Homomorphism through (Partly)
Iterative Events
Ingebjorg Tonne, University of
Oslo
ESSLLI 1997
1.
Introduction
In this paper, I argue that one aspectual
impact of the subject is of an iterative nature. The iterative effect of arguments is
constrasted with the incremental theme-effect, and the contrast is used to show
in what way the subject and the direct object differ aspectually. The subject
matches the direct object in that there is a homomorphy between the referential
properties of the argument and the event of which it is a part. However, the iterativity-homomorphism
induced by the subject is a repetition of the event measured out by the direct
object, i.e. the two constituents seem to induce homomorphisms at different
levels. This latter point fits in
spirit into the view of aspectual asymmetry argued for in Verkuyl (1993) and
elaborated in Dimitrova-Vulchanova (1996).
The matter is complicated by the fact that also the direct object may
induce iterative events, however.
In Verkuyl (1993, 1996) the iterative nature of the subject is
handled by a special (p-) function. Although such a function reflects
well the iterativity measuring out effect of a plural subject, it does not take
into account mass terms, which induce incremental theme readings if they
function as direct objects, but not as subjects. Furthermore, the analysis is burdened by
the less attractive approach to the semantics of the NPs, namely the
[±SQA]-opposition based on the presence or absence of a cardinality statement in
the representation of the denotation of the NP. It is argued here that the higher level
of homomorphism, i.e., the iterativity measuring out effect, may be well taken
care of in a framework like that of Verkuyl (1993), although it needs a
different semantic analysis of the NP. The lower level homomorphism, that
between the incremental theme and the event, is not satisfactorily handled by
the analysis in Verkuyl (1993), since mass terms contrasted with count terms
constitute the base for the aspectual contrast on this non-iterative level, and
in Verkuyl (1993) mass terms are not treated. The analysis in Krifka (1992) is
viewed as a better choice. A
semantic analysis of the NP is found in Krifka (1992), and an extension of
Krifka (1989,1992) in direction of separating singularity and plurality and introducing aspectual levels is
attempted here.
This work in progress is eventually
forming part of a thesis on aspectuality in Norwegian, hence the object language
in this paper is Norwegian.
2.
Iterativity and Levels of Aspectuality
A bare plural subject may induce what I
call a partly iterative reading:
(1) (Ulike)
studenter fant løsningen hele uka.
(atelic)
(Different) students discovered the solution all
week.
In (1), the adverbial all week forces an atelic reading of the
sentence. The verb, however, is
instantaneous (and telic, see below), and the event can only be extended through
iteration of the verbal activity.
(1) is atelic due to the possibility of partial iteration opened for by a
distributive reading of the subject.
(1) is a partial iteration, since the agent is not the same in
each iteration. The way that
this is understood is through the recognition of different levels of
aspectuality.
I recognize three aspectual levels. One is the lexical level, and it
pertains to what aspectual potential the verb carries with it. A stative verb,
for example stay, has much less
potential for taking part in a construction describing a telic event, than has
an activity verb, e.g. paint. Furthermore, in the lexical aspectual
specification, more than a binary distinction[1] seems to be necessary, since, in addition
to the two types exemplified, there are activity verbs that alone imply a telic
single event. Examples are discover, cross, explode.
The next two levels up are the verb phrase
and the sentence, following Dimitrova-Vulchanova (1996:2):
"Thus, basically two types of processes are
distinguished: those geared towards
[telicity] and which are primarily operative at the VP level, as opposed to
the processes operating at clausal
level which 'undo' [telicity]. The former type of process will be referred to as
aspectual composition, whereas the
latter will be dubbed 'aspectual
modelling'. Of the two, only
aspectual modelling can be seen as a kind of 'view operator' (cf Verkuyl's 1993
'perspective', and Smith's 1991 'viewpoint', for comparison)..."
In the light of such a view of various
levels of aspectuality, it is possible to explicate the ways in which the
various parts of the sentence contribute to the total aspectual understanding of
a sentence. With respect to
sentence (1), the verb itself carries a great aspectual potential, i.e., is
telic, in the sense that a discovery event cannot be though of as cut off before
its completion, nor lengthened, and still count as an instance of a discovery
event. Krifka defines telic events
through the notion of terminal point:
Both the event of running and the event of running a mile have a terminal
point, i.e. they end at some point in time, but only the event of running a mile
is telic. Let TP be the function
that maps events to the last time point in their run time. A telic event, then, is an event such
that all subevents which fall under the predicate have the same terminal point.
(See Krifka (1992: 34-35) for details.)
I take it as a prerequisite for an event
to be iterative or partly iterative that the event-parts that make up the total
event share the same thematic relations, and that each is telic. Since the verb itself in (1) is telic,
the latter condition is satisfied.
The event-parts making up the total event in (1) share thematic
relations, since all the students making the discovery play the same
discovering-part, and the solution stand in the same being-discovered-relation
to each student. The relation
between the verb and the direct object is what is iterated in (1), and the
iteration is triggered by the distributive reading of the
subject.
3.
The Subject and the Direct Object
The direct object has been extensively
studied with regard to its aspectual impact of the sentence[2], and the object position found to be the
typical grammatical site for the 'incremental theme'. I.e., a mapping has been noted from the
entity denoted by the direct object to the event, a homomorphism between the
direct object and the event.
An example of the aspectual contrast, also found in Norwegian, induced by the change in the direct
object is seen in (2):
(2) a. John spiste
brødskiva. (telic)
John ate the slice of bread.
b. John
spiste brød.
(atelic)
John ate bread.
The aspectual difference can only be
attributed to the differences between the direct objects in the two
sentences. In (3), the effect of a
bare plural in object position is seen.
I view this effect as parallel to what we saw in (1) for the subject,
i.e., partly iterative:
(3) John
oppdaget søte små landsbyer i årevis. (atelic)
John discovered quaint little villages for years.
The subject, however, does not have the
incremental theme properties. A
mass term in subject position may not open for an atelic reading in the same way
as a mass term in object position:
(4) Vann vasket
vinduet på to minutter/?i to minutter.
(telic/?atelic)
Water cleaned the window in two minutes/for two minutes.
(5) Olje fylte
tanken på to timer/*i to timer.
(telic/*atelic)
Oil filled the tank in two hours/for two hours
It is seen that whereas both of the
grammatical functions, the subject and the direct object, may stand in an
iterativity-type of homomorphism relation to the event in which they are parts,
only the direct object may stand in an incremental theme-type of homomorphism
relation to the event. The iterativity-homomorphism induced by the subject is a
repetition of the telic event measured out by the direct object, i.e. the two
constituents seem to induce homomorphisms at different levels.
This asymmetry between the subject and the
direct object should be reflected in the aspectual analysis. In the works of both Verkuyl (1993,
1996) and Krifka (1989, 1992), the works that I discuss in this paper, the
intentions have been to make a semantic analysis of the NPs and connect that
analysis to the aspectual analysis of the other parts of the sentence. My points are to see how their theories
can be expected to deal with the single and iterative type of aspectuality and
the asymmetry between the subject and the direct object alluded to above. I find the theory of Krifka (1989,1992)
worth expanding to deal with the facts presented here.
4.
Verkuyl (1993, 1996)
Verkuyl (1993, 1996), is interesting
because, to my knowledge, he is the only one to include the iterative effect of
the subject in the aspectual analysis.
Verkuyl places his work in the extension of Generalized Quantifier Theory
(Barwise and Cooper, 1981). He
claims to have found a way to characterize the difference between the two types
of NPs that are relevant for aspectual analysis, namely [+SQA] and [-SQA] NPs,
representing the former with a cardinality statement and the latter without a
cardinality statement. Krifka
(1996) points out a problem with this analysis in his review article (Krifka
(1996: 446)):
[Verkuyl] classifies a phrase like a sandwich as [+SQA] because the way its semantic object is
described contains a cardinality statement (in this case the statement "|W|=1",
where W denotes a sandwich in this case), and he classifies a phrase like sandwiches as [-SQA] because the
description of its semantic object does not contain such a cardinality statement
about the set W. (...) Notice that,
for example, the lack of any cardinality statement for W is logically equivalent
to the statement $n[ |W| =
n], where n ranges over the natural numbers, and this statement does contain a
cardinality statement; hence Verkuyl's criterion does not yield the expected
result.
In addition to this problem with the
NP-analysis, the theory of Verkuyl (1993) suffers from the lack of a treatment
of mass terms. Although in the
literature[3] mass terms are stressed as having similar
effects aspectually as bare plurals in object position, the importance of
±cardinality statement in the representations of NPs in Verkuyl (1993), prevents
the analysis to cover mass terms and this generalization is missed. On the other hand, his functions
relating the verb with the direct object and the VP with the subject, reveals
the iterative effect of the bare plurals. As opposed to what is argued in this
paper, he sees an asymmetry between the subject and the direct object with
regard to the iterativity-effect. The function p
takes as its domain the subject NP-denotation assigning to each element x in the
denotation a unique l. l, the
VP-denotation, is a function that can be characterized as a set of pairs
<i,p> such that x is in the position p (in the direct object) at i. l
thus defines a path for the x.
(6) Verkuyl
(1996:13):
p: for all (singletons) x Î [|
NP |] ext(ernal
argument) :
p(x) = lx, where
lx := {<i,p> : [| AT(p) (x) |] M,i = 1}
Each member of the denotation of a bare
plural subject will get its own path through the members of the direct object,
and the iterativity effect is taken into account.
5.
Krifka (1989, 1992)
In Krifka (1989, 1992) the homomorphism
between the denotation of the verbal arguments and the event is effected through
the mapping from the domain of events to the domain of objects and the mapping
from the domain of objects to the domain of events. The definitions of the properties
uniqueness of objects, mapping to objects and mapping to events are those needed
to in turn define the thematic role known as incremental theme. These
properties are defined as follows (Here, the symbol
ÍE is used for the part-of-event relation,
and Íofor the part-of -object relation (Link (1983))). (The numberings are from Krifka
(1992)):
(P27) "R[UNI-O (R) « " e, x, x'[R(e,x) Ù R(e, x') ® x=x']]
(P29) "R[MAP-O (R) « " e, e', x[R(e,x) Ù e'
ÍE e ®
$x'[x' ÍOx Ù R(e',
x')]]
(P30) "R[MAP-E (R) « " e, x, x'[R(e,x) Ù x' ÍOx ®$e'[e' ÍE e Ù R(e', x')]]
(Krifka(1992: 39))
(P27), uniqueness of objects, says that a
thematic relation R between an event e and an object x satisfies the property
uniqueness of objects if the event is related to a specific object, and nothing
else in the same thematic relation.
(P29), mapping to objects, says that every
part of an event, eat an apple, say, corresponds to a part of the
apple.
(P30), mapping to events, says that every
part of an object, in our example, an apple, corresponds to a part of the event
of eating an apple.
That the thematic relation that holds
between the event and the incremental theme actually holds is a necessary
condition for there to be a homomorphism between the argument and the event,
i.e. that the extension of the argument is mapped onto the extension of the
event. The thematic relation is
not, however, sufficient to decide whether the sentence is telic or atelic,
since the thematic relation is the same in the two sentences below, although one
is telic and the other atelic.
(7) a.
John drank a glass of milk.
(telic)
b.
John drank milk.
(atelic)
In addition to the thematic relation, one
needs to take into account the referential properties of the incremental theme
argument.
Krifka (1989,1992) bases this other part
of his work on the well-known idea (e.g. Bach (1986)) that there are striking
similarities between the meanings of nominal and verbal expressions, and that
the mass (+ bare plural) vs. count distinction in the nominal domain is
reflected in the verbal atelic vs. telic distinction. Krifka (1989,1992) does what was
not spelled out in Bach (1986), namely,
he explicates the mapping from the nominal to the verbal properties. He
defines the referential properties quantized and cumulative of the
incremental theme argument. If w is
cumulative, like in wine, then wine will also describe a part of w, for
instance w'. Then it should be
possible to apply the expression drink
wine, not only to e, but also to a part of e, i.e., e'. On the other hand, if w is quantized,
for example a glass of wine, no part
of w can be described by the same expression a glass of wine, and therefore no part
of e can be described by drink a glass of
wine. In Krifka's analysis both
bare plurals and mass terms are covered and both come out as cumulative. The referential properties of the
arguments are in turn mapped onto the event.
6.
Krifka (1989,1992) and Beyond: (Partly) Iterative Events
Krifka (1989, 1992) does not treat the
aspectual impact of the subject specifically, but he does include a definition
for iterative events:
(8)
"e, x, R[ITER(e, x, R)
«
R(e, x) Ù $e', e'', x'[e' ÍE e Ù e'' ÍE
e Ù -e'=e'' Ù x'Ío
x Ù R(e', x') Ù R(e'', x')]]
"It is a relation between an event e, an
object x and a thematic relation R saying that at least one part of x is
subjected to at least two different parts of e."(Krifka (1992:39-40)) This is intended to cover e.g. the
reading of a book if at least one part of the book is read twice. The definition
does not include the subject, and hence focuses on the direct object as being
the source of the iteration. There is not intended to be a restriction on the
iterative events of Krifka that each different part be telic. As he uses this
definition to count out events as iterative, as part of a proof for
showing that a given event is telic, the telic/atelic distinction on the event
parts is not relevant. The telicity-condition on the event-parts may, however,
be imposed in addition, to describe sentences like (9) as atelic through
iteration, the iteration triggered by igjen:
(9) Ola leste
boka igjen og igjen.
(atelic)
Ola read the book again and again.
(9), by the way, contrasts with another
construction in Norwegian which does not presuppose a complete reading of the
book on each repetition:
(10) Ola leste i boka igjen
og igjen. (atelic)
Ola read in the book again and again.
To categorize sentences as describing a
telic or atelic event, (8) is one step towards categorizing an event as a
subacategory of atelic events. In
addition to categorization, the representation shows in what way the event that
complies with (8) is atelic, i.e., that there are parts of the total event and
that each shares the thematic relations with the total
event.
To define partly iterative events
specifically, I propose the following elaboration of (8):
(11) "e, x, y, R, P[PART_ITER(e, x, y, R, P) « R(e, x) Ù P(e, y) Ù
$e', e'', x', x''[e' ÍE e Ù e''ÍE
e Ù -e'=e'' Ù x'Ío
x Ù x''Ío
x Ù -x'= x'' Ù
R(e', x') Ù R(e'', x'') Ù P(e',y) Ù P(e'', y)]]
(11) specifies that one of the arguments,
either the subject or the direct object, is kept constant when the other varies
in each event-part. (11) applied to
example (1) says that there are at least two events, e', and e'', that are parts
of the whole (partly iterative) event, e, and two individuals, x' and x'', that
are parts of the plural individual denoting students, and for the two events, e'
and e'', one has one group of students, x', doing a discovery of y, the
solution, and the other another group of students, x'', doing another discovery
of y, the solution.
Complying with (11) is a prerequisite for
an event to be categorized as the
partly iterative type of atelic events. In addition, some conditions have to be
imposed on the representations of (partly) iterative events for them to function
as aspectual checkers. A condition
for the event to be taken as (partly) iterative at all is that the subevents of
e have to qualify as telic. The overall event will be atelic if the
iterativity-inducing argument is cumulative, telic
otherwise.
(11) is indifferent to whether the
iterativity-inducing argument is the subject or the direct object. Being defined
through (8) and (11), iterative and partly iterative events may be seen as being
subjected to a homomorphism between the arguments and the event, at a different level than the
homomorphism between the incremental theme and the event in which it takes part.
This is so because, procedurally speaking, sentences describing events with
incremental themes do not comply with the (partly) iterativity-definition, and
will therefore not go through that extra step in calculating the aspectual
value. All sentences will be
checked for the incremental theme type of aspectuality, where (P27), (P29) and
(P30) settles the thematic relation question. The referential property of the entity
(corresponding to the grammatical arguments) complying with either the property
cumulative or quantized and the subsequent mapping of that property to the event
settles the atelic vs. telic question.
The incremental theme question is thus settled at the level of 'aspectual
composition' (Dimitrova-Vulchanova (1996)) alluded to in section 2, and
corresponds to a processing of the singular part of the event. The plurals are considered to be part of
the level of 'aspectual modelling' (ibid.).
The way that the asymmetry between the
subject and the direct object must be handled in a system as the one described
in this section, is that on the aspectual composition level, only the direct
object is taken into consideration.
7.
Conclusion
At this point it seems like the functions
of Verkuyl (1993, 1996) stand out as a possibility for showing the interaction
of the verb with its arguments when it comes to the homomorphism between the
bare plurals and the event, and with some opening for asymmetric treatment of
the subject and the direct object. Parts of the analysis of Verkuyl (1993,
1996), however, in particular those colored by the problems connected to the
[±SQA]-contrasts, are in need of replacement. Furthermore, the lack of treatment
of mass terms, which is one of the contrasting parts of the incremental theme /
aspectual composition-level is a major drawback of Verkuyl (1993, 1996). If the analysis of Krifka (1989, 1992)
can be extended in ways indicated in this paper, such a framework, with a sound
semantic analysis of the NP-arguments of the verb, and a mapping of the
referential properties of the arguments onto the event, is a way to categorize
iterative events as atelic, and explicate in what way the different parts and
properties of the sentence contribute to such a
categorization.
8.
References
Bach, Emmon, 1986: "The Algebra of Events",
in Linguistics and Philosophy 9, pp. 5-16.
Barwise, Jon, and Robin Cooper, 1981: "Generalized Quantifiers and Natural
Language", in Linguistics and Philosophy 4,
159-219.
Dimitrova-Vulchanova, Mila, 1996: Verb Semantics, Diathesis and Aspect,
Dr. art. thesis, Dept. of Linguistics, NTNU,
Trondheim.
Dowty, D., 1979: Word Meaning and Montague
Grammar, Reidel Publishing Company, Dortrecht,
Holland.
Dowty, David, 1991, “Thematic proto-roles and
argument selection” in Language, Vol.67, number 3.
Krifka, Manfred, 1989: "Nominal Reference, Temporal
Constitution and Quantification in Event Semantics", in R.Bartsch et
al.(eds.)"Semantics and Contextual Expression".Foris,
Dortrecht.
Krifka, Manfred, 1992: "Thematic relations as links between
nominal reference and temporal
constitution”, in Ivan A.
Sag and Anna Szabolcsi: Lexical Matters, Stanford
University.
Krifka, Manfred, 1996: Review article in Studies in Language
20:2, 443-454.
Link, Godehard, 1983: "The Logical Analysis of Plurals and
Mass Terms", in R. Bäuerle, Ch. Schwarze, and A. von Stechow (eds.),
"Meaning, Use and Interpretation of Language", pp.
302-323.
Smith, C., 1991: The Parameter of
Aspect, Kluwer Academic Publishers.
Vendler, Z., 1967: Linguistics in Philosophy,
Ithaca: Cornell University
Press.
Verkuyl, H. J., 1972: On the compositional nature of the
aspects. Reidel,
Dordrect.
Verkuyl, H. J., 1993: A theory of Aspectuality. The
interaction between temporal and atemporal structure, Cambridge University
Press.
Verkuyl, H. J., 1996: "Events as dividuals: Aspectual Composition and Event
Semantics", ms, Institute for Language and Speech OTS, University of
Utrecht.