r a i n t t h a t a n y a r g u m e n t or relation that a p p e a r s in the c o n d i t i o n s 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 s i t u a t i o n by t h e 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 t h r e a d e d before predicates. For e x a m p l e both the s u b j e c t N P a n d o b j e c t N P of a s i m p l e sentence will be t h r e a d e d l)e- fore the VP. In eontrmst in [6] tile V P c o m e s before a o b j e c t 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 deter- m i n e d (i.e. a free variable).

T h e other s t r u c t u r a l relations are r a n g e a n d b o d y Each d e t e r m i n e r u t t e r a n c e s i t u a t i o n a p p e a r s in exactly one r a n g e - r e l a t i o n and e x a c t l y one b o d y - r e l a t i o n . Tile second a r g u m e n t t o these relations are u t t e r a n c e 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 a n y 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 s i t u a t i o n is a flmction of t h e DRSIn I)I?~S plus i n f o r m a t i o n f r o m the r a n g e a n d b o d y related threads, hi t h e e v e r y d e t e r m i n e r case tile DRSOut, c o n s t r a i n t is

* S : [ S ! S != < < D R S B u t , S , * D R S O u t : : *DRSInType It

[DS ! DS != <<every,*RangeDRS, *BodyDRS, l > > ] , 1>>]

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<~

*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 : : * D R S I n T y f m , I > >

S !~ <<aem,S,every,l>>],

TS : ITS !

TS != < < b o d y , * S , * B o d y : :

IS ! S != < < D R S O u t , S , * B o d y D R S , I > > ] , i > > TS }= < < r a n g e , * S , * R a n g e : :

IS ! S != < < D R S D u t , S , * R a n g e D R S , I > > ] , I > > ] While for the indrtlnite d e t e r m i n e r the DRS0ut sits- ply c o n t a i n s all the conditions f r o m t h r DRSin, r a n g e a n d b o d y related utterances.

* s : [ s ! s != < < D R S U o t , S , * D R S 0 u t : : *DRSlnType • *DRSRType • *DRSBType, 1>>] <=

* S : [ S ! S ! - < < c a t , S , n e t e r ~ i n e r , l > >

S !~ < < D R S I n , S , * D R S l n : : * D R S I n T y p e , I > > S != < < ~ e m , S , s o m e , l > > ] ,

T,q: [TS !

TS != < < b o d y , * S , * B o d y : : [IS ! S != <<DRSihlt,S,

* [ ] o d y D R S : : * D R S B T y p e , i>>] , I>>

TS != <<range,*S,*Ilange: : [S ! S != <<DRSIIut,S,

*ltangeDRS : : *DRSRType, 1 >>] , 1 >>] .

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, r u c t u r c ( v i a Ih(, d a u g h l ~ e r relations). At, the same tim(' the t h r e a d ilig inforlllatioll can be COllStrllCLl!d. Each ilttl!rallc(! s i t u a t i o n is related to I, wo o t h e r s I)y (lie relations n e e d mid o u t . Th(! n e e d r(!Iation id('ntities tJ.' ut

t e r a n c ( s i t u a t i o n (either itself or o n ( of its d a u g h - ters) which requires an i n t e r n i n g tin'end while o u t identifies which s i t u a t i o n is to be t h r e a d e d on to the next p a r t of the discourse. A I I h o u g h th( n e e d and o u t r e l a t i o n s 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 t h r e a d e d to t h e 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

c o n t r a s t w i t h [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 " h i

t.erance" t h a t is to be tlu'('a(led in. lh're w('

giv('

a } > o t t o l l l t i p 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

t h r e a d relation dr~twn as a r r o w s to show the flow of information t h r o u g h the disconrs(~

D

,* , n a n like,~ l l . ) , . k o

in adclition, D S t a r t is t h r e a d e d to D, N and NP2. T h e m a i n discourse t h r e a d will go t h r o n g h D. T h e r e are two o t h e r t h r e a d s e n d i n g at NP1 and S. D will be related to NP1 by the relation r a n g e and to S by the

relation body, llence th(~ o u t p u t D R S f r o m t h e sentence (from the d e t e r m i n e r "a" by the c o n s t r a i n t s given s h o v e ) 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 a n d body relations).

P r o n o u n s a n d A c c e s s i b i l i t y

Unlike o t h e r u t t e r a n c e s i t m t t i o n s , p r o n o u n s do n o t j u s t 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 i n t r o d u c e d in the context, q b put it s i m p l y there m u s t be a suitable o b j e c t m t h e i n c o m i n g I ) R S t h a t the pro- 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 ;L~

*S: [S S !" < < D R S o u t , S , * D R S o u t : : *DII.S InType •

[DS ! DS != < < i s ) * X , * Y , I > > J , I > > ]

* S : ( S S != < < c a t , S , P r o n o u n , l > > S != < < t y p e , S , * T Y P E , t > > S != < < s e m , S , * X , l > >

S ! ~ <<DRSIn, S, *DRSIn: : *DIISInType, 1>> S !~ < < a c c e B s i b l e , 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

r t e u t e x 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 s i t u a t i o n 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 p o i n t 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 s i t u a t i 0 n U are defined ( i n l o r m a l l y ) m~ follows:

If U is a noun (or p r o p e r n o u n ) the accessible m a r k e r s are from t h a t noun plus the acces- sil)le m a r k e r s li'on, the i n c o m i n g t h r e a d . 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 t h e acc(,ssihl[~ m a r k e r s are those f r o m t h e 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 t h r e a d of (he relatrd d e t e r m i n e r .

if U is an ind('lini).(~ d('.terminer tim accessible nlarkers are thos(~ of the end of the b o d y t h r e a d

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 f r o m its i n c o m i n g t h r e a d (i.e. does . o r inclmh: Oar m a r k e r s i n t r o d u c e d in Lhe r a n g e and body threads).

otherwise the accessible m a r k e r s are those of the i n c o m i n g t h r e a d

T h e s e couditiolis can e~Lsily be represented by ASTL ¢ O l l s t , r a i n Ls

C~iven the abow! descriptions: a s y n t a c t i c back- b o n e a I)RS represent, aLien, t h r e a d i n g a n d definition for accessibility) we can refill I ) R S s 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 d o n k e y 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 u t t e r a n c e s i t u a t i o n is.

(5)

every(

~ith(NA1,DA1) _donkey(DA1) mnn(MAl)

l i k e (NA1 ,PN1) i s (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 prop- ertics 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 in- tuition 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].

S u m m a r y

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

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 dis- cussing 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. A c k n o w l e d g e m e n t s : 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.

R e f e r e n c e s

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Partial and Dynamic Semantics HI, DYANA

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[2] J. Barwise and J. Perry. Situations and Atti-

tudes. MIT Press, 1983.

[3] A. Black. A situation theoretic approach to computation semantics, forthcoming PhD the- sis, 1)ept of AI, University of Ediuburgh, 1992. [4] R. Cooper. Information and g r a m m a r . Techni- cal 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 and parsing. In COLING8g, Bonn, 1986. [7] H. Kamp. A theory of truth and semantic

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Study of Language. Mathematical Center, Am-

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[8] R. Muskens. Meaning and Partiality. PhD tim- sis, University of A m s t e r d a m , 1989.

[9] 11. Nakashima, H. Suzuki, P-K. Halvorsen, and S. Peters. Towards a computational interpreta- tion of situation theory. In FGCS, ICOT, 1988.