Tense, Aspect and the Cognitive Representation of Time 
Kenneth Man-kam Yip 
Artificial Intelligence Laboratory 
Massachusetts Institute of Technology 
545 Technology Square 
CamOridge, MA 02139. 
ABSTRACT 
This paper explores the relationshiDs between a 
computational meory of temporal representation (as developed by 
James Alien) and a Iormal linguiStiC theory Of tense (as developed 
by NorOert Hornstem) and aspect. It aims tO prowde exphcit 
answers to four lundamental Questions: (1) what ts the 
computational lustd~cat=on for me or=mmves of a hngu=stIc theory; 
(2) what ~s the computational explanation of the formal 
grammatical constraints; (3) what are the processing constraints 
~ml3osed on the learnabdity and marKedness of these theoretical 
construCtS: and (4) what are the constramnts that a hnguist=c theory 
imposes or. representat¢ons. We show that one can effectively 
exploit (n~ ,nterface between the language faculty and the 
cognmve faculties by using hngu=stic constra,nts tO determine 
restrtcuons on tile cognitive representations and wce versa. 
Three mare results are cbtalned: (1) We derive an 
explanation of an oOserved grammabcal constrmnt on tense .. the 
Linear Order Constraint -- from the reformation monotonicity 
property of the constraint propagation algorithm of Allen's 
temPoral system: (2) We formulate a principle of mart~edness for 
the 13as=c tense structures Ioased on the computational efficiency 
of the temporal representations: and (3) We snow Allen's 
interval-Oased temporal System =s not arbitrary, bul it can be used 
to exolair, ;nctependently motwated lingulst~c constraints on tense 
and aspect interpretatmns. 
We also claim that the methodology of research developed in 
tins study -- "cross-lever' investigation of independently motivated 
formal grammatical theory and computational moclets -. is a 
¢owerful paradigm with which to attack representational problems 
=n oaslc cognitive domains, e.g.. space, t~me, c~u:~ality, etc. 
1. Objectives and Main Results 
One malor effort m moclern hnguistlcs Is tO hmlt the class of 
possible grammars to those that are psychologically real. A 
grammar Is PSyChOlOgiCally/real if it ts (a) realizaole - possessing 
a computational model that can reproduce certain psychological 
resource complexity measures, and (b) learnable . capable of 
Oemg acquired (at least, m principle) despite the poor quality of 
input linguistic data. A shift of eml3nasis from the pure 
characterization problem of grammar to the realization and 
leamability problems naturally bnnga linguistics closer tO AI work 
in na:ural language understanding Concerned wfth computational 
models of language use and language acquisition Computational 
study =Sm principle complementary tO more formal and aOstract 
grammatical theory. Each should contribute to the other. 
The purpose of this loader ~s to work Out an example of how 
formal grammatical meory and computational models can 
effectively constrain eacn diner s reoresematJons. In ~3artJcular, I 
seek to exolore four !undamental ~ssues: 
t. How ~s the cho=ce of onmmve structures m grammatical 
theory to be lustified? 
2. What ~s the explanation of the rules and constramts that 
have to Oe stiI3ulated at the grammatical level? 
3. HOw are these knowledge structures acau~red? 
4. What are the theoretical constraints ~moosed by the 
grammar on the representational scheme of the 
computation theory? 
What I hope tO snow is that structures and prmcJoles that 
have to be sttoulatgG '~t the grammatical level fall out nalurally as 
consequences of the proDert=es of the algorithms and 
representations of the underlying comoutahonal model. In sO 
doing, I will also restnct the class of plausmle computational 
models tO those that can exclam or incorporate the constraints 
=m;3osed by the formal grammatical theory. 
There are a numoer of requirements that must be met m 
order for such "cross.lever' study to succeed. First, there is a 
sizable collection of fzcts and data from the target domain to be 
explained. Second. there =s ,ndeDendent motwauon for the theory 
of grammar .. =t ~s empmca:ly adequate. And, third, the 
computational model =s also ,nrJeoendently motivated by ioemg 
sufhc=ently express=re and computatlonally efficient. 
With these considerations, I have chosen two domains: (1) 
tense and (2) aspect. Tense concerns the Chronological ordering 
Of situations with resnect tO some reference moment, usually the 
moment of s!3eech. Aspect =S the study of situation types and 
perspectives from which a particular situation can be viewed or 
evaluated (cf. Comrie75) The point of departure of this study is 
two papers: (1) for tl~e theory of tense, Hornstetn's "Towards a 
theory of Tense" (Homstem77) and (2) tor the cognitive theory of 
time. James Allen's "°Towarcls a General Theory ot Action and 
18 
Time" (Allen84). 
In the following, I shall list the main results of this study: 
1. 
2. 
A better theory of tense with revised primitive tense 
structures and constraints. 
We derive an exDlanatmn of Hornstein's Linear Order 
Constraint, an oioserved formal constraint on lingu=stic 
tense, from propert=es of the constraint propagat=on 
algorithm of Allen's temporal system. This shows this 
formal grammatical constraint need not be learned at =1. 
We also show that the rule of R.germanence follows 
from the hypothes=s that only the matrix clause anti tl~e 
suocategortzaDle SCOMP or VCOMP can introduce 
distract S and R points. Finally, we prove that certain 
boundedness condition on the flow of mformatmon Of a 
grocassmg system leads d=rectly to the locality properly 
of a constraint on secluences of tense. 
3. A prmczole of markedness for tense structures based on 
the comoutat=onal efficiency of the temporal 
representation. The prmciple pred,cts that (1) of the stx 
basic tenses m Enghsh, future perfect =s the only marked 
tense, and (2) the not=on of a dastant future tense, lust 
like the s=mple future. =s alSO unmarked. 
A better account of the state/event/process d=st=nct=on 
based on Allen's interval-based temporal Iogac and the 
=dea that the progress=ve aspect sl~ec,hes the 
perspect*ve from wh=ch the truth of a s~tuation is 
evaluated. 
An account of theoretical constraints on the 
representation of hme at the comDutat=onal level, e.g., 
three distract t=me points are necessary to charactenze 
an elementary tensed sentence, and the d~stmctmn 
between instantaneous and non-instantaneous t=me 
intervals. 
2. Tense 
We begin Dy hrst outhmng Hornstem's theory of tense. In 
sect=on 2.1. we describe the 13rtmtt,ves and constramnts on tense of 
h~s theory. In sectzons 2.2 and 2.3. we snow how the 0nmit=ves 
and constraints can be denved from computat=onal 
conszderat=ons. 
2.1 Revcs,ons to Hornstem's Theory of Tense 
Hornstem develops a theory of tense w#th#n the 
Re~cnenbachlan framewcrk whtch postulates three- theoretical 
entit~es: S (the moment of speech}, R (a relerence point}, and E 
(the moment of event). The key ~dea =s that certain linear 
orOenngs of the three t~me I:}o=nts get grammat=cahz.,~l mid the smx 
bas=c tenses oi Engl,sh. 1 The following ~s the last of basic tense 
strOctures: 
1. SIMPLE PAST E,R_S 
2. PAST PERFECT E_.R_S 
3. SIMPLE PRESENT S,R,E 
4. PRESENT PERFECT E_S.R 
5. SIMPLE FUTURE S_R,E 
6. FUTURE PERFECT S_E~R 
The notation here demands some explanation. The 
underscore symbol "~" is interpreted as the "less-than" relation 
among time points whereas the comma symbol .... stands for the 
"teas-than-or-eQual-to" relatmn. As an illustration, the present 
perfect tense denotes a situation in winch the moment of speech 
is either cotemporaneous or precedes the reference point, while 
the moment of event =s strictly before the other two moments. 
Note that Hornstem also uses the term "assoc=ation" to refer to 
the comma symbol ",". 
Geven the bas=c tense structure for a s=mole tensed sentence, 
the mterpretat=on of the sentence that arises from the interact=on 
of tense and time adverbs ~s represented by the modihcatmn of the 
posit=on of the R or E points to form a new tense structure wh=Ch 
we call a aermeO lense structu,e. In two papers (Hornstem77 & 
Hornstem81), Hornstem proposes three formal constraints that 
hmlt the class of derived tense structures that can be generated 
from the bas=c tense structures m SuCh a way as to capture the 
acceptabd=ty of sentences containing temporal adverbs (e.g.. now, 
yesterday, tomorrow), temporal connechves (e.g., when. before, 
after), and md=rect speech. In the rest of tins sect=on, I shall 
examine the adeouacy of these constraints. 
2.1.1 Linear Order Constraint 
The Linear Order Constraint (LOC) states that t!~.523-4): 
(1) The linear order of a clenved tense structure must be the same 
as the hnear order of the basic structure. 
(2) NO new assoc=at=on ~s ;roduced =n the clerfved tense structure. 
LOG IS st=oulated to account for examoles cons=st=ng Of a 
single temporal adverb such as (4a) and those w~th two hme 
adverbs such as ~'32). 2 
4a. Jonn came home i. "now, at this very moment 
i. yesterOay 
iii. "tomorrow 
32 a. Jonn left a week ago \[from\] yesterclay. 
h. \[From\] Yestertlay, Jonn left a week ago. 
c. °A week ago. Jonn left \[from\] yesterday. 
The basic tense structure for 4(ai) is: 
E,RoS (sim\[ole past: Jonn came t~ome) 
NOw modifies E or R so that they become cotemporaneous with 
ll~e moment of speech S with the clerived tense structure as 
1. Hornstem actua=ly ksNid tone ~a~l¢ ter~ Put I *.,gmk U~e Dn~otes3~ve Oo~onQs 
to tfle Dromnce of asoect fqltrtet flqn te~. 2. The ,num~nnOs are Homstlm~'s. 
19 
follows: 
E,R,S (BAD: violates LOC since new 
association is produced) 
On the other hand, 4(aii) is acceptable because the modifier 
yeslerOay leaves the tense structure unchanged: 
yesterday 
E,RIS -- E,RIS (OK: does not 
violate LOC) 
The crucial example, however, ms 5(c): 3 
5c. John has come home i. ?right now 
ii. "tomorrow 
iii. yesterday. 
LOC predicts (wrongly) that 5cii is good and 5ciii bad. 4 But LOC 
gives the wrong prediction only on the assumotmon that the basic 
tense structures are correct. To account for 5c. i propose to save 
the LOC and change the following SRE assocmatmon with the 
present perfect: 
PRESENT PERFECT E_R.S 
With the modified basic tense structure for present perfect. LOC 
will give the correct analysmS. 5cii =s bad because: 
romp r row 
E__R.S -- EIS~R (linear order 
violated) 
5ciii is acceptable since: 
yesterday 
E__R.S -- EIR__S 
(OK: no new linear order and no new comma.) 
The questmon that naturally arises at this point ms: Why does 
Hornstein not choose my prooosed SRE structure for the present 
perfect? The answer, I befieve, will become apparent when we 
examine Hornste,n's Second constra, nt, 
2.1.2 Rule for Temporal Connectives 
The rule for temporal connectives (RTC) states that 
(p.539-40): 
For a sentence of the form Pl.conn-P 2 where "conn" ~s a 
temporal connectmve such as "when" "before", "after" etc.. line 
up the S pomt~ of Pt and F 2, that IS. wnte the tense structure of 
Pl and P2' lining uP the S points. Move R 2 to under R 1, placing 
E 2 accorc=ngiy to preserve LOC on the bes=c tense structure. 
It can be easily seen that my proposed tense structure for present 
3. See- toot;tote 7 ~ 11 Of Morn~Itein'$ ~IO~'. 
4 There rely Oe clouOts ~ re0a~s II~ ac=~ta~ilily of 5dii. An ~ui¥1m~ t~ ot 
5¢iii ~ a¢clmtal~ ,~ Dan~ (JeSl~lrJI4ll~. D.271\]. A~IO. in French, IRe I 
~'e~t moment (Comne76, D.al). 
perfect does not work with RTC since it produces the wrong 
predictions for the following two sentences: 
\[1 \] "John came when we have arrived. 
\[2\] John comes when we have arrived. 
For \[1\] the new analysis is: 
E.R~S --- E,R~S 
I I 
E~R. S EIR~S 
which does not violate the RTC and hence predicts (wrongly) that 
\[1 \] =s acceptable. Similarly, for \[2\], the new analys,s is: 
S.R,E -- S.R.E . (violates RTC) 
I I 
E~R. S EIS, R 
which prediCtS (wrongly) that \[2\] is bad. 
This may explain why Hornstem decides to use E_S,R for 
the present perfect because =t can account for {1 } and {2\] with no 
difficulty. However. I suggest that the correct move snould be to 
abandon RTC which has an asymmetrical property, I.e., it matters 
whether Pl or P2 =s put on top, and does not nave an obwous 
semanttc explanatmon. (See Hornstetn's footnote 20, p.54,.3). My 
second proooTw31 is then to replace RTC with a Rule of 
R.permanence (RP) stating that: 
(RP): Both the S and R points of Pl and P2 must be ahgned 
without any mamp-latmn of the tense structure for P2" 
Thus sentence \[3l: 
{3\] .John came when we had arrivecl. 
~s acceptable because its tense structure does not v=otate RP: 
E.R__S (OK: S and R points are 
EIRI$ already aligned) 
NOW, ~et us reconsider sentences \[1\] and \[2\]. Sentence \[1\] is not 
acceptable uncler RP and the new tense structure for present 
perfect since: 
E.R._S (violates RP: r.ne two R's 
EIR.S are not aligned) 
Sentence \[2\] ,s still a problem. Here I snail maKe my third 
proposal, namely, that tne simple present admits Iwo Ioas~c tense 
structures: 
SIMPLE PRESENT S.R.EandE.R,S 
Given this modification, sentence \[2\] will now be acceptable since: 
E.R,S (S and R points are aligned) 
E~R. S 
20 
To examinethe adeouacy of RP. letuslook at more examples: 
\[4\] John has come when i. "we arrived 
if. "we had arrived 
iii. we arrive 
iv, we have arrived 
v. "we will arrive 
The corresponding analysisisasfollows: 
\[4'\] i. E__R.S (BAD) 
E. RmS 
if. E__R.S (BAD) 
E__R__S 
iii. E__R.S (OK) 
E.R.S 
iv. E~R.S (OK) 
EoR, S 
v. E~R,S (BAD) 
S~R.E 
We can see that the proposed theory correctly predicts all ol the 
five cases. There ts. however, an apparent counter.example to RP 
which, unlike RTC, is symmetncal, Le., it does not ma~ter which Of 
the Pi's =s put on the top. Cons=der the following two sentences: 
\[5\] i. John will come when we arrive. 
if. "John arrives when we wi11 come. 
RP predicts both 5i and 5if will be unacceptable, but 5i seems to 
be good. It ts examples like 5i and 5if, I believe, that lead 
Hornstem to propose the asymmetrical rule RTC. But I think the 
data are m~slead=ng because =t seems to be an ,diosyncrasy of 
Enghsh grammar that 5i =s acceptable. In French, we have to say 
an ecluwatent of "John will come when we wdl arrive" with the 
temporal adverb=al expl=c~tly marked with the future tense 
(Jespersen6~, p.264). Thus. the acceptability of sentences like 5i 
can be explained Oy a !ormc=ple of Economy of Speech allowing us 
to om=t the future tense of the temporal adverbial if the matrix 
clause is already marked w~th the tuture tense. 
2.1.3 Sequences of Tense 
Now, we clescribe the third and final grammatical constraint 
on sequences of tense. Consider the following sentences: 
\[6\] John said a week ago that Mary 
(a) will leave in 3 days. 
{b) would 
In the (a) sentence, the temporal interpretatmn of the embedded 
sentence is evaluated w=th respect to the moment of speech. 
Thus. for instance, \[6a\] means that Mary's leaving is 3 days alter 
present moment of speech. On the other hand, the (b) sentence 
has the temporal intemretatlon of the embedded sentence 
evaluated with respect to the interpretation of the matrix clause, 
Le., \[6b\] means that Mary's leaving is 4 days before the moment of 
speech. 
To account for the sequence of tense in reported speeCh, 
Hornstein proposes the following rule: 
(SOT): For a sentence of the form "P1 that P2"' assign S 2 with 
E 1 • 
In general, for an n.level embedded sentence, SOT states that: 
assign S n with En. 1 (Hornslem81, p.140). With the SOT rule, \[6a\] 
and \[6b\] will be analyzed as follows: 
\[6a'\] a week ago 
I 
Et.RluS 1 
S2__R2,E 2 ==> E 2 is 3 days 
\[ after S I 
in three days 
\[s~'\] a week ago 
I 
EI.RI~S l 
I 
S2uR2.E 2 
I 
in three days 
==> E 2 is 4 days 
Defore S I 
The local property of SOT, Le., linking occurs only between 
nth and (n-1)th level, has a n~ce conseouence: ,t ex0tams wny a 
third level nested sentence like \[7\]: 
\[7\] John said a week ago (a) 
that Harry would 0elieve in 3 days (b) 
that Mary 
(i) will leave for London in 2 days (c) 
(ii) would 
has only two temporal readings: (1) sn 7(ci). Mary's leaving is two 
days after the moment of speech, and (2) m 7(cii), Mary's leaving Js 
two clays Oetore the moment Of speech. In part=cular, there ~s not 
a temporal reading corresponding to the situatmon fn which Mary's 
leaving ms hve days before the moment of speech. We would 
obta,n the th=rd reading if SOT allowed non-local hnking, e.g., 
ass=gned S 3 with E 1 . 
2.2 Explanations of the Formal Constraints 
In the prewous section, we have examined three formal 
constraints on the denvatmn of complex tense structures from the 
Oas,c tense structures: (1) LOC. (2) RP, and (3) SOT. NOw, I want 
to show how the LOC falls out naturally from the computat=onal 
propertms of a temporal reasoning system along the line 
suggested by Allen (Allen84, Allen83), and also how the RP and 
SOT constraints have mtuitwe computat=onal motwation. 
The bes,s of Allen's comDutat=onal system ts a temporal logic 
based on intervals instead of time points. The temporal logic 
cons=stS of seven basic relations and their mveraes (Allen84, 
D.129, figure 1): 
21 
Relation svmbol symbol for meaninQ 
inverse 
X Oefore Y < > XXX YYY 
X equal Y = = XXX 
YYY 
X mee~s Y m mi XXXYYY 
X overlaps Y o oi XXX 
YYY 
X during Y d di XXX 
YYYYY 
X starts Y s si XXX 
YYYY 
X finishes Y f fi XXX 
YYYY 
The reasoning scheme tsa form of constraint propagation in a 
network of event nodes hnKed by temporal relat,onsmps. For 
instance, the situat=on as clescribed in the sentence "John arrived 
when we came" is represented by the network: 
A -- (> < m mi =) --> B \ / 
(<)~,~ (<1 
L/ NOW 
where A = John's arrival and B = Our coming 
This network means that both event A and event B are before now, 
the moment of speech, while A can be before, alter or 
s=multaneous with B. 
When new temporal relatlonsmos are added, the system 
maintains consistency among events by orooagat,ng the effects of 
the new relatmnsmos wa a TaO/e ol Translt~wty Re/at~onsmps that 
tells the system how to deduce the set of adm=ss=ble relat=onsmos 
between events A and C given the retatlonsh=ps between A and B, 
and between B and C. Thus, for instance, Irom the relationships 
"A during B" and "B < C", the system can deduce "A < C". 
One orooerty of the constraint propagation algorithm 
generally =s that further mlormatlon only causes removal of 
members from the set of admissible labels, i.e., teml=orat 
relatlonsmDs, between any two old events (Allen83, p.8,35). NO 
new label can De added to the admissible set once it is created. 
Let us call Ires property of the constraint propagntlon algor, tnm 
the Delete Labei Condit=on (DLC). DLC can be mteroreted as a 
k=nd of reformation monotonicity condition on the temocral 
representation. 
Let u5 further restrict Allen's temooral logic to instantaneous 
intervals. ~.e.. each event corresponds to a single moment of time. 
The restricted logic has only one or,mitwe relat,on, <, and three 
ctner denved relat,ons: <, >, and >. There is a straightforward 
:ranslat=on of Hornstein's SRE notation =nto the network 
re=)resenta'Jon, namely, replace each comma symbol "," by < (or 
>. witr the event symbols reverse their roles) and each 
underscore symbol "~" by > (or < with similar a¢liustment on the 
event symbols). Thus, a tense structure such as: E_R,S can be 
represented as: 
s -(>)->E 
(> =) (>) 
R 
With this representation scheme, we can prove the following 
theorem: 
~1) DLC--LOC 
Proof 
Let A and B range over { S, A1 E } and A = B. There are five 
bas=c types ol violations of the LOC: 
1. A_B -- B_A 
2. A B -, A,B 
3. A_B --., B.A 
4. A,B -- B,A 
5. A,B -., B_A 
We can see that each of these cases ~s a v=olatlon of the DLC. To 
spell this out. we have tt~e following operations on the constraint 
network corresponding tO the above vlolat=ons of the LOC: 
f'.A-(<)-)'B --A-(>)->B 
2'.A-(<)->B --A.(< = ).)B 
3'.A.(<).>B -- A.(> = )->B 
4'.A.(< = ).>B --A-t> = )->B 
5".A.(< = )->B --A.(>)->B 
In each of these cases, the operation involves the addihon of new 
members to the adm=ss=Dle set. Th=s =s ruled out Ioy DLC. Thus, 
we have the result that if LOC =s wolated, then DLC =s v=olated. In 
other words. DLC -- LOC. 5 --I 
The second constraint :o be accounted for is the RP which 
effecbvely states that (a) the 50omts of the matrix clause and the 
temporal adverb=al must be ~clent=cal. and (b) the IR !0dints of the 
matrix clause and the temporal aOverbml must be ~dent=cal. One 
nypothests for th,s rule is that: 
(H1) Only the matrix clause mtrocluces distract S and R points. 
in other words, the non-subcate<Jonzable temporal adjuncts do 
net ado new S and R points. 
H1 has to be modifieO slightly to taV, e the case of embedded 
sentence =nto account, namely, 
{Revised RP): Only the matrix clause and the subcategorizable 
SCOMP or VCOMP can introduce d=stinct S and R points. 
where SCOMP and VCOMP stand for sentent=al complement and 
S. The ¢om,e~e o~ thss Ihe~n ~' nm true. 
22 
verbal complement respectively. The interesting point is that both 
the rewsed RP and the locality property of SOT can be easily 
implemented ,n processing systems which have certain 
Oounoeoness constraint on the phrase structure rules (e.g., 
,nformation cannot move across more than one bounding node). 
To illustrate this. let us consider the following tense interpretation 
rules embedded in the phrase structure rules Of the 
Lexlcal-Funct,onal Grammar: 
S -- NP VP 
($ S-POINT) = NOW 
VP -- V (NP) (ADVP) (S') 
($ S-POINT) = { 
(T E-POINT) if ($ tense) = PAST 
NOW 0tnerwise 
ADVP ~ Adv S 
S' -- COMPS 
Adv ~ when 
(T T-REL) = { <.>.=,m.mi } 
before 
(T T-REL) = { > } 
The S rule introduces a new S point and sets its value to now, The 
VP rule has two effects: (I) it does not introduce new S or R points 
for the temooral adveriolal phrase, thus imohcltly incorporating the 
revised RP rule, and (2) it looks at the tense of the embedded 
sentential comolement, setting the value of its S point to that of the 
E point of the higher clause if the tense is past, and to now, 
otherwise. Thus. tn th~s way, the second effect accomplishes what 
the SOT rule demands. 
2.3 Implications for Learning 
If the revisions to Hornstem's theory Of tense are correct, the 
natural cluest=on to de asked is: FlOW dO speakers attain such 
Knowledge? This Question has two Darts: (1) How do spea~ers 
acquire the formal constraints on SRE derivation? and (2) How do 
speakers learn to associate the appropriate SRE structures with 
the baszC tenses of the language? 
Let us consider the first sub-Question. In the case of LOC, 
we have a neat answer .. the constraint need NOT be learned at 
all! We have shown that LOC falls out naturally as a consequence 
of the architecture and processing algorithm ot the computational 
system. AS regards the constraint RP. the learner has tO acquire 
something similar to Hr. But H1 IS a fairly simple hypothes~s that 
does not seem to require induct=on on extenswe hngmstic data. 
Finally, as we have shown =n the previous section, the 
boundeQness of the flow of information ol a orocessmg system 
leads directly to ~he locality orooerty of the SOT. The partTcular 
linking of S and E points as stipulated by the SOT, however, is a 
parameter of the iJnwersal Grammar that has tO be fixed. 
What about the second sub.question? How do speake~ 
~earn to pair SRE conhguratlons wllh the basic tenses? There are 
24 possible SRE configurations seven of which get 
grammat,calized. Here I want to prooose a principle of 
marKeOness ol SRE structures that has a natural computational 
motivation. 
Let us recall our restrictive temporal logic of instantaneous 
interval with one primitive relation, <, and three derived relations: 
<, >, and >. Represent a SRE configuration as follows: 
S ~ E 
The admissible labels are among { <. < =, >, > = }. So there are 
altogether 64 possible configurations that can be classified into 
three types: 
(1) Inconsistent labelings (16). e.g.. 
S\--( > )-~ E ? 
(<) (<) 
R 
(2) Labelings that do not constrain the SE 
given the labelings of SR and RE (32), e.g.: 
s--( ?)-.~ E 
(<) (>) 
R 
link 
(3) Labelings that are consistent and the SE )ink 
is c0nstra~ned by the SR and RE \]~nk (16), e.g.. 
s -(<)-> E 
(<) (<) 
R 
If we assume that labehngs of the third type corresPOnd tO the 
unmark, ed SRE configurations, the following division of unmarKeO 
and marked configurations is obtained: 
UNMARKED MARKED 
E~R~S 
E. RoS 
EIR.S 
E,R.S 
S,R.E 
S, RoE 
S~R.E 
S~RoE 
PAST PERFECT E~SoR 
SIMPLE PAST E.SoR 
PRESENT PERFECT EoS,R 
SIMPLE PRESENT E.S,R 
SIMPLE PRESENT SIEoR 
SIMPLE FUTURE SoE. R 
S, EmR 
S.E.R 
RoSoE 
Ro$.E 
R~E~S 
R~E,S 
R, E~S 
R.SmE 
R,E.S 
R.S.E 
FUTURE 
PERFECT 
There are only eight unmarked tense structures 
corresponding to the sixteen SRE netwo~ configurations of type 3 
23 
because a tense structure can be interpreted by more than one 
network rebresentations, e.g., the Past Perfect (E_R_S) has the 
tollowing two configurations: 
S--t:>).-* E S-i(> =)--> E 
(>) .,VI (>) (>)~ ;>) 
R 
The interesting result is that five out of the six basic tenses 
have unmarked SRE configurations. This agrees largely with our 
pretheoretlcal intuit=on that the SRE configurations that 
correspond to the basic tenses should be more "unmarked" than 
other possible SRE configurations. The fit. however, is not exact 
because the future perfect tense becomes the marked tense in 
this classification. 
Another prediction by this principle of markedneas is that 
both the simple future (S_R.E') and distant luture (S_R_E) are 
unmarked. It would 0e interesting to find out whether there are 
languages =n which the distant tuture actually gets 
grammat=calized. 
The final point tO be made =s about the second type of 
labelmgs. There are two Other possible ways of grouping the 
laOehngs: (1) given SR and SE. those labehngs ~n winch RE ~s 
constrained, and (2) given SE and HE. those in which SR is 
constrained. But these types of grouping are less likely because 
they would yield me s~mple present tense as a marked tense. 
Thus. they can be ruleO out iOy relatively few linguistic data. 
3. Verb Aspect 
In cons=clenng the problem of tense, we have restricted 
ourselves to a subset of Aliens temporal logic, namely, using a 
temporal structure <:T._<> with hnear oraenng of time points. TO 
make use of the full Dower of Allen's temporal logic, we now turn 
to the problem of verb aspect. 
The two mare problems of the study of verb aspect are the 
correct charac!erizat~on of (1) the three funclamental types of verb 
predtcatlon according to the situation types that they signify .. 
state, process and event, and (2) the p(=rspectwes from which a 
situation ts viewed, or its truth evaluated -- s~mpte or progreSSive. 6 
in the first part of his paper. Allen attempts to prowde a formal 
account of *he state/process/even', d~s~mctlon using a temDoral 
logic. However. I beheve that htS charactenzahon fa¢ls to capture 
welt.Known patterns of tense =mot;cations, and does not make the 
distinction ioetween situation types and perspective types 
funclamental to any adequate account of verb aspect. In the next 
3ect=on. I will present some data that an,/ theory of verb aspect 
must be able to explain. 
3.1 Data 
3.1.1 Tense Implications 
1, Statives rarely take the progressive aspect 7 , e.g., 
I know the answer. 
"1 am knowing the answer, 
2. For verb predications denoting processes, the progressive of 
the verb form entails the perfect form, i.e., 
x is V.ing -- x has V-ed. 
For instance, 
John ts walking ---, John has walked. 
3. For verb predications denoting events, the progresswe of the 
verb form entads the negation of the perfect form, Le., 
x is V.mg -- x has not V.ed. 
For instance, 
John ~s bumidmg a house ~ John has not budt the house. 
3.1.2 Sentences containing When 
Sentences containing clauses connected by a connective 
such as "when" have different aspect tnterpretat~ons depending 
on the s~tuatlon types and perspective types revolved. 
\[9\] John laughed when Mary drew a circle. 
Situation/Per~oechve type: 
X = process/simple; Y = event/s~mple 
Inl\[ernretatlon: 
X can oe before, after or s=multaneous with Y 
\[10\] ,;ohn was laugnmg when Mary drew a circle, 
Situation/P~rsoective type: 
X = orocess/progresswe; Y = event/s=mble 
Int~roretatte, n: 
Y occurs during X. 
\[11 } ,John was angr'! when Mary drew a cwrcle. 
Situanon/Persoectwe Woe: 
X = s=ate/slmole: Y = event/simple 
Interr~retatton: 
X can Ioe before, after, simultaneous with or during Y. 
\[ 12\] John was laugnmg when MaP/was drawing a circle. 
~it~atmn/Pe~cective Woe: 
X = croces~/~rogresswe: Y = event/progresswe 
Inte,pr~ta'~lon: 
X must be s~multaneous with Y. 
3.2 Formal Account of the State/Process/Event 
distinction 
Define: 
6. Some of tl~ oener worlu~ are: Vcmdledr/. C~mne78. ~78. 
?. It ~ ofllm been ~ OUl trill some Slal~ves do ta~e the oro~'es..~ve form. 
E.G., "I am rnmkmg aOoul U~ exam.'. "The doctor ts se~ng a pauenl." Ploweves,. 
a ~lut=l~l¢~ slucly ~ ~ that ~ tam*~ar stal,ve= rarely occur ~ln the 
prl)gress~ve aspect -. ~ thin 2% ol me lm~ (01,1~=3. secUon 2.2) 
24 
{a) X C Y ,,.-* Xd Y V XsY V Xf Y 
(b) X C Y *-, X C Y V X e~ualY 
(c) mom(t) ".-. t is an instantaneous ,nterval, i.e., consists of a 
smgle moment of time 
(d) per(t) '-- t is a non-instantaneous interval 8 
where X and Y are generic symbols denoting state, event or 
process. 
3.2.1 Progressive 
(PROG): OCCUR(PROG(v,t)) -- morn(t) A ~ OCCUR(v,I) A (3 
r)(t d t' A OCCUR(v,t')) 9 
The progresswe aspect ss the evaluation of a situation from an 
interior oOmt t of the s~tuatlon which has the prooerty that though 
the sentence ts not true at that instantaneous ~nterval, ~t =s true m a 
nonqnstantaneous ~nterval r properly containing t. 
3.2.2 State 
(Sl): OCCUR(s,t) -- (V t')(mom(t') A t' C t -- OCCUR(s,t')) 
A state verb is true at every instantaneous interval of t. The 
clefmitlon is slmttar to Aliens H. 1 (Allen84, 13.130). 
The following theorem shows that state verbs do not occur with 
the progressive aspect. 
(S.THEOREM): "OCCUR(PROG(s,t)) 
Proof 
CCCUR(PROG(s.t)) 
morn(t) A -'~ OCCUR(s,t) A (~1 t')(t dt' A OCCUR(s.t')) 
-- OCCUR(s.t') tor some t containing t 
-- OCCUR(s.t) (by S1) 
'. contradiction. -t 
This theorem raises the tollow=ng quest=on: Why do some 
statlves occur w~th the orogresswe? I th~nK there are two answers. 
First, the verb in question may nave a use other than the statwe 
use (e.g. "have" is a statJve when tt means "possess=on", and not 
a s,*atlve when it means "experiencing" as ~n "John =s having a 
good time tn Paris.") Second. the English progressive may have a 
second meamng m addit,on to that cnaractenzed by PROG above. 
A freouent usage of the progresSwe =s to and=care short duration or 
temporariness, e.g., m "They are hying m CamDrldge"/"They live 
=n Cambridge". 
8. This SeCtIOn loenehL~ from the Ins~lhtS o! ear~ Taylor ("rayldrT~. 
9 & rewewet O! this oaOer po,nts out tnot me PI::IOG axiom seems to imDty tRat if 
something IS IO I~rOCJtlL~, II f'flg..~l complete. Thus. ,f Max is Oraw,ng a circle. II'=en at 
some. tuture time. ne must nave drawn the cIn:le. This =nt~ence =S clearty false 
because ;~efe ~ noth,ng contradiCtOry aJoou! "Max was Orawmg a ca:tie Out he 
never drew ,t." For ,ns\[aoce. Max ml(Jnt su!tef a heart altaclL anti ~J auOOe~y. 
This =met.ante problem of the orogressNe 'orm ot a evenl veto =s xnown as If~ 
,rnDertectlve paraoox in the hteralure One way oul is to Oeny mat ~a, was really 
drswmg a circle wflen ne oleti Rather ne was drawing sornelhmCJ ~'hlCh woulo 
nave deed a circle had I~t not d~¢l. This type ot analySiS would involve some 
machinery trom'Posslote WOlIO SemanUc$. 
3.2.3 Process 
A process verb can be true only at an interval larger than a single 
moment. This property differs crucially from mat of the statwes. 
(Pl): OCCUR(p,t) -- per(t) 
(P2): OCCUR(p,t) -- (V t')(per(t') A r C_ t -- OCCUR(p,t')) 
The following theorem shows that for a process verb, the 
progressive verb form entails the perfect form. 
(P.THEOREM) OCCUR(PROG(p,t)) -- (3 t')(per(t') A t'< t A 
OCCUR(p,t')) 
Proof 
OCCUR(PROG(p,t)) 
-- morn(t) A "~ OCCUR(p.t) A (3 t')(t d t' A OCCUR(p.t')) 
--... OCCUR(p.t') for some r such that t d t' 
-- 3m 1 Et'.m l<t (slncetdt') 
-- 3m 2Et'.m l<m 2<t (bydensltyoft=mepolnts) 
Let t" be the interval \[m 1 .m2\] Then. we have t" ( t and t" C t'. By 
(P2). we have OCCUR(p,t"). That is, 0 has occurred. --I. 
The charactenzat,on of process verb by Allen (ms O.2) is less 
sat=slactory because ~t combines both the notion of Drogresswe 
asDect (his "OCCURRING") and me process verb into the same 
axiom Furthermore. the difference between me predicate 
"OCCUR" and "OCCURRING" ~s not adequately exolamed in his 
paper. 
3.2.4 Event 
An event verb shares an ~moortant proDerty with a brocess 
verb. namely. ,t can be true only at a non.instantaneous interval. 
(El): OCCUR(e.t) -- !bet(t) 
(E2): OCCUR(e.t) -- (V r)(per(t') A r C t -- "~ OCCUR(e,r) 
The following theorem snows that the ~rogresslve form of an 
event verb entads the negal~on of the perfect form. 
(E-THEOREM): OCCUR(PROG(e.t)) -- '-,(3 r)(per(t') A r< t A 
OCCUR(e,t')) 
Proof 
AS in the ~roof of (P.THEOREM). we can find a non-~nstantaneous 
interval t" such that t" < t and t" C t' But |or any such t". we have 
OCCUR(e.t") Pecause of (E2). That is. it cannot be the case 
t11at e has occurred. --I. 
Again the crucial property (El) is not captured by Allen's 
charactenzat=on of events (ms O.1 ). 
3.3 Constraint on temporal interpretations involving When 
To account for the variety of aspect interpretations as 
presented in section 3.1.2, I propose the following constraint on 
25 
situation/perspective type: 
(C-ASPECT\]: Let "dynamic" stand for a process or event. 
(a) simple/dynamic .-* morn(t) 
(b) simple/state ..- per(t) 
(c) progressive/dynamic -.-* per(t)/k _C 
PerspeCtive is a way of looking at the situateon type. For process 
or event, the simple aspect treats U~e situation as an 
instantaneous interval even though the situation ~tself may not be 
instantaneous. For state, the simple aspect retains its duration. 
The progressive aspect essentially views a process or event from 
its inter=or, thus requiring a stance in which the situation is a 
non.instantaneous interval and the admissible temporal 
relationship to be the C_ relations, i.e., s, s~, I, fi.d. di, eoual. 
Let me show graphically how C.ASPECT accounts for the 
aspect interpretations of sentences {9\] to {12\]. 
\[g'\] simple/process WHEN simple/event 
Admissible relations: 
( m : mi 
X Y XY X YX 
Y 
) 
Y X 
\[to'\] 
AOmissib\]e relations: 
progressive/process WHEN slmple/event 
si di fi 
XXX XXX XXX 
Y Y Y 
\[11'\] simple/state WHEN s~mple/event 
Admissible relations: 
> mi si di fi 
Y XXX YXXX XXX XXX XXX 
Y Y Y 
m < 
XXXY XXX Y 
\[12'\] prog/process WHEN prog/event 
Admissible relations: 
: f fi s si 
XXX XXX XXXX XXX XXXX 
YYY YYYY YYY YYYY YYY 
XX XXXX 
YYYY YY 
4. Conclusion 
In this paper, I nave exam=ned two problems regarding 
linguistic semantics: tense and asDect. Important relationships 
between al~s;ract constra,nts governing lingu=st,c behavior and a 
computational scheme to reason aDout temporal relationships are 
discussed. In particular, I have shown that certain formal 
constraints, such as the Linear Order Constraint on tense, fall out 
naturally as a consequence of some computational assumptions. 
The interesting result =s that this formal constraint need not be 
learned at all, 
Another important role of a representation scheme in 
explaining phenomena that exist on a entirely different -. linguustic 
-- level is illustrated by the formulation of the C-ASPECT constraint 
to account for ~nterpretatlons of sentences conta,ning temporal 
connectwes. 
The study of linguistic semanhcs also sheds light on a 
representation of tJm~ hy reveahng the fundamental distractions 
that must be made, e.g.. a tensed sentence revolves three distract 
time points, and the aspectual interpretations reclu~re 
instantaneous/non-instantaneous ~nterval distinction. 
Acknowledgments 
; would like to lh:.mk Prof Robert C. BerwIck lor his insi(.Jhtful 
sugge'.';hon Ihat lhe r(flahonshlp t)~.~lwHP.n a co(jnd~ve mP..ory Of lime 
all(l a hll(llLll.'3tlC theory of lense ts a Irullhll 'and mq)ortam area for 
research. He also contrtbuled 5ut)stam~;.llly to lhP. presenlalion of 
lhLs paper Finally, I LIIso thank Nort)eft Hornstem who prowded 
useful comments durm(j the revision el this paper. 
5. References 
\[Allen84\] james Allen, "Towards a General Theory of Action 
and Trine", AI JournBI , Vol 23, No. 2, July, 1984. 
\[AlienS,3} "Maintaining Knowledge aJ3out Temporal 
Intervals". CACM Vol 26. No. 11. NOV, 1983. 
\[Comrm76\] Bernard Comne, A~oect, Camior=dge University 
Press, 1976. 
\[Hornstem81 \] Norioert Hornstem. "The study of meaning m 
natural language", in: Exolanabon tn (~tnculstlcs, 
Longman, 1981. 
\[Hornstem77} "Towards a Theory of Tense", Lmqu~st¢c InQuiry, 
Vol 8, No. 3, Summer 1977. 
{Jesi3ersen65\] Otto Jcspersen, The Phdosoohv of Grammar, 
Norton L~brary 1965. 
IMoure=;~tOS78} AP.D. Mouremtos, "Events, processes and 
soates '', L.:noutsttC3 and Ph=losoohv 2, 1978. 
\[Ota63\] KJra eta, Tense and AsPect Of Present Day 
American Enqil~h, Tokyo. 1963. 
\[TaylorTTJ ~arry Taylor, "Tense and Continuity", LinQuistics 
and Philosochv 1, 1977. 
\[Vendler67\] Zeno Vendler. Linaufstics and Philosgghy, Comell 
University Press. 
26 
