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<?xml version="1.0" standalone="yes"?> <Paper uid="C88-1050"> <Title>An Unexpectedly Simple Solution Suggested by Second- Order Prolog Constructs</Title> <Section position="2" start_page="0" end_page="247" type="ackno"> <SectionTitle> Abstract </SectionTitle> <Paragraph position="0"> Sentences a, ith crossing coreference (Bach-Peters-sentences) are notoriously difficult to eq/lain ill a natural nmnner. An intriguing parallel with certain properties of t'mlog suggests a modificatiml to Discour~ Represenlation Thexn'y which allows a simple and coherent explanation of these, and related, sentences.</Paragraph> <Paragraph position="1"> The Probteln In English there is due type of sentence that has caused major problems for practically all linguistic theories that have tried to explain it, and none of Ihe explanations put forward is very convincing. The sentences in question are those with cross'lag corcferenee, the so-called Bach-Peters-sentences. The standard exampies arc: l) &quot;The htutter who shot al:, it hJl; the \]ion that chased him and, with cxpiicit quarldfier expressions: 2) Every man who wants it will get the prize he deserves What is the difficulty wilh this type of sentence? 'Illey contaiu two uoun phrases each of which contains a pronoun that refers to the other notnl phrase, and tile first pronoun is filrthermore a case of &quot;backwards anaphora&quot;, or &quot;cataphonl&quot;. These sentences are admittedly tare, bet sentences with simple (non-crossing) camphora are quite frequent ill real world English (Carden 1982). And Bach-Peters-sentences are nevertheless perlectly reguhu', and so they should find a natural exph/nation. Moreover, they are key exanlplcs of sentences where Gala. pllora cannot, in principle, be mphlced by anaphora (cf. also Mittwoch 1983).</Paragraph> <Paragraph position="2"> This is imporlant because one of tile standard approaches to cataphora has been to define it away as stylistic variant of anaphm'a, which can be &quot;rectified&quot; by a simple transposition. Ill other words: Since we have to find a way to explain cataphora for Bach-F'eters-sentences anyway, we carl save us the lfouble to devise such tricks for the siutpler cases.</Paragraph> <Paragraph position="3"> Are Bach-Peters-Pronouns Descriptional l'ronouns? The non-reAucibility of cataphofic to anaphoric pronouns in Bach-Peters-sentences becomes clear if we try to explain them in tile traditional manaer. It seems that both of/tie two traditional interpretations of prononns, tile &quot;de~:riptional&quot; as well as the &quot;denotafionar' one, fail to explain the intuitive truth condilions of Baeh-l'ete~.-sentences. In Transformational Grammar the deseriptional approach is taken, trod pronouns are always expanded to the sl,rface syntax form of the norm pbaase they anaphoric~dly refer to (in other words, pronominalization is an obligalxlry cyclic rule). But then we get, for tile example above, a double infinite embedding of relative clauses: The hunter who shot at (the lion that chased (the hunter who shot at (tile lion that chased . . . ) ) ) hit the lion that chased (the hunter who shot at (the lion that ohased (the hunter who shot at ... ))) This analysis is patently uselc,ss. K,'u'ttuuen shows (Karttunen 1971) that dropping the requirement that pronominalization is a cyclic rule alleviates the problem somewhat, but at a cost: II would make sentence 1 derivable from (at least) two different deep structures, viz. fi'om file deep structures corresponding to the sentences 3) Tile hunt;~r who shot at the ll.on that chased him hit it: d) The lJ.on thai: chased the hlnlter who shot at it was hit by him This would mean that 1 has to he mnbiguous between the meanings of 3 and 4. This is what Karttuncn assumes, but it is a highly duhious claim as Karttunen himself scculs to fcel (Karttunen 1971:167 it. Moreover, the strnctum of I co,ld also be derived from a deep stractm'e corresponding to 5) The hunter who shot at the l~on hit the lion that chased tile hunter But Oils sentence is considered by nuuly informants to l~e simply ungramnmtical (Karttunen 1971:178), aud ill is not acceptable at all under the corefblvnce relations that should obtain between tile noun phrases. Finally, the assonlption that l is three ways ambiguo,s bctwceu 3, 4 and 5 is unaccellml~le, too, Ill urder to show this, and in order to underslanll better what these three sentences really nlean, we Call USe a set of data hascs (after Karttnaen 1971) which eitller contain, or do not contain, well-definexl referents for the varimm defiaite uoun phrases occtnriag iu/lie example sentences. We will see that I is not alnhiguous hclwccn 3 anti 4, \[lilt that the three sentences have three distinct n/eanings which Call lie derived directly fl'onl their syniactic stractllre. This proves, at tile same time, lha! cataphoric prououns are irreducible ill Bach-Peters-sentences. Let us first consider tile dcfiuite nonu phrase &quot;the hunlor who shot at tile lion dmt chased him&quot; (fiont 3) consisting of an embedding of two definite noun phrases. Since each singular definite noun phrase presupposes that there is a nnique retereut for it, this phrase cau refer to a pah&quot; &quot;hnnter H - lion I/' in the case whom lion L is the only lion chasing huuter tl, and this hanter H shot at this very lion L. Ill the fol lowing dam base (Karttunen 1971:166) there is one such pair.</Paragraph> <Paragraph position="4"> hun to r (hl) . chased ( L 1 ~ h3 ) . \]ion ( ~ t ) .</Paragraph> <Paragraph position="5"> hunter (h2) . chased (12, h \] ) . \] J on ( \]2 ) .</Paragraph> <Paragraph position="6"> hunter (h3) . chased (13,112) . lion {13) .</Paragraph> <Paragraph position="7"> shot; _at (hl, ill . shot_at (h2, \] 1 ) . shot at (h2, \] 3 ) .</Paragraph> <Paragraph position="8"> shotat (hl, 13) . shot; at (h3r \]3) . shotat (h3, 12) .</Paragraph> <Paragraph position="9"> \]?;or each hnnter, there is a single lion chasinj~ him but only elm hunter ~dso shoots at this lion, viz. hnnter 2 who shoots at lion 3. I{unter 2 S}IOOIS at Oilier lions, as well (e.g. at lion 1) but lieu I doesn't chase hunter 2 (although it does chase other hunters, e.g. hnnlm&quot; 3). Hence it can be said (Dik 1973:320) that tile delinite uonn phrase &quot;the hnnter who shot at tile lion that chased hiuf' has a well-defined referent in ally data hase which contaius fl~st one contigllration of the type shoots C/'~ &quot;-&quot; 7-~'deg&quot; ~t,.. hunter 4 ..... ~ lion ~</Paragraph> <Paragraph position="11"> This rules out that other lions chase the hunter, bat it leaves open tile possibility that the hunter shoots at other lions, that the lien chases other hunters aml, in particular, that other hunters shoot at the lion. On the other hand, example 4, &quot;The lion/lint chasexl tile bunter who shot at it was hit by him&quot;, is not intelllretnble in the data base given above, lts subject, &quot;the lion that chased the hnnter who shot at it&quot;, Nils to refer properly: There is only one lkm for which/llere is a huater we can call &quot;the hunter who shot at it&quot;, viz. lion 2 (the other two lions are both being shot at by nlm'e than one hunter), but lion 2 does not chase &quot;die hmlter who shot at it&quot; (viz. hunter 3), and so tile enfile noan phrase fails to refer. A data base where there is a referent for this noun phrase couhl look like that: hunter (hl) . chased Ill., hl) . llon lilt .</Paragraph> <Paragraph position="12"> hunter (h2) . chased ( 13., h3 ) . \] ion (12) .</Paragraph> <Paragraph position="13"> hunter (h3) . chased(12,hl) . lion (13) .</Paragraph> <Paragraph position="14"> shot_at (hl, \].2) . chased (\],2, h3) . chased (\].3, h2) .</Paragraph> <Paragraph position="15"> shot_at (h2, ii) . shot. at (h3, 13) . chased(13, hl) .</Paragraph> <Paragraph position="16"> The definite nouu phrase &quot;trio lion that chased the hanter who shot at it&quot; has a well-defined refereat ill troy data base which contains just one configuration of tile type 7: ,, o..~. ..~ * ,, *</Paragraph> <Paragraph position="18"> Exmnple 1 cannot be inter0reted in either ttle first or/lm second data base. It is interpretable only in a dam base which contains at most one confignratkm like 8 which combines restrictions 6 and 7:</Paragraph> <Paragraph position="20"> Are Bach.Peters-Pronouns &quot;Bound Variable&quot; Pronouns? Since the unmodified as well as the modified descriptional interpretations of pronouns in Bach-Peters-sentences do not allow us to represent these distinctions they cannot be accepted. But how do the &quot;deep&quot; approaches to pronouns, the so-called &quot;denotational&quot; interpretations, fare? The prototypical denotational interpretation of pronoans is the one suggested by Fh'st Order \[x)gic, where bound variables ate seen as the logical counterpart of pronouns in Natural Language. If we use iota-operators, we could try to translate</Paragraph> <Paragraph position="22"> The trouble is that iota-operators bind their variables, making them inaccessible for reference from the outside. Hence we cannot refer forward from the term &quot;shot at(Z,W)&quot; to the &quot;W&quot; in the second iota-expression, nor can we refer backward from &quot;chased(W,Z)&quot; to the &quot;Z&quot; in the first iota-expression. If we add equality to First Order Logic there is a way out. We could re-phrase 9 as</Paragraph> <Paragraph position="24"> chased(W, iota V: \[hunter(V) ^ shot_at(V,W)\])\]) But in cases 11 and 12 part of the expression must be repeated, namely the one stating the uniqueness of the hnnter-chasing lion, and of the lion-shooting bunter, respectively. This is a very unattractive way to express this sort of thing, and Karttauen agrees: &quot;One is tempted to think that one of \[these repeated definite descriptions\] could be eliminated by a more clever use of variables, especially when variables in predicate calculus are generaUy used very much the same way as pronouns in natural language. \[_.\] \[But\] the second appearance of the same description cannot be avoided, because, in predicate calculus, there is no way to refer back to the first.&quot; (Karttunen 1971:176).</Paragraph> <Paragraph position="25"> McCawley's suggestion: Referential indices But this is the point where other people disagree. McCawley (McCawley 19&quot;10), for instance, argues (for other reasons), that the semantic representation of sentences should not be east in terms of First Order Logic, but rather in terms of the overall proposition of a sentence plus referential indices. The proposition would define the relationship that exists between the different objects talked about in the sentence, but these objects would be represented independently by referential indices that correspond to the &quot;intended reference&quot; of the noun phrase. These indices are &quot;identified&quot; by the noun phrases in the sentence, i.e. their values are determined by the nonn phrases. A sentence such as &quot;The man killed the woman&quot;, would be translated as A surface sentence would be generated from this structure by replacing die referential indices in the proposition by the noun phrases identifying them. As for Bach-Peters-sentences, example 1 would be represented as 14) s I proposition(hit(Xl,X2)), np(Xl: the hunter who shot at X2) np(XZ: the lion that chased Xl)) Here the referential indices are identified by noun phrases which themselves conrain referential indices. \]f we want Ix\] generate a surface senteuee from this structure we will have to ~'eplaee the referential indices by their identifying nmm phrases, but we will not be able to replace systematically all referential indices this way, because fltis would lead tit the same kind of infinite embedding that we encountered above. We will rather, at some point in the derivation, have to tncn some of the refereoti~d indices into pronouns (talOns into account case, gender and number). The point at which we stop replacing referential indices by full noun phrases and start turning them into pronouns will determine which of several possible paraphrases of a sentence we will obtain. The distinction between &quot;proposition&quot; on the one hand and &quot;referential index&quot; with the accompanying &quot;identifying noun phrase&quot; on the other hand allows McCawley to overcome the problem with repeated components: The &quot;identifying noun phrase&quot; of a referential index is memioned only once, independently of how many times the referential index itself is used elsewhere in the representation.</Paragraph> <Paragraph position="26"> Dik's Modificatio~ of McCawle/s Theory This approach has been criticized on different coums. First, it is not clear at which point referential indices may begin to he tarued into l)mnouns rather than being replaeexl by identifying expressions. Second, and more importantly, McCawley's suggestion allows all three sentences (1, 3, and 4) to be derived from the same semantic representation, which would require that they are all synonymous. Hence all the problems we encountereA with the descriptional interpretation of pronouns are hack with a vengeance. Does that meau that we have to return to the standmd First Order Logic representation with all its unattractive features (repetition of components)? Dik 1973 suggests a mothfication of McCawley's approach that takes care of the empirical fact that file three sentences mentioned above are not synonynrous.</Paragraph> <Paragraph position="27"> The main syntactic diffel~nce between the three example sentence,; is the way in which tfie different full noun pllrases are embedded in each other. In particular, in the Bach-Peters-sentence there are no embedded full noun phrases; tile only embedded noun phrases are pronouns (&quot;who shot at it&quot;, &quot;that chased him&quot;). This kind of distinction is lost in McCawley's original notation, which is the reason why he has to ch'fim that the examples sentences axe all synonymous. Dik's first (and main) modification of McCawley's notation makes sm'e that this, cnlcial, distioction is not lost. The way to achieve this goal is by iuiroduciug what might be called (not Dik's expression) &quot;annotated variables&quot; to take the place of McCawley's referential indices, which are constants. The annotation of a variable indicates how tile value of the variable is to be computed. Thus &quot;X2(X2=iota Z: (lion(Z) ^ chased(Z,Y)))&quot; is an annotated vari~thle. This would give as, for 3,</Paragraph> <Paragraph position="29"> ~hot at(Y, X2(XZ=iota Z: (\].ion(Z) A chased(Z,Y))))) As in McCawley's system, refereotial indices umst be replaced by the corresponding identifying expressions, and any variables remaining after this step are tnmed into pronouns. In addition, we have the usual convention that functional expressions are to be evaluated from the inside out. But what is gained by faithfuUy copying a certain syntactic structure (viz. embedding) into the deep representation? Are the interpretation rules given by Dik really sufficient to interpret the resulting expressions correctly? If we perform the replacement, lbr instance, in 15 we get 16) hit(iota Y: (hunter(Y) A shot at(Y,X2lX2=iota Z: (lion(Z) A chased(Z,Y))))l,X2) Now, if we wanted to generate a surface sentence from tiffs representation we would turn the remaining unbound varinble, i.e. &quot;X2&quot;, into a pronoun, and everything would be in order. But what if we wmtted In evaluate this statement over one of the data bases? The X2 on the level of the proposition, i.e. &quot;hit(...,X2)&quot; is clearly outside the scope of the &quot;almotntion&quot; defining its value, and so we would expect it to remain unbound alter the annotation itself has been evaluated. This is, after 'all, precisely the reason why Karttunen thought it necessary to reintroduce the duplication of logical expressions that McCawley had tried to gel rid of: To provide the second, outer, occurrence of this variable with a value. We need an interpretation rule which specifies how variables of this kind can be bound, and this rule is not provided by Dik.</Paragraph> <Section position="1" start_page="246" end_page="246" type="sub_section"> <SectionTitle> An Unexpectedly Simple Solution Suggested by Second- Order Prolog Constructs </SectionTitle> <Paragraph position="0"> As it turns out, the additional interpretation rule that makes the correct interpretation of Bach-Peters-sentences virtually &quot;fall out&quot; is the definition of second-order operators, and the general interpretation rules of Horn Clause Logic, as implemented in starutard Prolog: Instead of &quot;Z=iota X: (Y)&quot; we use &quot;setof(X,Y,\[Z\])&quot;, where the nniqueness reqltirement is built into the definition of &quot;setof', and singularity is enforced by requiring the result list to consist of exactly one element. Annotated variables on the other hand are &quot;multiplied out&quot; in the relational spirit of Prolog, i.e. instead of &quot;predicate(X,Y(Y=Z))&quot; we write &quot;(predieate(X,Y), Y=Z)&quot;. Combining these two steps we get, for the expression above, 17) hit(Xl,X2), setof(Y, (hunter (Y) , setof(Z, (lion(Z), chased(Z,Y)), \[X2\]), shotat (Y, X2) ) , \[Xl \] ) or, with a more suggestive choice of variable names and a more efficient ordering of the goals</Paragraph> <Paragraph position="2"> Now the desireal truth conditions come out corrccdy. We can see this if we treat 18 as a Prolog query: We lind, first, a lmnter CH&quot;) who shoots at something CTL&quot;). Then we check whether this entity is identical with the set of exactly one lion C\['IL\]&quot;) ttmt chases someone CTH&quot;) who mast then tam out to be identical with the hunter who is the only such hunter C\[TH\]&quot;). Finally we check whether this hunter also hits this lion. The other sentences are represented the same way: 4 and 1 (the Bach-Peters-sentence) give 19) setof (L, (lion (L) , uhased(L, Tn) , setof (H, (hunter (H) , shotat (H, TL) ) , \[TH\] ) ) , \[TL\] ) , hit (TH, TL) .</Paragraph> <Paragraph position="3"> 20) setof (n, (hunter (H) , shot at (H, TL) ) , \[TH\] ) ,</Paragraph> <Paragraph position="5"> Now we get, without any additional stipulations, the three different interpretations for the tlnee example sentences. The sentences are neither collapsed into one single meaning repre~ntation (with three synonymous surface sentences), as with McCawley's approach, nor into two different ones (with two distinct and unambiguous, :rod one ambiguous, surface sentence), as with IGarttanen's approach. The simple fact that in Bach-Peters-sentences the full definite descriptions are not embedded, forces them to evaluate to two distinct, independently unique, values, and this ensures that these sentences are true only over data bases meeting condititm 8.</Paragraph> <Paragraph position="6"> But how can this unexpectedly straightforward solution be explained? The main problem that McCawley's representation, and Dik's modification of it, tried to overcome was: How can variable values be communicated into iota-expressions from the outside, despite the fact that, in First Order Logic, variables within the scope of an operator or quantifier are shielded from the outside? Now, in Horn Clause Logic nil variables of a clause are, implicitly, universally quantified (which means that variables in a query, i.e. in a negated clause, are existentially quantified), and the scope of the implicit quantifiers is the entire clause. The bindings of variables &quot;spread&quot; tlvoughout the clause, irrespective of how deep a variable may be. embedded. This also applies to the setof-operator: All its variables are accessible from the outside, within the given clause. The variables can, of course, still be unbound when the evaluation of the setof-expression begins, and then it is the evaluation of the setof-expression that will establish bindings for these variables. But they can also get bound elsewhere, before the operator is used, and &quot;spr~td forward&quot;. And then a proof of tim setof-expression treats these pre-established I~indings as constraints to be satisfied. This is the Prolog way to implement the cataphoric pronoun in Bach-Peters-sentences, In this, last, respect the setofoperator in Prolog is treated as just another predicate, and its being second order is irrelevant. The difference is that the interpretation of the setof-operator uses Prolog's meta-callfacility. Or, to put it differently: A piece of code (the entries in the second argument of the semf-operator) isfirst treated as &quot;data&quot; (variable bindings are communicated with the outside world), and then it is treated as a piece of &quot;program&quot; that is executed (using the variable bindings that are established at this point in time). And in this the Prolog setof-operator differs fundamentally form the iota-operator as used in First Order Logic. The iota-operator has, a~ fro&quot; as variable binding is concerned, the same force as a quantifier: A variable in its scope is immune from any outside interference.</Paragraph> <Paragraph position="7"> Now it is clear why we need not repeat any expressions in the representation of the example sentences, and yet the variables all get properly bound: In the example above, the two terms of 18 (i.e. rite setof-expression and the expression &quot;hit(TH,TL)&quot;) are part of the same clause, and values for variables created in either of them will spread to the other. In particular, the value which the variable &quot;TL&quot; takes during the evaluation of &quot;shot_at(H,TL)&quot; is still available during the evaluation of the embedded &quot;setof(L,(lion(L),chased(L,TH)),\[TL\])&quot;, and later during the evaluation of &quot;hit(TH,TL)&quot;.</Paragraph> </Section> <Section position="2" start_page="246" end_page="247" type="sub_section"> <SectionTitle> Mapping Variables onto Pronouns </SectionTitle> <Paragraph position="0"> If we want to generate surface sentences from these stmctares, we must distinguish between two uses of variables: First there are those uses which are merely an artefact of the relational way of representing functional application, and, second, there are those that correspond to true anaphoric relations in language.</Paragraph> <Paragraph position="1"> The first use is simple: If we want to represent functional applications such as plus(times(3,2),4) in a relational language, we must &quot;multiply out&quot; the embedded expression and create auxiliary variables for the intermediate results, e.g. &quot;X&quot; and &quot;Y&quot; in times(3,2,X), plus(X,4,Y) Thus we had to use 20, with auxiliary variables &quot;TH&quot; and &quot;TL&quot;, instead of a functional representation such as, for instance, 21) hit (set (H, (hunter (H) , shot .at (H, L) ) ) , set(L, (lion(L) , chasod(L,H) ) ) ) These &quot;auxiliary&quot; variables are situated on the same level of embedding (by definition: their purpose is to flatten embeddings). Co-occurrence of such variables on the same level of embedding maps, in simple cases, onto concatenation (&quot;^&quot;) in surface structure: Thus the fonuwing occurrences of variables &quot;TI.&quot; and &quot;TH&quot; in 20</Paragraph> <Paragraph position="3"> ferent levels of embedding, however, cannot be encoded as simple concatenation.</Paragraph> <Paragraph position="4"> These cross-references map onto pronouns. (The conver~ does not hold: There are pronouns that do not correspond to this kind of cross-reference; e.g. descriptional pronouns.) Thus the level-crossing co-occurrence of the variable &quot;TL&quot; in</Paragraph> <Paragraph position="6"> must map onto a pronoun (&quot;The hunter who shot at it&quot;). A problem arises when we try tO translate 19 back into English. If we begin the translation process wiri~ &quot;hit(TH,TL)&quot; and map the level-crossing variable &quot;TH&quot; onto a pronoun we get &quot;He hit the lion that chased the hunter who shot at it&quot;, which is not acceptable under the intended interpretation (i.e. coreferentiality of &quot;he&quot; and &quot;the hunter ...&quot;). This corresponds to a well-known syntactic restriction on the use of cataphoric pronouns. Here we need a rule that works for syntax generation rather than for analysis. The following rule is a bit ad-hoc, but it is sufficient for the present purpose: We require that the translation of the entire set of expressions must begin with the expression defining the top relationship between the individual set expressions (i.e. with the expression corresponding, in most cases, to the main verb of the surface sentence), and that level-crossing occurrences of variables in this term are la'anslated last. If this restriction makes it impossible to translate these variables from, say, left to right (as in the case of example 19, where the first variable &quot;TH&quot; is a level-crossing occurrence), it is done right to left. This requires that the surface verb form is passivized but it gives the grammatieally correct ordering of full noun phrases and pronouns (i.e. we get rite original passive sentence 4 for 19). In Bach-Peters-sentences such as 20 both the active and passive versions are admissible under this restriction, in keeping with the linguistic facts.</Paragraph> </Section> <Section position="3" start_page="247" end_page="247" type="sub_section"> <SectionTitle> Second-Order Prolog Constructs and Discourse Represen- </SectionTitle> <Paragraph position="0"> tation Theory The painless way in which the correct truth conditions of Bach-Peters-sentences and the related sentences virtually fall out of the standard Prolog interpretation rules and the definition of the second-order setof-operator is m)t just a lucky coincidence. It is rather another case of the intriguing parallel between Natural Language and Horn Clause Logic which has become particularly clear in Discourse Representation Theory (DR'I). The main hypothesis of DRT is that noun phrases (and articles) have no quantificational force on their own but are implicitly quantified by the context. This allows DRT to explain, with remarkable ease, so-called donkey-sentences, a type of sentence that does not yield to the traditional interpretation of noun phrases as quantified statements. The correspondence between the logic underlying DRT, and Horn Clause Logic is, in this respect, almost one-to-one: In DRT, (indefinite) noun phrases introduce discourse refcreuts which are quantified by the (discourse) context in the same way as variables in Horn Clause Logic are implicitly quantified by the (chnlse) context.</Paragraph> <Paragraph position="1"> How do Bach-Peters-sentences fit into DRT? First, we notice the parallel between McCawley's ideas and DRT: His &quot;referential indices&quot; correspond, in their intended fllnction, to tile discourse referents in DRT, and &quot;propositions&quot; correspoud to the DRT &quot;conditions&quot; on discourse referents. In the Prolog version of Dik's modification of McCawley's ideas, discourse referents correspond ~ the value of the third argument in a setof-operator, and the &quot;conditions&quot; of a Discourse Representation Structure (DRS) to the expression(s) in its second argument. All this applies, for the time being, only to definite noun phrases and their representation. If we want to incorporate this into DRT, we must first provide for the possiblity to explicitly represent the embedding of noun phrases.</Paragraph> <Paragraph position="2"> This kind of explicit embedding was the main reason why we got the right truth conditions in the Prolog representation of the example sentences. We must, in other words, be allowed to use embedded &quot;conditions&quot; in a DRS. Traditional DRT allows for the embedding of entire DRSs, hut not of individual conditions.</Paragraph> <Paragraph position="3"> While a sentence like &quot;If John owns a donkey that dislikes him, he beats it&quot; is traditionally represented as aflat DRS like</Paragraph> <Paragraph position="5"> (cf. Kamp 1981, Kanrp 1983, Frey 1983, Guenthner 1983, Guenthner 1985, Kolb \]985, Guenthner 1986, Pinkal 1986, Root 1986) this will not do-for the sentences with embedded definite noun phrases considered above. We must somehow represent this embedding. And we must, obviously, provide for the interpretation rules to use them. These rules will crucially rely on Prolog's meta-call facility to implement the double use of embedded set-expressions, as data structures on the one hand and as &quot;executable procedures&quot; (i.e. as provable assertions) on the other.</Paragraph> <Paragraph position="6"> In traditional DRT mostly indefinite and universal noun phrases (and proper names) are used while the Bach-Peters-sentences considered above all contained definite noun phrases. But for some of them there are versions with indefinite noun phrases, too, and all of them have corresponding plural versions. In order to cover all these cases we must introduce, instead of the &quot;conditions&quot; of DRT, generalised set expressions without the totality implication of Prolog's &quot;setof&quot; (cf. also Webber 1983). We use &quot;set(Def,Card,Gdr,Var,Int,Ext)&quot;, where &quot;Def&quot; can take the values &quot;def'(inite) or &quot;indef&quot;(inite), and &quot;Card&quot; either an explicit dumber, &quot;plur&quot;, or a quantifying expression Call&quot;, &quot;some&quot; etc.). &quot;Gdr&quot; gives the gender of the main noun. &quot;Var&quot;(iable),&quot;Int&quot;(ension) and &quot;Ext&quot;(ension) correspond to the three arguments of the setof-operator. The variable &quot;Ext&quot; can imw stand for sets as well as for individuals.</Paragraph> </Section> <Section position="4" start_page="247" end_page="247" type="sub_section"> <SectionTitle> Mapping Pronouns onto Variables </SectionTitle> <Paragraph position="0"> So far we have mentioned how pronouns correspond, statically, to certain semantic objects of oar modified DRSs (i.e. to the level-crossing occurrences of variables). But it is one of the main goals of DRT to give a unified account of what the procedures that actually perform the resolution of pronouns should look like.</Paragraph> <Paragraph position="1"> This problem is much harder than the converse one, i.e. the mapping of level-crossing variables onto pronouns. The central idea used hel~ by DRT is simple (it goes back to Karttunen, together with the term &quot;discoarse referent&quot;): Indefinite noun phrases in &quot;assertive&quot; contexts create discourse referents which &quot;live on&quot;, and which can he accessed by anaphoric expressions from points later in the sentence or discourse. Discourse referents, however, that are created by indefiuites in universal, conditional, and negative contexts, &quot;die oft&quot; when the sentence in which they occur is processed. This idea corresponds closely to Prolog's concept of variables and Skolem constants (the latter standing for existentially quantified variables): During the interpretation of a program variables remain accessible by name within the clause where they occur. This corresponds to the limited fifespan of discourse referents created in universal, condifional, and negative contexts. For Skolem constants in Prolog, however, the scope is the entire program; they &quot;live forever&quot;, in the szune way as discourse referents created by iarlefinites in assertive contexts. And whenever a (definite) pronoun or definite noun phrase is encountered, a suitable antecedent must be located among the discourse referents still &quot;alive&quot;. Its value is then replaced by the value of the discourse referent found. If several pronouns access the same discourse referent, they get, of course, the same value. This is the DRT counterpart of unificatiou.</Paragraph> <Paragraph position="2"> If we want to have, in our modified notation, discourse referents &quot;float on the surface&quot; of the corresponding DRSs, accessible lot later anaphoric reference, we could write, for the indefinite version of 3, viz. &quot;A hunter who shot at a lion that chased him hit it&quot; 19a) \[TL, TH: set (indef, 1, masc, H, (hunter (H) , shot_at (H, TL) , set (indef, 1, neutr, L, (lion (L) , chased (L, TH) ) , TL) ) , TH) , hit (TH, TL) } But there are fimdamenml differences between the treatment of variables in Prolog and DRT: During the interpretation of a Prolog program, bindings of a given variable spread throughout a clause to all occurrences of the same name, forwards and backwards. DRT, however, allows mdy torwards, &quot;anaphoric&quot;, spreading of values. Since a pronoun is processed as soon as it is encountered, it can &quot;look for&quot; antecedents exclusively in the DRSs built up by the preceding discourse. The interpretation procedures of DRT thus implement, implicitly, the syntactic rule that a pronoun can refer auaphorically to a preceding noun phrase that c-commands it. Becausc this is, at the same time, the only case where anaphora is allowed, the~ interpretation rules block, correctly, cataphora from tile pronoun to the indefinite noun phrase in 23) He said that a boy had taken the book But legitimate cases of cataphora, such as those in Bach-Peters-sentences, are blocked by these interpretation rules of DRT, as well. Hence we must weaken the accessibility restrictions for anaphoric l~ronominal references somewhat, but not too much: If we modelled them on Prolog's unrestricted variable sharing, 23 would go through in its coreferential reading.</Paragraph> <Paragraph position="3"> Accessibility rules of DRT not only block certain correct interpretations, they also allow certain blatantly incorrect ones. They would allow, for instance, the sentence above with a definite noun phrase, i.e.</Paragraph> <Paragraph position="4"> 24) He said that the boy had taken the book to get an interpretation where pronoun and definite noun phrases are coreferential. Why? The correct interpretation of this santence (no corefcrence between &quot;he&quot; and &quot;the boy&quot;) requires that the definite noun phrase will be able to find an antecedent among the pre-existing discourse referents. But then the sentence-initial &quot;he&quot; would be equally capable of accessing them, and this would allow the prohibited coreferential, cataphoric, reading of the &quot;he&quot; (i.e. &quot;pseudo-cataphora&quot; via a common antecedent). The same thing holds for &quot;He hit the lion that chased the hunter who shot at it&quot;.</Paragraph> <Paragraph position="5"> The prohibited reading of this type of sentence can be ruled out on the basis of purely syntactic information. The standard rule about pronouns says that a pro~aoun cannot be coreferential with an noun phrase if it both precedes and c-commands it. This rules out the cataphoric use of a pronoun if it c-commands its target noun phrase but it allows cases of eataphora such as 25) ~len he got up, John felt hungry (which are reducible to anaphora) as well as Bach-Peters-sentences (which are not), but it blocks the prohibited coreferences in &quot;He hit the llon that chased the hunter who shot at it&quot; and &quot;He said that the boy had taken the book&quot;. Mittwoch (1983) has shown that lhese purely syntactic criteria are not sufficiently general to cover all relevant occurrences of cataphora. In many cases, discourse considerations are needed to explain why eataphora is allowed. The pronoun can occur, for instance, in a sentential constituent which is demoted, by explicit discourse subordlnation markers, to a lower position than warranted by syntax. Thus, in 26) I haven't seen him yet but John is back (from Mittwoch 1983) the &quot;but&quot; functions as an overt marker of topicality for the second sentence, demoting the first sentence, and in 27) He may not represent the US at the United Nations anymore, but that does not mean that Andrew Young has slowed hia pace (fi'um Macleod 1984, quoting li'om &quot;Tium,&quot;) Ihe &quot;but&quot;, together with the modal &quot;may&quot;, even lnallages to laake calaphora acceptable fronl a sentcnee.iuifial sab. ject position (at l~ast ill journalese). The common element of all lhese examples of catapltoric proaouus is that they occur in discourse conditions, ht simple, cases this coiacides wilh senteulial conditions (&quot;if' etc.), and rely often with subseateotial condilious (ill particular with postmodifie~s 0f norm phrases, such as reslrictive relative elanses, prepositioual phrases, or nonlinite cla,scs). Ilut Ihe pictare is complicated by tile lhct flint the &quot;antecedent&quot; of cataphota mnst bc definite if ~he sea~.ence is specific. Conlllare 28) ?? A hu,lh~-r l.lho shot at: .1.t h~t a \]lon i.hat ch~s,ed h:im 29) A \]lllrlher ,./he shot o./; Jt hit thC/~ \]ion th&t ~:ha;~:d hi.hi 30) ?? When h,? 1;as poor a farme~: t ez~le<1 to ove~woJ:k his do~ null koy \[{I) Whon lie w~s poor tile fa~7111or tendod to ov{~<wo,Tk his <loll key In general (and ill mauy generic) scutences this restriction does not hold. The following sentences ale fine although the &quot;all|cl:edcnt&quot; norm illn'ases are indetinile: 32) A hun~:e~- who .~;ho.t~ al: it wSll l~t a lion ch~L ch.~:;,-,.'~ hllfl 33) Zf he is ~oo~: ~t f/l~:mer will t:{~nd Lo ovezwork hSs donk0y What seems to Im\[llmn here it that. intntivC/ly spe~tking, the calallhoric I)rononn sets np an &quot;expectation&quot; for a t~lllowing nonn i)lnase which is specilic or noaspecific, dependin!~, on the st~cilicity of the coudillnnaI context in which the pro. norm fiilds itself. The specilicity of the pronoulhnll context is deteralino:l (mainly) by tile m~pect of the velb there: &quot;who shoots&quot; vs. &quot;who shul&quot;, &quot;if hc is lloer '' vs. &quot;when he wax poor&quot;, etc. A spccitie expeclalion requires a delinite notal phl~dSC or a proper uaule Ill its &quot;auteceAlent&quot;. while a non..specilic one accepts either an indefinite or a delinite nonn phrase.</Paragraph> <Paragraph position="6"> Required Moflilications to Discourse Representatio.</Paragraph> <Paragraph position="7"> Theory llow conld I)RT incoi0oratc Ihis kind of iuionuation in order to determine more, reliably tile range of permissible anallhora aud cataphora, while rnling out the illegal coreferential reading in sentences like &quot;lie said that the boy had taken the book&quot;? The R)llowing it &quot;l list of requirements fl)r an implementation Ihat wonld take tllese additional condilions lute account; At ill traditional \])P,T, tile iuconling sentence otx;ns a new DRS, which defines tile space where all newly created discourse, referenls Call survive. Nouu phrases creme sot extlressic, ns (tile &quot;conditides&quot; of standard dleory): hldefinite and detinite noun lltnases give rise to norulal set expressions, while pro\]floons create set expressions Of a special type. Indefinite noon plnases give rise, in additioa, to discern'so referenls, which are, deposited in tim DRS nnder coustraction. Traditional DRT has proper uame,s create discourse reli:rents, toll. Whether this is the best possible decision is open to d0bale. It would, iu lnany respects, t)(3 more consistent to lreat protx:r nailles Oil a par widl detiui\[e uouu phrases. Discoarse referents shoald contain all the illform'.ttiou that can become relevant tbr tim resolntion of prenuminal nnallhora, i.e. at least ntnnber aud gender. Definite set eXllressions delived from full nonu phrases without co*~ditional modtihers, as well as those delJved fl'onl definite pronouns, are evalualed as soon as Ihcy are created, i.e. they try to find tlleir ',mtee,edenls among tile pre..exisling (liscourse reforeuts. \[{xpressions for pronouns whose autecedents have been fotuld tire renloved, once they have done Iheir duty as value shariug ch;mnels. So fIlr nothing really new.</Paragraph> <Paragraph position="8"> But now tile first modificatiou of standard theory is ueeded: Delinite full noun phrases are uot aiR,wed to look lbr their antec(xlenls inside file 1)RS still under CouslxnctiOll, wheu;as pr(lllOUnS ntay do so. Sdcond, wllen any definite UOHU phrase (fnl\[ noah phrase or pronoun) Ilas iomld tilt ton'oct discourse rcfercllt, it drags it into the DRS umler couslruclion. These two chauges make sure that two full noun phrases within Ihe same clause ate, never interpreted as corefemntial. They tdso block ealaphora in &quot;lie said that a boy had token the book&quot; (tile &quot;he&quot; has dragged file aptwopriate discotmse referent inlo the DRS, where it is &quot;iuvisible&quot; to the subseqnent &quot;tile boy&quot;). And, liually, it brings a discourse refereut accessed by a definite uoun phrase lute focus and makes it the prime caudiate for sllbsequcnt aaaphoric reference by ploaouns. The lhird modiiication to standard I)RT is tills: Bccat~: proaollnS ill uon-gene,ric contexts cequire delinite iloan phrases at ante, cedcnts (see examples 28 to 311, di~;oulse refereuls ulnst a/so calry information m~out tile definiteness of ~he noun phrase from which they were derived. Set expressions derived from prl)nOUllS will use this infornlaliou tO detennioe whedmr a giveu discourse referent is a possible ~mtece,dent. Thefou*th modification, linally, takes case of cataphora: Wheoever all expression denoling a contrition (on tile disconrse, sentence, or sab-sentential level) is encountere,d, uo embedded DRSs are created (as it is done in standard DRT for &quot;if&quot;- and &quot;every&quot;seuteuces) and the production of discourse referents goes on, but evaluation of all new set eXflressions is suspendexl. In particular, no filrther attempts at ,'maphora resolulJou ale nlade, aud all llronuuns encountered from now on are stored ill the DRS ouder cousttllctiou as unevahlated set expressions. It is only when die end of file chaise, is reacll0xl tllat unevahlated set expressious are processext. Aluoug the set expressions and disconrse refereuls &quot;in SUSlmnded animation&quot; within a DRS, any reference, (backwards and lorwards) is permitted, as/one as the coedilions oullincd above ale fullilled. This allows calaphura to be modelled, while the classical syutacti( reslriclious (calaphora only fi'om a non C/-eomnlauding COllSlittlent) are StlllSlllllOAI. Lastly, dlose discourse refere,nls thai are allowed In live (Ihose from assertive, i.e. non-conditional, contexts, and those that were.</Paragraph> <Paragraph position="9"> dragged ill l?om Ihe out.side) are released into the universe of discoarse re,ferents.</Paragraph> </Section> </Section> class="xml-element"></Paper>