Partial Orderings and Aktionsarten in Discourse Representation Theory 
lOtrt EBERLE 
Institut for Maschinelle Spraehverarbeitung 
Universit~it Stuttgart 
Keplerstr.17 
7000 Stuttgart 
West Germany 
Abstract 
This paper presents an approach to deal with the underspecification of 
Aktionsarten in German sentences. In German the difference between an 
accomplishment and the associated progressive state is often not marked 
on the sentence level. This distinction is important for correctly 
interpreting texts and for translation into languages which provide 
morphological markings of Aktionsarten. To maintain compositionality we 
suggest a two-step analysis of a text with respect to the temporal relations 
and the classification as events or states. This analysis is guided by the 
Discourse Representation Theory developed by Kamp and makes use of 
world knowledge and an inference component. 
The problem of classification can be reformulated as the problem of 
finding an embedding function f from the representational entities onto 
the domain of a model. The models we use are structures built from 
intervals of time, events and individuals. Considering intensional models of 
this type will allow us to give truth-conditions for progressive states related 
to corresponding accomplishments. We restrict ourselves to progressive 
states of intentional actions and use the beliefs of the agent. 
1) Introduction: 
The influence of the criterion "Aktionsart" with respect to the temporal 
relations of temporal entities often seems to be overemphasized. On the 
one hand the correct dassiftcation is a problem, on the other hand, it 
seems that in more cases than assumed the influence of world knowledge 
is necessary to disambiguate the temporal relations. 
In this paper an approach is preseuted based on a two-step anal~Ls of a 
text. The first step consists in constructing a partial ordering on the basis 
of an approximate classification of the temporal units on sentence level, 
using the framework of D(iscourse) R(epresentatlon) T(heory)/cf.Kamp 
1981a/. In the second step we try to obtain possible linear readings, using 
background-information, provided by a database, and an inference 
component that. is an extended version of the "event-calculus" 
/cf.Kowalski,Sergot/. 
The subdivision into two steps enables the temporal resolution 
component to work without a great number of inferencing processes. This 
contributes to a more modular-like structuring of the natural language 
processing-system. The goal is to represent ambiguous readings as such. 
The progressive state reading of an accomplishment leads to the problem 
called "imperfeetive paradox". Using the beliefs of the agent we try to give 
a solution for the subclass of intentional actions. The problem here is to 
deal with the time dependency of the content of someone's belief. 
160 
2) Partial Event-Structures 
The starting point of this paper is the conviction, following Kamp and 
others, that within the temporal units, events are primordial, and time is 
abstracted from them. The construction of pure temporal units can be 
based on the ultra-filter-construction introduced by Wiener /cf.Kamp 
1979,1981b,van Benthem/: In order to model the natural 
underspecification of human perception, only the relations < , o 
(temporally smaller or overlap) are given within the event-structures in 
/Kamp 1979/along with the following axioms: 
A1 V el,e 2 e I < c 2 - > ~ e 2 < e 1 
A2 Vel,e 2 e 1 <e 2 & e 2< e 3 -> e I < e 3 
A3 Vel,e 2 e lee 2 -> e 2oe 1 
A4 V e 1 e I o e 1 
A5 Vel,e 2 e I <e 2 -~. ~e lee 2 
A6 Vel,e2,e3,e 4 e l< e 2 & e 2oe 3 & e 3< e 4 -> e 1 < e 4 
Including the axiom of linearity 
A7 Vel,e 2 e l< e 2 ; e lee 2 ; e 2< e I 
other relations llke "subset" or "temporal equivalence" can be defined out 
of these basic relations. This shows the fundamental significance of the 
relations < and o. 
The addition of new events can allow a more accurate statement o~ the 
temporal relations. If we start with an uttered relation of vague 
simultaneity between two events e I and e 2 expressed by e 1 o % and if it 
becomes clear from later passages of the text that there are events e 3 and 
e 4 with e 3 < e 2 < e 4 and e 3 o e 1 and e 4 o e 1 we can deduce by the Wiener 
construction, that the event et, seen as punctual at the beginning, consists 
of at least three moments of time tl, t2, ty Thus the internal structure of 
such events can become more elaborate as the text proceeds. In addition 
we can specify with greater precision the relation between events. In the 
case of e I and e 2 we are now able to conclude, that the overlap of the 
beginning has to be understood as a subset-relation between e 2 and e 1. 
In the following we will make use of this conception within the definition 
of our models for representations of texts. 
The Akfionsarten, redefined by Vandler, have frequently served as 
criterion to correctly construct tlme-structures from natural language- 
texts./cf.Dowty 1986,Hiurichs,Par tcc/. 
The opinion is not tenable however that telic events (accomplishments, 
achievements), in the absence of temporal adverbials, shift the reference 
time for new temporal units forward, and that activities, or so-called atelic 
events, and states do not. This is often argued in the literature. 
Exampte 1 : 
(e O) John I,~rote a program. (e 1) Ite togged in, 
(e z) opened his file and 
(e 3) began writing and correcting by using his papers. 
ExampLe 2: 
(e O) Yesterday a tot of things happened. 
(e 1) John bought a bicycte, 
(e 2) Mary den~tished Stantey's microwave oven. 
In example 1, el,...,e 3 are internally ordered subevents of e 0. In example 2, 
no obvious ordering between e I and e 2 exists. 
Without infereneing and using a detailed analysis of discourse fimctions 
as "continuatiolf' or "elaboration" we can not establish the right ordering 
relations for =:uch cases. 
It is ewm harder to state correctly temporal relations within a 
compositions t approach: 
Exar%t~ \[ e 3: 
(e O) John took the ptane to Frankfurt. 
(e 1) Then he took the train to Stuttgart. 
(s 1) As he'd had nothing to eat since breakfast 
(e 2) he bought e sandt~ieh at the station. 
e) 
(e\]) Then he bordered the train. 
b) 
(e 3) Then he 19aoned his uife to say that he=d arrived, 
(e 4) before tsking the tram horle. 
Only when p,'ocessing the fourth sentence of example 3 (lo we discover 
that e 2 is an elaboration of e 1 in the case of a), whereas in b) e 2 is a 
continuation ~)f e 1. 
Thus what we should do in the first step of the analysis is to construct an 
underspecified ordering hoping that in the second step, on the basis of the 
representation* of the whole text, we can refine the conditions. We restrict 
ourselves to cases as in example 1 and 3, becansc here it suffices that one 
reference point is provided by the representation of the preceding text. 
To repret;ent the ambiguity between continuation and elaboration we 
need a relation "not-before". However to define "not-before" as a transitive 
relation the disjunction of < and o (< ; o) is not sufficient. This becomes 
clear from e:mmples 1 and 3 which would then be expressed by the 
following: 
%0 (<;o) e 1 (<;o) e 2 (<;o) e3" (e 3 not-before e 2 not-before el... ) 
Because o is not transitive, for an admitted reading "e 0 o e 1 o e 2 o e3" 
(which would be true in cases where e 1 is a subevent of Co, e x a subevent 
of e 1 and so on) one cannot exclude the possibility that "e 3 < el" , which is 
surely not the case for such episodic readings. 
Exempt e 4: e 3 
-- e 2 
e 1 
Thus we have to require: 
V el,e 2 ( e 2 not-before e 1 
<->e l<e 2;(e lee 2a(Ve s e s<e 1->e 3<%))). 
This suffices for transitivity as easily can be shown. 
Nevertheless we intend to tackle the problem in a second way; first 
because we want to be able to state a relation of isomorphy between event 
structures and Allen's interval structures /cf.Allen/, and second, because 
we want to make use of the eveut calculus of Kowalski and Sergot within 
our inference component. In their approach events are fike points. To this 
end we need extensions of pure event structures. 
It has been proposed, by Moens and Steedman among others 
/cf.Moens,Steedman/, partly with the intention of making Kowalski and 
Sergot's event calculus available for natural language systems, to represent 
the extent of structured events, i.e. accomplishments and activities, thereby 
conceding them starting and final events Cstart-events" and "stop"- or 
"culminafion-events"). This method is also adopted within our approach. 
In combination with the Wiener method of constructing pure time units, 
this finer granulation allows us to conceive the o-relation as art 
equivalence relation for so-called secondary events, which, as we will see, 
is another way of solving the problem of "not-before". 
The model for DRS's used here is an extended version of the point- 
event-structure model with a domain of individuals proposed by Kamp. 
The version in this paper is a continuation of the modcl in/Reylc/. 
An extended point-event structure with a domain of individuals is given by: 
<E, 'l;,d, U,&b, <,o, start, end, F, G > 
where Ihe following is the case: 
* E is tile set of events and is subdivided into primary and secondary 
events: Primer, Seeev. 
* Primer is subdivided into Acc (accomplishments), Act (activities) and 
Ach (achievements). 
* start, end are partial functions over the primary events with values in the 
domain of the secondary events such that each element of this 
domain is a value of one of these fimctions. 
* Secev is subdivided into the subclasses Start (start-event), Stop (stop- 
event) and (htl (culmination-event). 
* S is the set of states. 
* P(T) stands for the set of periods which can be formed from the 
elements in T, which is the set of atomic, purely temporal units, 
whereby 
* T contains all atomic elements which arc constructed out of E and S 
through the Wiener constrnction. 
* d is a (<,o)-homomorphism, which relates the events in E and the states 
in S to the corresponding purely temporal entities in P(T). 
*//is the set of individuals 
* The following holds: 
every accomplishment x is assigned exactly one start-event x I and either 
one stop-event x 2 or one cul-event x2, 
every activity x is assigned exactly one start-event x I and one stop-event ~, 
every achievement x is assigned exactly one cul-event x2, 
whereby tile assignment of secondary events to primary events, in 
combination with conditions about the relations <,o can be graphically 
illustrated as follows: 
x 
x 6 Acc, or x 6 Act: ......... 
x I x 2 
tx 1 <x2&x 1 ox&x2 ox& (VyEEUSUP(7") 
(y < x ~-> y < Xl) & (x < y <-> x2 < y))) 
161 
x 
× EAch: .... 
x Z 
(x2ox&(VyEEUSUP(T) (x < y <-> x2 < y))) 
* The secondary events are considered as atomic: 
VxESecev, y,z~EUSUP(T) : ~(yox&zox&y<z) 
The axiom s A1 - A6, extended to all temporal units of the domain, hold 
for the relations <,o, such that it follows that, with the inclusion of the 
linearity axiom : 
A7 Vx,yEEUsUP(T):(x<y;xoy;y <x) 
o has the characteristic of being an equivalence relation, restricted to the 
secondary events. 
One can thus define: 
Vx,yESecev:x=py <-> xoy 
This allows the abbreviation "x <p y" for elements of Secev with "x < y" or 
"x =p y". 
*/7, G are interpretation functions, such that 
F assigns every n-ary relation R a function over P(T),which assigns every 
i E P(T) a subset of U n 
G assigns every n~ary relation R a set of n+l-tupels out ofExU n 
* b is a function which assigns in a one-to-one-correspondence every state 
s E S a pair <i,<R,Ul,,..,un> > with <ul,...,Un> ~ F(R)(i) 
* In addition, the following correlation principle should hold: 
For every n-ary verb R and every n+l-tupel <e,ul,...,Un> E G(R) there 
exists a state s E S and an interval i E P(T) such that b(s) = 
<i,<R',ul,...,Un> > and either "i c d(e)" or "i < d(e)" , whereby R' 
represents the progressive variant ProgR of R. 
On the other hand, there should exist for every R', which is the 
progressive variant of an R and which is assigned an s by b, an n+l- 
tupel E G(R) with the corresponding ordering and individual relations. 
In the system proposed here, a narrative text without any additional 
specifications which includes a series of events e I E Acc, e 2 E Ach, 
e 3 EAcc would be assigned the following semantic representation: 
end( e 1 ) 
/ 
< / 
/ <p <p < 
start(el) ....... end(e2) ...... start (e3) end(e 3 ) 
Thus, the underspecification which is necessary in examples such as 1 
and 3 is maintained without the side-effect of example 4. 
More exact relations can be established in a second step, using 
pragmatic knowledge, which completes the structure. In the case of 
example 2 we assume an indicing which does not allow an internal 
ordering. 
An advantage of this representation, using secondary events, for 
underspecified texts, over a representation with differentiated ordering 
relations, such as Allen's interval structures/eft.lien/, is, for example, its 
notational efficiency: 
If el,e 2 E Ace, then the following holds: 
start(el) <p start(e2) is equivalent to e 1 (= ;< ;o;s;siBdi;fi) e 2 
162 
Using the further restriction 
V e EAch, e 2 ESecev: 
end(e) = e2-> (VyEEUsUP(T): y < e 2 <-> y < e) 
one can show easily that within the event substructure of the extended 
point-event structure the relations that Allen uses can be defined in terms 
of o and < such that a relation of isomorphy holds between such extended 
event structures and Allen's interval structures. (In general this is not the 
case for the original event structures). 1 
3) The imperfectlve paradox and the ambiguity of the Aktionsarten in 
German 
No attempts to solve the paradox that I an~ familiar with have been able 
to reduce the validity of a sentence in the progressive form to the validity 
of the same sentence without a progressive, which was the intent. 2 
Moens and Steedman, with their aspectual net, have proposed a solution 
in which progressives are only generated from the activity readings of 
events. I will adopt this view to a certain extent, but will take it one step 
further, by bringing in beliefs, in order to create the possibility of 
reestablishing a direct relation at least for some kinds of accomplishments. 
The basic idea is that it is often only on the level of a text that the hearer 
can decide whether or not the culmination of an accomplishment, which 
has been introduced by a progressive, has actually been reached. Some 
texts will leave this decision open, others will force the existence of a 
culmination, and still others will force ihe nonexistence of a culmination. 
Especially in this last case, it is necessary to question the justification of 
the use of the progressive state for an accomplishment: how do we know 
the goal of an action if it is not attained? These possible characteristics of 
a text should be reflected by the different possibilities of assigning an 
embedding function relative to a DRS in a model M. 
We therefore require for a function f, which maps discourse referents of 
a DRS K onto entities in an expanded point-event structure with a domain 
of individuals, in addition to the usual features/eL Reyle/, the following: 
M I=f, K start(e) < end(e) iff startM(f(e)) <M endM(f(e)) and either 
endM(f(e)) E Stop M or endM(f(e)) E Cul M 
In addition the DRS construction algorithm must contain the rule: 
For all e E Ace, e' E E U S U P(T) : end(e) <p e' -> end(e) ~ Cnl 
If one requires, as in the correlation principle, that every state 
introduced by the progressive of an accomplishment verb be contained by 
an event, then the question whether e has a culmination (that is, 
represents a true accomplishment) or just a stop-point (that is , 
corresponds to the activity reading of an accomplishment), is transformed 
into the question of the existence of the corresponding f. 
Compat~ to this end the analogous approach in/Schulz/. In a subsequent paper we want 
to generalize the result with respect to the whole temporal substructure of an extended 
point-event structure. 
2 Dowty's attempt using ~i~tcrtia worlds ~ seen'~s to lead to difficulties with respect to the 
correct non-subjective definition of the notion of an inertia world/el.Dowry 1970\]. 
On the other hand, the question whether a corresponding expression in 
German is to bc read as the progressive of an accomplishment or as a real 
accomplishment will not necessarily be decided on tiae sentence level. We 
enter start(e) < end(e) and make the interpretation of end(e) depend on 
the possibility oi? finding an embedding ftmction f, 
Exampie 5: 
(e I) gans OberoDerte die Strasse. 
(liana crossed/was crossing ti~e street) 
(e 2) Ein Last~a~len schoss our ihn zu ut~l 
tA Lorry ai~proached him at speed and) 
(e 3) Oberrottte ihn auf der HShe des MitteLstreifens. 
tran him o./er in the middte of the road.) 
(e 4) Er storb aHf der Stetle. 
(Death was instantaneous.) 
In this constell~tion, the compositionally constructed e:t c- Ace cannot be 
truly interpreted as an accomplishment sittce Hans never arrived at the 
other side of the street. A simplified representation ha our system would 
give the followitig: 
~.~od( e I ) 
/ 
< / 
I <p <p <p 
starttel) ..... .. etxtt e2) ....... end(e3) ....... endt e4) 
Incorporating a spatial-temporal inference component (ill the second step 
of the analysis) which uses rules that deal with presuppositions and 
resltltiug state,,, with respect to events and states, one would get, in psetulo- 
prolog notation: 
loe(stort(el),h,sidel(street)) 
end(e 1) G Cut -> loc(endtel),h,side2(street)) 
I oct end(e3), h, i n(st reet)) 
i oc(end(e4), h, i n(st reet)) 
term(e4,exists(h)) 
t rue(end(el ), exi st s(h)) 
On the basis of these facts one can conclude that no linear ordering of 
the secondary events can exist if end(el) C Cul lmlds. Therefore we make 
use of an extended version of the event-calculus by introducing for each 
finear reading which is to be tested "auxiliary" events to get endpoints for 
the introduced states if needed. If such events contradict with respect to a 
story an assumption wtfid~ one could call the relevance-principle, the 
proposed linear reading is rejected. This relevance-principle for instance 
would predict that in a story in which the agent crosses the street but is 
nevertheless later located in the street, an event of reentering the street 
should be mentioned. 
Tiros, every embedding function f, on the basis of the appropriate 
axioms, must map end(ca) onto an element from Stop M. e I is interpreted 
as a non-real accomplishment and this part of the text is no longer 
ambignous. When translating this representation into a natural language, 
the corresponding state-marker and not the corresponding twent-marker 
must be considered 3. 
~A technical vm'iant of this alethod (with different embedding conditions) assigns every 
accomplishnleat a culmination point. The CuJlllillation points of accolnplishn'tetus which 
cannot be assigned a linear reading call be undel~tood as entrance points to an inertia 
world /cf. Dowry ~970/. For the sake of completeness, one would then have to generate 
additional stop l~fiats for such e's anti label them as norl-real acconxplishtllents~ as ill the 
first variant. 
4) luteusionul model of a DRS 
Although the correlation principle implies a relation between a sentence 
wilh tire progressive form and the same sentence without, it also makes 
dependent on f the question of whether the corresponding event to a 
progressive form of an accomplishment can be read as a real 
accomplishment or not. 
If not, one must ask according to which criteria the special 
determinability of assertions about accomplishments is justified, since 
without the possibility of checking the result, the descriptions of 
progressives such as: 
Exampte 6: 
a) "Hans war dabei auf don gerggipfel zu kLettern" 
b) "lions ~al' dabei auf die Iluette unterhaib des Gipfels zu klettern.", 
in case the corrcspondiug events are not completed, collapse into the 
description of a perception of an activity: "Hans klctterte". 
What are the criteria for considering one state to be fulfilled at time t 
and the other not? It seems to me that one possibility of cwthtating such 
cases could consist in referring to beliefs. Thcrc is no doubt that not all 
accomplishments inw}lve agency, and even in the case of agency there is 
not always intcntionality by the agent (cf. Dowty's nolion of 
"controllahility"). But on thc one hand intentionality and associated activity 
can serve as a sufficient condition for the validity of a progressive state. 
On the other hand, in other cases, the introduction of beliefs can serve to 
represent expectations of the speaker or mentioned protagonists 
connected to tire introduction of such progressive states. Thus we get at 
least a further instrument to represent ambiguous readings. Our aim is uot 
to provide the correct truth-conditions for nonintentkmal cases. Here 
further research is needed. Wc restrict ourselves to the description of 
cases as in example 6 and we will concentrate on the notion of belief in a 
framework where time comes into play. 
For cases as in example 6 we require that: 
"Hans ist dabei attf den Berggipfel zu klettern" be true at t 
if 
an activity e of climbing by Hans in the direction of the peak exists where 
tce. 
and 
if Iqans has the intention of climbing the motmtain at t, i.e. in the 
"belief state" of llaus at t there exists an (:vent e wlfich he wants to 
accomplish. 
A DRS-Notation: 
IHans(tO I Berg(v) 
Is: JProg ktettern_auf(u,v) I 
Is':l p I 
Jbet ieve(u,p) 
\[ IP:" i r e n 
I le: Iktettern_auf(i, r ) 
J JAc~te) Cut(end(e)) 
I l:t:rtv (°) ..... 
d(s) =Jd(s') .................... 
ig3 
For the interpretation of such DRS's it is useful to expand the concept of a 
DRS model. Extending the model of/Asher/, we define: 
Intensional point-event structure with a domain of individuals: 
< w,n,// //cc// //r> 
The following holds: 
* Wis a set of worlds 
*D=U(Dw:WEW ) 
* Dw = < <E,T,d,U, <,o, start, end, S,b>w,K,K',K"> 
For every w E W <E,T,d,U, <,o, start, end, S,b > w is a point-event structure 
with a domain of individuals and the corresponding conditions. 
K is a set of DRSs. 
K' is a set of "delineated" DRSs. 
K" is a set of "predicative" DRSs. 
(For our porposes K' is of interest. K and K" m'e mentioned only for the 
sake of completeness). 
*////G maps every relation R onto a function, which assigns to every w 
E W an element out of the powerset of 
U ~N(~wXUwn U U" U K" U K'" U K""). 
*////F maps "believe" onto a function which assigns to every w e W a 
function which assigns to every i E P(T)w a subset of 
(U w x powerset(K')), 
maps "start","end","d" onto functions, which assign to every 
w E W a function from E w onto Ew, resp. from E w onto P(T)w, 
(b w as b above), 
maps every relation R onto a function, which assigns to every 
w E W a function which assigns to every i E P(T)w a subset of 
Uw". 
f is an embedding function of a DRS K in an intensional model if 
f maps/ 
all individual reference markers of U k onto elements of U Uw, 
all event reference markers of U k onto elements of U Ew, 
all state reference markers of U k onto elements of U Sw, 
all DRS reference markers of U k onto elements of K, 
all n-place condition reference markers of U k onto n-ary predicative 
DRS's in K", 
all belief reference markers of U k onto sets of "delineated DRS's" in K'. 
The decisive requirement on a belief-state such as above: 
ra I =w,e,K s' : IS' (p ~ u(IS'), p:IS E Con(IS'), 
where U(K0' ) is the universe and Con(is') the set of conditions of K0' ) 
iff 
3 g ,f ~ g: g(p) = {k r' \[ r' E I} for some set of indices I, 
and 
bw(f(s)) = <i,<believe,f(u),g(p)> > 
such that <f(u),g(p)> ~//believe//F(w)(i) 
and 
3 k z' V k r' ~ {kr' I r' ~ I} such that k 2' < k r' (1~' is a proper portion of kr'), 
such that < f(u),k2'> E//believe//F(w)(i) 
and 
V k r' E {kr' I r' ~ I} q i r e i such that < f(u),kr'> E//believe//F(w)(ir) 
and 
k 3' < k 2' such that H/0,0,Ug(p),M/(k3' ) ~ H/g,Uk0,0,M/(IS ) 
and 
H/0,0,Ug(p),M/(k3'* ) $ 0 
164 
The essential but simplified principle is to be described as follows: 
f is, as usual, an embedding function from U k into the domain of a 
point-event structure, indexed here with w. Beliefs are assigned structures. 
Since the beliefs of the agent can change within the considered time- 
interval we require that the value of p be a set of structures, {k r' \[ 1 < r' _< 
m}. For the description of the belief - K 0 - to be true it is necessary that 
there is a proper portion - k 2' - that all the different belief-states have in 
common. One part of that portion - k 3' - should be described by K 0. We 
state that the description of the belief - K 0 - is correct when the set of 
possible worlds in which the corresponding part of the portion - k 3' - is 
true is contained in the set of possible worlds in which the description is 
true. The treatment of "internal anchors" remains to be integrated. 
For a more detailed review compare the basic model in lasher~, where, 
in particular, the function H is defmed along with the remaining truth 
conditions. 
5. Conclusion: 
The system considered here allows a solely partial ordering of events anti 
states on the representational level, which can be completed on the basis 
of world knowledge stored in a data base, with respect to the ordering and 
the dassiflcation into Aktionsarteu. The compositionality principle for the 
construction of a semantic representation can thereby be maintained. 
Ambiguous readings are kept as such, impossible readings are rejected. 
The expansion to an intensional model for DRS's not only would permit in 
a certain way the restatement of the relation between some kinds of 
accomplishments and the corresponding progressive states , but it also 
would allow, through the use of the belief predicate, an extended version 
of the theory to correctly represent ambiguities such as is made clear in 
the following examples through the use of different indices. 
Exampte 7: 
"Mary saw OswaLd shoot Kennedy" 
a) Mary saw Oswald/Mary shoot KennedY/Mary 
so~ooe 
b) Mary saw /Mary shoot KennedY/Mary 
Osws ld/speakcr 
a) and b) are to be represented by different instantiatlons of the 
arguments for the predicate "believe". A further possible expansion, also 
relating to incomplete accomplishments, is the incorporation of unfinished 
objects. 

Bibliography

ASItEILN.(1986), Belief in Discourse Representation Theory, in: Journal of 
Philosophical l,ogic 15 (1.986) pp.127-189 

ALLEN,J.(1983)~ Maintaining Knowledge about Temporal Intervals, in: 
Comm.ACM 26 (1983) pp.832-843 

VAN BENTItEM, I.(1983), The Logic of Time. Dordrecht : Reidel 

DOWI~',D.(1970), Word Meaning And Montague Grammar. Dordrecht : Reidet 

DOWf'¥,D.(19~R;), The Effects of Aspectual Class on the Temporal 
Structure of Discourse, in: Linguistics and Philosophy Vol.9, No,l (1986) 
pp.3%62 

~IINRICItS,E.(1986), Temporal Anaphora in Discourses of English, in: 
Linguistics and Philosophy Vol.9,No.1 (1986) pp.63-82 

KAMP,H.(1979), Events,lnstants and Temporal Reference, in: 
Baeuerle,R./El,,li,U./von Stechow,A. (eds.) Semantics from Different 
Points of View. Berlin : Springer, pp.376-417 

KAMP,rI.(1981a), A Theory of Truth and Semantic Representation, in: 
Groenendeijk ~t al (eds.) Formal Methods in the Study of Language. 
Mathematical (\]entre Tract, Amsterdam 

KAMP,H.(1981b), Ev6nements, repr6sentation discarsives et rdf6rence 
temporelle, in: Language 64 

KOWALSKI,R.,SI!!RGOT, M.(1985), A Logic-Based Calculus of Events, in: 
New Generation Computing 4(1) (1985) pp.67-95 

MOENS,M.,S~I'EEI)MAN,M.(1986), The Temporal Dimension in Information 
Modelling and Natural Language Processing, Acord Deliverable 2.5, 
Edinburgli,1986 

PARTEE,B.(19g4), Nominal and Temporal Anaphora, in: Linguistics and 
Philosophy Vol.7,No.3 (1984) pp.243-287 

REYLE,U.(\]986), Zeit uud Aspekt bei der Vcrarbeitung natuerlicher 
Sprachen. Dk,;sertation Institut fuer Linguistik der Universitaet 
Stuttgart,1986 

SCHULZ,K.(\]I.987), Event- and Interval Structures A Mathematical 
Comparision. FNS-Bericht-87-18 Forschuugsstelle for nafftrlich- 
sprachliche Sys! eme, Universitht Tflbingen,1987 
