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<?xml version="1.0" standalone="yes"?> <Paper uid="H93-1027"> <Title>INTERPRETING TEMPORAL ADVERBIALS*</Title> <Section position="4" start_page="0" end_page="140" type="metho"> <SectionTitle> 2. SYNTAX AND SEMANTICS OF TEMPORAL ADVERBIALS </SectionTitle> <Paragraph position="0"> We first discuss the basic interpretive mechanism, using yesterday as an example, and then generalize to other types of temporal adverbials.</Paragraph> <Paragraph position="1"> 2.1. The Basic Mechanism As indicated in the following fragment of a GPSG-like sentence grammar, we treat all adverbial adjuncts as VP-adjuncts at the level of syntax. 1 (Aspectual feature agreement is assumed, but not discussed till section 3.)</Paragraph> <Paragraph position="3"> However, despite this surface syntax, the semantic rule (ADVL' VV), specifying functional application of the ADVLtranslation to the VP-translation, may lead to either predicate modification or sentence modification at the level of immediate logical form. In particular, manner adverbials (e.g., with lIn sentences like &quot;Yesterday Mary left,&quot; we treat the proposed ADVL as topicalized, i.e., as &quot;extracted&quot; from post-VP position. However, we may want to treat modal and attitude adverbials (as in &quot;Oddly, Mary left&quot;) as sentencemodifying. This does not affect our discussion here.</Paragraph> <Paragraph position="4"> a brush, hastily, etc.) are uniformly interpreted as predicate modifiers at the level of immediate LF, while temporal (and locative) adverbials are all interpreted as sentence modifiers.</Paragraph> <Paragraph position="5"> How such sentence-modifier interpretations are formed from</Paragraph> <Paragraph position="7"> (adv-e stands for 'episode-modifying adverbial'. 2 More on this later.) From these rules it is clear that the logical translation of yesterday, as an adverbial adjunct, is ZPZx((adv-e (during Yesterday)) Ix P\]).</Paragraph> <Paragraph position="8"> In the interpretation of a sentence such as &quot;Mary left yesterday,&quot; this A-abstract would be applied to predicate leave (initially paired with unscoped tense operator past), yielding lx((adv-e (during Yesterday)) \[x <past leave>\]), and this in turn would be applied to term Mary (translating the NP Mary), yielding the formula ((adv-e (during Yesterday)) \[Mary <past leave>\]).</Paragraph> <Paragraph position="9"> Here, (during Yesterday) is a 1-place predicate (the result of applying the 2-place predicate during to the indexical constant Yesterday, allowable in the&quot;curried function&quot; semantics of EL). adv-e maps this 1-place preedicate into a sentence modifier; i.e., (adv-e (during Yesterday)) denotes a function from sentence meanings to sentence meanings. In the present case, the operand is the sentence \[Mary <past leave>\], written in the square-bracketed, infixed form that is the preferred sentence syntax in EL. 3 The above indexical (context-dependent) logical form is obtained quite directly as a byproduct of parsing, and is subsequently further processed-- first, by scoping of ambiguously scoped quantifiers, logical connectives, and tense operators, and then by applying a set of formal deindexing rules, which introduce explicit episodic variables into the LF, and temporally relate these based on tense operators, temporal adverbials, and context structures called tense trees. These tense trees, described in \[10, 22\], supply &quot;orienting relations&quot; between episodes introduced by different clauses, such as the relation that exists between successively reported events in a narrative. We should emphasize that our treatment of time adverbials is fully compatible and integrated with the treatment of tense, but we will neglect tense o~rators and tense trees herein as far as possible. We do need to mention, though, that tense operators are generally assumed to take wide scope over adverbials in the same clause. Thus, after scoping, we get 2Certain feature principles are assumed in the grammar--namely, certain versions of the head feature principle, the control agreement principle, and the subeategorization principle. Notice that in our system, features are treated as trees; e.g., the subtree rooted by feature mod-vp has daughters pre-vp and post-vp, and the subtree rooted by feature e-rood has daughters temp-loe, dur, time-span, freq, card, eyc-time, etc., where temp-loe in turn has daughters def-time, indef-time, etc.</Paragraph> <Paragraph position="10"> 3In general, \['r. n: 1:1 ... 'r~l\] is an equivalent way of writing Or x, ... 'r.), Which is in turn equivalent to 6.- ((g lrl)x2) ... &quot;rn). See \[9, 11\]. (past ((adv-e (during Yesterday)) \[Mary leave\])).</Paragraph> <Paragraph position="11"> Since the deindexing rules &quot;work their way inward&quot; on a given indexical LF, starting with the outermost operator, the past tense operator in the sentence under consideration will already have been deindexed when the adv-e construct is encountered.</Paragraph> <Paragraph position="12"> In fact we will have (2e1: \[el before ul \] \[((adv-e (during Yesterday)) \[Mary leave\]) T ** eli), where ul denotes the utterance event for the sentence concerned, and T denotes the current tense tree. Note that we use restricted quantitiers of form (Qa: * it0, where Q is a quantitier, a is a variable, and restriction * and matrix ~P are formulas. At this point the following deindexing rule for adv-e is brought to bear (we omit the second half of the rule, specifying the transformation of the tense tree T ; see \[9, 11\]): For lr a monadic predicate, and * a formula, adv-e: ((adv-e g) ~)r ~ \[VlrT ^ ~r-T\] This rule essentially splits the formula into a conjunction of two subformulas: one for the adverbial itself, the other for the sentence modified by the adverbial, much as in Dowty's system \[4, 5\]. To provide an intuitive explanation of how this works, we need to mention the operators '.' and '**', which are central to EL. Roughly, \[~ * 77\] means that * is true in episode r I (or, 4~ describes rl), and \[el, ** 7/\] means that el,, and only O, is true in episode 71 (or, * characterizes 7/). (For details, see \[9, 11, 12\].) Now the expression &quot;nT on the RHS of the deindexing rule for adv-e is a sentential formula (formed from predicate ~T) which Can be read as &quot;~T is true of the current episode (i.e., the one at which vg T is evaluated).&quot; In view of this, the combination \[Vnr ^ ~,~.r\] ** 7/\] is equivalent to \[\[\[71 ~T\] ^ @~.T\] ** 71\]. Note that nT is now predicated directly of episode 71. In the example above, we obtain (3e1: \[el before ud \[\[\[el during Yesterdayr\] A \[Mary leave\]\] ** ed), and this leaves only Yesterdayr to be deindexed to a spdcific day (that is, (yesterday-rel-to uO).</Paragraph> <Paragraph position="13"> To make the semantics of ,v,,,., and'**' a little more precise, we mention two clauses from the truth-conditional semantics: 1. For * a formula, and rl a term,</Paragraph> <Paragraph position="15"> where these conditionals become biconditionals (iffs) for s an exhaustive (informationally maximal) situation.</Paragraph> <Paragraph position="16"> 2. For s e S, and lr a predicate over situations, l\[V~ &quot;= I\[~&quot;', i.e., ~lr~(s)(s), where S is the set of possible situations.</Paragraph> <Paragraph position="17"> Also, a few relevant axioms are (for lr, rr&quot; 1-place predicates, 71 a term, and * a formula): Like adverbials of temporal location, durafive adverbials are also translated as (adv-e re). For instance, &quot;John slept for two hours&quot; becomes (with tense neglected) ((adv-e (lasts-for (K ((num 2) (plur hour))))) \[John sleep\]). Like during, lasts-for is a 2-place predicate. Here it has been applied to a term (K...), leaving a 1-place predicate. Just as in the case of (during Yesterday), the deindexed LF will contain a predication stating that the episode characterized by John sleeping lasts for two hours. (The details of the term (K...), denoting the abstract kind of quantity, two hours, need not concern us here. K as used here corresponds to K1 in \[9, 11\].) Time-span adverbials (as in &quot;John ran the race in two hours&quot;) are treated in much the same way, using predicate in-span-of.</Paragraph> <Paragraph position="18"> The translation of cardinal and frequency adverbials involves the sentence-modifying construct (adv-f re). re is a predicate which applies to a collection of temporally separated episodes. It may describe the cardinality of the episodes or their frequency (i.e., their relative density), periodicity or distribution pattern. So, for instance, we have ((adv-f ((num 2) (plur episode))) \[John see Movie3\]) for &quot;John saw the movie twice,&quot; and ((adv-f ((attr frequen0 (plur episode))) \[John call Mary\]) for &quot;John called Mary frequently.&quot; (num is an operator that maps numbers into predicate modifiers, and plur ('plural') is a function that maps predicates applicable to individuals into predicates applicable to collections; cf., Link \[13\]. agtr ('attributive') is an operator that maps predicates into predicate modifiers.) Table 1 shows lexical rules and PP and ADVL rules handling large classes of frequency adverbials, including periodic ones such as every two hours and synchronized cyclic ones such as every spring.</Paragraph> <Paragraph position="19"> The deindexing rule for adv-f is as follows: For re a monadic predicate, and cb a formula, adv-f: ((adv-f re) ~)T ~ \[&quot;rer ^ (mult On.T)\] As illustrated in Table 1, re could take various forms, mult on the RHS side of the rule is a function that transforms sentence intensions, and is defined as follows.</Paragraph> <Paragraph position="21"> e.g., in two hours&quot; = J!.PAx((adv-e (in-span-of (K ((num 2) (plur hour))))) \[x P\]) ADV\[card, post-VP\] ~-- tw/ce; (adv-f ((num 2) (plur episode))) N.B. 'adv-n' used in \[9\] is no longer used.</Paragraph> <Paragraph position="22"> ADV\[freq, mod-VP\] ~ frequently; (adv-f ((attr frequent) (plur episode))) ADV\[freq, mod-VP\] ~- periodically; (adv-f ((attr periodic) (plur episode))) ADV\[freq, post-VP\] ~--- Det\[every\] N\[lbar, time-length\] ; (adv-f As\[\[s ((attr periodic) (plur episode))\] ^ \[(period-of s) = (K N')\]\]) e.g., twice&quot; = APAx((adv-f ((nurn 2) (plur episode))) \[x P\]) e.g.,frequently&quot; = APgx((adv-f ((attr frequent) (plur episode))) \[x P\]) e.g., every two hours' = AP2x((adv-f 2s\[\[s ((attr periodic) (plur episode))\] ^ \[(period-of s) = (K ((num 2) (plur hour)))\]\]) Ix P\]) N\[indef-time\] ~--- spring; spring NP\[cyc-time\] ~--- Det\[every\] N\[lbar, indef-firne\] ; <Deg N'> PP\[post-VP\] ~-- NP\[cyc-time\] ; (during NP') ADV ~- PP\[cyc-tinae, post-VP\] ; (adv-f 2s(3e \[\[e member-of s\] ^ \[e PP'\]\])) e.g., every spring&quot;</Paragraph> <Paragraph position="24"> Sentences (1)--(5) below illustrate the rules stated in Table 1.</Paragraph> <Paragraph position="25"> The (a)-parts are the English sentences, the (b)-parts their immediate indexical LFs, and the (c)-parts the deindexed ELFs.</Paragraph> <Paragraph position="26"> (1) should be fairly transparent at this point. (2c) says that &quot;some time before the utterance event, there was a 2 monthlong (multi-component) episode, that consists three episodes of type 'John date Mary'.&quot; (3c) reads similarly. (4c) reads as &quot;there was a 10 day-long episode that consists of periodically occurring subepisodes of type 'John take medicine', where the period was 4 hours.&quot; (5c) is understood as &quot;at the generic present there is a collection of episodes of type 'Mary bake cake', such that during each Saturday within the time spanned by the collection, 4 there is such an episode.&quot; (We take verbs of creation such as bake as predicate modifiers.) (1) a. John worked for three hours yesterday.</Paragraph> <Paragraph position="27"> b. (past ((adv-e (during Yesterday)) ((adv-e (lasts-for (K ((num 3) (plur hour))))) \[John work\]))) c. (3e1: \[el before u,\] \[\[\[el during (yesterday-rel-to ul)\] ^ \[el lasts-for (K ((hum 3) (plur hour)))\] ^ \[John work\]\] ** eli) (2) a. Mary visited Paris three times in two months.</Paragraph> <Paragraph position="28"> b. (past ((adv-e (in-span-of (K ((num 2) (plur month))))) (4) a, John took medicine every four hours for ten days. b. (past ((adv-e (lasts-for (K ((num 10) (pinr day))))) ((adv-f As \[\[s ((attr periodic) (plur episode))\] ^ \[(period-of s) = (K ((num 4) (plur hour)))\]\]) We emphasize again that ELFs are completely deindexed, and so allow effective inference. EPILOG \[20\], the computer implementation of EL, makes inferences very efficiently, based on such ELFs and world knowledge, aided by a &quot;time specialist.&quot; For instance, given &quot;There is a train to Boston every two hours,&quot; &quot;A train left for Boston at 2:30,&quot; and appropriate axioms, EPILOG Can infer that the next train would be at 4:30. 5 a. (Vs: \[s ((attr periodic) (plur episode))\] (~n: \[In number\] ^ \[n ~ 2\]\] Is ((hum n) (plur episode))\])) A periodic collection of episodes has at least two component episodes. This kind of reasoning is very important in the TRAINS project \[1\], one of our target applications.</Paragraph> <Paragraph position="29"> We also have a tentative account of adverbials such as consecutively and alternately, and some non-PP adverbials, but cannot elaborate within the present space limitations.</Paragraph> </Section> <Section position="5" start_page="140" end_page="142" type="metho"> <SectionTitle> 3. AN EXTENSION: TEMPORAL ADVERBIALS AND ASPECTUAL CLASS SHIFTS </SectionTitle> <Paragraph position="0"> So far, we have assumed aspectual category agreement between temporal adverbials and VPs they modify. We now discuss our aspectual class system and our approach to apparent aspectual class mismatch between vPs and adverbials, based on certain aspectual class transformations.</Paragraph> <Paragraph position="1"> We make use of two aspectual class feature hierarchies, stativeness and boundedness as below: 6 st at ivene s s boundedne s s</Paragraph> <Paragraph position="3"> factual star telic unbounded bounded Atemporal (or, unlocated) sentences whose truth value does not change over space and time are assigned the feature factual. Every tensed English sentence, e.g., &quot;Mary left before John arrived,&quot; in combination with a context, is considered factual. Untensed sentences may be stative or telic, depending on the type of the preedicate (i.e., achievement/accomplishment versus state/process predicates) and on the object and subject (e.g., count versus mass). Sentences describing states or processes are assigned the feature star, while those describing achievements or accomplishments are assigned the feature telie.</Paragraph> <Paragraph position="4"> By a co-occurrence restriction, factual formulas are unbounded, and telics are bounded. Statives are by default unbounded. Intuitively, a formula is bounded if the episode it characterizes terminates in a distinctiveresult state (result states are formally defined in \[11\].) This is a property we ascribe to all telie episodes as well as to some stative episodes (such as an episode of John's being ill, at the end of which he b. (Vk: \[k kind-of-timelength\] (Ve: \[\[e episode\] ^ \[\[e lasts-for k\]\] (3t: \[\[t time\] a \[(timelength-of 0 = k\]\] \[e throughout t\]))) An episode lasting for a certain length of time means there is a time of that length such that the temporal projections of the time and the episode are identical.</Paragraph> <Paragraph position="5"> c. (Ve(Vs: \[Is ((attr periodic) (plur episode))\] ^ \[s throughout e\]\] (Vp: \[(period-of s)=p\] (Vel: \[el member-of s\]</Paragraph> <Paragraph position="7"> A component episode of a sequence of episodes with periodp has an immediate predecessor/successor that is apart from it by p unless it is the firstllast element of the sequence. The distance between the first/last element and the begirdend point of the episode the sequence permeates is less than p.</Paragraph> <Paragraph position="8"> is not ill). Conversely, a formula is unbounded if the episode it characterizes does not terminate in a distinctive result state. For instance, was ill in &quot;John was ill when I saw him last week&quot; is unbounded as the sentence does not entail that John was not ill right after the described episode. However, when we say &quot;John was ill twice last year,&quot; we are talking about bounded &quot;ill&quot; episodes. 7 As has been discussed by many authors (e.g., in \[3, 6, 15, 17, 26, 27\]), vPs and temporal adverbials may not arbitrarily combine. Normally, durative adverbials combine with unbounded VPs; cardinal and frequency adverbials with bounded VPs; and adverbials of time-span with telic VPs. Thus, for instance, Mary studied for an hour. s *Mary finished the homework for a second.</Paragraph> <Paragraph position="9"> Mary called John twice I repeatedly l every five minutes.</Paragraph> <Paragraph position="10"> Mary wrote the paper/n two weeks.</Paragraph> <Paragraph position="11"> Note, however, that we also say Mary sneezed for Jive minutes.</Paragraph> <Paragraph position="12"> Mary stepped out of her office for \]fve minutes.</Paragraph> <Paragraph position="13"> Mary was ill twice \[ repeatedlyl every two months.</Paragraph> <Paragraph position="14"> The latter group of sentences show that VPs often acquire an interpretation derived from their original, primitive meaning. More specifically, when &quot;stative&quot; adverbials are applied to telic VPs, usually iteration is implied, as in the first sentence. However, in the case of the second sentence, the preferred reading is one in which the adverbial specifies the duration of the resultant episode, i.e., &quot;the result state of Mary's stepping out of her office&quot; (i.e., her being outside of her office), rather than a reading involving iteration. Next, when cardinal or frequency adverbials (i.e., &quot;bounded&quot; adverbials) are applied to unbounded-stative VPs, those VPs are interpreted as boundedstatives. Thus, the third sentence above means that the kind of episode in which Mary becomes ill and then ceases to be ill occurred twice, repeatedly, etc.</Paragraph> <Paragraph position="15"> To be able to accommodate such phenomena, the syntactic parts of our grammar use stat and bounded as agreement features. The semantic parts introduce, as needed, operators for aspectual class transformation such as result-state, iter (iteration), bounded, etc. (In place of iter, we may sometimes use a habitual operator, It.) Adverbials of temporal location like yesterday or last week may combine with either bounded or unbounded formulas (with unbounded ones, these imply a throughout reading; with bounded ones, a sometime during reading). For instance, in &quot;John left last month,&quot; the &quot;leaving&quot; episode took place sometime during last month, but in case of &quot;Mary was ill last month,&quot; Mary's &quot;ill&quot; episode may be either sometime during 7Semanticany, stativeness and boundedness play an important role with respect to the persistence of a formula. In general, stafive formulas are inward persistent (modulo granularity), and bounded formulas are outward persistent. (Polarized ones are exceptional, however.) See \[11\] for further discussion.</Paragraph> <Paragraph position="16"> SHowever, *Mary resembled her mother for five years, even though &quot;resembling&quot; is a typical stafive VE This indicates that compatibility between predicates and adverbials involves more than just the aspeetual class compatibility; that is, pragmaties and world knowledge need to be considered. or throughout last month (corresponding to bounded and unbounded readings of the VP). Synchronized cyclic adverbials like every spring or every time I saw Mary may combine with bounded or unbounded formulas.</Paragraph> <Paragraph position="17"> Secondly, an application of certain temporal adverbials often induces shifts in the aspectual classes of the resultant VPs. Frequency adverbials transform bounded sentences into unbounded-stative ones, while durative adverbials normally yield bounded VPs and synchronized cyclic ones yield unbounded-statives. Thus, John {{was ill twice} in three years}.</Paragraph> <Paragraph position="18"> ?John { {was ill twice} for three years}.</Paragraph> <Paragraph position="19"> John { {was frequently ill} for three years}.</Paragraph> <Paragraph position="20"> ?John {{was frequently ill} in three years}.</Paragraph> <Paragraph position="21"> John { {worked for five hours} three times} last week.</Paragraph> <Paragraph position="22"> We now rewrite the VP adjunct rules introduced earlier to accommodate the interaction between vPs and adverbials and possible shifts in aspectual classes. 9 We also show VP rules that perform aspectual class shifts. Note that aspectual class features (stat, bounded, etc.) are head features.</Paragraph> <Paragraph position="24"> These rules allow transitions in aspectual class and VPadverbial combinations somewhat too liberally. We assume, however, that undesirable transitions and combinations may be ruled out on semantic grounds. We now show some additional sentences and their initial translations (with tense neglected) to illustrate the above rules.</Paragraph> <Paragraph position="25"> (6) a. Mary was ill twice in December b. ((adv-e (during (in-time December))) ((adv-f ((num 2) (plur episode))) \[Mary (bounded ill)\])) (7) a. Mary received an award for three years b. ((adv-e (lasts-for (X ((num 3) (plur year))))) \[Mary (iter 2x(3y: \[y award\] \[x receive y\]))\]) (8) a. Mary became unconscious for five minutes b. ((adv-e (lasts-for (X ((num 5) (plur minute))))) \[Mary (result-state (become unconscious))\]) (9) a. Nobody slept for eight hours for a week b. ((adv-e (lasts-for (K week))) (No x: \[x person\] ((adv-e (lasts-for (X ((hum 8) (plur hour))))) Ix sleep\])))) e. ((adv-e (lasts-for (X week))) (No x: Ix person\] \[x (iter Xy((adv-e (lasts-for (K ((hum 8) (plur hour))))) \[y sleep\]))\]))) d. (No x: \[x person\] ((adv-e (lasts-for (R week))) \[x (iter Ay((adv-e (lasts-for (K ((hum 8) (plur hour))))) Notice that (9) has at least three readings: first, during a certain week-long event, nobody had an 8-hour snooze; second, a situation in which nobody slept regularly for 8 hours persisted for a week1deg; and third, there is no one who slept daily for 8 hours for a week. (9b), (9c) and (9d) provide these three readings (distinguished by the scope of the quantifier No and the adverbial for a week). Note now that in (9a), the inner durative adverbial for eight hours transforms the unbounded VP to a bounded one. Being another durative adverbial, however, the outer for a week requires that its argument be unbounded. This is not a problem as shown in ELFs (9b, c, d). That is, in (9b), the argument is a negated formula which is normally considered to be stative-unbounded, and in (9c) and (9d), the iter operator produces stative-unbounded formulas.</Paragraph> </Section> class="xml-element"></Paper>