suggestions and comments in connection with an earlier version of this paper.

Transcription

1 UNDERSPECIFIED PRESUPPOSITIONS 1 Frank Keer Centre for Cognitive Science University of Edinburgh keer@cogsci.ed.ac.uk Abstract In this paper, van der Sandt s (1992) account of presupposition as anaphora is reconstructed in Underspecified Discourse Representation Theory (UDRT). We show that UDRT readiy provides the means for representing presuppositiona anaphora, making redundant a specia α- structure as empoyed by van der Sandt. Our account is non-procedura, fuy monotonic, and offers an underspecified representation for ambiguities arising from presupposition accommodation. In this approach, presupposed materia is integrated directy into underspecified discourse representation structures. Presupposition binding and accommodation take pace by adding subordination restrictions to these underspecified structures. This aows us to capture certain instances of presupposition denia, as we as exica variation in the behavior of presupposition triggers. 1 Introduction The need for underspecified representations of semantic ambiguities is widey recognized both in semantic theory and in computationa inguistics. An underspecification-based approach to semantics on the one hand shoud offer the representationa devices to effectivey express underspecified meanings, and on the other hand shoud inherit the expanatory power of more traditiona semantic theories. 1 Thanks go to David Beaver, Anette Frank, Jonas Kuhn, David Miward, and Uwe Reye for suggestions and comments in connection with an earier version of this paper. Francis Corbin, Danièe Godard, and Jean-Marie Marandin (eds.). Empirica Issues in Forma Syntax and Semantics: Seected Papers from the Cooque de Syntaxe et de Sémantique de Paris (CSSP 1995), Bern: Peter Lang,

2 An instance of such an approach is Underspecified Discourse Representation Theory, initiated by Reye (1993). It extends the formaism of standard Discourse Representation Theory (DRT, Kamp and Reye 1993) to incude the means for underspecifying the scope reations between Discourse Representation Structures (DRSs). UDRT has been appied to ambiguities arising from scrambing (Frank and Reye 1992, Reye 1993) and pura noun phrases (Frank and Reye 1995a,b, Reye 1994). The goa of this paper is to show how an account of presupposition can be integrated into a UDRT setting, the underying assumption being that presuppositions are best treated as anaphora in the spirit of van der Sandt (1992). Our key idea is that anaphora can be regarded as scope-bearing eements, and that anaphora resoution corresponds to the disambiguation of anaphora scope. Presuppositiona anaphora have the specia property of remaining scopay underspecified if they cannot be bound to an antecedent. An unresoved presuppositiona anaphor then corresponds to an accommodated presupposition in van der Sandt s theory, with accommodation ambiguities remaining underspecified where van der Sandt recurs to disjunctive representations. In this section, we outine the two frameworks on which our account of presupposition reies: section 1.1 gives a brief overview of UDRT, section 1.2 introduces the anaysis of presupposition by van der Sandt and Geurts (1991) and van der Sandt (1992). 1.2 Overview of UDRT In DRT, the subordination of DRSs is represented graphicay with the hep of boxes and their nestings reative to each other. UDRT makes this subordination reation expicit by using abeed DRS-conditions of the form :γ where is a abe (a constant) and γ is a DRS-condition (or a discourse referent). The abes for the conditions in an Underspecified DRS (UDRS) are arranged in a attice through the reation. A subordination restriction of the form m > n states that the condition abeed n is stricty subordinate to the one abeed m. Weak subordination (incuding the possibiity of equa nesting) is expressed accordingy by m n. In standard DRT, scope ambiguities are expressed by disjunctive DRSs which differ in the nesting of the sub-drss they contain. In UDRT, the aim is to avoid disjunction by eaving the nesting, i.e., the subordination reations 2

3 underspecified: an ambiguous discourse is assigned a singe underspecified representation, on which inferences can be drawn directy (Reye 1993, 1995). This can be iustrated using exampe (1): (1) Everybody didn t pay attention. (Frank and Reye 1995b) The DRT representation for the two readings of (1) is as foows: (2) a. b. x human(x) x pay attention(x) human(x) pay attention(x) If we reformuate the same representation in UDRT, we get the structures in (3). Here, the subordination reation is represented by upwards arrows meaning : (3) a. b. x human(x) x human(x) pay attention(x) pay attention(x) These two UDRSs can be represented by a singe structure, hence eiminating the need for disjunctive representations: (4) x human(x) pay attention(x) We give the forma definition of a UDRS (foowing Reye 1993:162): 3

4 (5) A UDRS K is a pair L, D consisting of the subordination restrictions L = L, and the UDRS-conditions D, where L forms an upper semi-attice with 1-eement, L is a set of abes, and D a is set of conditions of the foowing form: a. :x, where L and x is a discourse referent b. :x 1 = x 2, where L and x 1, x 2 are discourse referents c. :P(x 1,, x n ), where L, x 1,, x n are discourse referents, and P is an n- pace predicate d. : 1, where, 1 L e. : 1 2, where, 1, 2 L f. : 1 n, where, 1,, n L Using this definition, the UDRS depicted in (4) can be restated by giving the subordination restrictions L and the UDRS-conditions D: 2 (6) 1 : T 1 11 :x 1 > 11 1 > :human(x) 11 > 12 2 : 21 T 2 2 > 21 3 :pay attention(x) As UDRT uses a subordination attice to represent scope ambiguities, disambiguation corresponds to adding more subordination information to the attice. An unambiguous structure is achieved if the attice is eventuay reduced to a inear order. In exampe (6), the two readings ensue by adding the constraints 12 > 2 and 21 > 1, respectivey. 1.3 Presuppositions as Anaphora An exampe for presupposition triggers are persona pronouns such as his. The foowing sentence presupposes that a rabbit exists which is owned by Theo: (7) Theo oves his itte rabbit. In this exampe, the presupposition is accommodated, i.e., the existence of a rabbit is asserted and the respective conditions are added to the discourse 2 Note that we assume that the scope of a quantifier is subordinate to its restrictor, expressed by the constraint 11 > 12 in this exampe. This is an extension of the definition of subordination proposed by Reye (1993) and Frank and Reye (1995a,b), which is necessary for our definition of accessibiity (the referents in the restrictor of a quantifier have to be accessibe from its scope, cf. van der Sandt 1992). 4

5 representation buit so far. However, if such an anima has aready been mentioned in the discourse, the presupposition gets canceed (or neutraized), i.e., his itte rabbit is interpreted as referring to the pre-estabished rabbit, and does not introduce a new one. This is the case for the exampes in (8), where a rabbit is mentioned in the first conjunct and in the antecedent of the impication, respectivey: (8) a. Theo has a itte rabbit and his rabbit is grey. b. If Theo has a itte rabbit, his rabbit is grey. (Van der Sandt and Geurts 1991:259) With reference to such exampes, van der Sandt and Geurts (1991) and van der Sandt (1992) argue that presuppositions behave in the same way as anaphora. They consider the foowing cases of pronomina anaphora, which are cosey anaogous to the exampes of presupposition canceing in (8): (9) a. Theo has a itte rabbit and it is grey. b. If Theo has a itte rabbit, it is grey. (Van der Sandt and Geurts 1991:259) Here, the pronoun it is bound to the antecedent a itte rabbit. In much the same way, the presupposition trigger his rabbit in (8) can be regarded as an anaphor which is bound to the antecedent a itte rabbit, and therefore gets neutraized. Hence, van der Sandt and Geurts concude, presuppositions are not reay canceed (i.e., retracted from the DRS), but rather bound to existing referring materia in much the same way as pronouns. The crucia difference to pronouns is that a presuppositiona anaphor can be accommodated if it fais to find a suitabe antecedent: in this case, its content is added to the DRS buit so far. Presuppositions possess this possibiity of being accommodated because they bear descriptive content of their own and hence can introduce a new discourse referent. This is not the case for pronouns, since these are semanticay void (apart from agreement information). To formaize the intuition that presuppositions behave ike anaphora, van der Sandt and Geurts (1991) modify standard DRT as foows: Conventiona DRSs are pairs of a set of referents and a set of conditions K = U(K), Con(K). Van der Sandt and Geurts use α-drss K = U(K), Con(K), A(K) instead, where A(K) is the anaphora structure (α-structure) of the DRS, which is again an α-drs. Instead of the top-down construction agorithm with integrated anaphora 5

6 resoution of Kamp and Reye (1993), van der Sandt and Geurts (1991) empoy a bottom-up construction mechanism using a categoria grammar. An α-drs is buit for one sentence at a time, its anaphora are coected in the α-structure, but not resoved. Then the α-drs is merged with the DRS of the preceding discourse, and its α-structure is resoved bottom-up. The treatment of presuppositions takes pace in the resoution of the α- structure. It is subdivided into two parts: The resoution starts with the most deepy embedded anaphor and tries to bind it in the usua way, i.e., by ooking for an antecedent which is suitabe and accessibe (in the sense of Kamp and Reye 1993:154). The agorithm tries to bind as ow as possibe: it inks the anaphor to the antecedent which is cosest on its projection ine. If no binding is possibe, the anaphor has to be accommodated. Accommodation proceeds top-down: the information contained in the respective α-drs is added to the highest DRS possibe. The accommodation site is constrained by conditions on possibe and admissibe DRSs (cf. van der Sandt 1992:365ff for definitions of these notions). In addition to van der Sandt and Geurts's (1991) rather procedura view of resoution and accommodation, a more decarative formuation is suggested by van der Sandt (1992). We wi draw on this version when we present our proposa for anaphora binding in section 2. We demonstrate how van der Sandt and Geurts s account works using the foowing exampe: (10) Every man oves his wife. (Van der Sandt 1992:366) The unresoved α-drs for (10) is given in (11a): (Thick ines mark α- structures.) (11) a. b. x man(x) ove(x, y) y wife(y) poss(z, y) z x z z = x man(x) ove(x, y) y wife(y) poss(z, y) 6

7 Now the α-structure of (11a) is processed. The most deepy embedded referent is z which arises from the pronoun his. It can be bound to x and is removed from the α-structure. This yieds (11b). Then, we try to bind the remaining α- DRS for wife. No suitabe antecedent can be found, thus accommodation has to take pace. We start top-down and try to accommodate in the top DRS, which is impossibe since z woud be a free variabe. Hence the accommodation has to take pace in the restrictor DRS (intermediate accommodation), yieding (12a): (12) a. b. x y z z = x man(x) wife(y) poss(z, y) ove(x, y) x z z = x man(x) y wife(y) poss(z, y) ove(x, y) According to van der Sandt (1992), there is aso the possibiity of oca accommodation: the α-drs for wife can aso stay further down the projection ine and be accommodated in the scope of the quantifier, which yieds (12b). 3 2 Underspecified Presuppositions In this section, we propose a reconstruction of the account of presupposition as anaphora put forward by van der Sandt and Geurts (1991) and van der Sandt (1992). We show that UDRT readiy provides the means for representing presuppositiona anaphora, making redundant a specia α-structure as empoyed by van der Sandt and Geurts. Our account is non-procedura, fuy monotonic, and offers an underspecified representation for ambiguities arising from presupposition accommodation. It can be used to capture certain instances of presupposition denia, as we as exica variation in the behavior of presupposition triggers. 3 It has to be pointed out that the existence of these two readings is not uncontroversia, Beaver (1994a,b, 1995) gives exampes where the intermediate reading is not avaiabe and argues that this reading is not triggered by presupposition but rather reated to the information structure of the discourse. He shows that discourse topic and focus affect the accommodation of presuppositions. 7

8 2.1 Against α-structure The use of a separate α-structure to store anaphora unti they are resoved can be criticized for severa reasons: The theoretica status of the unresoved anaphora in the α-structure is uncear. In particuar, van der Sandt and Geurts (1991) and van der Sandt (1992) give no semantic interpretation for α-drss, they assume that ony fuy resoved DRSs (where A(K) is empty) have truth vaues. 4 In contrast to that, our underspecified account of presupposition requires no storage mechanism comparabe to the α-structure. UDRSs have a truth-conditiona semantics and are equipped with a proof theory (Reye 1993, 1995). In van der Sandt and Geurts 1991, a very procedura view of anaphora resoution is put forward: the proposed agorithm searches a DRS first bottom-up and then top down, the order is crucia. 5 This is remedied to a certain extend in van der Sandt 1992, where a set of restrictions is provided to repace the agorithm. We try to improve on this, as our anaysis attempts to factor out as much decarative constraints as possibe, so as to keep the account independent of a certain processing strategy. Order-dependence shoud be postuated ony where absoutey necessary. 6 Van der Sandt s resoution mechanism is non-monotonic: the content of the α-structure is deeted and reocated to another part of the DRS ( semantic move-α, Beaver 1995:125). 7 We wi show that an account using UDRSs 4 But cf. Bos 1994, where van der Sandt s (1992) notion of α-drs is expicated and semanticay interpreted, aowing α-drss to act as underspecified representations for anaphoric materia. But Bos (1994) sti assumes a separate (procedura) accommodation component and accommodation ambiguities have to be represented disjunctivey. 5 The same is true for the extensions of the van der Sandtian account in Bos Cf. Krause 1995 for an eaboration of this criticism and an aternative proposa which integrates van der Sandt s approach into a type-theoretica framework, where presupposition resoution is treated as abductive inference. 7 Bos (1994) proposes a copying mechanism as an aternative: presuppositiona information is accommodated or resoved by copying the content of the α-drs to the reevant accommodation site (whie eaving the origina intact). This eads to a monotonic account but dupicates the 8

9 can preserve monotonicity: binding and accommodation take pace by adding subordination restrictions to the structure buit so far, no information has to be deeted or copied. 2.2 UDRSs instead of α-drss To improve on the representationa framework of van der Sandt, we reconstruct the theory of presupposition as anaphora in UDRT. Our account differs in the foowing respects from van der Sandt s (1992) origina proposa: We assume that anaphora resoution operates on underspecified structures. Anaphora are integrated into the UDRS right from the start, with their scope eft underspecified. This obviates the need for a separate α-structure. The presuppositiona UDRSs we assume can be constructed straightforwardy by a modified HPSG grammar (Poard and Sag 1994), as detaied in Keer We specify a resoution function which attempts to determine a suitabe antecedent for an anaphor. If it succeeds, UDRS-conditions and subordination constraints are added to the UDRS buit so far, thereby fixing the reference of the anaphor (whie preserving monotonicity). Anaphoric materia which cannot be resoved is accommodated. In this case, the resoution function adds no further information, the scope of the anaphor is eft underspecified. This is desirabe in the ight of the data we present in section 2.3: further subordination constraints (to disambiguate the accommodation site) shoud be added ony if this is necessary to create an antecedent or to maintain the consistency and informativeness of the discourse Representation We assume that presuppositions have a particuar scope potentia in much the same way as other scope-bearing eements, e.g., indefinites and quantifiers. Lexica and syntactic constraints restrict the scope of these eements by setting the minima abe min and the maxima abe max as ower and upper scope boundaries (cf. Reye 1993, 1994 for detais). anaphoric information, hence introducing undesirabe redundancy. 9

10 As an exampe consider (13), where the indefinite can take arbitrariy wide scope, hence its min is the bottom eement of the attice, and max is its top eement. This can be rendered in UDRT as shown in (14). (13) A probem about the environment preoccupies every serious poitician. (Reye 1993:132) (14) x serious poitician(x) y probem about the environment(y) preoccupy(y, x) The scope of an indefinite can be more restricted than in (14), e.g., if the indefinite is part of a negated cause. We assume that the scope of presuppositiona anaphora is essentiay unrestricted: the upper imit to its scope is the top box, i.e., max = T hods. Its ower imit corresponds to the position of the presupposition trigger. (15a) iustrates this by giving the UDRS for van der Sandt s exampe in (10) (again, thick ines indicate anaphoric materia which has to be resoved by a separate resoution component): (15) a. b. T T 1 x man(x) z y wife(y) poss(z, y) 2 1 x Theo(x) y rabbit(y) poss(x, y) 3 4 z 4 ove(x, y) 10 5 ove(x, z) In this exampe his introduces the pronomina referent z and triggers an anaphoric UDRS in which the NP argument of his is estabished as presupposed. In (15a), the reevant UDRS is {y, wife(y), poss(z, y)}. Consider

11 another exampe, which has anaphoric materia both in the subject and in the object NP: (16) Theo s rabbit doesn t ove him. The UDRS for this exampe is depicted in (15b). Here, the pronoun him introduces an anaphoric eement, and both the proper noun Theo and the genitive morphoogy trigger presuppositions. In Keer 1995, we propose an HPSG grammar which constructs the UDRSs given in this section. This is achieved by a set of syntactic and exica constraints introducing the appropriate subordination restrictions and UDRSconditions. The exica entries for presuppositiona eements mark the abes of the reevant UDRS as anaphoric, which then triggers the anaphora resoution component Binding After the underspecified representation for a sentence has been constructed, the anaphora it contains have to be resoved reative to the discourse processed so far. We assume that this is done by a separate anaphora resoution function, which is subject to the foowing constraints: 8 (17) Let K = L, D be the UDRS for the discourse buit so far and K s = L s, D s the UDRS of a newy added sentence. Let A s L s be the set containing the abes of the anaphoric expressions of K s. 9 Then K is updated to K' as foows: K' = K K s res(k K s, A s ) (18) res( L, D, A) = L' { = '}, {:x = y} A where the foowing conditions have to hod: (19) a. {:x, ':y} D b. y suit(d, x) c. ' acc(l, ) and L' = or ' acc(l, ) and ' acc(l L', ) with L' = {' = ''} for some '' L (20) suit(d, x) = {y {γ {:x, :γ(x)} D} {γ {:y, :γ(y)} D}} (21) acc(l, ) = {' { '', ' ''} L} 8 We use a generaized union operator which appies not ony to sets but aso to tupes of sets: A 1,, A n B 1,, B n = A 1 B 1,, A n B n 9 In Keer 1995, we expicate how the set A s is constructed by the syntactic component. 11

12 As stated in (17), the UDRS for the discourse buit so far is updated by merging it with the UDRS of the newy incoming sentence and possiby adding conditions to resove the anaphora contained in the new UDRS. 10 The conditions to be added are computed by the function res defined in (18): to bind the anaphoric referent x to the referent y, the condition :x = y and the subordination constraint = ' are added, which has the effect hat the two discourse referents are identified, and their respective UDRSs merged. Further subordination constraints may be added via L'. To ensure proper anaphora binding, res is subject to a number of constraints: (19a) seects a pair of referents in the set of UDRS-conditions D. (19b) ensures that the antecedent y is suitabe for x. In cause (20) we define suit(d, x), the set of suitabe antecedents for an anaphor x under the conditions D, as foows: a referent y is suitabe for x if the conditions attached to x are a subset of the ones attached to y. 11 (19c) requires either that ', the abe of the antecedent, is accessibe from, the abe of the anaphor, or that ' can be made accessibe by adding a further subordination constraint. 12 The first possibiity is the standard case: no additiona subordination constraints are added, L' is empty. The second possibiity arises since an anaphor can fix the (underspecified) scope of its antecedent (cf. the exampes in section 2.3.1). This is the case if there is a abe '' such that adding L' = {' = ''} to L makes ' accessibe from. 13 Our definition of accessibiity given in (21) is different from the one empoyed 10 The case of ambiguities arising from mutipe binding sites for the same anaphor is not covered by this definition. We eave this issue aside. 11 This is of course ony a rough approximation. We wi not eaborate on the conditions for suitabiity any further here. 12 Note that this condition does not aow to add arbitrary equations to make ' accessibe: of course ony such additions are possibe which resut in a we-formed subordination attice, for instance by coapsing to =. Hence this condition is not as permissive as it seems at first gance. 13 A simiar proposa is put forward by Kamp et a. (1995), who suggest that the need to bind a pronoun to a certain antecedent might promote this antecedent to top position. 12

13 by van der Sandt (1992): we cannot define accessibiity in terms of subordination, since the representations we construct eave the scope for anaphora underspecified, i.e., an unresoved anaphor is subordinate ony to the top abe T. We therefore draw on the fact that an anaphor is anchored to a subordinate UDRS-condition (the verb in the case of exampes (15a)), which is aso subordinate to the materia which has to be accessibe for the anaphor. Hence (21) states that acc(l, ), the set of abes accessibe from in a attice L, contains the abes for which a abe '' exists that is subordinate both to and to the accessibe abe '. 14 Note that (in contrast to van der Sandt 1992) our anaphora resoution component contains no conditions to prevent the unbinding of variabes: this is unnecessary as we construct UDRSs in a way which ensures that a variabes remain bound. An exampe for this is (15b): here the referent x in the condition 2 :poss(x, y) is bound correcty since 2 is subordinate to 1, where x is introduced. The reevant subordination constraint is added exicay. The same hods for the condition 3 :ove(y, z). Here a syntactic condition, the Cosed Formua Principe, ensures that the correct subordination constraints are introduced and y and z are bound (cf. Keer 1995 for detais). Furthermore, we do not need van der Sandt s (1992:365) additiona conditions to ensure that anaphora are processed bottom-up and eft-to-right: these conditions are remnants of the procedura formuation of his theory which carry over to his decarative reformuation. They disappear if we dispense with the α-structure. We use the exampe (10) to iustrate how anaphora resoution works according to our proposa. First consider the subordination constraints and conditions L, D of (15a): 14 For this definition to work, the UDRSs we construct have to contain the mentioned anchoring reations for anaphora. This has to be taken care of in the syntactic component. 13

14 (22) 1 : T 1 11 :x 1 > 11 1 > :man(x) 11 > 12 2 :z T 2 3 :y :wife(y) 3 :poss(z, y) 3 :ove(x, y) The set of the abes of the anaphoric expressions for this exampe is A = { 2, 3 }. The appication of the resoution function res (cf. (18) (21)) yieds the foowing resut: (23) res( L, D, A) = { 2 :z = x}, { 2 = 11 }, In this exampe, z can be resoved to x as x is suitabe for z according to definition (20), and 11 is accessibe from 2 according to definition (21), since there is the abe 4 which is subordinate to both 2 and 11. In contrast to this, y cannot be resoved, as no suitabe antecedent can be found, and therefore no condition for y is added. The updating of the constraints in (22) eads to the constraints in (24), depicted in (25). (24) 1 : T 1 11 :x 1 > 11 1 > :man(x) 11 > 12 2 :z T 2 2 :z = x 2 = 11 3 :y :wife(y) 3 :poss(z, y) 3 :ove(x, y)

15 (25) T 1 x man(x) y wife(y) poss(z, y) 4 ove(x, y) We give another exampe, where the presupposing materia triggered by his rabbit can actuay be bound: (26) Theo has a itte rabbit. Everybody oves his rabbit. The processing of the first sentence give rise to the UDRS in (27a). No anaphora resoution is possibe at this stage. Then the second sentence of (26) gets processed and is assigned the UDRS in (27b). (27) a. b. T T 1 v Theo(v) 2 w itte(w) rabbit(w) 4 x human(x) z y rabbit(y) poss(z, y) 3 poss(v, w) 7 ove(x, y) The UDRSs in (27a) and (27b) are merged and anaphora resoution is performed, the abes of the anaphoric expressions being A = { 5, 6 }. The appication of the function res produces the resut in (28): 15 (28) res( L, D, A) = { 1 = T, 5 = 1 }, { 5 :z = v} { 2 = T, 6 = 2 }, { 6 :y = w} Here, both z and x are bound to antecedents pre-estabished in the discourse. Note that in both cases the antecedents are not directy accessibe, but first have to be raised to the top eve by adding the constraints 1 = T and 2 = T, 15 In addition to that, we get the reading where z is bound to x, as in (15a). 15

16 respectivey. This is a (trivia) exampe for how the resoution of an anaphor can disambiguate the scope of its antecedent. The second disjunct of condition (19c) takes care of this, as described above. The resuting UDRS is: 16 (29) T v w y z z = v y = w Theo(v) rabbit(w) itte(w) poss(v, w) 4 x human(x) ove(x, y) No anaphor is eft unresoved in (29), hence we get a inear subordination order corresponding to an unambiguous UDRS Accommodation We propose no additiona mechanism for presupposition accommodation. The assumption is that the resut of the anaphora resoution provides a suitabe (underspecified) representation of accommodated presuppositions. As an exampe consider the constraints in (24), graphicay represented in (25). Here, the resoution component faied to bind the referent y, no conditions were added for y. The representation in (25) corresponds exacty to the DRSs (12a) and (12b) proposed by van der Sandt for this sentence: the accommodation site of the presupposition triggered by his wife is eft underspecified, just ike quantifier scope can be eft underspecified in UDRT. The disambiguation of (24) is achieved by adding the restriction 3 = 11, which yieds intermediate accommodation, or by adding 3 = 12, which eads to oca accommodation. The first possibiity strengthens the exicay determined constraint 2 3 to 2 = 3, the second one entais 2 > 3. Note that accommodation higher in the attice (i.e., goba accommodation) is bocked due to the constraint 2 3 : this is correct, as it avoids the unbinding of the 16 We ignore the condition abeed 3, which is redundant in this representation. 16

17 variabe z. In addition to admitting the same accommodation sites as van der Sandt s account, our proposa has the foowing advantages: No separate accommodation mechanism is proposed, no fixed accommodation sites are predicted. This provides not ony an underspecified representation for accommodation ambiguities, but aso aows for the scope of accommodated materia to be disambiguated by information that is added ater in the discourse. Such disambiguation can occur if an antecedent for an anaphor is needed or if discourse consistency and informativeness has to be maintained (cf. section for exampes). The account of van der Sandt and Geurts (1991) and van der Sandt (1992), in contrast, computes a fixed accommodation site (viz., as far up the projection ine of the anaphor as possibe) and uses disjunctions to represent accommodation ambiguities. Their prediction is that once the site has been determined, it cannot be changed by the subsequent discourse. 17 In section 2.3.2, we give counterexampes invoving presupposition denia. Furthermore, our proposa can be extended to dea with presupposition triggers which are more restricted in the possibe accommodation sites they aow: as the subordination constraints for presuppositions are introduced exicay, additiona constraints can be stipuated for specific exica entries, thus exicay restricting accommodation behavior. Reevant exampes incude verbs which take a sententia compement, discussed briefy in section Note that van der Sandt s account does not aow to determine the accommodation site exicay, as his α-structure together with his accommodation agorithm predict that a presuppositions are accommodated in a uniform way, depending ony on the structure of the present discourse. As far as grammar architecture is concerned, our account has the advantage of readiy offering an interface to other components of the grammar: 17 However, extensions of the van der Sandtian account are conceivabe which assume a component that triggers a revision of the accommodation site if this is necessitated by incoming new information. In such an approach, van der Sandt s mechanism woud ony compute the preferred accommodation site, without actuay fixing it. However, this resuts in a nonmonotonic system. 17

18 inferencing components or modues deaing with pragmatic or word knowedge can simpy add UDRS-conditions or subordination constraints to the UDRSs buit by the syntacticosemantic component, thus extending or disambiguating the discourse representations Empirica Issues Certain empirica consequences foow from the assumption that unresoved presuppositiona anaphora remain underspecified in scope, rather than being accommodated. In this section, we wi provide some data to support this view on anaphora Disambiguation by Anaphora Resoution The resoution of an anaphor can disambiguate the scope of its antecedent. A standard exampe for this is: (30) Every cassmate of mine fancies a gir in the sixth form. We, it is true, she is very attractive. (Kamp et a. 1995) The indefinite a gir is no presupposition trigger, i.e., no anaphora resoution is performed when the first sentence of (30) is processed. The resuting structure is anaogous to the one in (14), where the scope of the indefinite remains underspecified. But when the second sentence is processed, the need to find an antecedent for she disambiguates the indefinite a gir to its wide scope reading: it is accessibe for the pronoun ony if it takes wide scope. Consider an anaogous exampe invoving a presupposition trigger: (31) * Every man oves his wife. We, it is true, she is very attractive. The UDRS for the first sentence of (31) is given in (25): the presupposition his wife triggers anaphora resoution, and once it is bound to every man, the presupposition is no onger accessibe to pronouns in the foowing discourse. Hence she cannot be bound and (31) is ungrammatica. Formay, this is achieved by the accessibiity constraint in the resoution function: condition 18 The data presented by Beaver (1994b) seems to point in this direction: he argues that intermediate accommodation is not triggered by presuppositiona information (as van der Sandt predicts), but rather by a more genera mechanism of topic accommodation. In our account, this coud be impemented by assuming a separate modue which handes topics in Beaver s sense and contributes subordination constraints for intermediate accommodation where adequate. 18

19 (19c) aows resoution ony if the antecedent is directy accessibe to the anaphor (which is not the case here) or if it can be made accessibe by adding a abe equation: this possibiity is bocked since the restrictor box is stricty subordinate to the top UDRS ( T 1 and 1 > 11 in (24)). A more interesting exampe is the foowing: (32) Theo doesn t ove his rabbit. His rabbit is grey. After anaphora resoution, we get the UDRS in (33a) for the first sentence of (32): (33) a. b. c. T T v w x y z Theo(x) rabbit(y) 1 x z poss(z, y) Theo(x) z = x z = x v = x 3 w = y 2 y rabbit(y) 3 poss(z, y) T 2 3 v x z Theo(x) z = x v = x y rabbit(y) poss(z, y) 5 ove(x, y) 5 ove(x, y) 5 ove(x, y) The scope of the negation is underspecified at this stage. But as soon as the second sentence of (32) is processed and its presuppositiona anaphor his rabbit gets bound, an unambiguous representation ensues: the boxes abeed 1 and 2 have to be raised to top eve to make them accessibe, which yieds (33b). Given the ambiguity of the UDRS in (33a), we expect that the negation can take wide scope over the boxes abeed 1 and 2. Evidence for this comes from exampes with presupposition denia as in (34). Here, the UDRS in (33a) is disambiguated to yied the structure in (33c): 19 (34) Theo doesn t ove his rabbit. In fact, he doesn t have a rabbit. 19 The question arises whether the existentia presupposition of proper names can be denied in the same way. This seems to be the case. Consider the foowing sighty macabre exampe: (i) Peter doesn t ove Mary anymore. She was kied in a traffic accident yesterday. 19

20 2.2.2 Presupposition Denia Exampes of presupposition denia as the one in (34) are not covered by van der Sandt and Geurts (1991) and van der Sandt (1992): in their account, one sentence is processed at a time and a fixed accommodation site is computed for each unbound presuppositiona anaphor. A presupposition cannot be canceed once its site is fixed, and the subsequent discourse shoud not be abe to infuence its scope. Therefore, they predict exampes such as (35a) (anaogous to (34) above) and (35b) to be ungrammatica, since the denia of the existentia presupposition shoud ead to inconsistency: (35) a. The king of France is not bad. France does not have a king. (Van der Sandt 1991:332) b. If John invites the king of France for dinner, he wi come. But there is no king of France, of course. The underspecified anaysis proposed here can cope with exampes ike these. The definite description the king of France introduced by the first sentence in (35a) and (35b) is initiay ambiguous between goba and intermediate accommodation (in the top box or in the restrictor/negation box). The second sentence then disambiguates the scope of the definite by excuding goba accommodation, since this woud ead to inconsistency (the existence of the king of France both being asserted and denied). A simiar effect is found in (36), where the existentia presupposition is not directy negated, but part of a conditiona: (36) If John invites the king of France for dinner, he wi come. If there is a king of France, that is. In this case, the second sentence forces disambiguation on grounds of informativity: if the existence of a king of France was aready given by the first sentence (goba accommodation), then the second sentence woud be uninformative, since the existentia assertion is embedded in the restrictor of a conditiona. 20 Again, intermediate accommodation of the king of France offers 20 Van der Sandt uses an anaogous argumentation in terms of informativeness to rue out exampes ike: (i) * John has a dog. If he has a dog, he has a cat. (van der Sandt 1992:368) 20

21 a way out and renders (36) grammatica. 21 As mentioned earier, Beaver (1994a,b, 1995) gives data that cast doubt on the existence of intermediate accommodation for presuppositions embedded inside universa quantifiers or conditionas. He assumes that an exampe ike the one in (37a) can ony be interpreted as accommodating her Cadiac ocay, i.e., (37a) can ony have the reading gossed in (37b). (37) a. Every woman who buys a car wi se her Cadiac. (Beaver 1995:117) b. Every woman who buys a car owns a Cadiac and wi se it. Exampe (38) seems to provide counter-evidence: it suggests that the subsequent discourse can enforce intermediate accommodation: 22 (38) Every woman who buys a car wi se her Cadiac. Ony if she owns a Cadiac, of course. Just ike in (36), the utterance of the second sentence of (38) forces intermediate accommodation for the first sentence: oca accommodation woud ead an inconsistent discourse. We take this as evidence that intermediate accommodation is indeed an option in certain marked cases, and hence that our account is right in aowing it (but oca binding seems to be the defaut case, as argued for convincingy by Beaver). The question remains how to formaize the notions of consistency and informativity. A suitabe suggestion is van der Sandt s (1992:367) concept of admissibe resoutions, and its reformuation by Beaver (1995:107), which can easiy be integrated into the present account (cf. Keer 1995 for detais). 21 However, the proposed approach to presuposition denia is counter-intuitive in that it treats denia in the same way as ambiguity resoution, i.e., in a competey monotonic fashion. Intuitivey, denying a presupposition invoves retracting information which is aready estabished. This intuition is not captured by the proposed account and it might be argued that a van der Sandtian approach pus a non-monotonic mechanism for denia is more adequate (cf. footnote 17). 22 Exampes invoving generics are interesting in this respect: cf. (i), which seems to aow for an intermediate reading even without a particuar context: (i) Everybody takes their pram into the supermarket. (Beaver 1995:118) 21

22 2.2.3 Lexica Restrictions on Accommodation An advantage of the presented approach is that it aows to specify exica restrictions on the accommodation and binding of presuppositions. The exica entry of a presupposition trigger introduces a set of subordination restrictions that determines its accommodation behavior. This gives us a hande on exica variation in presupposition triggers, which can be used, for instance, to account for the diverse properties of sententia compement verbs. According to Karttunen (1974:185), three casses of sententia compement verbs have to be distinguished according to their projection properties: (39) a. Verbs of saying: say, ask, te, announce, etc. b. Verbs of propositiona attitude: beieve, fear, think, want, etc. c. Other compementizabe verbs: factives, semi-factives, modas, aspectua verbs, etc. Karttunen s generaization is that verbs of type (39c) require that the context of the matrix cause satisfies the presuppositions of the compement cause, whereas this is not the case for verbs of type (39a) and (39b): verbs of saying impose no restrictions on the context of utterance, whie propositiona attitude verbs require that the subject of the matrix cause hods a beief which satisfies the presupposition of the compement cause. In the framework of underspecified presuppositions, this generaization can be captured by making use of exicay introduced subordination restrictions. A tentative account aong these ines is presented in Keer Concusion We presented a reconstruction of the van der Sandtian account of presupposition in Underspecified Discourse Representation Theory. Our account is non-procedura and fuy monotonic. In particuar, it eiminates van der Sandt s α-structure and repaces his rather procedura notion of anaphora binding. Furthermore, it requires no specia mechanism for presupposition accommodation and provides an underspecified representation for ambiguities arising from mutipe accommodation sites. This was shown to have empirica advantages over the use of fuy resoved structures as of van der Sandt s. In the framework proposed here, three components of the grammar contribute subordination constraints and UDRS-conditions to the semantic representation of a discourse: 22

23 The exica entries provide an initia set of UDRS constraints and conditions. This can be used to account for exica variation among presupposition triggers, an exampe being the variance in the presuppositiona behavior of sententia compement verbs (cf. section 2.3.3). Syntactic principes add further subordination constraints. This possibiity is not used in the approach outined here, but is necessary, e.g., to account for syntactic restrictions on quantifier scope or for scrambing phenomena (Frank and Reye 1995a,b). Finay, the semantic component can contribute additiona UDRS constraints and conditions. This is used by our anaphora resoution function and can be iustrated with respect to disambiguation by anaphora resoution (cf. section 2.3.1) and presupposition denia (cf. section 2.3.2). References Beaver, David. 1994a. When Variabes Don t Vary Enough. In Mandy Harvey and Lynn Santeman, eds., Proceedings of the 4th Conference on Semantics and Linguistic Theory. Rochester, NY. Beaver, David. 1994b. Accommodating Topics. In Rob van der Sandt and Peter Bosch, eds., Proceedings of the IBM/Journa of Semantics Conference on Focus. Institute for Logic and Linguistics, IBM Heideberg. Beaver, David Presupposition and Assertion in Dynamic Semantics. Ph.D. thesis, University of Edinburgh. Bos, Johan Presupposition and VP-Eipsis. CLAUS Report 37. Department of Computationa Linguistics, University of the Saarand. Frank, Anette and Uwe Reye How to Cope With Scrambing and Scope. In Günther Görz, ed., Proceedings of KONVENS-92, Springer, Berin. Frank, Anette and Uwe Reye. 1995a. Principe Based Semantics for HPSG. In Proceedings of the 7th Conference of the European Chapter of the Association for Computationa Linguistics, 1 8. Dubin. (Short version.) Frank, Anette and Uwe Reye. 1995b. Principe Based Semantics for HPSG. Working Papers of the SFB 340. University of Stuttgart. (Long version.) Kamp, Hans and Uwe Reye From Discourse to Logic. Introduction to Modetheoretic Semantics of Natura Language, Forma Logic and Discourse Representation Theory. Kuwer, Dordrecht. Kamp, Hans, Uwe Reye, and Antje Rossdeutscher Underspecified Representation, Discourse Inference and Lexica Meaning. Unpub. ms., Institute for Computationa 23

24 Linguistics, University of Stuttgart. Karttunen, Lauri Presuppositions and Linguistic Context. Theoretica Linguistics 1: Keer, Frank Integrating an Underspecified Account of Presupposition into HPSG. In David Beaver, ed., The DYANA Integrated Impementation. DYANA-2 Deiverabe R3.7, ILLC/Department of Phiosophy, University of Amsterdam. Krause, Peter Presupposition and Abduction in Type Theory. In Suresh Manandhar, Werner Nutt, and Jörg Siekmann, eds., Proceedings of the Workshop on Computationa Logic for Natura Language Processing. Centre for Cognitive Science, Edinburgh. Poard, Car and Ivan A. Sag Head-Driven Phrase Structure Grammar. University of Chicago Press, Chicago and CSLI Pubications, Stanford, CA. Reye, Uwe Deaing with Ambiguities by Underspecification: Construction, Representation and Deduction. Journa of Semantics 10: Reye, Uwe Monotonic Disambiguation and Pura Pronoun Resoution. In Hans Kamp, ed., Eipsis, Tense and Questions, DYANA-2 Deiverabe R2.2.B, ILLC/Department of Phiosophy, University of Amsterdam. Reye, Uwe On Reasoning with Ambiguities. In Proceedings of the 7th Conference of the European Chapter of the Association for Computationa Linguistics, Dubin. Van der Sandt, Rob Denia. In Lise M. Dobrin, Lynn Nichos, and Rosa M. Rodriguez, eds., Papers from the 27th Regiona Meeting of the Chicago Linguistic Society. Vo. 2: The Parasession on Negation, Chicago. Van der Sandt, Rob Presupposition Projection as Anaphora Resoution. Journa of Semantics 9: Van der Sandt, Rob and Bart Geurts Presupposition, Anaphora, and Lexica Content. In O. Herzog and C.-R. Roinger, eds., Text Understanding in LILOG, Springer, Berin. 24