INTERPRETING TEMPORAL ADVERBIALS* 
Chung Hee Hwang & Lenhart K. Schubert 
Department of Computer Science, University of Rochester 
Rochester, New York 14627-0226 
Abstract 
We take for granted that sentences describe situations \[2, 12\]. One 
of the most important properties of situations are then their tempo- 
ral locations, which are indicated by tense and aspect and temporal 
adverbials in the surface form. In \[10, 22\], we offered a formal the- 
ory for English tense and aspect and an algorithm that computes the 
temporal relationships between the situations implicitly introduced 
by a text. In the present paper, we propose a systematic approach to 
temporal adverbials, fully integrated with our tense-aspect theory and 
the inte~retive algorithms, using the Episodic Logic (EL) formalism 
\[9, 11, 12, 211. 
1. INTRODUCTION 
Previous theoretical work on temporal adverbials has mostly 
concentrated on adverbials specifying temporal locations (e.g., 
"yesterday"), durations (e.g., "for a month") and time spans 
(e.g., "in three hours"). It appears that interest in the first kind 
of adverbial originated from the desire to correct the erroneous 
analyses provided by Priorean tense logics, in particular, their 
treatment of the interaction between time adverbials and tense. 
The second and third kinds of adverbials were often consid- 
ered in connection with the aspectual classes of the vPs or sen- 
tences those adverbials modify (e.g., durative adverbials may 
modify only stative sentences, whereas adverbials of time span 
may modify only accomplishment sentences). However, other 
kinds of temporal adverbials have received little attention, in- 
cluding ones specifying repetition: 
The engineer shut down the motor twice yesterday. 
The engine frequently broke down. 
The operator checked the level of oil every half hour. 
The inspector visits the lab every Monday. 
On our analysis, these sentences describe complex events, 
consisting of a sequence of subevents of specified types, and 
the given adverbials modify the structure of these complex 
events: the cardinality of component events ("twice"), the 
frequency or distribution pattern of component events ("fre- 
quently," "regularly," "every half hour," etc.), and the temporal 
location of cyclic events that occur synchronously with other 
recurrent time frames or events ("every Monday" or "every 
time the alarm went off''). 
Other issues that deserve further investigation are the interac- 
tions between multiple temporal adverbials, and various kinds 
of aspectual class shift due to aspectual class constraints on 
the use of adverbials (occurring singly or jointly with others). 
The following sentences illustrate these issues. 
*This research was supported in part by NSF Research Grant IRI- 
9013160 and ONR/DARPA Research Contracts No. N00014-82-K-0193 and 
No. N00014-92-J-1512. The authors benefited from example sentences by 
Greg Carlson and Phil Harrison. 
John ran for half an hour every morning for a month. 
John stepped out of his office for fifteen minutes. 
Mary is going to Boston for three days. 
Mary won the competition for four years. 
John saw Mary twice in two years. 
Our aim is to provide a uniform analysis for all kinds of tem- 
poral adverbials. Our approach is compositional in that the 
lexicon supplies meanings at the word level (or possibly at the 
morpheme level, e.g., for '-ly' adverbs), and the meanings of 
adverbials are computed from the lexical entries by our GPSG- 
like grammar rules. The grammar rules take care of aspectual 
compatibility of adverbials with the VPs they modify. The re- 
suiting indexical logical form is then "deindexed" (converted 
to an explicit, context-independent form) by a set of recursive 
rules. The resultant episodic logical form (ELF) is formally in- 
terpretable and lends itself to effective inference. We now con- 
sider the syntax and the semantics of temporal adverbials. We 
first show logical form representations of temporal adverbials, 
in both indexical and deindexed form, and how to obtain them 
from the surface structure, together with a brief discussion of 
semantics. Then, we discuss an extension of our system that 
accommodates aspectual class shifts to properly handle the in- 
teraction between temporal adverbials and aspectual classes. 
2. SYNTAX AND SEMANTICS OF 
TEMPORAL ADVERBIALS 
We first discuss the basic interpretive mechanism, using yes- 
terday as an example, and then generalize to other types of 
temporal adverbials. 
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.) 
NP ~- Mary ; Mary 
V\[lbar, past\] ~ left ; <past leave> 
VP ~ V\[lbar\] ; V' 
VP ~ VP ADVL\[post-VP\] ; (ADVL" VP') 
S ~---NPVP; \[NP" VP'\] 
However, despite this surface syntax, the semantic rule 
(ADVL' VV), specifying functional application of the ADVL- 
translation to the VP-translation, may lead to either predicate 
modification or sentence modification at the level of immedi- 
ate logical form. In particular, manner adverbials (e.g., with 
lIn sentences like "Yesterday Mary left," we treat the proposed ADVL as 
topicalized, i.e., as "extracted" from post-VP position. However, we may want 
to treat modal and attitude adverbials (as in "Oddly, Mary left") as sentence- 
modifying. This does not affect our discussion here. 
138 
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. 
How such sentence-modifier interpretations are formed from 
VP adjuncts is easily seen from rules such as the following: 
NP\[def-time\] ~ yesterday ; Yesterday 
PP\[post-VP\] (-- NP\[def-time\] ; (during NP') 
ADVL (-- PP\[e-mod, post-Ve\] ; APZx((adv-e PP3 \[x P\]). 
(adv-e stands for 'episode-modifying adverbial'. 2 More on 
this later.) From these rules it is clear that the logical transla- 
tion of yesterday, as an adverbial adjunct, is 
ZPZx((adv-e (during Yesterday)) Ix P\]). 
In the interpretation of a sentence such as "Mary left yester- 
day," this A-abstract would be applied to predicate leave (ini- 
tially 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)) \[Mary <past leave>\]). 
Here, (during Yesterday) is a 1-place predicate (the result of 
applying the 2-place predicate during to the indexical con- 
stant Yesterday, allowable in the"curried function" semantics 
of EL). adv-e maps this 1-place preedicate into a sentence mod- 
ifier; 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 ob- 
tained quite directly as a byproduct of parsing, and is subse- 
quently 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 tempo- 
rally relate these based on tense operators, temporal adver- 
bials, and context structures called tense trees. These tense 
trees, described in \[10, 22\], supply "orienting relations" be- 
tween 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 ad- 
verbials 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. 
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) ... "rn). See \[9, 11\]. 
(past ((adv-e (during Yesterday)) \[Mary leave\])). 
Since the deindexing rules "work their way inward" 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. 
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 con- 
cerned, and T denotes the current tense tree. Note that we use 
restricted quantitiers of form (Qa: • it0, where Q is a quanti- 
tier, a is a variable, and restriction • and matrix ~P are formu- 
las. 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 "nT on the RHS of 
the deindexing rule for adv-e is a sentential formula (formed 
from predicate ~T) which Can be read as "~T is true of the 
current episode (i.e., the one at which vg T is evaluated)." 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). 
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, 
~ • 7/\]\] s = 1 only if Actual (~rl~, s) and \[\[~n~ = 1 ; 
= 0 only ifNonactual(lrl\],s) or IIO\]\] ~n\] ~ 1, 
where these conditionals become biconditionals (iffs) 
for s an exhaustive (informationally maximal) situation. 
2. For s e S, and lr a predicate over situations, 
l\[V~ "= I\[~"', i.e., ~lr~(s)(s), 
where S is the set of possible situations. 
Also, a few relevant axioms are (for lr, rr" 1-place predicates, 
71 a term, and • a formula): 
139 
\[\] 13~ ** 7/\] 
~-~ \[\[~ * 7/\] A --1 (3e: \[e proper-subep-of 7/\] \[* • e\])\] 
\[\] \["re A "re'\] ~ VZe\[\[e re\] A \[e re'\]\] 
\[\] \[lYre ^ ~\] ** 77\] ~ \[\[\[7/re\] A ~\] ** 7/\] 
2.2. Adverbials of Duration, Time-span, and Repetition 
Like adverbials of temporal location, durafive adverbials are 
also translated as (adv-e re). For instance, "John slept for two 
hours" 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 "John ran the race in 
two hours") are treated in much the same way, using predicate 
in-span-of. 
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 fre- 
quency (i.e., their relative density), periodicity or distribution 
pattern. So, for instance, we have 
((adv-f ((num 2) (plur episode))) \[John see Movie3\]) 
for "John saw the movie twice," and 
((adv-f ((attr frequen0 (plur episode))) \[John call Mary\]) 
for "John called Mary frequently." (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 ('at- 
tributive') 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 pe- 
riodic ones such as every two hours and synchronized cyclic 
ones such as every spring. 
The deindexing rule for adv-f is as follows: 
For re a monadic predicate, and cb a formula, 
adv-f: ((adv-f re) ~)T ~ \["rer ^ (mult On.T)\] 
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. 
For r 1 an episode, and ~ a formula, 
O \[(mult ~) ** 7/\] 
\[\[7/(plur episode)\] ^ 
(Ve: \[e member-of ri\] 
\[\[~ ** e\] ^ ~ (3e" \[\[e" ~ e\] ^ \[e" member-of ~/\] ^ 
\[e" overlaps eli)\])\], 
Table 1: GPSG Fragment (Adverbials) 
% VP Adjunct Rules 
ADVL ~-- PP\[e-mod, post-VP\] ; APAx((adv-e PP') \[x P\]) 
ADVL <-- ADV\[e-mod, mod-VP\] ; APAx(ADV" Ix P\]) 
VP ~--- VP ADVL\[mod-vp\] ; (ADVL', VP') 
% Temporal ADV, PP Rules 
NP\[def-fime\] ~ yesterday; Yesterday 
PP\[post-VP\] ~-- NP\[def-time\] ; (during NP') 
e.g., yesterday" = APAx((adv-e (during Yesterday)) \[x P\]) 
N\[time-unit, plur\] ~-- hours; (plur hour) 
ADJ\[number, plur\] ~--- two; (num 2) 
N\[lbar, time-length\] ~ ADJ\[number\] N\[time-unit\] ; (ADJ" N') 
NP ~ N\[lbar, time-length\] ; (K N') 
P\[dur\] ~---for ; lasts-for 
P\[span\] ~-- in; in-span-of 
PP\[e-mod, post-VP\] ~ P NP\[time-length\] ; (P' NP') 
e.g.,for two hours" = gPAx((adv-e (lasts-for 
(K((num 2) (plur hour))))) Ix P\]) 
e.g., in two hours" = 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. 
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" = APAx((adv-f ((nurn 2) (plur episode))) \[x P\]) 
e.g.,frequently" = 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" 
= APgx((adv-f As(3e \[\[e member-of s\] ^ \[e during <V spring>\]\])) 
Ix P\]) 
Sentences (1)--(5) below illustrate the rules stated in Table 1. 
The (a)-parts are the English sentences, the (b)-parts their im- 
mediate indexical LFs, and the (c)-parts the deindexed ELFs. 
(1) should be fairly transparent at this point. (2c) says that 
"some time before the utterance event, there was a 2 month- 
long (multi-component) episode, that consists three episodes 
of type 'John date Mary'." (3c) reads similarly. (4c) reads as 
"there was a 10 day-long episode that consists of periodically 
occurring subepisodes of type 'John take medicine', where the 
period was 4 hours." (5c) is understood as "at the generic 
140 
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." (We take verbs 
of creation such as bake as predicate modifiers.) 
(1) a. John worked for three hours yesterday. 
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. 
b. (past ((adv-e (in-span-of (K ((num 2) (plur month))))) 
((adv-f ((num 3) (plur episode))) \[Mary visit Paris\]))) 
c. (3e2:\[e2 before u2\] 
\[\[\[e2 in-span-of (K ((hum 2) (plur month)))\] ^ 
\[e2 ((num 3) (plur episode))\] ^ 
(mult \[Mary visit Paris\])\] ** e2\]) 
(3) a. John regularly dated Mary for two years. 
b, (past ((adv-e (lasts-for (K ((num 2) (plur year))))) 
((adv-f ((att~ regular) (plur episode))) \[John date Mary\]))) 
e. ~e3:\[e3 before u3\] 
\[\[\[e3 lasts-for (K ((num 2) (plur year)))\] ^ 
\[e3 ((attr regular) (plur episode))\] A 
(mult \[John date Mary\])\] ** e3\]) 
(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 \[\[s ((attr periodic) (plur episode))\] ^ 
\[(period-of s) = (K ((num 4) (plur hour)))\]\]) 
\[John take (K medicine)\]))) 
c. (3e4:\[e4 before u4\] 
\[\[\[e4 lasts-for (K ((num 10) (plur day)))\] 
\[e4 ((aUr periodic) (plur episode))\] ^ 
\[(period-of e4) = (K ((num 4) (plur hour)))\] n 
(mult \[John take (K medicine)\])\] 
** e4\]) 
(5) a. Mary bakes a cake every Saturday. 
b. (gpres ((adv-f 2s(Vd: \[d Saturday\] 
(3e \[\[e member-of s\] A \[e during d\]\]))) 
\[Mary (bake cake)\])) 
c. (3es: \[es gen-at us\] 
\[\[(Vd: \[d Saturday\] 
~e \[\[e member-of es\] A \[e during d\]\])) A 
(mult \[Mary (bake cake)\])\] 
** es\]) 
We emphasize again that ELFs are completely deindexed, and 
so allow effective inference. EPILOG \[20\], the computer im- 
plementation of EL, makes inferences very efficiently, based 
on such ELFs and world knowledge, aided by a "time special- 
ist." For instance, given "There is a train to Boston every two 
hours," "A train left for Boston at 2:30," and appropriate ax- 
ioms, EPILOG Can infer that the next train would be at 4:30. 5 
4This constraint on the Saturdays under consideration is assumed to be 
added by the deindexing process for time- or event-denoting nominals, but 
has been omitted from (5c). 
5The following kind of meaning postulates are assumed: 
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. 
We also have a tentative account of adverbials such as con- 
secutively and alternately, and some non-PP adverbials, but 
cannot elaborate within the present space limitations. 
3. AN EXTENSION: TEMPORAL ADVERBIALS AND 
ASPECTUAL CLASS SHIFTS 
So far, we have assumed aspectual category agreement be- 
tween temporal adverbials and VPs they modify. We now dis- 
cuss our aspectual class system and our approach to apparent 
aspectual class mismatch between vPs and adverbials, based 
on certain aspectual class transformations. 
We make use of two aspectual class feature hierarchies, 
stativeness and boundedness as below: 6 
st at ivene s s boundedne s s 
i 'I I I I i 
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., "Mary left 
before John arrived," in combination with a context, is 
considered factual. Untensed sentences may be stative or 
telic, depending on the type of the preedicate (i.e., achieve- 
ment/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. 
By a co-occurrence restriction, factual formulas are un- 
bounded, and telics are bounded. Statives are by default un- 
bounded. 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 as- 
cribe 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. 
c. (Ve(Vs: \[Is ((attr periodic) (plur episode))\] ^ \[s throughout e\]\] 
(Vp: \[(period-of s)=p\] (Vel: \[el member-of s\] 
\[\[(3e2:\[e2 irnmed-suecessor-in el s\] 
\[(dist (begin-of el) (begin-of e2)) = p\]) v 
\[(dist (begin-of e 1) (end-of e)) < p\]\] ^ 
\[(3e3:\[e3 immed-predecessor-in el s\] 
\[(dist (begin-of • 1) (begin-of e3)) = p\]) v 
\[(dist (begin-of el) (begin-of e)) < p\]\]\])))) 
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. 
6Our aspecmal class system resembles Passonneau's \[18\] in that it makes 
use of two orthogonal feature hierarchies, although the actual division of fea- 
tures is different from hers. 
141 
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 "John was ill when I saw him last week" 
is unbounded as the sentence does not entail that John was not 
ill right after the described episode. However, when we say 
"John was ill twice last year," we are talking about bounded 
"ill" 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 com- 
bine. 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. 
Mary called John twice I repeatedly l every five minutes. 
Mary wrote the paper/n two weeks. 
Note, however, that we also say 
Mary sneezed for Jive minutes. 
Mary stepped out of her office for \]fve minutes. 
Mary was ill twice \[ repeatedlyl every two months. 
The latter group of sentences show that VPs often acquire an 
interpretation derived from their original, primitive meaning. 
More specifically, when "stative" 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., "the result state of Mary's stepping 
out of her office" (i.e., her being outside of her office), rather 
than a reading involving iteration. Next, when cardinal or fre- 
quency adverbials (i.e., "bounded" adverbials) are applied to 
unbounded-stative VPs, those VPs are interpreted as bounded- 
statives. 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. 
To be able to accommodate such phenomena, the syntactic 
parts of our grammar use stat and bounded as agreement fea- 
tures. 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 some- 
times 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 
"John left last month," the "leaving" episode took place some- 
time during last month, but in case of "Mary was ill last 
month," Mary's "ill" 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. 
SHowever, *Mary resembled her mother for five years, even though "re- 
sembling" is a typical stafive VE This indicates that compatibility between 
predicates and adverbials involves more than just the aspeetual class compat- 
ibility; that is, pragmaties and world knowledge need to be considered. 
or throughout last month (corresponding to bounded and un- 
bounded readings of the VP). Synchronized cyclic adverbials 
like every spring or every time I saw Mary may combine with 
bounded or unbounded formulas. 
Secondly, an application of certain temporal adverbials of- 
ten induces shifts in the aspectual classes of the resultant 
VPs. Frequency adverbials transform bounded sentences 
into unbounded-stative ones, while durative adverbials nor- 
mally yield bounded VPs and synchronized cyclic ones yield 
unbounded-statives. Thus, 
John {{was ill twice} in three years}. 
?John { {was ill twice} for three years}. 
John { {was frequently ill} for three years}. 
?John {{was frequently ill} in three years}. 
John { {worked for five hours} three times} last week. 
We now rewrite the VP adjunct rules introduced earlier to ac- 
commodate 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. 
VP <-- VP\[stat, unbounded\] ADVL\[dur\] ; (ADVL' VP') 
VP\[bounded\] ~ VP\[stat, unbounded\] ADVL\[dur\] ; (ADVL' VP') 
VP ~ VP\[bounded\] ADVL\[span\] ; (ADVL" VP') 
VP ~ VP\[bounded\] ADVL\[card\] ; (ADVL" VP') 
VP\[stat, unbounded\] ~ VP\[bounded\] ADVL\[freq\] ; (ADVL' VP') 
VP\[stat, unbounded\] ~ VP ADVL\[cye-time\] ; (ADVL' VP') 
VP\[bounded\] ~-- VP\[stat, unbounded\] ; (bounded VP') 
VP\[stat, unbounded\] ~-- VP\[bounded\] ; (iter VP') 
VP\[stat, unbounded\] ~ VP\[telic\] ; (result-state VP') 
These rules allow transitions in aspectual class and VP- 
adverbial 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. 
(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))))) 
\[y sleep\]))\]))) 
9Similar kinds of shift in aspeetual classes have previously been discussed 
in the literature; first in \[24\], and subsequently in \[15, 23\]. 
142 
Notice that (9) has at least three readings: first, during a cer- 
tain week-long event, nobody had an 8-hour snooze; second, 
a situation in which nobody slept regularly for 8 hours per- 
sisted for a week1°; 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 du- 
rative 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. 
4. CONCLUSION 
Much theoretical work has been done on temporal adverbials 
(e.g., \[4, 5, 7, 14, 16, 19\]). There is also some computation- 
ally oriented work. For instance, H0bbs \[8\] provided sim- 
ple rules for some temporal adverbials, including frequency 
ones. Moens and Steedman \[15\], among others, discussed the 
interaction of adverbials and aspectual categories. Our work 
goes further, in terms of (1) the scope of syntactic coverage, 
(2) interaction of adverbials with each other and with tense 
and aspect, (3) systematic (and compositional) transduction 
from syntax to logical form (with logical-form deindexing), 
(4) formal interpretability of the resulting logical forms, and 
(5) demonstrable use of the resulting logical forms for infer- 
ence. 
Our initial focus in the analysis of temporal adverbials has 
been PP-adverbials. Remaining work includes the analysis 
of clausal adverbials. Also, interactions with negation and 
aspect (perfect and progressive) have not been completely 
worked out. Negations of statives are statives, but negations 
of bounded sentences may be either bounded or unbounded 
(cf., "We haven't met for thre e years" versus "I have friends I 
haven't met in three years"). The interaction between present 
perfect and multiple adverbials of temporal location also cre- 
ates some subtle difficulties. E.g., in "Mary has jogged {at 
dawn} {this month}," the inner time adverbial modifies the 
"jogging" episode, while the outer one modifies the interval 
that contains the "jogging" episode as well as the utterance 
time. See \[11\] for some relevant points. Another issue that 
requires thought is adverbials involving implicit anaphoric 
referents. Consider, e.g., "Shortly, Mary came in," "John 
came back in ten minutes," and "After three years, John pro- 
posed to Mary." These adverbials involve an implicit refer- 
ence episode. Such implicit referents may often be identi- 
fied from our tense trees, but at other times require inference. 
Another important remaining issue is the interaction between 
event nominals and frequency adjectives (along the lines of 
\[25\]). 
1°Here, iterated sleep is understood as daily sleep--something that must 
be determined by pragmaties. 
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