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ITERATION, HABITUALITY
AND VERB FORM SEMANTICS
Frank
v~n Eynoe.
University oi Leuven
Mar=a-Theresiastraat, 21
3000
Leuven
Belgium
ABSTRACT
The veto forms are o4ten claimeo to convey two
;inds o+ information :
I. w~et'~er the event Oeecribed in a sentence is
present, past or future (= oeictic information
2. whether the event described in a sentence is
oresente~ as completed, going on, just starting
or
being ,inished (= espectual information)
[t will be ~emonstrated in this paper that one
has tl ado a rhino component
to
the analysis of
verb ~orm meanings, namely w~e~ner or no~ they
e>press
habltualitv.
The
4ramewor~
04
the analysis is mo~el-
theoretic semantics.
BACKGROUND

The analwls of
iteration and ha~ituality in
this ~aper
is
part of a comprehensive semantic
ar~Ivsis of temporal expressions in
natural
kanguage. The research on this topic is carried
ob~ in ~he framework of EUROTRA, the MT project o4
the
European Community.
It
is reporteo on
e, tensi~,eiv in Van
Eynde
(lqBT).
The original motive for s~arting this research
~as the fact that verbal tenses ann temporal
a,:~:ili~ries
do
not corresponO one-to-one in toe
ienguages that EUROTRA has
to
deal with. Compare
for in~taqce
,i EN ne has lived in Copenhagen for 20 years
,Z, Dk nan nan boer i KmOenhavn i 20 ~r
~it~ tnelr equlvaients in
the
fokiowlng languages

• S~ DE er wonnt seit 20 Jahren in Kopenhaoen
~i FR ii haDite ~ Copenhaoue Oepuis 20 ans
~5, NL nij woont sinds twintlg jaar in Kopenhagen
When translating from
Englieh
or Danish
to
German,
~rench or Dutch the present perfect has to Pe
replaceO by a simple present,
Di&~ererces like these can be handled In one o;
two eaVs either by Oefinlng complex mappings
from source language to target language forms in
transfer or Oy Oeflnlng mappings Oetween language
specific forms and Interlingual meanings in the
monolingual components.
SL ~orm ) TL form
complex
mmpc~ngs
meanlng ) meanlng
,[ identity I
mapping mapping
SL ~orm TL form
Because c* EUROTR~ s ao~erence to the principle
o~ "simPle t~ansfe ~" it was quite OOVlOUS ~rom the
start that
the
interlingual
approa~ was the one
to opt ~or. It will, hence, be adopted in thls

paper a~ well.
The paper consists
of
t~ree
parts.
In .ths flrst I will present a formalism for the
representation
of
time meanings, together with
mooel for the interpr~tatlon o~ those
representations. In the seconp this forma|ism wiil
be extenOeO so that it can also Pe use~ for the
ana]~slS o~ iteration an¢ habitL, alit~. Ann In th~
third pert
I
~i~i show how the extendeo formalis~
can
be l,~'
~or a~
!n[erllnoua~ a~alvsis
O~
the
ver~ fo~.S,
THE CORE FORMALISM
A Temporal Model
T~e formalist tha: ~ill oe use: here has oee~
de~ineo e~pilcitiy i~, van Eynce, aes TomDe Q Maes
~5). irk th!s
p~per i
will on!y give a

s~or~
In~ormai present~zion of tDe formailS~
CO%Cemtratlrlg On
th~se
partS ~ICh will De neeOe~
In
the
se~onO
pert,
270
The model
COnSIStS
of
a set of
linearly oroerep
irtsrvals.
An interval
~s
a continuous
set
of time points
on the time axis :
I
, )
A la limite it might consist of one moment o6
tlme :
I
For an~ pair of ~ntervaie one can Oeflne tnelr
interlection
as the set of tlme points which

the'/ share:
i J
Inj
Tn~s set m~g~t also be empty, as in
I J
it
Is, furthermore, possible to define some
b~narv relations between intervais, such ae
l
preceoence ' , , ~} I be4ore O ( ~i,J:
O J after i
;.~J,i;
I
~dent~ty
"t
I
)
I simui .] =(l,a)
O
I
contain , , ' ) I part-of J c~I,J.,
d 0 contain I ~(J,I;
I
overlap
' , ~
, )
I leftover J ~<(I,J)
O J rightover I >>(O,l)
T~ese relations are also useO
in

Bruce (1972).
A Format for Representation
For the semantic analysis of the temporal
expressions i wili start from tne assumption t~at
every sentence can be analvseo in two parts : the
temporal informal:on expressa~ by the tenses.
auxiliaries anO ao~erbials on t~e one hano. anp
~as~o atempora! proposition on the ot~er hand.
(b; the cat sat on t~e mat
w~.i. for instance, be analyseo in a basic
proposition "the cat sit on the met" and
the
~n~ormation conveyed Dv the past tense.
The relation between both is established in two
steps : the basic proposition is first relateO to
the interval ~or whicn it is said to be true, the
socalled time of event (E), and then this interval
is related to the time Of speech ~S) :
3 E :,E,S) ~ AT(E,the cat sit on the mat)3
This formula states that "the cat sit on the mat"
i~ true at an interval E which precedes the tlme
of speech S.
Following Reichenbach (1947) I will furthermore
assume that the relation between the time of event
and the time of speech is mediated by a thiro kind
o~ interval, namely the time of reference (R), So,
instead of the simple ReI(E,S) we w111 have a
composite ReI~E,R) & RefeR,S).
Ne.t to thls relational information tn~
tempore: expreeslons can also give specific

informatlon about the iocatlon or the length of
the reie~ant intervals. This is typically Oone by
means o~ t:me aOverbiais, such as "next year", "in
the
spring':, "for t~o years", "till Christmas",
etc. T~is in~ormatlon will be represented bY means
o~ one-place preOicates over intervsls : Freo(E)
and Pred~),
~n exception ~s tc be ~ade here +or the time o,
speec~. ~nose precise location or length is never
spec~fleo
b,
iinQo~stic means, bu[ rather bv
pragmatic factors. A possible way
to
reelect tn~s-
In the &oc~,allsm is to trest it as an unbouno
variable.
In sum, the general format for the
representatlon of temporal information looks as
follows :
3 R,E [Rei(R.S) ~ Pred~R; & ~eI(E,R) ~ Prep(E)
AT(E,p)]
where p is a basic atemporal proposition
An example ;
~T we will vielt Moscow next year
3
P,E [,~R,S~ & ne~t vear~R) ~ =~E,R) &
A ~ E,we visit Moscowi]
271

As it stanos this format is not adequate yet
fo ~ the ~epresentatlon of sentences like
(8~ last year they played
chess
every week
(e~ he was always late
The basic propoe~tions "they play chess" and
"he oe late" do not hold for one particular time
of event E, but rather for a set of intervals
wnicn are spread in time in some way specifieo
by
"every week" in (8) and "always" in (9).
In the following part I will introduce an
exter.oeO formalism which can OeaI with these typos
04 iteration.
THE EXTENDED
FORMALISM
Cyclic
Iteration
Cyclic iteration is marked by aoverpials like
"caiiv", "every Monday", "each year", etc. In
~virk
e.a. (1972) they
are
callao periodic
frequency
adverbials.
For the analysis of these adverbials I first
IntroOuce the notion Crams time. The frame time ie
the interval which contains all the instances of

the event describeo in the basic proposition. In
(8~ last year they played chess every week
t~e ~rame time is last year. In the general forma~
t.e frame time occupies the same place as the time
c~ event in non-iterative interpretations (= the
E-i~tervai~,
~ext, I de~ine a set of distinct, non-
overlapping subintervals ~I~ which are all part o+
the frame time. In (8~, these intervals have a
length of one week each. This gives the following
,preliminary) representation :
5
R,E [ (R,S) & last year(R~ & =(E,R) &
I [c'i,E) & nI:~ & week,i) x
AT~i,they play chess;]]
R S
similar analysis can be found in Stump (198i
where t~e aoverbial frequency ad~ectlvee (P) ere
given the following truth condition :
F~' is true in a world w at an interval I
i~4 ,~m is true in w at non-overlapping
subintervals
o$
i
distriOuteO throughout
i
~t perioOs of a speci$ieo
length
I.
"

[Stump 1981, 226]
5t~mp s i-interval corresponds to my frame
time. and his non-overlapplng subintervals
correspond to my I-intervals.
As a representation of (B) this formula is not
sufficient, though, since the instances of chess
pla~ing do not have to take a whole week for (B~
to. be true. A more adequate paraphrase is to say
that every week contained at least one subinterval
(e~ during which they played chess :
,,o
l[c(l,E~ & nl=~ & week!i) >
e[c~e,l) & AT(e, they play cness)]]
An argument in favor of this refinement is that
languages have special means for specifying the e-
times. In
~I(' last year she arrived at ~ c clock every da~
the
aoverbia2
"at
eight
o ¢ioc~" denotes the
locatlOn 04 t~e e-intervai
;
B
Notice tha~ the pro~artlee of e are constant
within 'the 4tame time : the aoverDial "st eight
o clot!" specities t~e time of each o¢ her
arrlvals cf last year.
The general format for the representation of

cyclic iteration is, hence~
3 R,E [ReI~R,S) & PreO~R~ & Rei(E,Ri & Pred~E} &
I [c(l.E~ & ni=O & P(1)
e ~:~e~I~ ~ M(e) 2 AT~e,p;]]]
where P is replacec ov the head o4 a periooic
~requencv aoverbial, specifying the
location
or
the
iengtn o~
I
Io -optlona}l~i replaced ov ~ ti~,a
advero~6i, sPecifYin~ the length cr the
igcatlon C.f e
~n
im[,ortar~t
property of
this
format is it ~.
chain-like structure
:
272
R is oef~neo with respect to S : ReI~R,S~
E as defined with respect to R : ReI(E,R~
I is defineo w~th respect to E : ~(I,E)
and e is oefineo with respect to I : c(e.I~
As
it
stands, the format does not provioe any
means for stating a direct relationship between

the intervals inside the frame time ~I and e~ ano
the intervals outside the frame time (S anO R~. As
consequence, the formal~sm predicts that
temporal adverbials w~ich are in the scope o~ a
frequency adverbial (: the e-specifiers~ cannot
refer
ba~K
to
the
speech
t~me or the
eeference
time: * Rei(e,S) and * Rel(e,R~,
gooo p;ece of evidence for this hypothesis ~s
pr~ioed by the WHEN-aoveroiais. In general one
can distinguish two kinde of those adverbials :
t~e relational
ones,
which express a relation
Oetween the reference time and the speech time,
such as "~esterday" a'nd "tomorrow", and the non-
relational ones, which identify the location o~ an
:nterval without any reference to the speech t~me,
suc~ as "between 8 and 9" and "at two o clock".
The interesting thing now is t~at only the
latter adverbials can occur in the scope of a
frequency adverbial. Compare
:iI~
she arrived every day between 8 anq 9
e

*(12~ she arrived every day yesterday
e
The fact that the relational WHEN-adverbials
cannot occur in the scope of a frequency aoverb~al
prcviOes some positive evioence ~or not inciuoln§
direct relations between e ano S in the formal~em.
The chaln-like structure of the representation
format Is, hence, i~nguistically motivated.
Temporal Quantifiers
The format Oeveloped for the analysis of cvclic
iteratlon can also be useo for the analysis o~ the
temporal ~uantifier$,
such
as "miway~",
"scmetlmes", "never", "seldom" ano "often". The
~rmetion they proviOe is less specific than the
ona p~ovioed by the period frequency aOverb~ais,
ar, d t~s should be refiecteO in their
representation.
As a starting point I take the general ~ormat
~or the representation o~
sentences
w~th a
periodic frequency adverbial :
~ i [c(l.E~ & nI=~ & P(li >
3
e [cie,li &Mie) & AT(e,p)]]
For a semantlc analysis of the temporal
quantiflers this format has to be generalieeo.
The most important change is the replacement of

the universal ouanti;ier bv a variable :
Q
I C=(I,E)
where Q can be any of the follo~ing quantiflers
always
3 eometimes
-3
never
Few selOom, rarely, now ano then
Many o~ten, frequently
Most usuallv, mostly, generally
.=,is sixfold dzvis:on is taken beer from Lewis
~1975).
This analysis account~ for the anomaly of
sentences like
o ,13} we sometimes played chess every wee~
3
? (141 they often met every month
Many
(15p we always plaveO chess every week
9
These sentences are eemantlceiiy anomalous
oecauee t~e sa~e ~ino o* In*ormation. namely the
v~iue o~ ~. is epec~lec twice. This leaps to
:~cons~etenc~ ~ ~13) and (14} where the Q-
ve~ia~ie IB s~l~ to be both universal anO non-
~r;vers~i at tme same time,
and
it leaos to
pleonasm in (15~ where the Q-variable is twice

sago to Oe u~,iversal.
The ne, t question is whethe," thP temporal
quant!~iers introduce any extra-conqitions on
those Intervals, ouch ms c~l,E), ~I=~ and P~i~.
The f~rst of t~ese conditions appears to Pe
relevant : the temporal quantifiers are ~ndeeo
interpreteO wi~ respect to some given frame time.
In
~x
he was
al~ays late
"always"
ooesnot oenote AL~ possible intervals.
but onl~ all possibie intervals ~n the past.
The conoit~on that the subintervals may no~
overlap does not seem to be relevant, though, in
(16, quaOratlc equations are aIweye s~mple
273
the Instances for whlon "quadratic equations Pe
~imple" are true are no~ temporally ordereo at
all. it, is m~gnt indicate, Ov the way, that the i-
objects ~re not necessarily intervals, but rather
cases
or occasions wnlcn can but need
no:
be given
m temporal interpretation (of. Lewis 1975i.
The third conOition concerns the properties of
t~e I-objects. In the case of the periodic
• ,equency aOverblals the relevant properties

concern the location or the length
of
the
interval. In the case of the temporal guantiflers
one could think of specifying a relevance
conoiticn~ for a sentence like
~ he was always
late
ones not mea= that he was late at any possible
occasion in the past, Put rather that he was late
on all occasions on which his being late or timel~
could nave mattered.
in Aqv~st, Hoepelman & Rohrer (1980) one can
~ind a proposal to incorporate this information in
the semantic representation, but I will not adopt
t~is proposal here, since the conditions o~ the
,non)relevance
of
the occasions are typicaliv
determined O~ pragmatic factors, in
~:" he
always leaves o~-~ twelve
the relevant occasions (1) could just as well oe
all
occasions on which he leaves as all occasions
on
Wnlch ne leaves
for
work as a!i occasions on
~hish he leaves for watching the home game of nls

~avourlte footOaii team.
As a result of the foregoing reductions ar~o
changes the general format for analysing tempo, al
cuantifiers looks as follows :
3 ~,E [ReI(R,S) & Pred(R) & ReI(E,R) & F'reoiE) &
Q I [c(l~E) >/&
3 e [c~e,I; & M~ei & AT(e,p!]]]
,here O is replaced by any of {V, 3, "3, Most,
Few, Many}
M is replaced by some time adverbial
which specifies the location or the
length of e (if there is anv~
Habituality
The sentences oiscusse~ so
far all
contain an
explicit indication of iteration. !he presence of
SL~Ch an IndlCatlOn Is,
however, not necessary
for
deriving an iterative interpretation. Take, ÷or
instance,
(in~ he leaves at twel~e
This sentence cannot only mean tnat he will
leave at twelve, but also that he has the habit of
leaving ~-* twelve.
in the representation of
interpretation the time adverbial
specifiss the t~me of reference :
the former

"at twelve'
3 ~,E [:(R,S) & at twelve(R) & :(E,R) &
AT(E. he leave~]
E
S R
in the representation of tne habitual
i~terpretation~ on tne other hand, tne time
adverolal shouls be tal~en to specify the multiple
e-tlme,
for
the sentence Ooes no~
report on one o~
his ieavzngs at twelve, out rather on several of
socn :ea,es. As a representation of this
interpretation I propose :
~,=st ;
[ ~I.fJ ,
_ e Lc~e,I) ,~ at twelve~e
& AT~e, he leave, l]
R
(19~ he leaves at twelve
is t-eaten as synonymous with
(20, he usually leaves at twelve
If this is felt to be undesirable, one cam
introGuce a special quantifier for marking
habituaiitv, but at this moment ~ do not see an~
reason for SUCh a move.
274
The general format for the representation of
habitual ~nterpretat~one Is, hence,

3 R,E [ReI(R,S) ~ Pred(R) & Rel~E.R> ~ Preo(E)
Most i [c~I,E) >
3 e [c~e,I) ~ Pred(e) & AT~e,p)]]]
The Assignment of Representations to Sentences
On
t~e
basis of the given analyses one
O:stinguls~ three kinds of sentence meanings :
no iteration
no ~ i [ l/periodic
cyclic
i~eration
\
Q I [ ]
\indefi-,te
can
is specified
F is not specified
Q is any of {~,3,
"3,~ost,Manv,Few}
The assl~nment of these meanings
to
particuiar
sentences is fairly straightforward when the
sentence contains a frequency adverOial or a
temporal quantifier, but if there is none o~
those~ then the sentence is amOiguous Oetween a
non-lterative and an habitual interpretation ~cf.
the two interpretations of "he leaves at tweive"~.
It, practice there are some oisambiguatlng

~. I* the basic proposition (p) denotes a state,
~r. er, the sentence can not have an habitual
ir~erpreta~ior~ Compare
:i;~
ne leaves at twelve
,21 ne is in jei!
~1~
can be interpreted
as
meaning that he has
the naPlt of leaving at twelve, bu~ (21i cannot Oe
interpreted ms meaning that he has the habit of
bel=g in
jail.
~,
Certain verb forms can biock
the
Oerivation o~
one of t~s two possiole interpretations. Compare
~2~ he is drinking coffee
12]) he drinks coffee
(22, can Oenote a single instance of drinking as
wei" as a recent habit of him to drink:: coffee ~cf.
in the sense of "he
is.
drinklng coffee nowadays").
(2;,, on the other hand, can only denote a habit;
it cmnnot be used to report on a single instance
o~ drinking.
This demonstrates the need to

distingulsn
oi4ferent types of verb forms : the ones that will
aiways elicit an habitual interpretation, the ones
that block the derivation o~ an habitual
interpretation, and the ones that admit both kinds
of interpretmtions. The firs~ are unequivocall~
[+habitual], the second C-habitual[ and the last
will be given the feature [+/-habitual].
THE INTERLINSUAL
ANALYSIS
OF THE VERB FORMS
The Meanings of the Verb Forme
In the previous parts i have presente¢ a
formaliem for the representation of temporal
information in sentences. This formallsm is
especially deeigned for the anaiyeis of natural
language, but not for the analysis o~ any
particular natural language, such ae English,
Dutch or Kiswahili.
Its mmin purpose is to provide
a
conceptuall~
well-defined language for de;ining and comparln~
the ~eanings of te~poral expressions in different
natural l~nguagee. In order to serve this purpose
it is not s~fficlent ~o have a formalism, ~nouon.
What is also needed is a general specification o4
now the semmntic representations relate to tnelr
imnguage specific co~nterpmrts, i.e. the tenses,
the temporal auxli:ries and t~e time aoveroials.

The ÷orme~ two wiil furcner de caileO
veto forms,
For c {'is~ ~n~, those verb forms are summec up in
the followlng rL~ie :
Vero form ~. [+/-F'ast] (wi11+ir.f)
(have+EP) ({be+iNS to+frill)
~e going
T, hi_'¢ rule ylelds 24 (=2x2x2x3) 'verb forms.
Their role in the semantic interpretation of
sentences .:an easily de expressed in terms of the
given formalism. They specify
i. the relation Petween reference time anO speech
time : ~eI(R,S) (= oeictic information)
2. the relation between event time and reference
time : ReI,E,R) (= aspectual information~
5. whether the sentence has an habitual and!or ;
non-iterative ~nterpretaZlon
275
The meaning of a verb form can, hence, be
representeO as a triple ~x,y,z> where x and v are
substi~uteO for one of the possible dinar,
-elations oe~ween intervals, and where z is one of
the three poesible habituali~y values.
The aame
verb ~orm can, of course, have
oifferent meanings
and
will,
hence,
Oe

assoclateO
~th a set of such triples.
The details o~ this association have
been
discL:ssed elsewhere~
at
]east
for the x ann ¥
values ~cf. Van Eynde, des Tombe & Maes 1985i. In
tnls paper I will only discuss the z values in
some detail.
The Mabituality Value
A good starting point for demonstrating the
relevance
of the habituality value is provided by
the following iist of sentences. They are taken
from hess (1985).
~) a text editor makes modifications to a text
file
~25) a text editor is makin~ modifications to a
text file
~26) a text editor made mooiflcatione to a text
file
• 27~
a text editor has made modifications to a
text file
In L24) it is said "that a text editor ma~es
modifications
to
a text file in general, almost

by
Oefinition. We might read this sentence in a
re~erence manual" (Hess 1985, 10).
In (25-27), on the other hand, it is said "that
there
is, or was, a case of a text editor mankind
modifications to a text file. These remarks might
~e made by a system operator, watcnlng ~is screen'
(lb.).
Hess concludes from these observations that the
quantifier of the subject is universal in (24) and
e~:isten~ial in (25-27), However~ this conclusion
does not foliow automatically. In terms of the
formalism presented in this paper one could sa~
that (24) has an habitual interpretation, whereas
the
other sentences have a non-iterative
interpretation, In the former case the existential
quantifier of the subject will be in the scope o~
the Most-quantifier, whereas in the latter case it
wlii not be in the scope of any non-existential
quantifier, and this accounts for the difference
in interpretation without havinq to postulate two
possiole meanings for the indefinite article.
Hess s examples are
useful
in this
context,
t~ough, because they clearly illustrate the roie
of the vend for~ in the interpretation. Since it

is the only variable part in the sentences, the
~ifferences in interpretation can only be ascribeo
to them, more specifically to their habltuaiity
value.
;or the
assignment of an
habltuality value to
a
given verb form one has to test whether it can or
cannot elicit an habitual interpretation in some
given context. In testing this one should
i. always use sentences with a non-stative basic
proposition, for i~ the latter is stative the
sentence can never be habitual (of. supra) ;
2. pay attention to the other interilngual values
of the verb form. The English simple present.
for instance, is uneouivocally [+habitual] in
its sim~Itaneoue meaning, but in its posterior
meaning it can be [-naoitual] too (of. the
non-iterative interpretation of "he leaves at
twelve"~.
The relevance of the [+/-Habitualitv]-
distinction has so far only been demonstrated from
a monolln~ual semantic point of view. It is,
however, possible to give some translational
evidence
for this oletinctlo= as well.
The relevant cas~s are tne ones where the
corresponding verb forms have Oi~ferent
habi:~allty values. A good example of this is the

translation of
the
Dutch simple present in
En~ilsh.
The Dutch simple present can be both habitua}
and ~on-hacitual in It~ simultaneous meaning :
28; hi~ o,'inxt aileen whisky <simui,y,~haOitual~
"he
drinks only whisky'
29, Liji~,
hij
dr!nit k~4ie
.,simul,/,-habltuai>
"look, he Orinks co,fee"
The English simple present, on the other hand,
s always habitual in its simultaneous meaning
unless in sentences Oee:ribing states, of course
(~0~ he only drinks whisky <slmui,y,+habitua~.
*~31) iooi:, he drinks ~o~fee <simul,y,-ha~itual
Pot the expression of slmul~aneous non-
iterativity one has to use She progressive :
32) look, De is crinking coffee
As a conseoue~ce. ~e mapping of (29) to ~32)
in~ol~es a non-~riviai tense replacement, and it
il o~e of the merits o~ the given formaliem that
it car handle this ir an lnteriingual way.
276
REFERENCES
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Bruce Bertram (1972), "A model for temporal
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program",
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Lemis David ~1975~ "Adverbs of ouantification",
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Cambrioge University Press,
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~u!rk
Randolph, Greenbaum Sioney, Leech Geoffrey
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Relcnenoach
Hans
(1947~
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of
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277