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Centre for Cognitive Science

Negation and ordering relations: the case of until L.M.Tovena Research Paper EUCCS/RP-68 September 1994

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The University of Edinburgh

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Negation and ordering relations: the case of

until

L.M.Tovena1 Centre for Cognitive Science The University of Edinburgh 2 Buccleuch Place Edinburgh EH8 9LW UK [email protected]

Research Paper EUCCS/RP-68 September 1994

Centre for Cognitive Science The University of Edinburgh

c 1994 Copyright Centre for Cognitive Science The University of Edinburgh

Centre for Cognitive Science The University of Edinburgh 2 Buccleuch Place Edinburgh EH8 9LW UK

Negation and ordering relations: the case of

until

L.M.Tovena

Contents

1 Introduction 2 Core cases

2.1 Until as a binary operator . . . . 2.2 Simple and complex operators . . 2.2.1 Until in positive contexts 2.2.2 Until in negative contexts

3 More data 3.1 3.2 3.3 3.4

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The use of two operators . . . . . . . Scoping relations . . . . . . . . . . . From concurrence to postpositioning Until and implicatures . . . . . . . .

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4 Conclusion 5 References

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24 24 Abstract

This study argues in favour of a uni ed analysis of until as a binary time operator sensitive to the characteristics of the eventualities instantiating its arguments. It is further argued that until, as an ordering operator, interacts directly with negation, an order reversing operator. Such an interaction produces a complex operator whose semantics is like the original, except for the ordering that is reversed. The analysis is supported by cross-linguistic data. Material contained in this study was presented at the Pionier Colloquium on Negation and Polarity, in June 1994 at the University of Groningen. Thanks to Sheila Glasbey, Elisabet Engdahl, Janet Hitzeman and Ivan Derzhanski for comments or discussions. Thanks to Ulrike Hahn for assistance with data from German. 

1

2 Negation and ordering relations: the case of until

1 Introduction Until is sometimes classi ed as a special negative polarity item (NPI) which, contrary to all other temporal expressions considered sensitive to polarity, is subject to further aspectual restrictions. This is the treatment proposed in (Karttunen 1974) and (Linebarger 1980). According to such a treatment, the contrast in (1) is explained by considering until an NPI, and ruling out (1b) as licensing failure. The lack of contrast in (2) is then accounted for by postulating two dierent words, a durative and a punctual until, and by imposing extra requirements on the types of verb with which the latter, i.e. the NPI, must co-occur.

(1) (2)

a. b. a. b.

He did not awake until the alarm went o. *He awoke until the alarm went o. She did not sleep until the sun rose. She slept until the sun rose.

Several points make this analysis unattractive. The main criticisms from the point of view of tense and aspect analysis are summarised in (Hitzeman 1991). They are that it does not provide an explanation for the acceptability of example (2a), because until in the scope of negation requires what Karttunen calls a `punctual' verb, and that, again following his terminology, it leaves open the question of what causes the impression of a shift in `focus' between the a. and b. examples in (1) and (2). A further weakening point is that the functioning of the phenomenon of polarity, to which this treatment appeals, is still under discussion, hence the appeal itself could be interpreted as a way of pushing the issue one step back without solving it. Although it is common practice to split up items considered of negative polarity into a PS part and a non-PS one1 , at least in this case the assumption of such a lexical ambiguity is not supported by clear semantic arguments. No explanation is provided for the similarities between the two `dierent' until s. Finally, as noted above, this item has to be given special status, with constraints that don't apply to any other NPI. Another trend of analysis, referred hereafter as the tense and aspect analysis, see (Klima 1964), Mittwoch's (1977) reply to Karttunen, (Hitzeman 1991) and references therein, treats until as a unique element. The characterization of until as a durative adverbial rests on the crucial assumption that negated eventualities are duratives. Our proposal has points in common and in contrast with both trends. We shall argue against the double-until approach, showing that a uni ed treatment of until is possible once it is recognized that this item is an ordering 1

Any oers a clear example in point.

Core cases 3

operator, and that the characteristics of the instantiators of its arguments aect the felicity of the relation. We will make use of Hitzeman's analysis of until as a binary operator which orders its arguments, A and B, without subscribing to her idea of selectional restrictions on them. The restrictions observed in the distribution of this item will be derived from general conditions of compatibility between the roles imposed by until on its arguments and the characteristics of the eventualities2 instantiating them. Thus, the issue of the characterization of negated eventualities is independent from the analysis proposed here. We will further argue that the interaction of until with negation produces a complex operator, obtained by function application of negation to the functor until. As a result, the original ordering is reversed. The impression that the perspective moves between (1a) and (1b), or (2a) and (2b), follows from B's identifying either the end or the beginning of A, depending on the direction of the order.

2 Core cases

2.1 Until as a binary operator In her paper on aspect and adverbials, Hitzeman (1991) introduces a treatment of the prepositions heading temporal adverbials as binary operators. The idea is to treat these adverbials as operators that take eventualities as arguments. This allows her to keep the perspective of the analysis on the properties of the eventualities, rather than on the properties of their intervals. With respect to this point, Hitzeman highlights the relevance of the distinctions between eventualities with well-de ned and poorly-de ned termination points. She observes that the primary function of temporal adverbials is to order events, and derives from there the relevance of their borders in the assessment of the relation. She also shows that this type of analysis applies to temporal adverbials in general. We subscribe to this idea of temporal adverbials as binary operators and to the conviction of the relevance of the terminating point of eventualities. Where we part is when she claims that until is an instance of the schema [A P B], where A and B are eventualities and P is a preposition of class i, i.e. a preposition that orders the events in one of the three modes classi ed as `prepositioning', `postpositioning' or `concurrence'. Our disagreement stems from the fact that we consider the roles for the two arguments of until to be asymmetric. In our analysis, until temporally locates the eventuality instantiating argument A, i.e. it assigns A an event time in a reichenbachian i

i

2 We use the term eventuality in the sense adopted in (Bach 1986), i.e. to cover states and events.

4 Negation and ordering relations: the case of until analysis, by establishing an anaphoric relation with respect to the location of either the point in time or the eventuality instantiating argument B. In other words, until positions or orders A with respect to B depending on whether B is an interval or an eventuality. However, since the time axis is represented by a directed line, the relation can always be considered as an ordering. As a matter of fact, when discussing until, Hitzeman usually refers to the eventuality in A and a well-de ned point within B, hence introducing in practice the asymmetry not acknowledged in theory. In the next section it will be shown how the observation that the role of arguments A and B is asymmetric enables us to account for the dierences in the possible instantiators of A and B, as well as to explain the behaviour of the ordering with respect to negation.

2.2 Simple and complex operators The rst half of this section is devoted to a discussion of the use of until in positive contexts. First, until is described as expressing a relation of precedence between its arguments. Then this position is somewhat nuanced, because of the dierent possible instantiators of the two arguments. The second half describes the eects of the presence of negation. It is argued that the interaction between the ordering operator until with the order reverser negation results in a modi cation of the direction of the ordering.

2.2.1 Until in positive contexts Until temporally situates the eventuality instantiating argument A by de ning its position relative to the point in time provided by B. The instantiator of A, e.g. his walking in (3), stretches up to B, e.g. three in (3a), or a point in it, often the beginning, when B is an interval identi ed for instance by the eventuality occurring over it, e.g. his feeling tired in (3b), or by a time expression denoting an interval, e.g. the evening in (3c). A schematic representation of the operator and its arguments is provided in (4), similar to the schema adopted by Hitzeman.

(3)

a. He walked until three. b. He walked until he felt tired. c. He walked until the evening.

(4)

A UNTIL B

In (5a), her sleeping (A) lasts up to the calling from the butler (B), i.e. A  B with the additional requirement that the two together constitute

Core cases 5

a uninterrupted interval. Argument A must be instantiated by a durative, hence (5a) is ruled in and (5b) out. It seems that until `introduces' a stopping point for the eventuality in A, and that this point cannot coincide with a well-de ned termination point of the whole eventuality, hence the need for duratives. (5)

a. She slept until the butler called her. b. *He awoke until the butler called him.

With respect to examples (6) and (7), the relevance of the dierence between telic and atelic events is to be noted. The verb clap in (6) can be interpreted only as doing many claps. Similarly, dance in (7a) means doing many dances or an endless one, as explicitly stated in (7b). (6)

He clapped until his hands were sore.

(7)

a. She danced until the sun rose. b. She kept dancing until the sun rose.

The duration in A is obtainable also via iteration, cf. (8). The question relevant to the issue under examination is not the type of borders of the events forming the iteration, because in (8) they have well-de ned termination points and this should disqualify them from instantiating argument A. The question is that the whole iteration instantiates argument A. For instance, in the case of (8) or (9), the bare plural in either subject or direct object position allows in nite repetition, i.e. free recursion. Hence, the iteration has a poorly-de ned termination point. (8) (9)

Guests arrived until midnight. a. She ate just sandwiches until she got an advancement. b. She wrote letters until she fell asleep.

Of course, free recursion can be obtained in other ways, see for instance (6) and (10). (10)

The polling was repeated several times until a consensus was reached.

If the recursion is limited to a precise number of times, for instance because one of the arguments of the predicate is stated to be instantiated a xed amount of times, the result is an iteration with a well-de ned termination point. Thus, the sentence is ill-formed, see (11a). In such a case, the

6 Negation and ordering relations: the case of until presence of a bare plural in one of the arguments of the predicate seems not to be enough to rescue the sentence because of the cumulative reading which arises, see (11b), instead of free recursion.3 (11)

a. *She ate ve sandwiches until noon. b. *Girls ate twenty sandwiches until noon.

Similarly, the collective reading is not available in example (12). (12)

Many guests arrived until midnight.

In the discussion of example (3), it was noted that argument B can be instantiated by expressions of time, as three, or by eventualities. As a consequence of the asymmetric roles of A and B, expressions of time denoting moments may never occur in A, cf. (13). Argument A has to be eventuality denoting because it contains the `entity' which is to be mapped. (13)

a. *Noon until she arrived. b. *Noon until she did not arrive. c. *It was noon until she arrived.

However, not any eventuality is a suitable instantiator of B either. The instantiator of B must provide an identi able point, hence the ill-formedness of example (14) suggests that states cannot always be used to identify a precise point in time4 . The same must be said for activities. (14)

*Daniel studied until he stayed in his mother's house.

Hitzeman says that the prepositional object of until must \introduce an eventuality true over an interval which is or contains a well-de ned termination point"(Hitzeman 1991:113). However, it is not clear how to reconcile the constraint on the termination point with the role of B as providing information on the stopping point of A. On the contrary, once such a function of B has been established, and it has been acknowledged that until is sensitive to the characteristics of the instantiators of its arguments, it follows that When context gives enough support and makes the free recursion reading available, the sentence becomes acceptable. For instance, in the improbable case of a Guinness booklike competition between teams of several twenty-sandwiches-eaters, it becomes possible to attribute to sentence (11b) the interpretation that the team of girls performed until noon. 4 There is another reading, not relevant for the current discussion, where his staying at his mother's is interpreted as an event. In this case, sentences (14) and (17) below, become acceptable. 3

Core cases 7 until is sensitive to the existence of a prominent point corresponding to the eventuality described by B, with no need of imposing selectional restrictions on B. In this way, example (15a) can be reconciled with (15b) in a uni ed treatment, and the potential ambiguity of (15c) is predicted. The preference for B contributing its end in (15c) is due to its being an accomplishment, but the other option is also possible with supportive context, as shown in (15d).

(15)

a. b. c. d.

Joe was unhappy until Irene started to build him a house. Joe was unhappy until Irene nished building him a house. Joe was unhappy until Irene built him a house. The old man was unhappy until the City Council built him a house. I saw him at the cerimonial laying of the rst stone and he was glowing.

2.2.2 Until in negative contexts The con guration presented in (16) represents the main way in which until interacts with negation. As anticipated at the beginning of this section, their interaction is due to the fact that until is an ordering operator and that negation is an order aecting operator. (16)

A [ : UNTIL ] B

A key point for our analysis is that negation is an operator sensitive to the characteristics of its argument. In the literature, negation is an operator whose core function is always characterised in the same general way, namely as the complementation function, but whose role has been analysed in dierent ways. It has been treated as a boolean operator, cf. (Keenan and Faltz 1985), but also as an ordering reverser, a function investigated in particular by Fauconnier (1975) and Ladusaw (1979) in connection with polarity sensitivity (PS) phenomena. The former aects truth value assignment, the latter scalar ordering. Because of the still controversial nature of NPI, it is not clear how to connect the latter role with the function of licenser, one of the open questions in the study of PS phenomena. The idea adopted in this study is that the dierences in role of negation originate from the variations in the arguments to which it applies. In other words, the treatment we propose is not a case of shifting a presumed ambiguity from until onto negation. The data seem to support the hypothesis that there is a preference for negation interacting with the ordering operator rst. In (16), negation applies to the functor until, and form a new complex operator. More precisely, it is a case of function application of negation to the ordering operator. The result is an operator which has the characteristics

8 Negation and ordering relations: the case of until of the simple one, with the dierence that the ordering relation is reversed. Now B marks the beginning of A. Because of their new relative positions, the constraints on the types of the arguments are modi ed: B must identify a point in time which is the beginning of A, so A must possess a clearly identi able beginning. The constraint on B remains the same, compare (17) with (14). (17)

*Daniel did not study until he stayed in his mother's house.

Finally, the perspective has not been changed, i.e. it is still A which is the eventuality that has to be mapped, but, as said, it is to be situated on the interval beginning at the point individuated by B. Hence, we have the feeling that the focus has moved. The idea of function application of not to another element is not entirely new. Our complex functor bears some similarities to a proposal made by Hoeksema (1986) with respect to the interaction of not with the quanti er all. Hoeksema argues that the monotonicity of the generalized quanti er not all students can be accounted for compositionally if one adopts the structure [[not all] students], with a complex determiner, rather than [not [all students]] where the negation modi es the NP. In the second part of this study, we shall provide further data that show that negation can modify the type of ordering imposed by a temporal adverbial. When until interacts with negation, a second consequence of the asymmetric roles of A and B discussed above becomes apparent. The application of negation to an ordering relation reverses the direction of the ordering, so the order  becomes >. We have shown above that in positive contexts until can be interpreted as establishing the order  between its two arguments. It has also been shown that this interpretation is a little too simplistic, because it does not provide motivations for the dierent range of instantiations available for A and B. This observation has led us to the conclusion that until allows for the possibility of mapping A on the time axis by de ning its position relative to B. Hence, A stands in an anaphoric relation with respect to B5 . This anaphoric relation is part of the semantics of until, and is not modi ed by the presence of negation. Furthermore, until is sensitive to the presence of a prominent point in B, which usually is at the beginning or at the end of B, and because of that the relation between A and B turns out to be either < or , in positive clauses. When the negation and until are fused, the resulting order is >. Whenever this reversed order is combined with the referential use of the left border of B, the relation expressed by the complex function is A  B. 5 Strictly speaking, it is a cataphoric relation, because B acts as antecedent and usually occurs second in linear order.

Core cases 9

Let us go back to examples (1) and (2), repeated here as (18) and (19). It can be seen that our proposal accounts for the judgements of (18) with respect to the question of the aspect of the verb, because the event of his awakening has a well-de ned termination point, so it cannot occur as a rst element of the ordering, see (18b). With respect to the question of the predictions for polarity licensing, (19a) is grammatical because her sleeping is the second element of the ordering. (18) (19)

a. b. a. b.

He did not awake until the alarm went o. *He awoke until the alarm went o. She did not sleep until the sun rose. She slept until the sun rose.

In addition to accounting for the distribution of until, our treatment accounts also for the distribution of the readings of the verbs. The inchoative reading of sleep in (19a), and its absence in (19b), are explained because only in (19b) is her sleeping rst in the ordering. In this case its right border is relevant for the assessment of the relation, whereas the inchoative reading focuses on the left border, i.e. the inception. The inchoative reading in (19a) is predicted because B identi es the beginning of the interval occupied by A and indicates the convergence of the left borders of B and A. Similarly, the inchoative reading in (20) is due to the fact that the border of B identi es the end of the interval occupied by A. There is no need to invoke a presupposition of his awakening in (18a), because its eective occurrence follows from A being the eventuality to be ordered. (20)

She sang until the baby slept.

The situation is even clearer in Catalan, a language that also has a unique lexical element to perform the simple and complex functions, namely ns, but which makes an overt distinction between inchoative and durative verbs, see (21). (21)

a.

El nen ha dormit ns a les 9. `The boy slept until 9.' b. El nen no s'ha adormit ns a les 9. `The boy did not sleep until 9.' c. *El nen no ha dormit ns a les 9. `The boy did not sleep until 9.'

Similarly, the verb clap in (22a) can have the meaning of striking the palms together once or of starting to applaude, because A is second in the ordering. In (22b) A is rst in the ordering, and clap has the durative meaning of applaud.

10 Negation and ordering relations: the case of until (22)

a. He didn't clap until everybody was ready. b. He clapped until everybody was ready.

It becomes possible to say something about (23) too. The only way of interpreting example (23) is by attributing to continue the meaning of resume, which is consistent with the positioning of A as second of the ordering. (23)

The rehearsal did not continue until three, when all the artists had come back from lunch.

The con guration discussed above is the one responsible for the shift in perspective already noted in the literature, cf. (Karttunen 1974) among others. The assumption that negated eventualities are atelic is no longer as crucial as for former uni ed treatments of until, and the failure of polarity licensing in (18b) becomes irrelevant. It is also possible to accommodate the intuitions that A does not necessarily follow B, but may be co-temporal with it. When discussing example (15c), it was noted that, taken in isolation, the sentence is potentially ambiguous. The ambiguity is there also in a sentence like Joe was not happy until Irene built him a house, as predicted by our treatment. This ambiguity does not seem to be expected in Hitzeman's treatment. Although there are similarities between her treatment and ours, for instance until is always considered an operator and the characterisation of negation as a complementation function is central in both, there are also signi cative dierences in what such a function applies to. Hitzeman combines the negation together with the until B compound, and claims that the interval selected for placing A in the negated case is the complement of the interval identi ed by the compound. However, the process of selection of the well-de ned point within B used by until is treated as a selectional restriction on B, i.e. choosing the prominent point, and the reader is led to believe that this well-de ned point is unique and no ambiguity may ever occur, contrary to data like (15d). Furthermore, the selectional restriction for a durative A forces her to assume that, in cases such as (18b), negation also combines with the eventuality instantiating A and turns it into a durative. This is to say that the same occurrence of negation has two eects, one outside and one inside A, namely selecting a complement interval and performing an aspectual transformation. This is also to say that the eect of negation on the instantiation of A is taken into account only for the purposes of the restriction on A, and not with respect to the whole relation. In fact, as Hitzeman herself states explicitly (Hitzeman 1991:117), it is the eventuality in A, and not the negated eventuality, that is mapped in the complement interval. So, negation both does and does not aect the instantiation of A, which is contradictory.

Core cases 11

Our proposal presents several advantages. First, it does not require the assumption of a double until, with the connected problems of motivating their common form and partially common semantics. Second, as just noted, it does not rest on the assumption that the negation of an achievement turns this eventuality into a duration, which is far from undisputed. Third, nothing need be added to ensure that A will actually occur at the switching point, as shown by the unacceptability of (24). (24)

*He did not sleep until three, when he gave up and made himself a cup of coee.

Example (24) constitutes evidence against the assumption that the shift in perspective is produced by inference. In fact, sentence (24) would require an appeal to presupposition, in the sense of non defeasible inference, in order to account for the ungrammaticality. However, it will be discussed how such an appeal would cause us problems in the case of a sentence like (44) below. Further evidence against an explanations in terms of inferences is provided by the observation that the interpretation of sentence (25a) is as paraphrased in (25b) and not as (25c). (25)

a. Joe did not sleep until midnight. b. Not until midnight did Joe sleep. c. Joe kept not sleeping up to midnight.

The similarity in meaning between (25a) and (25b) has already been discussed in (Hitzeman 1991), hence does not require further commenting. On the other hand, it could be objected that sentence (25a) cannot be analysed as (25b) precisely because English `has' (25b) as a perfectly grammatical sentence. However, this objection would ignore the fact that the two examples have similar meanings as far as the ordering goes, but they dier in focus. Sentence (25b) will be preferred in case one want to convey the information that Joe should have been asleep well before midnight, whereas (25a) will be selected for a more neutral report. Furthermore, our analysis provides a beginning of solution for the problem Hitzeman raises and leaves open at the end of her paper, in her example (82), here (26). The question asked by Hitzeman is why sentence (26) is ungrammatical, given the fact that until supplies its argument A with a well-de ned termination point and that in requires an eventuality with a well-de ned termination point as input. (26)

*Joe slept until noon in two hours.

In our opinion, a pointer to a possible answer is the observation that the main function of until is to order the eventuality in A, thereby providing it

12 Negation and ordering relations: the case of until with an event time. The mapping causes the output to be an eventuality with a well-de ned termination point, but such is not the main purpose of the operator until. If one consider time adverbials as mapping operators, one sees that it is not possible to map the same eventuality twice. It could be objected that it is not exactly the `same' eventuality that is mapped twice, since in the rst case it is sleep and in the second sleep until noon. However, if Joe's sleeping occurs in the interval terminating at noon, there is no guarantee that this is not contradictory with its starting in two hours. Dowty (1982:39) treats the question of multiple time adverbials as reducible to a cyclic application of the same time adverbial rule which forms a new sentence out of a sentence by adding a time adverbial to it. The repeated application is allowed only if it is possible to nd a single reference time which meets all the requirements of the various adverbials. Considering example (26), it can be said that there is no way to ensure the uniqueness of the time referent. Furthermore, because of the dierent orderings the two operators de ne, until and in select dierent readings of the verb sleep, namely durative the former and inchoative the latter. The reading of in two hours as a time-span adverb, which could be compatible with a durative reading of the verb, is also ruled out for (26), because in such a case the adverbial requires an eventuality whose well-de ned termination point is not set temporally. This analysis allows us to distinguish the use of until in con guration (16) from that of before. So, although both (27a) and (27b) are compatible with the situation were the party started at nine, only (27b) is compatible with a party having started at ten. In fact, B indicates the rst point of A. As said above, from there follows also the veridicality of until. (27)

a. The party did not start until nine. b. The party did not start before nine.

The presence of a `factive' and a `counterfactual' reading of before (Heinamaki 1972) might be reduced to the fact that before identi es a point on the time axis without distinguishing between which of the branches stemming from that point will be or is the actual one, thinking in terms of possible worlds. Finally, our treatment does not require the stipulation of any operations or assumptions special for the case. The combination of the two operators is just a case of function application of negation to until. The semantics of the compound is a function of the semantics of its constituents and the way these constituents are combined. The nature of scalar reverser of negation is a point largely studied in connection with polarity phenomena and does not require further comments. It seems also possible to reduce example (28) to the complex function case represented in (16). This step is motivated by the bridging property of

Core cases 13

neg-raising expressions. (28)

a. I don't think the child woke up until the mother called her. b. It is unlikely that he will arrive until after the show.

One may consider an analysis of neg-raising verbs in terms of functions characterised by the property of consistency, which Kas (1993:101) attributes to Zwarts. On the basis of this property, reproduced in (29), negation can be interpreted as occurring in clausemate position with until, and can apply to it. (29)

f

(?X)  ?f (X)

At this point, two questions remain to be discussed. One is the convergence of the left borders of A and the point provided by B in the reversed order con guration, and the other is the presumed `disappearance' of the constraint of duration on argument A in the reversed order. The rest of the section is devoted to them. Negation changes the relation from prepositioning to postpositioning. Strictly speaking, however, the relation may turn out to be a case of parallelism, when the end of B is considered in the direct order, or the beginning of B is considered in the reversed order. In any case, there is a constraint on A and B sharing an interval. However, there seem to be two types of examples where this constraint is overruled. One case is presented in (30)6. (30)

Nancy did not marry until she met Henry.

This example is a case where it is dicult to identify the relevant point, rather than a counter-example. We agree with Karttunen who says that meet has to be taken with a particular interpretation. Indeed, as shown by the unacceptability of (31a) and (31b), meeting is to be interpreted as getting acquainted with rather than bumping into a person. Sentence (31c) has been included because it shows an interesting change in interpretation with respect to (30). In fact, (30) implicates that Nancy eventually married Henry, whereas this implication is a great deal weaker in (31c). Our explanation is that in (31c) the second meeting with Henry provides just a point for mapping Nancy's getting married. In (30), the meeting is a complex event which indirectly supplies an instantiation for the role of patient of the verb marry. (31) 6

a. *Nancy did not marry until she rst met Henry. b. *Nancy did not marry until she last met Henry. c. Nancy did not marry until she met Henry for the second time.

The example is from (Karttunen 1974).

14 Negation and ordering relations: the case of until The second type of example contains a verb of phase transition in argument A. In this respect, it may be worth considering the issue of the preparatory period of A in the assessment of the point identi ed by B. (32)

He did not nish university until he went to live on his own.

The second question we want to discuss is that of the constraint of duration and atelicity on argument A, which are present in positive contexts, but which seem to disappear when until is combined with negation. We have two types of answer to this question, which do not contradict each other. The rst one is that the asymmetric roles of A and B is involved in the change. The operator until introduces either a stop or a start for its argument A, depending on the direction of the ordering. Therefore, argument B identi es the termination-point or the beginning of A. When it identi es its beginning, conditions on the terminating point of A lose relevance. The second one, which is not an answer strictly speaking, is related to a characterization of the relation established by until in positive and negative sentences as from prepositioning to postpositioning. It is interesting to notice that there are cases of items used as counterparts of until, where negation changes the type of ordering relation. Two cases, Hungarian and Italian, will be presented in section 3.3.

3 More data This section opens with some data showing that there are languages where the complex function not: : :until is realised as a lexical unit, and simple and complex functions are independent. Then we discuss other ways in which negation can aect a sentence containing until. The third part presents data from languages where the ordering relation expressed in English by until is obtained by applying negation to an operator expressing a relation of cotemporality. Finally, the last part raises questions about the implicatures of sentences containing until.

3.1 The use of two operators We have analysed until either as a simple operator, or as a complex one obtained by composition of the simple one with negation. A prediction that could be made on the basis of such a treatment is that there should be languages in which the complex operator is lexically realized as a unit. This unit may express the same meaning as not: : :until by following a dierent strategy. In this section, two dierent strategies will be presented. The rst one is identifying the beginning of the suitable interval using expressions

More data 15

like `only since'. This is the strategy adopted by German7. The item bis is used to indicate the terminating point, and erst um the starting one8 , see example (33). The perspective being xed for each of the items, the interaction with negation does not give origin to order reversion. Negation modi es the truth value of the relation and not the direction of the ordering. (33)

a.

Der Junge schlief bis 8 Uhr. `The boy slept until 8.' b. Der Junge wachte erst um 8 Uhr auf. `The boy did not awake until 8.'

In these cases, negation does not form a complex function with the two temporal operators, see examples (34)9 and (35). (34) (35)

Die Prinzessin wachte nicht auf, bis ich sie um 9 Uhr weckte (bis 9 Uhr). `The princess didn't wake up until when I woke her up at 9 o'clock.' Ich will nicht erst um drei gehen. `I do not want to go only at three.' (i.e. I want to go before then)

Another strategy is identifying the end of the unsuitable interval, the preferred choice in French.10 French uses the expression jusqu'a to indicate the termination point, and the expression ne: : :que for the starting one, see (36). (36)

a.

La jeune lle a dormi jusqu'a 8 heures. `The girl slept until 8.' b. Elle ne s'est reveillee qu'a 8 heures. `She did not awake until 8.

The reason for there being only ne without pas before que is that full negation sets to false the truth value of the relation, cf. (37a). In (37b), ne just controls the left border of the rst eventuality, preventing it from 7 We agree that these data do not provide crucial evidence either for or against homonymy. As a matter of fact, (Karttunen 1974) uses them to support his claim of the existence of two distinct until s. 8 Strictly speaking, this expression could also be considered complex, because erst provides the `only'-part of the meaning, and um the `since'-part. It must be noted that erst is the `only' which applies to ordered sets, whereas nur, which also means `only', applies to unordered sets. 9 Example (34) comes from (Karttunen 1974:fn.8). 10 As a matter of fact, French can exploit the rst strategy too, via the expression seulement. A possible reason why this strategy is less preferred in French could be that seulement, like only and unlike erst, applies to ordered and unordered sets indierently.

16 Negation and ordering relations: the case of until sliding back beyond B. So, although, at rst sight, the French strategy bears similarities to the one followed by English, their functionings do not match. The dierent eect of full negation in French with respect to English follows from the impossibility of reverting the direction of the ordering imposed by the operator in the former case. (37)

a.

Le moteur n'a pas tourne qu'a trois heures, mais a midi aussi. `The engine did not work only at three, but also at noon.' b. Le moteur n'a tourne qu'a trois heures. `The engine did not work until three.'

However, a similar control over the movements of A explains the contrast in (38), already noted in (Karttunen 1974). A comparison between (38) and (39) shows that here in the case of the operator until, as it was the case in the discussion of the generalized quanti er not all students in (Hoeksema 1986), the dierent directions of inference can be accounted for compositionally. ( the earliest. (38) The princess didn't wake up until 9 at at the latest. ( the earliest. (39) The princess slept until 9 at at the latest. A word should be added with respect to examples (40) and (41). They do not constitute a counterexample to the previous statement on the monotonicity of A UNTIL B, because what is highlighted in (40)11 and (41) is the monotonicity of the argument B and not of the whole. So, (40) shows the eect of negation, whereas (41) shows the lack of monotonic properties of argument B. (40) (41)

a. b. a. b.

She didn't wake up until at least 9. *She didn't wake up until at most 9. She slept until at least 9. She slept until at most 9.

The dierence between (39) and (41) is that in the former the modi ers aect the relation directly, whilst in the latter they aect the instantiation of B, and only indirectly the relation. 11

Example (40a) is taken from (Mittwoch 1977).

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3.2 Scoping relations Negation can interact with until in two main ways. It can either interact with it directly, in what could be seen as a wide scope relation, or with its arguments, a kind of narrow scope one. In the latter case it can negate either of the arguments. However, a formulation of the questions in terms of scope relations may run into problems in cases where the sentence contains other operators. We have already discussed one case in which negation interacts with until. A second way of interacting, mainly induced by stress, is what the literature calls metalinguistic negation12 . It expresses a denial of the truthfulness of the relation established by until on its arguments. This case may be represented by the con guration presented in (42). (42)

: [ A UNTIL B ]

In this respect, there is no dierence between metalinguistic or contrastive (McCawley 1991) use of negation, see (43). (43)

a. He DIDN'T sleep until two. b. *He DIDN'T awake until two. c. He didn't sleep until two, but ran until three.

Sentence (44) provides another example of con guration (45). (44)

The party didn't last until midnight.

Example (44) contains an instance of a durative verb, which is atelic and non distributive, hence the eventuality cannot be said to happen at every subinterval. Therefore, the eventuality of the party's lasting cannot be placed by referring to its left border, which makes it unsuitable for being the second element of the order. The only interpretation available is to consider negation as applying to the truth value of the sentence. Con guration (42) per se is of reduced interest for the current study. However, it is worth pointing out that we have seen cases, such as (24), where the presumed inference of A holding after B is not defeasible, and cases, such as (44), where the inference is not only not `obligatory', but also not possible. More interesting is the observation that until can also take `wide scope' over the negation. This situation is realized as the con gurations in (45) and (46). 12

This use of negation has been treated extensively in (Horn 1989).

18 Negation and ordering relations: the case of until (45) (46)

[ : A ] UNTIL B A UNTIL [ : B ]

The con guration in (45) is the trickiest, so to speak, because it has to `compete' with (16), which is the preferred one. Motivation for asserting the existence of such a preference comes from the fact that speakers constantly report the feeling of a switch in perspective in sentences analysable as instances of con guration (16). On the other hand, evidence of the existence of con guration (45) comes from the negative polarity side, for instance, see example (47). (47)

He did not lift a nger until the teacher scolded him publicly.

Con guration (45) is also favoured by the presence of a universal quanti er in argument A. As usual, everybody outscopes the negation, and no special explanation has to be provided for the dierence in preferred interpretation between (48a) and (48b), which share the same context. (48)

a. Everybody did not eat cakes until the end of Lent. b. Daniel did not eat cakes until the end of Lent.

Finally, there is the case of inversion, see (49), which makes the interpretation of the sentence according to con guration (45) at least as plausible as (16). (49)

He promised to buttress his claim with evidence, and until then Daniel won't believe him.

Examples of con guration (46) are presented in (50). In this con guration the linear order rules out an application of negation to until. (50)

a.

He kept harassing her on the phone until she did not answer it any more. b. We had a correspondence until she did not write to me any more.

It is interesting to notice that the acceptability of the sentences in (50) degrades if the expression any more is suppressed. The change is not entirely surprising if one considers the position we have adopted in this study. The proposed choice for con guration (16) rather than (45) as the main analysis implies the consideration that the preferred interpretation does not refer to `negated' eventualities, i.e. the duration of the not happening of an eventuality, but to eventualities standing in various relations. This position holds

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with respect to argument A as well as argument B. Therefore, it is expected that in (50), instead of the interval over which B does not happen being used for the mapping, the cessation of the eventuality in B is used, which is precisely what is made explicit by the presence of any more. This position allows us to account also for the contrast in (51), due to the dierent ways in which French expresses the reference to the end of the preceding negative interval and the beginning of the subsequent negative interval. The element plus highlights the switch between a `positive' and a `negative' phases, whereas pas selects the negative phase, possibly terminated by a positive one. (51)

a.

L'enfant a crie jusqu'a n'avoir plus de voix. `The child screamed until s/he lost her/his voice.' b. *L'enfant a crie jusqu'a n'avoir pas de voix. `The child screamed until s/he had no voice.'

The contrast in (52) provides further evidence for the crucial role of the switch time in the assessment of the relation. The presence of deja in (52b) forces the interpretation that the screaming of the child stopped at some time past the time when the light went out, thereby causing the unacceptability of the sentence. (52)

a.

L'enfant a crie jusqu'a ce qu'il n'y ait plus de lumiere. `The child screamed until all the lights were out.' b. *L'enfant a crie jusqu'a ce qu'il n'y ait deja plus de lumiere. `The child screamed until all the lights had already been out.'

3.3 From concurrence to postpositioning We have seen that negation changes the relation expressed by until from what can be generally described as prepositioning to postpositioning. Hungarian and Italian provide other cases where negation brings about a change in the type of ordering imposed by a temporal adverbial, primarily from concurrence to postpositioning. Pi~non (1991) provides the following data on Hungarian, as evidence that the temporal connective amg, whose meaning is rendered as `while', see example (53), performs a function equivalent to that of the English until when the subordinate clause contains a negation, see (54). The function of the item addig is to double the marking of the relation, and its occurrence is optional. (53)

a.

Boldog voltam, amg Mari a felesegem volt. happy was.I while Mary the wife.my was `I was happy while Mary was my wife.'

20 Negation and ordering relations: the case of until (54)

a.

(Addig) olvastam, amg Janos le nem fekudt. that.till read(PST).I while John PREV NEG lay `I read until John lay down to sleep.' b. (Addig) beszelgettunk, amg Mari fel nem hvott. that.till talked.we while Mary PREV NEG called `We talked until Mary called us up.'

The main issue Pi~non is investigating in his paper is the presence of the broken order, i.e. the con guration where negation breaks the preverb{ verb sequence by occurring right before the verb, in the subordinate clause introduced by amg. This order is usually used to express emphatic negation, and appears also in the clause introduced by certain lexical elements, e.g. amg. The issue Pi~non addresses is how to reconcile the presence of the broken order with the absence of emphasis in the subordinate. However, as Pi~non (1992:254) himself notes, there is also the possibility of ordering the preverb after the verb in subordinate clauses introduced by amg, a sequence which produces a dierent interpretation, compare (55) with (54a). (55)

(Addig) olvastam, amg Janos nem fekudt le. that.till read(PST).I while John NEG lay PREV `I read while John was not lying down to sleep'

A line of research that is suggested by the approach we have adopted in this paper takes into consideration the changes in verb aspect brought about by the pre/post positioning of the preverb with respect to the verb, and the interaction with negation. The placement of the preverb before the verb indicates perfectivity, and the broken order comes about because negation goes in front of the verb. Imperfectivity is indicated by positioning the preverb after the verb. It seems promising to study the variation of the type of relation expressed by amg with respect to the perfectivity or imperfectivity of the subordinate clause. Italian possesses at least three ways to express the not: : :until relation. Two follow the same strategy noted for French, namely non: : :che and solo `only'13 , with the dierence that their degree of preference is the opposite of the French. They both express the feeling that the beginning has happened after the expected time, and can also convey the disappointment of the speaker for this delay. There is a third way, which is the most common and does not carry feelings of frustrated expectation. The expression in question is no/ nche, 13

Hungarian too has this last possibility. The expression is csak `only'.

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depending on the syntactic role that it has to perform, i.e. introducing respectively a prepositional phrase or a sentence. In positive sentences, nche can be paraphrased as as long as, and expresses cotemporality of the two eventuality, with identity of the terminating points, see (56). As shown by the ungrammaticality of (57), the two eventualities must be atelic. (56)

(57)

a.

Dormo un po' nche leggi. `I sleep a little while you read.' b. Leggo un po' nche dormi. `I read a little while you sleep.' a. *Dormo nche parti. `I sleep while you leave.' b. *Parto nche dormi. `I leave while you sleep.'

It is worth noting that the concurrence can be established from or to a certain moment, by de ning a point to (a) or from (da) which the relation is holding. However, the constraint of duration on argument A remains, as shown by the ungrammaticality of (59). (58)

(59)

a.

Ti aspetto no alle tre. `I wait for you until three.' b. Ti aspetto n dalle tre. `I have been waiting for you since three.' a. *Si e svegliata no alle tre. `She awoke until three.' b. *Si e svegliata n dalle tre. `She awoke since three.'

In conjunction with negation, nche expresses the meaning of until, see example (60). The perspective is on the interval up to B. (60)

Leggo il giornale nche non ritorni a casa. `I read the newspaper until you come home.'

With two negations, on both sides of nche, the meaning is until and the perspective is on the interval from B onwards, see example (61), which could be a bedtime conversation between a parent and a little child. (61)

a.

Non parto nche non dormi. `I do not go until you fall asleep.' b. Finche non parti non dormo. `As long as you do not leave I will not fall asleep.'

22 Negation and ordering relations: the case of until It is worth noting that there are strong similarities between the use of one or two negations with nche in Italian, example (62), and the use of one or two negations with amg in Hungarian, see (63). (62)

a.

Abbiamo parlato nche Maria non ci ha chiamato. `We talked until Mary called us.' b. Non abbiamo parlato nche Maria non ci ha chiamato. `We didn't talk until Mary called us.'

(63)

a.

Beszelgettunk, amg Mari fel nem hvott. talked.we while Mary PREV NEG called `We talked until Mary called us up.' b. Nem beszelgettunk, amg Mari fel nem hvott. NEG talked.we while Mary PREV NEG called `We didn't talk until Mary called us up.'

3.4 Until and implicatures In this section we will consider two issues related to the possible implicatures that arise from sentences containing until in positive and negative clauses. First, let us make a minor point about negated eventualities and complements. The termination point of the eventuality in the rst argument of until, is identi ed by the second argument. Strictly speaking, anything else can carry on or start after that point, apart from the eventuality instantiating the rst argument. However, the termination of this eventuality does not imply the beginning of what is pragmatically seen as its complement. For instance, when one is not asleep, one is not necessarily awake. Sentence (64) oers a relevant example. Hence, analyses based on inferences cannot account for the fact that the awakening will de nitely take place in (65), and are forced to call presupposition into play for this type of cases. (64)

The patient slept quietly until ve, when he went into a coma.

(65)

The patient did not awake until ve.

A case that requires further examination is that of sentences containing other types of negative items, e.g. nothing or no, in the matrix clause, see (66a) and (67a). We would rather not treat these examples as cases of function composition of the negation with until, because this would require an operation of lexical decomposition of the negative quanti er into a negative part and what would presumably be an inde nite, prior to the function composition itself. The alternative would be to suggest that the

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strong implication of something appearing on the screen after the button pressing event in (66a) is to be connected with the role of this event as identi er of a meaningful moment, rather than being attributed to the reversed ordering produced by some sort of function application. The negative element is instantiating one argument of the predicate contained in A, and the implication arises because of the dichotomous partitioning of the time axis induced by until. Support for this analysis comes from the presence of a similarly strong implication in the corresponding sentence in German, see (66b), where the order is never reversed because function application does not takes place. The same must be said for (67a) and the corresponding German sentences in (67b) to (67d). (66)

(67)

a.

Nothing appeared on the screen until Louise pressed the green button. b. Man konnte nichts auf dem Bildschirm sehen, bis Luise den grunen Knopf one could nothing on the screen see until Louise the green button druckte pressed a. Tom ate no potatoes until he was sixteen. b. Tom hat, bis er 16 war, keine Kartoeln gegessen. Tom had, bis he 16 was, no potatoes eaten c. Tom a keine Kartoeln, bis er 16 war. Tom ate no potatoes bis he 16 was d. Erst mit 16 hat Tom Kartoeln gegessen. Erst with 16 had Tom potatoes eaten

Such a proposal would gain conclusiveness if it could be shown that (67a), for instance, is dierent from (68) inasmuch as the inference can be cancelled in the former but not in the latter. This seems to be the case if one considers example (69). (68) (69)

Tom did not eat any potatoes until he was sixteen. Until he was sixteen, Tom only ate no meat, after that he ate neither meat nor sh.

Sentence (69) shows that it is possible to cancel the inference that Tom will eat meat after his sixtheenth birthday. As argued in section 2.2, this would not be possible if the sentence were to be analysed as a case of function composition, i.e. as a case of con guration (16). However, we have to

24 Negation and ordering relations: the case of until agree that the argument is not as strong as we would wish. Sentence (69) degrades when the order of the arguments is altered. As we noted in section 3.2, inversion facilitates a reading where negation aects only argument A. So, although the need for inversion is motivated by the observation that the emphasis is on argument B, the possibility of providing independent motivation for analysing example (69) as a case of con guration (45) weakens our argument.

4 Conclusion Our proposal of a uni ed account for the behaviour of until, allowing this operator to interact with negation, can be considered a way of putting together the two trends of analysis discussed in the literature, without taking in the burden of their special assumptions. We are sympathetic with the idea of negation interacting with until, proposed by approaches based on negative polarity. The main dierences are that we do not postulate a split into two lexical items; and that instead of a `passive' relation between the two operators, as in licensing, we propose an `active' relation, as in function application. We subscribe to the idea of a unique until, common in approaches more concerned with aspectual facts. The main dierence here is that we let negation interact with until rather than with the verb, so we do not have to take a stand on the issue of negated eventualities. As a result, our proposal can account for a wide range of data, both distributional and interpretational, without requiring special assumptions.

5 References Bach E., 1986, The Algebra of Events, in Linguistics and Philisophy, Vol.9, pp. 5{16 Dowty D.R., 1982, Tenses, Time Adverbs, and Compositional Semantic Theory, in Linguistics and Philisophy, Vol.5, pp. 23{55 Fauconnier G., Pragmatic Scales and Logical Structure, in Linguistic Inquiry, Vol.6, pp. 353{375 Heinamaki O., 1972, Before, in Papers from the Eighth Regional Meeting of the Chicago Linguistic Society, pp. 139{151 Hitzeman J., 1991, Aspect and Adverbials, in Proceedings of SALT I, Cornell University, pp. 107{125

References 25

Hoeksema J., 1986, Monotonicity Phenomena in Natural Language, in Linguistic Analysis, Vol.16, pp. 25{40 Horn L., 1989, A Natural History of Negation, Chicago University Press, Chicago Karttunen L., 1974, Until, in Papers from the Tenth Regional Meeting of the Chicago Linguistic Society, pp. 284{297 Kas M., 1993, Essays on Boolean Functions and Negative Polarity, Doctoral dissertation, University of Groningen Keenan E., L. Faltz, 1985, Boolean Semantics for Natural Languages, Reidel, Dordrecht Klima E.S., 1964, Negation in English, in Fodor J.A. and J.J. Katz (eds.) The structure of language, Prentice Hall, New Jersey Ladusaw W., 1979, Polarity sensitivity as inherent scope relations, Ph.D Thesis, University of Texas at Austin, published by Garland Publishing Inc., 1980 Linebarger M.C., 1980, The grammar of negative polarity, Ph.D. diss., MIT, published by Indiana University Linguistics Club, 1981 Mittwoch A., 1977, Negative sentences with until, in Papers from the Thirteenth Regional Meeting of the Chicago Linguistic Society, pp. 410{ 417 McCawley J.D., 1991, Contrastive negation and metalinguistic negation, in Proceedings of the Parasession on Negation, CLS 27, pp. 198{206 Pi~non C.J., 1991, Presupposition and the syntax of negation in Hungarian, in Proceedings of the Parasession on Negation, CLS 27, pp. 247{262