TEMPORAL CENTERING 
Megumi Kameyama 
SRI International AI Center 
333 Ravenswood Ave., 
Menlo Park, CA 94025 
megumi©ai.sri.com 
Rebecca Passonneau 
Dept. of Computer Science 
Columbia University 
New York, NY 10027 
becky¢cs.columbia.edu 
Massimo Poesio 
Dept. of Computer Science 
University of Rochester 
Rochester, NY 14627-0226 
poesio©cs.rochester.edu 
Abstract 
We present a semantic and pragmatic account 
of the anaphoric properties of past and perfect 
that improves on previous work by integrating dis- 
course structure, aspectual type, surface structure 
and commonsense knowledge. A novel aspect of 
our account is that we distinguish between two 
kinds of temporal intervals in the interpretation 
of temporal operators -- discourse reference inter- 
vals and event intervals. This distinction makes 
it possible to develop an analogy between center- 
ing and temporal centering, which operates on dis- 
course reference intervals. Our temporal property- 
sharing principle is a defeasible inference rule on 
the logical form. Along with lexical and causal 
reasoning, it plays a role in incrementally resolv- 
ing underspecified aspects of the event structure 
representation of an utterance against the current 
context. 
The Problem 
The past tense has been compared with anaphoric 
definite pronouns (\[20\] \[22\]) and definite noun 
phrases (\[27\]). The supporting observation is 
that in two consecutive past tense descriptions of 
events, as in (1) below (from \[18\]), the second sen- 
tence refers to a time (t') whose identity depends 
on the time (t) of the event described in the first 
sentence. 
(1)a. The Lone Ranger got on his horse. (t) 
b. He rode off into the sunset. (t') 
Tense interpretation also involves common- 
sense inferences in that the specific relation be- 
tween the two event times may vary. In (1), the 
relation inferred to hold is temporal progression (t 
-~ t'), but other ordering relations are also possible 
(see \[6\] \[27\]). Any temporal relations are in fact 
possible for two consecutively described events in 
discourse. 
A number of factors affect the interpretation 
as to whether successive past tenses are anaphor- 
ically related, and if they are, what the relative 
order of the associated events is. The determinant 
factors have been argued to be discourse struc- 
ture (\[27\] \[14\]), aspectual type (\[61 \[12\] \[17\]), sur- 
face structure (\[7\] \[14\]), and commonsense knowl- 
edge (\[19\] \[271 \[13\]). However, no account has ad- 
equately addressed all four factors. 
The problem in tense interpretation that we 
address is illustrated with Example (2) (from \[27\]). 
(2)a. John went over (el) to Mary's house. 
b. On the way, he had (t2) stopped (t3) by the 
flower shop for some roses. (t3 -~ t2 (=tl)) 
c. Unfortunately, they failed (t4) to cheer her 
up. (t3 -~ tl -~ t4) 
c'. He picked out (t4') 5 red ones, 3 white ones 
and 1 pale pink. (t3 -< t4' -< tl) 
(2c) and (2c') are alternative third sentences. Al- 
though both are in the simple past, and both evoke 
events of the same aspectual type (transition event 
\[23\]), they are interpreted differently. We refer 
to the contextually established time that a past 
tense is resolved against as the "discourse refer- 
ence time." A discourse reference time (tl) is in- 
troduced in (2a) with the event of John going to 
Mary's house at tl) The past perfect in (2b) in- 
troduces two times: John's stopping at the flower 
shop (t3) precedes the time t2 (t3 -~ t2), and t2 is 
typically inferred to be equal to the time of going 
over to Mary's house (tl); hence t3 ~ tl. In (2c), 
the time of failing to cheer Mary (t4) is inferred 
to occur just after tl, whereas in the parallel ver- 
sion (2c'), the time of picking out roses (t4') is 
inferred to occur during or just after t3, thus be- 
fore tl. Thus, as noted by Webber \[27\], a past 
perfect evokes two temporal referents (e.g., t2 and 
t3) and either of them can provide a discourse ref- 
erence time for a subsequent past tense. 
1Later we will see that although the first tense gen- 
erates a discourse reference time for the subsequent 
one, its temporal referent (here tl) is not precisely 
equivalent to it. 
70 
Another aspect of the problem in tense in- 
terpretation is illustrated with so-called extended 
flashbacks such as Example (3), similar to the one 
discussed in \[14\]. 
(3) John and Mary went to buy a lawnmower. 
Somebody had stolen theirs the day before. 
They had seen the thief go away. John had 
run after him to no avail. All the lawnmow- 
ers were too expensive. They decided they 
couldn't afford a new one. 
There are two narrative threads in (3), one de- 
scribing John and Mary's visit to a store, the other 
John's chase of the thief. These threads corre- 
spond to the repeated use of the past and of the 
past perfect, respectively. The return from the 
past perfect to the past in also coincides with the 
return to the earlier thread. Note that (i) not 
only the simple past but also the past perfect 
can achieve an effect of continuity and that (it) 
more than one discourse reference time needs to 
be maintained in order to account for the return 
to an earlier one. 
The general problem in tense interpretation 
that we address is how to keep track of all the po- 
tential discourse reference times in a context, and 
how to select the right one for a given anaphoric 
past tense. 
We argue that the choice of the discourse an- 
tecedent of a temporal operator is subject to cen- 
tering effects. We assume that each temporal op- 
erator in a sentence introduces a discourse refer- 
ence time into the discourse context. We claim 
that this set of times constitutes a list of poten- 
tial discourse reference times for the next sentence, 
which we'll later refer to as the temporal forward- 
looking center (TCf), and that the position of a 
temporal operator in the logical form of the sen- 
tence affects the choice of the antecedent through 
structural parallelism (as a case of the property- 
sharing effect in centering \[16\]). 
We formalize the effect of surface structure on 
the choice of temporal antecedent by means of de- 
feasible axioms. These axioms must be less specific 
than axioms encoding causal reasoning. We argue 
that the choice of discourse reference time is an 
instance of a general principle in defeasible rea- 
soning, namely, the Penguin Principle \[19\] that 
chooses the most specific axiom applicable. We 
support our claims with data from the Brown cor- 
pus. 
In the next section, we review the three ex- 
isting proposals most related to ours -- Webber 
\[27\], Lascarides and Oberlander \[19\], and Hwang 
and Schubert \[14\]. The next two sections present 
a review of centering followed by a discussion of 
the analogous effects of temporal centering. To 
account for temporal centering effects, we then 
present our tense rules and our account of how 
commonsense reasoning interacts with the default 
preferences generated by the surface structure. 
Related Work 
Webber \[27\] argues that temporal entities are 
subject to focusing processes analogous to those 
constraining the interpretation of definite noun 
phrases. She explicitly rejects, however, a more 
direct analogy to Sidner's \[26\] potential local foci, 
and assumes only one temporal referent in the 
temporal focus (TF). 
Lascarides and Oberlander \[19\] present de- 
feasible reasoning rules for narrative understand- 
ing that partly address the reasoning and control 
needs of Webber's model. For example, they argue 
that in the case of conflicting inferences regard- 
ing the temporal order of two times \[e.g., whether 
precedes, follows, or overlaps\], the most specific 
interpretation should be preferred. However, they 
do not address cases such as (2), where there are 
multiple possible discourse reference times and the 
choice of one interpretation over the other needs 
to be accounted for. 
Itwang and Schubert \[14\] intend to account 
for the role played by structural factors in the 
choice of anaphoric relations among distinct past 
tenses. They propose the contextual structures 
called tense trees built as a narrative gets inter- 
preted. Tense trees reflect the structural depen- 
dencies among the tense and aspect operators in 
the interpretation of the sentences. The events 
evoked by a sentence are "appended" to the tree 
nodes whose positions reflect the structural posi- 
tions of the corresponding temporal operators in 
the sentence. 
Webber \[27\] and Hwang and Schubert \[14\] dif- 
fer markedly regarding the relative weight they 
assign to commonsense inferences versus surface 
structure, but both have problems with examples 
like (2). Neither can readily account for the in- 
terpretation assigned to (2c'). Webber assumes 
that the TF of (2b) is initially tl, but shifts to t3, 
thus initiating an embedded segment, after (2c') 
has been processed sufficiently to recognize that 
TF=t3 yields a more sensible interpretation than 
TF=t2(=tl). She does not discuss how t3 comes 
to be considered as a potential TF in this case, 
much less how to reject t2(=tl). Like Webber, 
Hwang and Schubert assume that (2c') requires 
recognition of an embedded segment, but admit- 
tedly they have not resolved the conflict between 
the need for discourse segment recognition, a task 
for commonsense reasoning, and the clear sepa- 
ration of tense resolution from commonsense rea- 
soning that they advocate. They also fail to dis- 
tinguish betwen the hierarchical structures of sen- 
7\] 
tences and discourses in the tense tree. Tense tree 
thus overcommits in places where the rule should 
belong to defeasible preferences. 
Our approach is to formulate the structural 
preferences for tense resolution as defeasible rules 
analogous to centering preferences for pronoun res- 
olution. These structural preferences, which are 
overlooked in Webber's or Lascarides and Ober- 
lander's accounts, interact with the commonsense 
inferences used in tense interpretation. 
Centering 
Centering \[9\] is a refinement of Sidner's \[26\] local 
focusing model. It consists of a set of principles 
and rules for dynamically updating the local at- 
tentional state \[11\] in discourse processing. 
We assume the following general picture of 
discourse processing. A discourse consists of a se- 
quence of utterances uttl,..., uttn. The sentence 
grammar translates the content of each utterance 
utti into a (set of) surface logical form(s) contain- 
ing unresolved anaphoric expressions and opera- 
tors. We call it here a "surface" formula ¢i. This 
logical form is similar, in spirit, to Hwang and 
Schubert's \[14\] indexical formula and Alshawi's \[2\] 
quasi logical form, whose main motivations are to 
represent that part of the sentence meaning in- 
dependent from the particular discourse context. 
This "baseline" meaning representation acts as a 
clean interface to the pragmatic processing needed 
to resolve context-dependent expressions. Utter- 
ance interpretation takes place in a context, and 
outputs an updated context. Part of this dynamic 
context is the attentional state that represents the 
currently salient entities partially ordered by rel- 
ative salience. 
We say that each formula ¢i defines a transi- 
tion relation between the input attentional state 
ASi_I and the output attentional state ASi. An 
attentional state ASi contains the focus of atten- 
tion Foci whose most salient subpart is the center 
of attention. After resolving anaphoric expressions 
in ¢i, the center of attention contains a partially 
ordered set of forward-looking centers Cfi com- 
prising the entities realized in ¢i. A member of 
Cfi might (but need not) be the backward-looking 
center Cbi, the currently most salient entity. 
Centering has mainly been used to constrain 
how discourse anaphoric pronouns are processed; 
e.g., the centering rule \[9\] predicts that Cbl will 
be realized with a pronoun if Cbi=Cbi_l. 2 Also, 
when Cbi=Cbi-1 and both are realized by definite 
pronouns, it is predicted that both will be real- 
2Here we avoid the complication acknowledged in 
\[11\] that the two relevant utterances need not literally 
be adjacent. 
a. John went to the store. 
C fl =\[Johnl,storel\] Cbl=NULL 
b. He saw Bill. 
C f2=\[John ~,Bill'\] Cb2=John ~ 
Cb-establishment 
c. He walked towards him. 
C fj=\[John',BiW\] Cbz=John ~ 
Cb-retention 
c'. He appeared pale to him. 
Cfz,=\[Bill', John'\] Cb3,=Bill' 
Cb-establishment 
Figure 1: Illustration of Centering 
ized in a common grammatical role, with subject 
preferred over non-subject \[16\] \[24\]. A number of 
transition relation types have been distinguished 
in centering. In this paper, we will use the fol- 
lowing four types: Cb-retention, Cb-establishment, 
Cb-resumption, and NULL-transition. z 
In Cb-retention, the same entity is retained 
as the Cb: Cbi-1 = Cbi y£ NULL. In Cb- 
establishment, another member of Cf becomes 
the Cb: Cbi-1 ~ Cbl, Cbi E eli-1 (Cbi-1 may 
be NULL). These two are the most relevant to 
the present paper. In Cb-resumption, an old Cb 
not in Cf but in the current Foc is resumed. 
In NULL-transition, the output state has no Cb 
(Cbi=NULL). Centering posits a default prefer- 
ence for retention over establishment. We pro- 
visionally assume that establishment is preferred 
over resumption or NULL-transition. 
We illustrate centering with Fig. 1, where c 
and c' are alternative continuations of b. After a., 
C fl contains two entities, John ~ and storel. In b., 
John ~ is referred to with a subject pronoun, and 
is established as Cb2. In c., because John ~ is the 
current Cb, and because retention is preferred over 
establishment, centering predicts that a subject 
pronoun will refer to John ~ rather than to Bill( 
The default is overridden in c' and instead, the 
subject pronoun is inferred to refer to BiW because 
it is likely that the perceiver in the first perceptual 
state, see ~, remains the perceiver in the subsequent 
perceptual state, appear ~. " 
3Cb-retention and Cb-establishment are due to 
Kameyama \[15\] \[16\]. These two roughly correspond 
to the three \[10\] and four \[5\] transition types pro- 
posed elsewhere. Cb-resumption captures Sidner's \[26\] 
use of a discourse focus stack in the potential focus 
list, and can be analogously formalized as a Cb stack 
within the Cf. NULL-transition has been implicit in 
Kameyama's work but has not been made an explicit 
transition type. 
72 
a. John went over (tl) to Mary's house. 
TCfl=\[rl\] TCbl=NULL 
b. On the way, he had (t2) stopped (t3) 
by the flower shop for some roses. 
TC f2=\[r2=rl,r3\] TCb2=rl 
TCb-establishment 
c. Unfortunately, they failed (t4) to cheer her up 
TC fz=\[r4=rl\] TCbz=rl 
TCb-retention 
c'. He picked out (t4') 5 red ones, 3 white ones, 
and 1 pale pink. 
TCf3,=\[r5=r3\] TCbz,=r3 
TCb-establishment 
Figure 2: Illustration of Temporal Centering 
Centering effects in tense 
interpretation 
Our proposal is motivated by the parallel between 
example (2) above and the centering example in 
Fig. I. As illustrated in Figure 2, we would 
like to say that utterances (2a) and (2b) share 
the same discourse reference time rl that links t2 
to tl. The shared discourse reference time rl is 
thereby established as a backward-looking tempo- 
ral center (TCb). (2c) retains the TCb, linking t4 
to t2(=tl), whereas (2c') establishes a new TCb, 
linking t4' to t3. 
In order to establish a direct analogy between 
centering and temporal centering, however, we 
need to first clarify the nature of the temporal 
entities in the attentional state. Note that if (2c) 
retains the "same" TCb, this TCb cannot be iden- 
tified with either t2 of (2b) or t4 of (2c), since t2 
and t4 are distinct (tl=t2, tl -< t4). The TCb 
remains fixed while the event times within it may 
move forward or backward. The TCb is then quite 
different from the reference time as used in propos- 
als inspired by Reichenbach \[25\] such as Dowty's 
\[6\] and ttinrichs \[12\]). 4 Recall the extended flash- 
back example (3) above. There are two simulta- 
neous narrative threads, in the simple past and in 
the past perfect, and the former seems to remain 
somehow in the background while the latter is in 
the foreground. These examples seem to indicate 
that when processing a text a reader maintains 
a list of "potential foci" ordered by their relative 
salience, instead only one temporal focus, as in 
Webber's account. 
Further evidence in favor of the analogy was 
obtained by examining a random sample of dis- 
4A similar proposal is made by Kamp and Reyle \[17\], 
where they argue for the separation of the tem- 
poral perspective point ( TPpt) that is relatively fixed 
and the re\]erence point (Rpt) that moves with narra- 
tive progression. 
course sequences from the Brown corpus \[8\], a 
heterogeneous corpus that should yield unbiased 
data. Each multi-sentence sequence contained 
one of two types of trigger sentences with multi- 
ple temporal operators -- the past perfect matrix 
clause or the past matrix verb taking an embed- 
ded past or past perfect complement clause (e.g., 
John remembered that Mary had asked for roses). 
We observed that this trigger's output TCb was 
almost always the time associated with the super- 
ordinate operator. Following each trigger was a 
target sentence with a simple past matrix clause. 
This creates a sequence analogous to (2b-c) or 
(2b-c'). We analyzed each sequence to determine 
whether the discourse reference time for the past 
in the target sentence was introduced by the trig- 
ger's superordinate operator (as a case of TCb- 
retention) or by a subordinate operator (as a case 
of TCb-establishment). In the total of 80 exam- 
pies, we found 52 retentions (65%) and 12 estab- 
lishments 15%). Others included 9 cases of "nei- 
ther" (11%) (some combination of resumption and 
NULL-transition) and 7 undecidable cases (9%). 
These data are consistent with our hypothesis that 
in a sentence with multiple temporal operators, 
the relative likelihood that a given temporal op- 
erator provides the discourse reference time for a 
subsequent past depends on its syntactic promi- 
nence. The question is, how do temporal centering 
and commonsense reasoning interact to yield the 
observed results? 
Two levels of logical representation 
Our explanation for the interaction between tem- 
poral centering and commonsense reasoning rests 
on assuming two distinct levels of representation 
in sentence interpretation. One is the logical form 
independent from the context and obtained by a 
direct translation of the surface syntactic structure 
of the utterance. The other is a fully resolved log- 
ical expression that results from incrementally re- 
solving context-dependent expressions in the log- 
ical form. For simplicity, our discussion ignores 
anything but temporal operators. 
Much as in Hwang and Schubert's proposal 
\[14\], the logical form contains unresolved tempo- 
ral operators -- e.g., tense operators, PR~.S(ent) 
and PAST, and aspectual operators, PERF(ect) and 
PROG(ressive). It also represents the structural po- 
sition of the temporal operators in a sentence. The 
crucial difference is that we take each tense and 
aspect operator to also give rise to a discourse ref- 
erence interval (see below) that is contextually re- 
solved. Our logical forms for (2a) and (2b) are 
shown in (4). 
(4)a. (PASTrl 'John goes over to Mary's 
house ' ) 
73 
r(PASTr¢)=(3 e (e C r) A 
(e starts_before SuperNow) A 
(Las$In(r) orients e) \[e ~ r(¢)\]) 
r(PERFr¢)=(3 e (e C r) A 
(e starts_before SuperRef) A 
(LastIn(r) orients e) Ce ~ r(¢)\] ) 
Figure 3: Mapping rules for PAST and PERF 
b. (PASTr2 (PERFr3 'John stops by the 
florist for some roses')) 
The temporal operators in our logical forms 
are translated into the language of what we call the 
event structure representation (ESR). In essence, 
ESR represents the temporal and causal relations 
among the eventualities described in discourse. 
We will use Allen's \[1\] interval representation 
scheme for this representation level. Described 
eventualities correspond to event intervals and 
what we have been calling the "discourse reference 
times" correspond to discourse reference intervals. 
To represent relations among these temporal inter- 
vals, we use disjunctive subsets of Allen's thirteen 
relations. With Allen's representation, we can di- 
rectly represent vague or ambiguous temporal rela- 
tions expressed in natural language and incremen- 
tally resolve them to more specific relations using 
constraint propagation. Our discourse reference 
intervals coincide exactly with the computational 
role of Allen's reference intervals. 
Tense mapping rules 
Now we define the recursive mapping r be- 
tween the logical form and the event structure 
representation. 5 These tense mapping rules "un- 
pack" the relations among relevant event inter- 
vals and discourse reference intervals encoded by 
temporal operators in the logical form, and gen- 
erate the initial event structure representation. 
Although these rules look similar to IIwang and 
Schubert's tense deindexing rules, they play a very 
different role. Rather than performing sentence 
interpretation, as their deindexing rules do, our 
mapping rules specify the semantics of the logical 
form in terms of the event structure representa- 
tion. The v rules for PAST and PERF are shown in 
Fig. 3. 
We assume that formulas denote sets of time 
intervals. For every clause associated with a for- 
mula 0PC, where 0P is a temporal operator (PAST 
or PERF) and ¢ is a formula, there is an event inter- 
SThe use of r was inspired by the r translation in 
temporal logic \[4\]. 
val e corresponding to the specific time for which 
¢ is inferred to hold. We express this relation as 
e ~ ¢ (e supports ¢). A statement of this form 
evaluates to true if the denotation of e is an ele- 
ment of the denotation of ¢. 
Each event interval e is temporally included 
in a discourse reference interval r, semantically 
treated as an open variable -- the value of r is 
constrained by contextual factors such as tempo- 
ral centering and commonsense reasoning, as de- 
scribed in a later section. 
Superllo~ and SuperRef have values deter- 
mined by the position of the subformula 0PC in the 
logical form. SuperNow evaluates to the current 
utterance interval- the time interval in which 
the current utterance takes place. We assume that 
there is an updating mechanism for SuperNow de- 
fined for each utterance initiation including the 
onset of a quoted speech. $uperRef evaluates to 
the event interval evoked by the temporal opera- 
tor that immediately dominates the current one in 
the logical form. 
Starts.before, a disjunction of meets, pre- 
cedes and the inverse of finishes (m -~ fi), is 
the possible relation between e and Supe.rNow for 
any PASTe (or between e and SuperRef for any PERF¢), 
irrespective of the aspectual type of 4. 
Orients, borrowed from Hwang and Schubert, is 
the disjunctive set of all of Allen's thirteen re- 
lations. Both starts_before and orients may be 
further specialized after computing ¢'s aspectual 
type, which depends partly on the aspectual types 
of its constituents and partly on commonsense 
reasoning? We can state certain default speci- 
fications of orients. For example, involving two 
transition event intervals, orients defaults to pre- 
cedes (e.g., see (1) where t -~ t'). Stative inter- 
vals by default overlap other non-stative or stative 
intervals (cf. \[6\] \[12\]). 
LastIn(r) is a function defined over dis- 
course reference intervals, and evaluates to the 
most recent non-stative event interval in the dis- 
course reference interval r, where applicable. This 
event interval orients the new event interval e. 
LastIn(r) corresponds to the "reference time" that 
moves with narrative progression in approaches 
like Dowty \[6\] and Hinrichs \[12\]. 
How the mapping rules work 
Table 1 shows the logical form and the event struc- 
ture determined by the mapping rules for each sen- 
tence of (2) (repeated here). 
(5)a. John went over (tl) to Mary's house. 
6See \[23\] for a partial model of computing aspectual 
type; see \[21\] for a partial model of aspectual coercion, 
one type of commonsense reasoning. 
74 
¢i eC_ r Constraint 
a PAST a tl C_ rl tl (-~) u~ 
b PAST 
(PERFfl) t2 C r2 t2 (m fi) ub 
PERF ~ t3 C r3 t3 (-~) t2 
c PAST 7 t4 C r4 t4 (-<) uc 
c' PAST 7' t4'C_ r4' t4'(-~) uc, 
Table 1: Application of Rules to (2) 
b. On the way, he had (t2) stopped (t3) by the 
flower shop for some roses. 
c. Unfortunately, they failed (t4) to cheer her 
up. 
c'. He picked out (t4') 5 red ones, 3 white ones 
and 1 pale pink. 
The symbols a-7' correspond to the tenseless 
propositions of sentences a-c', and ua--ue, repre- 
sent the respective utterance event intervals. We 
explain the interpretation of sentence (25) ((5b) 
above) in detail. Applying the rule for PAST, we 
obtain t2 ~ T(PERF~), with discourse reference 
interval r2 such that t2 C r2. SuperNow evalu- 
ates to Ub, yielding t2 starts_before Ub. PERFfl 
is necessarily stative, so by default its event inter- 
val is assumed to persist up through the present. 
Thus t2 starts_before Ub is specialized to t2 
(m fi) Ub. Applying the PERF rule, we obtain t3 
fl, with discourse reference interval r3 such that 
Z3 C r3. Superl~ef evaluates to t2, the event in- 
terval of the dominating PAST operator, yielding 
t3 starts_before t2, which is then specialized 
to t3 ~ t2 due to the aspectual types of PERFfl 
and ft. 
The interaction between structural 
factors and causal knowledge 
We propose that defeasible rules producing hy- 
potheses about the interpretation of an utterance 
operate on both the levels of representation used 
in tense interpretation. On the event structure 
representation level, we assume the existence of 
axioms formalizing lexical semantics and other as- 
pects of commonsense knowledge (e.g., \[13\] \[19\]), 
and call them causal axioms. Simplified examples 
are given in (6) and (7) below. We use the default 
conditional > introduced by Asher and Morreau 
\[3\] and used by Lascarides and Oberlander \[19\]. 
(6) encodes the inference that people usually pick 
up flowers at the florist's. (7) say that people are 
usually at certain places as a result of their going 
there. 
(6) PICK-UP(X,flowers,%) > 
(AT(X,florist,t') A tCt') 
(7) AT(X,place,t) > 
(GO-TO(X,place,t') A t'-~t) 
The other, more novel, assumption we make 
is that there are defeasible rules that operate on 
the logical form, on the basis of structural infor- 
mation only. We formalize the effects of structural 
information in terms of what we call logical form 
axioms. Much as in the case of axioms formaliz- 
ing commonsense knowledge, logical form axioms 
can be defeasible. Although the effects of struc- 
tural factors on anaphora interpretation are widely 
acknowledged in linguistic theories (e.g., binding 
theory), the interest is more on indefeasible gram- 
matical principles. Our logical form axioms en- 
code grammatically derived defeasible preferences, 
the kind of structural effects that centering and 
temporal centering uncover. 
We assume the following architecture for sen- 
tence interpretation. Once the logical form has 
been obtained, logical form reasoning takes place. 
There are two kinds of rules in logical form reason- 
ing -- monotonic (or indefeasible) and defeasible. 
The former rewrite the logical form, and the lat- 
ter generate logical form hypotheses, that are addi- 
tional logical form expressions. All of the hypothe- 
ses resulting from logical form reasoning, as well as 
the original interpretation, are then mapped into 
event structure representations, and causal axioms 
are used to complete the interpretation. All com- 
plete interpretations of a sentence are compared 
to find the best hypothesis. 
We propose to encode temporal centering as 
defeasible logical form axioms that generate logi- 
cal form hypotheses about the interpretations of 
unresolved discourse reference intervals. To be 
more precise, we claim that the following principle 
holds: 
Temporal Property-sharing Principle (TPP) 
Resolve the current discourse reference interval 
rl against a discourse reference interval rj in the 
attentional state. By default, ri and rj should 
share the same properly reflecting the temporal 
position in the logical form. 
This general preference can be encoded by 
means of logical form axioms of the type shown 
in (8), whose intended interpretation is as follows 
-- Let uttn-1 and uttn be two consecutive ut- 
terances in discourse, lf(utt) be a function from 
utterances to their logical forms, (PASTrl ¢) be 
a subformula of l:~(uttn_l) , (PASTr2 ~) be a 
subformula of if (utt,), and pos (lf 1, lf2) be a 
function from pairs of a formula lfl and a sub- 
formula lf2 into the "temporal position" of lf2 in 
lfl. The temporal position of a subformula in a 
formula is the sequence of higher temporal oper- 
ators of the subformula. For example, in the for- 
75 
mula (PAST (PEP~F ¢)), the temporal position 
of (PAST (PERF ¢)) is the empty sequence (), 
that of (PERF ¢) is the sequence {PAST), and 
that of ¢ is the sequence (PAST,PERF). In a case 
where pos(u.-1,(PASTrl ¢) = pos(u., (PASTr2 
~)), the TPP generates the hypothesis that the 
two discourse reference intervals rl and r2 are the 
same. 
consecutive (utt._ 1 ,uttn), 
pos(If(utt._l), (PASTrl ~)) = 
(8) pos(lf(uttn), (PASTr2 ~)) 
¢.-+ 
uttn : (PASTr2=rl ~) 
A similar rule generates hypotheses about the 
identity of two discourse reference intervals both 
introduced by PERF operators in the same tempo- 
ral positions. 
Lascarides and Oberlander \[19\] propose the 
Penguin Principle as a way of choosing among 
conflicts generated by the application of defensible 
rules. The principle says that whenever a conflict 
between rules arises, the hypothesis obtained by 
applying the most specific rule should be chosen. 
The logical form axioms encode general knowledge 
of linguistic structures independent from particu- 
lar events or situations being described. Thus the 
information they encode is necessarily less specific 
than rules encoding lexical inferences and causal 
relations. Hence the following consequences on the 
TPP: 
The TPP applies in the absence of informa- 
tion about causal relation between the events. 
Any hypothesis that results from causal rea- 
soning is preferred over the hypothesis sug- 
gested by the TPP. 
This general pattern of interaction between 
causal and logical form axioms predicts the fol- 
lowing Temporal Centering Principle: 
Temporal Centering Principle (TCP) When ¢i 
evokes a set of unresolved discourse reference 
intervals rx,...,rn, each rk is resolved against 
the current atttentional state as follows-- (i) IF 
causal axioms generate a hypothesis, take it, (ii) 
ELSE IF the TPP generates a hypothesis, take 
it, (iii) ELSE rl,..., r, are new to the discourse. 
After resolution, rl, ..., rn are in the TCfl in the 
output context of ¢i. 
Case (i) of the TCP allows any of the four transi- 
tion types, retention, establishment, resumption, 
or NULL. A NULL-transition only result only 
from negative conclusions obtained from causal 
axioms. Under the TPP in the form of rule 
(8) that applies only on consecutive utterances, 
case (ii) would result in either TCb-retention 
or TCb-establishment, but not TCb-resumption. 
How does this accord with our corpus data dis- 
cussed earlier? In the most frequent (65%) TCb- 
retention, the discourse reference interval evoked 
by the matrix past tense is identified with an- 
other evoked by the matrix past tense in the pre- 
vious utterance. In the next frequent (15%) TCb- 
establishment, it is identified with the one evoked 
by the subordinate temporal operator. This sharp 
difference in frequency would be explained by the 
fact that the TPP supports the former but not the 
latter. 
Webber's example, revisited. 
We now go back to Webber's example (2) and ex- 
plain how the interactions of defensible rules result 
in the temporal centering transitions shown in Fig. 
2. The input consists of the logical forms from Ta- 
ble 1. 
(2a) For the initial sentence of discourse, only the 
NULL-transition can apply, rl is not identified, 
and remains as an open variable. AS1 contains 
TCfl=\[rl\]. 
(2b) The TPP can apply for PAST; resulting in 
TCb-establishment, with rl=r2. As a re- 
sult, TCf2=\[rl,r3\], TCb2=rl, and the value of 
LastIn(r2)=LastIn(rl) is tl. This yields tl 
orients t2, where tl is the transition event 
interval for (~) and t2, for a state (PERF /3). 
When a non-stative event interval orients a 
stative event interval, the former is partly cov- 
ered by (overlaps, starts, finishes, equals, during, 
or their inverses) the latter by default. 
(2c) The TPP, in the form of rule (8), generates 
the hypothesis expressed by the following log- 
ical form: (PASTr4=rl 'The roses fail to 
cheer her'). The causal reasoning generates 
the same conclusion, namely, in order to give 
somebody flowers, one has ~o be at somebody's 
place, so we conclude that the 'failing-to-cheer 
event' continues the "story" of John's going 
over to Mary's house. Either way, we have a 
TCb-retention, yielding TCf3 =\[rl(=r4)\] and 
TCb3=rl. The value of LastIn(r4) is now tl, 
yielding tl orients t4. Since tl and t4 are 
event intervals for transition events (a and 7), 
orients defaults to tl (-<) t4. 
(2c') There is a conflict. While the TPP would sug- 
gest a continuation of the story of John's visit 
at Mary's house, the causal rules such as (6) 
suggest that the event of picking up flowers 
takes place at the florist's, and the rules such 
as (7) suggest that being at the florist's results 
from the action of "stopping by" the florist's. 
The Penguin Principle now applies, resulting in 
TCb-establishment, and t3 (-4) t4. 
76 
Conclusions 
We have presented a semantic and pragmatic ac- 
count of the past tense that uniformly accounts for 
its discourse anaphoric properties. We distinguish 
between two kinds of intervals, discourse reference 
intervals and event intervals, which allows us to 
provide a direct analogy between centering and 
temporal centering. 
We introduce the notion of logical form rea- 
soning, which obviates the need for tense trees as 
the source for structural reasoning, and, at the 
same time, enables us to account for the interac- 
tion between the structural preferences and causal 
reasoning. By including in both logical form ex- 
pressions and event structure representation an ex- 
plicit indication of the contextual parameters to be 
resolved, rules can be formulated that exploit the 
kind of information available at each level. We 
can therefore factor out different sources of de- 
feasible preferences in tense interpretation. Rules 
operating on the logical form formalize the effects 
of structural factors, and rules operating on the 
event structure formalize the effects of common- 
sense knowledge. 
The ordering preferences in our model are con- 
sistent with data from a large, heterogeneous cor- 
pus. In the future work, we need to develop an 
evaluation method for our model, to specify more 
fully the knowledge representation and reasoning 
needs, and finally to clarify consequences that our 
model might have on a more unified model of at- 
tentional state to simultaneously account for nom- 
inal and temporal anaphora. 
Acknowledgement 
Each author would like to thank the other two 
authors for stimulating discussions and encour- 
agements. We would also like to thank Johan 
van Benthem, David Carter, Janet Hitzeman, Len 
Schubert, and ttenri~tte de Swart for helpful dis- 
cussions. 

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