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<?xml version="1.0" standalone="yes"?> <Paper uid="C92-4175"> <Title>Embedding DRT in a Situation Theoretic Frmnework</Title> <Section position="3" start_page="0" end_page="0" type="ackno"> <SectionTitle> ASTL </SectionTitle> <Paragraph position="0"> ASTL is a language based on situation theory. It takes a very conscrvative view of situation theory, admitting only some basic parts. Although ASTL may need to be extended later, it already can be used to describe simple versions of semautic theories (such ms situation semantics and DRT). 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 Grammar \[4\] while PRoslrr is designed more for knowledge representation than direct language processing.</Paragraph> <Paragraph position="1"> ASTL allows the following basic terms: Individuals : e.g. a, b, c.</Paragraph> <Paragraph position="2"> Parameters : e.g. X, Y, Z.</Paragraph> <Paragraph position="3"> Variables : e.g. *X, *g, *Z.</Paragraph> <Paragraph position="4"> Relations : e.g. see/2. Relation name and arity.</Paragraph> <Paragraph position="5"> i-terms : consisting of a relation, arguments and a polarity (0 or 1), e.g. <<sing,h, 1>>.</Paragraph> <Paragraph position="6"> AcrEs DE COLING-92, NANTES, 23-28 Ao~r 1992 1 l 1 6 PROC. OF COLING-92, NANTES, AUG. 23-28, 1992 tylms : consisting of an abstractioll ow!r proposi tions. For example</Paragraph> <Paragraph position="8"> That is tile type of situation which supports the fact that h sings and h sees that situation.</Paragraph> <Paragraph position="9"> Sitnatirms : written ,as names optionally followed by a type. e.g.</Paragraph> <Paragraph position="11"> tn addition to terms there are the following sentc~tccs: null Propositions : consisting of a situation and a type e.g.</Paragraph> <Paragraph position="12"> The selnantics of ASTI, (delin,~d fully ill \[3\]) are de lined in terms of a model consisting of individuals, relalions, parameters, situations slid a set coasisting of pairs of situations and facts, lnfflrmally, a proposition is true if the denotation of the situation supports 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 prop(. sition is true also. As it is currently defined ASTL has no bailt-in delinition with respect to coherence. that is there is no built-in mechanism that stops a situation SUl)l)orting bath a fact and its dual (the fact with the opposite polarity) Coastraints can be generalised using variabh,s.</Paragraph> <Paragraph position="13"> An example will help to illustrate this. If we define the folh)wing basic situation and constraint:</Paragraph> <Paragraph position="15"> hfforlnally the constrainl states that in ally situ ati(m where something smiles it. is also Imppy (m tlmt sanw situation). From the above bmsi(: axioms we can derive that tile following is true:</Paragraph> <Paragraph position="17"> llather than just 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, making complex objects nmch easier to view. In this notation we write situations its boxes with their names m a top left inset with facts written (in a more conventional predicate argmnent form) inside the box.</Paragraph> <Paragraph position="18"> Using the work of Cooper \[d\] we can process language in a situation theoretic way. Situation Theoretic Grammar takes the view that utterances can be represented by situations. For example</Paragraph> <Paragraph position="20"> That is, the use of the phrase &quot;llanako&quot; gives rise to a situation that supports the facts that it (the situation) is a ProperNoun and it is a use of the word &quot;Hanako&quot;. We call these utterance situaiions.</Paragraph> <Paragraph position="21"> As an utterance happens at a particular time and location this fact should also be recorded in the situation. In ASTL this temporal aspect is built-in to the language. A special form of constraint, grammar rules, can Ire used to constrain utterance situations~ (-;eneral constraints apply to any form of situation (utterance or otherwise) while grammar rules only apply to utterance situations. A grallilllar rllle betweea !ltLel-allce situations such a.,4</Paragraph> <Paragraph position="23"> t;tkes into accollllt that the two utterance situations occm next to each other It is possible to model all of this within the standard constraint system by adding facts almut start and end l)oints of utterances (in a mmihu, way that l)C(_~s arc interpreted in l'roh)g) but as one of the main uses of ASTL is language processing it w~s felt more elllcient to buiht utterance situations (and constraints on them) drredly into the language.</Paragraph> <Paragraph position="24"> A basic impienmntation has been made within Common I,isp which takes ASTL dcscriplions (deftnitions, basic situations and constraints) and allows queries to be made about their sets of constraints and I)itsic situations.</Paragraph> <Paragraph position="25"> Discourse representation theory Given a simple language like ASTL there is now the question about }low it can be used in rel)resenting other semantic theories. DRT \[7\] ota~rs a representat, ion lot discourses. A discourse rcprcsenlalion structure (I)RS) is dctined at each stage 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 markers in the top part and conditions below. For example a I)RS for the utterance &quot;a man</Paragraph> <Paragraph position="27"> The following description of I)RT in ASTL is based on lhe I)HT definition in \[6\]. First we need a syntactic backbone to be able to discuss the constructi(m of a I)RS for a discourse. As seen (briefly) above AS'I'I, oilers a basic grammar formalism. That is, grammar rules are Sl)ecilled as eoastraints betwet'n iltterance siluatiollS, AL'DAS DE COLING-92, NAI~'H~S, 23-28 aot~r 1992 1 I 1 7 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 markers c0.n be represenled as parallleters ill ASTI.. Ill situation theor3 parameters denote partially determined objects. Parameters can be anchored to other objects as information about tt~eir denotation is found. DRS conditions arc represented by i-terms. A DRS itself is represented as a parametric situation--a situation whose type contains parameters. Discourse markers are not explicitly listed in the 1)ITS representation. An ASTI. representation of the I)RS for % man stags&quot;</Paragraph> <Paragraph position="29"> This allows a siml)le semantics close to thai of a conven(.ional I)RS. That is an ASTL I)RS will be truc Ior some situation (i.e. a model) if there exists an anchoring for the parameters in it which make it a lype of the model-situation. A special definition will be needed for tile condition every (and possil)ly others if extensions to basic DI(I' are inehMed). It may be better to think of the situation nellie also as a parameter which gets anchored Io the model-sitnation. Hut as the semantics of ASTL relates situations names to situations (i.e. two sitm~t.ion nanles can denote the same situation) flmre is still a level of indirection.</Paragraph> <Paragraph position="30"> DHSs arc objects which are related to utter anee situations. They are not themselves representations of the utterances but representations of whal tile utterances describe.</Paragraph> <Paragraph position="31"> Threading An iml>ortant aspect of I)RT is how a I)RS is constructed from a discourse. Here (and in \[6\]) we use tile technique of threading. Tile general idea is that a DH.S gets passed through a discoarse being added to as the discourse l)rogresses.</Paragraph> <Paragraph position="32"> hi this description, a discourse consists of a set of utterance situations which call In' viewed tim)ugh a number of different structural relations, The tirsl is through tile relation daughter which defines tile syntactic structure of lhe discourse as defined by the grammar rules (immediate doininance and linear precedence). Secondly the thread rdal.ion defines an ordering of tile ntlerance situaliens used in the generation of the l)RSs. I,aslly there are two relations, range and body lined ill defining the logical structure of the discourse.</Paragraph> <Paragraph position="33"> The threading relation is a binary relation between utterance situations. We will say the first argument is threaded to tile second. Each utterance situation appears exactly once a,S the second argument in tile thread relation (i.e. il. has exactly one incoming thread). There is one exeeplion, a special situation called DStart which does not have an incoming thread (it is used to represent the null context at the start of a discourse), bm does appear as all incoming thread for one or more utterance situations. There are no cycles m threadhlg but as we shall see there may be more than one linked thread of utterances within a discourse. The actual construction of the threading relations is discussed later.</Paragraph> <Paragraph position="34"> Each utterance situation is related to two DRSs, through tim relations DRSIn and DRSOut. A DRSIn DRS is tim DRSOut DRS of the incoming thread.</Paragraph> <Paragraph position="35"> Tiffs constraint can be written in ASTL o~'-;</Paragraph> <Paragraph position="37"> *SI: \[S1 ! S1 != <<DRSBut,SI,*DRS,I>>\] .</Paragraph> <Paragraph position="38"> The relation between the two DRSs related to an utterance is also constrained, This is a core part of DRT. Basically the outgoing DRS contains the same information as the mcnming DRS plus any reformation the utterance adds to the discourse. In the cruse of a proper noun utterance situation we can capture this relation with the following constraint:</Paragraph> <Paragraph position="40"> hfformation is monotonically increasing m l)RSs as we traverse along a thread. We are not destructively modifying a DRS as the discourse progresses but constructing a new DRS which supports the same conditions as the incoming DRS. The constraint above forms the outgoing I)RS from the type (*DRSInType) of tile incoming one, which will contain all the conditions of the incoming DRS, plus a new condition introducing the parameter for the I)roper noun and a condition on its name.</Paragraph> <Paragraph position="41"> We also have tile constraint that any argument or relation that appears in the conditions of a DRS must be related to some utterance situation by the relation sere previously ill that thread. This condition means that argnments are threaded before predicates. For example both the subject NP and object NP of a simple sentence will be threaded l)efore the VP. In eontrmst in \[6\] tile VP comes before a object NP which means a I)RS is created with an argmnent in a condition which is not yet determined (i.e. a free variable).</Paragraph> <Paragraph position="42"> The other structural relations are range and body Each determiner utterance situation appears in exactly one range-relation and exactly one bodyrelation. Tile second argument to these relations are utterance situations that do not appear as first arguments in any threading relation (i.c. they are ends of threads). Tile DRS0ut of a determiner utterance situation is a flmction of the DRSIn I)I?~S plus information from the range and body related threads, hi the every determiner case tile DRSOut,</Paragraph> <Paragraph position="44"> While for the indrtlnite determiner the DRS0ut sitsply contains all the conditions from thr DRSin, range and body related utterances.</Paragraph> <Paragraph position="45"> *s:\[s ! s != <<DRSUot,S,*DRS0ut:: *DRSlnType * *DRSRType * *DRSBType, 1>>\] <= *S:\[S ! S !-<<cat,S,neter~iner,l>> S !~ <<DRSIn,S,*DRSln: :*DRSInType,I>> S != <<~em,S,some,l>>\], T,q: \[TS ! TS != <<body,*S,*Body: : \[IS ! S != <<DRSihlt,S, *\[\]odyDRS : : *DRSBType, i>>\] , I>> TS != <<range,*S,*Ilange: : \[S ! S != <<DRSIIut,S, *ltangeDRS : : *DRSRType, 1 >>\] , 1 >>\] . lhH }low is threading huilt? Thr granHnar rule~ sl)ecit 3' I,h(~ I)asic syntactir st, ructurc (via Ih(, daughl~er relations). At, the same tim(' the thread ilig inforlllatioll can be COllStrllCLl!d. Each ilttl!rallc(! situation is related to I, wo others I)y (lie relations need mid out. Th(! need r(!Iation id('ntities tJ.' ut teranc( situation (either itself or on( of its daughters) which requires an interning tin'end while out identifies which situation is to be threaded on to the next part of the discourse. AIIhough th( need and out relations are determined al the tillle a grall/ill~tr rule is realised the :-tetllaI t:hread, range and body relations Inay not be detrrmined locally. The utterance to be threaded to the need of an NP can not Ire realised until thr NI ) is put in context tn contrast with \[6) inslea(I of i)assing up the utter ante that needs a Ihrrad, they i)ass down the &quot;hi t.erance&quot; that is to be tlu'('a(led in. lh're w(' giv(' a }>ottolll tip definition rather 1111111 ~1.C/; ill \[(i\] a lop (\[own OIle.</Paragraph> <Paragraph position="46"> As seen ill the (Ollstraillts above Ill(' strtlctural \[a('ts whose relations are thread, range and body ar(~ colhx:t,ed in a siUiation called TS tlelow is an (!xanlp\[(! sent, eiicc showa ;is a sylll,ax tree willl the thread relation dr~twn as arrows to show the flow of information through the disconrs(~ D ,* ,nan like,~ ll.),.ko in adclition, DStart is threaded to D, N and NP2. The main discourse thread will go throngh D. There are two other threads ending at NP1 and S. D will be related to NP1 by the relation range and to S by the relation body, llence th(~ output DRS from the sentence (from the determiner &quot;a&quot; by the constraints given shove) is built from tile incoming l)tkq plus lhe outgoing l)}lSs from NP1 and S (which are related to I) via the range and body relations). Unlike other utterance sitmttions, pronouns do not just add new information to a I)RS. They also require existence of sonre referent already introduced in the context, qb put it simply there must be a suitable object m the incoming I)RS that the pro- null rteutex llow(~vcr, it. is not su/licient to sinlply check the conditions in the incoming l)lLq lbr some tnarkvt of the right type.</Paragraph> <Paragraph position="47"> The access+-b\].e relation is also dctined over the three(ling relations. Each utterance situation is re}ah!d to ;t situation that supports the facts about which markers are accessible at that point m the discotn'se. The accessible markers for an utterance situati0n U are defined (inlormally) m~ follows: If U is a noun (or propernoun) the accessible markers are from that noun plus the accessil)le markers li'on, the incoming thread. if U is the start of a thread whose end is related to a determiner by tile relation body then the acc(,ssihl\[~ markers are those from the end of thai determiner's range thread.</Paragraph> <Paragraph position="48"> if U is the' start, of a rmxge thread, the accessible markers are those froln tlw incoming thread of (he relatrd determiner.</Paragraph> <Paragraph position="49"> if U is an ind('lini).(~ d('.terminer tim accessible nlarkers are thos(~ of the end of the body thread if ( is an every determiner I,he accessible mark ers are those from its incoming thread (i.e.</Paragraph> <Paragraph position="50"> does .or inclmh: Oar markers introduced in Lhe range and body threads).</Paragraph> <Paragraph position="51"> otherwise the accessible markers are those of the incoming thread These couditiolis can e~Lsily be represented by ASTL C/Ollst,rain Ls C~iven the abow! descriptions: a syntactic backbone a I)RS represent, aLien, threading and definition for accessibility) we can refill I)RSs for simple (liscourses. The coverage is that of \[6\]. This still allows an example of donkey anaphora ;is ill &quot;every man with a do)lkey likes it&quot; The DRS0ut for the discourse utterance situation is.</Paragraph> <Paragraph position="52"> 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 &quot;all men.&quot; (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 every 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.</Paragraph> <Paragraph position="53"> 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\].</Paragraph> <Paragraph position="54"> 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 possible translation of I)I~T in ASTL is given. The coverage is that of \[6\].</Paragraph> <Paragraph position="55"> 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.</Paragraph> <Paragraph position="56"> 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.</Paragraph> </Section> class="xml-element"></Paper>