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<Paper uid="W06-2111">
  <Title>On the prepositions which introduce an adjunct of duration</Title>
  <Section position="3" start_page="0" end_page="73" type="metho">
    <SectionTitle>
PHRASE STRUCTURE GRAMMAR, en-
</SectionTitle>
    <Paragraph position="0"> riched with a number of devices which are familiar from DISCOURSE REPRESENTA-TION THEORY. The resulting analysis is demonstrated to be relevant for machine translation, natural language generation and natural language understanding. 1 A typology of PP adjuncts of duration In many languages the adjuncts of duration take different forms depending on the aspectual class of the VP which they modify. In English, for instance, they are introduced by for if the VP denotes a state or a process and by in if the VP denotes an accomplishment.</Paragraph>
    <Paragraph position="1">  (1) Maria played the piano for an hour.</Paragraph>
    <Paragraph position="2"> (2) Anna wrote that letter in half an hour.</Paragraph>
    <Paragraph position="3"> Orthogonal to this distinction, there is another one, which can be made explicit by comparing (1) and (3) with (4).</Paragraph>
    <Paragraph position="4"> (3) Laura will stay in Ohio for two months.</Paragraph>
    <Paragraph position="5"> (4) Silvia has lived in Paris for three years.  The adjuncts in (1) and (3) unambiguously specify the duration of Maria's activity of playing the piano and of Laura's stay in Ohio. The adjunct in (4), however, triggers an ambiguity: it can denote any three-year period in the past in which the state of Silvia's living in Paris held, but it can also denote a period which started three years ago and which includes the time of utterance (Kamp and Reyle, 1993, 567). The relevance of this distinction is clear from the fact that there are languages which use different prepositions for both interpretations. Italian, for instance, employs the preposition per in the translation of (1), (3) and the first interpretation of (4), whereas it employs da in the translation of the second interpretation of (4).  (5) Maria suon`o il pianoforte per un'ora.</Paragraph>
    <Paragraph position="6"> (6) Laura star`a per due mesi nell'Ohio.</Paragraph>
    <Paragraph position="7"> (7) Silvia ha abitato per tre anni a Parigi.</Paragraph>
    <Paragraph position="8"> (8) Silvia abita a Parigi da tre anni.</Paragraph>
    <Paragraph position="9">  For ease of reference I will call the adjuncts in (1), (3), (4a), (5), (6) and (7) floating: they denote a stretch of time whose position on the time line is not defined. The adjuncts in (4b) and (8), by contrast, will be called anchored, since their position on the time line is fixed: their right boundary is supplied by the time of utterance. As illustrated in (9-10), the right boundary can also be supplied by a temporal adjunct, such as a PP[a] or a subordi- null The distinction between floating and anchored adjuncts is also relevant for the PP[in] adjuncts. To show this let us compare (2) and (11) with (12).  (11) Pablo makes such a drawing in less than five minutes.</Paragraph>
    <Paragraph position="10"> (12) Leo will tune your piano in an hour.</Paragraph>
    <Paragraph position="11">  In (2) and (11) the PP[in] adjuncts are unambiguously floating, but (12) is ambiguous: it can either mean that it will take Leo one hour to tune your piano or that he will start the activity of tuning your piano in an hour from now. In the first interpretation, the adjunct is floating, as in (2) and (11), but in the second one it is anchored: the beginning of the hour which will pass before Leo starts tuning the piano is supplied by the time of utterance. The relevance of the distinction is, again, brought out by the Italian equivalents. While the floating PP adjuncts are introduced by in, as in the translation of (2), (11) and (12a), the anchored ones are introduced by fra, as in the tanslation of (12b).1  (13) Anna ha scritto quella lettera in mezz'ora. (14) Pablo fa un disegno come quello in meno di cinque minuti.</Paragraph>
    <Paragraph position="12"> (15) Leo accorder`a il tuo pianoforte in un'ora. (16) Leo accorder`a il tuo pianoforte fra un'ora.  The following table provides a summary of the data discussed so far.</Paragraph>
    <Paragraph position="13"> floating anchored</Paragraph>
    <Paragraph position="15"> The distinction between floating and anchored adjuncts is relevant for Machine Translation and for Natural Language Generation, since it conditions the choice of the preposition. At the same time, it is also relevant for Natural Language Understanding, since it bears on the issue of scope.</Paragraph>
    <Paragraph position="16"> More specifically, while the floating adjuncts can be in the scope of a VP quantifier, the anchored  conditioned by phonological factors. To avoid alliteration speakers tend to prefer fra when (one of) the surrounding words start with t(r), and tra when (one of) the surrounding words start with f(r).</Paragraph>
    <Paragraph position="17">  'Lea has lived in Rome for three years.' The PP[per] in (17) is in the scope of the quantifying spesso 'often': there are several one hour periods of my playing the flute. By contrast the PP[da] in (18) outscopes the quantifying sempre 'always', yielding an interpretation in which Lea's living in Rome is said to go on uninterruptedly for a period of three years. The same contrast can be observed in sentences with VP negation.</Paragraph>
    <Paragraph position="18">  '(S)he has not been playing the piano for an hour now.' The floating PP[per] in (19) is in the scope of the negation, yielding an interpretation which can be paraphrased as 'it is not the case that (s)he played the flute for an hour'. The anchored PP[da] in (20), by contrast, outscopes the negation, yielding an interpretation which can be paraphrased as 'for an hour it has not been the case that (s)he plays the piano'.</Paragraph>
    <Paragraph position="19"> To capture the semantic properties of the four types of durational adjuncts we need a framework for the analysis and representation of temporal expressions. As a starting point, I will use the HPSG framework, as defined in (Pollard and Sag, 1994) and (Ginzburg and Sag, 2000). This suffices to spell out what the four types have in common (section 2), but in order to also model what differentiates them (section 4) we will need some extensions to the standard HPSG ontology and notation (section 3).</Paragraph>
  </Section>
  <Section position="4" start_page="73" end_page="75" type="metho">
    <SectionTitle>
2 What the durational adjuncts have in
</SectionTitle>
    <Paragraph position="0"> common Since the adjuncts of duration are modifiers rather than arguments, they are not selected by their head sister. Instead, it is the head which is selected by the adjunct. Phrased in terms of the HPSG notation, a PP adjunct has a SELECT feature whose  value spells out the syntactic and semantic properties of its head sister.2</Paragraph>
    <Paragraph position="2"> Since the SELECT feature is part of the HEAD value, it is shared between the PP and the preposition. From this it follows that prepositions which introduce an adjunct can impose constraints on the SYNSEM value of the phrase which the adjunct modifies. Exploiting this possibility we can capture the syntactic properties of the prepositions which introduce a durational adjunct in terms of</Paragraph>
    <Paragraph position="4"> In words, the prepositions which introduce a durational adjunct take an NP complement and project a PP which modifies a VP. Besides these properties, which they share with many other types of PP adjuncts, there is the more specific requirement that the NP complement must denote an amount of time. This is modeled in terms of its MARK(ING) and its CONTENT values. Starting with the latter and employing the semantic ontology of (Ginzburg and Sag, 2000), in which the CONTENT value of a nominal is an object of type scope-object, the relevant constraint can be defined as follows:  In words, the index of the complement must be the argument of a predicate of type t-unit-rel. This is one of the intermediate types in the hierarchy of relations. Its subtypes are the predicates which express temporal units.</Paragraph>
    <Paragraph position="6"> The defining property of temporal units is that they succeed one another without interruption. A day, for instance, is a temporal unit, since it is immediately followed by another day, but a Friday is not, since it is not immediately followed by another Friday. The relevance of this distinction is illustrated by the fact that for a day and in ten minutes can be adjuncts of duration, whereas for Friday and in April cannot. Whether a PP[for/in] can be used as an adjunct of duration is not only determined by the semantic class of the noun, but also by the prenominals: for every day and in that month, for instance, cannot be used as adjuncts of duration. This is captured by the constraint that the NP must be indefinite, rather than universal or determinate. Evidence for making this threefold distinction and for modeling it in terms of the MARK-ING values is provided in (Van Eynde, 2005).4 A crucial factor in the semantic analysis of the durational adjuncts is their contribution to the meaning of the VP: the amount of time which is denoted by their NP daughter must somehow be related to the semantic properties of the VPs which they modify. To spell this out we first need a format for the semantic analysis of verbal objects.</Paragraph>
    <Paragraph position="7"> 4If the NP is determinate, as in for the last five years, for the whole morning and da lunedi 'since Monday', it does not denote an amount of time, but an interval or an instant. Such PPs have meanings which resemble those of the durational adjuncts, but their contribution to the semantics of the VP is nonetheless different.</Paragraph>
  </Section>
  <Section position="5" start_page="75" end_page="79" type="metho">
    <SectionTitle>
3 Times and temporal objects
</SectionTitle>
    <Paragraph position="0"> To model the semantic properties of verbal projections I extend the semantic ontology of (Ginzburg and Sag, 2000) with times and temporal objects.</Paragraph>
    <Paragraph position="1">  sem-object time interval instant scope-object temp-obj . . .</Paragraph>
    <Paragraph position="2">  The temporal objects belong to a subtype of scope-object and, hence, have an index and a set of restrictions on that index. Besides, they have a TIMES attribute, which takes a list of times as its value.</Paragraph>
    <Paragraph position="4"> The objects of type time denote temporal entities and come in two kinds: instants and intervals. This distinction does not concern any inherent properties of the temporal entities, but rather their mode of individuation. The objects of type interval have a beginning, an end and a duration.</Paragraph>
    <Paragraph position="5">  Since the value of the EXTENT feature is of type scope-obj it can be identified with the amount of time which is expressed in an adjunct of duration. Of the various times which figure in the list of a temporal object, the rightmost one has a special role, since it is the one which is linked to the index of the verb. For ease of reference I will call it the</Paragraph>
    <Paragraph position="7"> The verb's index ( a21 ) is comparable to a Davidsonian event variable, but has a slightly different role. It is, for instance, not only assigned to verbs and VPs which denote an event, but to all verbal projections, including the stative ones. The index is invariably the first argument of the relation which the verb denotes, as in greet-rel (i, x, y), and is linked to the V-time by means of the loc-rel relation. The function of this relation is to link the denotation of the V(P) to the time at which it holds. It is comparable to the overlap relation, familiar from Discourse Representation Theory: a21 a4 t.</Paragraph>
    <Paragraph position="8"> Since the temporal objects belong to a subtype of scope-obj, it follows that their indices are of the same type as those of the nominal objects. Given the ontology of (Ginzburg and Sag, 2000), this implies that they contain features for person, number and gender.5  The presence of these features in the CONTENT values of verbs may, at first, seem awkward, since they model properties which are typical of N(P)s. A form like greets, for instance, requires its NP subject to have a third person singular index, but does not have a third person singular index of its own, as argued in (Pollard and Sag, 1994, 82).</Paragraph>
    <Paragraph position="9"> Looking closer, though, the assignment of these features to verbs does have a number of advantages. One is that it accounts for the agreement in clauses with a verbal subject.</Paragraph>
    <Paragraph position="10"> (28) Forging banknotes is/*are/*am not easy.</Paragraph>
    <Paragraph position="11"> (29) To make mistakes is/*are/*am human.</Paragraph>
    <Paragraph position="12"> Since the form is requires a subject with a third person singular index, it follows that the nonfinite VPs in (28) and (29) have a third person singular index, and since phrases share their index with their head daughter, this implies in turn that the verbs forging and make have a third person singular index.6 To avoid misunderstanding, it is worth stressing that this does not mean that they require a third person singular subject, but rather that they 5The values of these features concern the mode of indivduation of a nominal's referent and should not be confused with properties of the referent itself. A person, for instance, can be individuated by means of a second person pronoun, but this does not mean that (s)he has the property of being a  second person.</Paragraph>
    <Paragraph position="13"> 6That forging and make are verbs is clear from the fact that they take NP complements; if they were nouns, they would take PP[of ] complements.</Paragraph>
    <Paragraph position="14"> 76 themselves are third person singular. This distinction is especially relevant for the finite verbs, as illustrated by (30) and (31).</Paragraph>
    <Paragraph position="15"> (30) That he/she snores is/*are/*am annoying.</Paragraph>
    <Paragraph position="16"> (31) That I/they snore is/*are/*am annoying.</Paragraph>
    <Paragraph position="17">  Also here the subjects are required to have a third person singular index, and since they are clauses which are headed by a finite verb, it follows that the finite verbs have a third person singular index. Moreover, this index is different from the one of their subject. Snore in (31), for instance, has a third person singular index, but requires its subject to have an index which is plural or nonthird person. In sum, one advantage of the assignment of a third person singular index to verbs is that it accounts in a straightforward manner for the agreement data in (28-31).</Paragraph>
    <Paragraph position="18"> Another advantage is that the indices provide a way to capture the distinction between the aspectual classes (Aktionsarten). To see this, let us first revisit the role of the indices in nominal objects. As argued in (Pollard and Sag, 1994), the indices are not only useful to model agreement between a finite verb and its subject, or between an anaphoric pronoun and its antecedent, but also between a determiner and its nominal head. The demonstrative these, for instance, requires a nominal with a plural index, whereas this requires a nominal with a singular index. A similar constraint holds for the combination of a quantifying determiner and its head. While every and a require their nominal head to be singular and count, much requires it to be singular and mass: every/a/*much table vs. much/*every/*a traffic. Despite the obvious similarity with the constraints for the demonstrative determiners, they cannot be modeled in terms of the indices of (Pollard and Sag, 1994), since their indices do not contain any information about the mass/count distinction. A natural move, therefore, is to redefine the indices in such a way that this distinction can be integrated. Independent evidence for this move is provided by the fact that the mass/count distinction concerns the mode of individuation of the referent(s) of the nominal, rather than an inherent property of the referent(s), see footnote 5. Another piece of evidence is the fact that the mass/count distinction closely interacts with the NUMBER distinction: most of the relevant constraints simultaneously concern a number and a mass/count value. To model this I add a COUNT-ABILITY feature to the objects of type number, adopting a proposal of (Van Eynde, 2005).</Paragraph>
    <Paragraph position="19">  In terms of this dichotomy the count nouns have bounded indices, whereas the mass nouns have unbounded indices. Nouns which are used either way, such as glass, have the underspecified value in their lexical entry; this can be resolved by the addition of a determiner, as in a glass or much glass.</Paragraph>
    <Paragraph position="20"> Returning now to the verbs, it automatically follows from the presence of an index in their CONTENT values that they also have a COUNTABIL-ITY feature. This is an advantage, since it provides us with the means to spell out the similarities between the count/mass distinction for nominals and the Aktionsart distinction for verbal projections. The states and processes, for instance, share the property of the mass nouns that their denotation is unbounded, whereas the accomplishments and the achievements share the property of the count nouns that their denotation is bounded (Bach, 1986). Exploiting the potential of this extended role of the indices I introduce a distinction between two types of temporal objects. The bounded ones have an index of type bounded and are subsumed by the following constraint:</Paragraph>
    <Paragraph position="22"> In words, the index of a bounded temporal object is temporally included in the V-time. Since inclusion is a special type of overlap, this is a more constrained version of (26). It corresponds to DRT's 'e a1 t'.</Paragraph>
    <Paragraph position="23"> The unbounded temporal objects obviously have an index of type unbounded, but the relation  of this index to the corresponding time is not sub-ject to any further constraints; it is subsumed by the generic loc-rel.</Paragraph>
    <Paragraph position="24"> With the introduction of times, temporal objects and the boundedness distinction we have paved the way for a more detailed analysis of the various types of durational adjuncts.</Paragraph>
    <Paragraph position="25"> 4 What differentiates the four types of durational adjuncts I first discuss the adjuncts which combine with an unbounded temporal object, and then the adjuncts which combine with a bounded temporal object. In the last paragraph I return to the issue of scope.</Paragraph>
    <Section position="1" start_page="77" end_page="78" type="sub_section">
      <SectionTitle>
4.1 The PP[for/per/da] adjuncts
</SectionTitle>
      <Paragraph position="0"> The PP[for/per/da] adjuncts select a VP which denotes an unbounded temporal object and specify the duration of the V-time.7  The restricton to unbounded temporal objects accounts for the fact that these adjuncts combine with states and processes, but not with accomplishments or achievements. Notice, though, that this restriction does not exclude the combination with VPs whose CONTENT value is the underspecified temp(oral)-obj(ect). This is important, since few V(P)s are inherently bounded or unbounded.</Paragraph>
      <Paragraph position="1"> It is usually by the addition of an adjunct that the underspecification gets resolved.</Paragraph>
      <Paragraph position="2"> That the adjunct specifies the duration of the V-time is illustrated by the examples of the first section. In (1), for instance, it is the time of playing the piano which is said to take an hour, and in (3) it is the time of Laura's stay in Ohio which is said to have a length of two months. The relation between this time and the index of the V(P) is required to be the one of inclusion (s a7 t). This accounts for the fact that (1) is only true if the playing of the</Paragraph>
      <Paragraph position="4"> abbreviation is used in (36) and (38).</Paragraph>
      <Paragraph position="5"> piano went on for at least an hour. The generic loc-rel is not sufficient for this purpose, since it only requires overlap: it would make (1) true if the playing went on for five minutes.</Paragraph>
      <Paragraph position="6"> For the floating PP[for] and PP[per] adjuncts there is nothing which need be added to (34).</Paragraph>
      <Paragraph position="7"> Their anchored counterparts, however, are sub- null In words, the interval whose duration is specified has a right boundary ( a21 ) which is related to the time of utterance. This relation can be the one of identity, as in (5b) and (8), or it can be mediated by a temporal adjunct. In (9), for instance, the right boundary is specified by the PP a quel punto, which precedes the time of utterance, and in (10) it is specified by the clause quando verr`a raggiunta da Ivo, which follows the time of utterance. To capture this variation I use the relation temp-rel. This stands for any binary relation between times.9 sem-object rel loc-rel in-rel incl-rel temp-rel m-rel ... f-rel As demonstrated in (Allen, 1984), the number of distinct binary relations between times is limited. He distinguishes seven basic relations: equal (=), before (a9 ), during (d), meets (m), overlaps (o), starts (s) and finishes (f). Each of these relations has an inverse: the one of before, for instance, is after (a10 ). This yields fourteen possible relations, but since equality is indistinguishable from its inverse, the number of distinct relations is 13. Of these 13 relations, only three are  loc-rel and its subtypes, which are relations between an index and a time.</Paragraph>
      <Paragraph position="8">  exemplified by (8-10), but most of the remaining ones are excluded by the constraint in (35) that the related times must be instants. This automatically excludes the relations in which at least one of the times must be an interval, such as overlap, during, start, finish and their respective inverses.</Paragraph>
    </Section>
    <Section position="2" start_page="78" end_page="78" type="sub_section">
      <SectionTitle>
4.2 The PP[in/fra/tra] adjuncts of duration
</SectionTitle>
      <Paragraph position="0"> The floating PP[in] adjuncts select a VP which denotes a bounded temporal object and specify the duration of the V-time.</Paragraph>
      <Paragraph position="1">  Since only intervals can have duration this constraint accounts for the fact that these adjuncts are not compatible with VPs which denote instantaneous events, as in: (37) ? The bomb exploded in two minutes.</Paragraph>
      <Paragraph position="2"> In contrast to their floating counterparts, the anchored PP[in] and PP[tra/fra] adjuncts do not specify the duration of the V-time, but rather of the interval which elapses between the time of utterance and the beginning of the V-time. In terms of Allen's ontology, this can be characterized as an instance of m(eets)-rel: m(x, y) is true if and only if x immediately precedes y.10  The leftmost interval is the one whose duration is specified. The rightmost time can be an instant or an interval. In (16) it is most likely an interval, since the tuning of a piano is bound to take some time, but it can also be an instant, as in the most plausible interpretation of (39).</Paragraph>
      <Paragraph position="3"> 10R is short for RESTR(ICTIONS), T for TIMES, BG for BE-GINNING and EX for EXTENT.</Paragraph>
      <Paragraph position="4"> (39) The bomb will explode in two minutes.</Paragraph>
      <Paragraph position="5"> Since the beginning of an interval necessarily precedes its end, the V-time (a1 ) must follow the time of utterance. This accounts for the fact that the English PP[in] can have the anchored interpretation in a clause with a future auxiliary, such as (12) and (39), or in a clause with a futurate present tense, such as we are leaving in a minute, but not in a clause with a past tense verb, such as (2), or in a clause with a non-futurate present tense, such as (11).</Paragraph>
    </Section>
    <Section position="3" start_page="78" end_page="79" type="sub_section">
      <SectionTitle>
4.3 Scope
</SectionTitle>
      <Paragraph position="0"> Having spelled out the properties of the anchored adjuncts we can now account for the fact that they cannot be outscoped by a VP quantifier. What makes this impossibe is the fact that the interval whose duration they specify is linked to the time of utterance. The link can be more or less direct, but it does not allow for the intrusion of other intervening intervals. The floating adjuncts, by contrast, apply to intervals which are not linked to the time of utterance and, therefore, allow the intrusion of intervening times, as in (17), where spesso 'often' outscopes per un' ora 'for an hour'.</Paragraph>
      <Paragraph position="1"> Of course, the fact that the floating adjuncts can be outscoped by a VP quantifier does not imply that they must be outscoped whenever there is such a quantifier. To show this let us have a look at (40).</Paragraph>
      <Paragraph position="2"> (40) We will train two hours a day for at least six months.</Paragraph>
      <Paragraph position="3"> While the adjunct two hours a day specifies the duration and the frequency of the V-time, i.e. the time of the individual training sessions, the PP[for] adjunct specifies the duration of the period in which the daily training sessions will take place.11 It, hence, outscopes the VP quantifier.</Paragraph>
      <Paragraph position="4"> This use of the adjunct is not covered by the analysis in section 4.1, since the latter only deals with those adjuncts which specify the duration of the V-time. To deal with the adjunct in (40) we would have to extend the hierarchy of temporal objects with a special subtype for the quantified temporal objects and add a constraint which captures the 11The floating nature of the PP[for] adjunct is clear from the absence of a specification (implicit or explicit) of its right boundary and from the fact that its Italian equivalent is per almeno sei mesi rather than da almeno sei mesi.</Paragraph>
      <Paragraph position="5">  properties of the durational adjuncts which combine with such objects. Spelling this out is left for future work.</Paragraph>
    </Section>
  </Section>
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