A VP expresses a property of events, and most or all properties of events expressed by VPs are either telic or atelic in a strong sense of anti-telic. Telicity, defined in terms of events, their parts and their runtimes, is a lexical aspect, or situation aspect, or an aktionsart. It is inherent.
An AspP, on the other hand, expresses a property of times, so the grammatical, or viewpoint, aspect transforms a property of events into a property of times, introducing a constraint of (im)perfectivity, defined in terms of the events' runtimes, the times and their parts.
Aktionsart – or lexical aspect, or situation aspect – is a built-in property of VPs. The main distinction is that between telicity and a(nti-)telicity.
Let us first say that a VP is telic if and only if it expresses a telic property of events (where a property of events is a function from worlds to sets of events).
The standard definition of (total) telicity is essentially the one proposed by Krifka (1998: 207):
(T) A property of events P is telic if and only if for all e and w, if Pw(e),
(T) any part of e e' such that Pw(e') is both an initial and a final part of e.
This presupposes that events form a part structure (a mereology) – events have parts.
Note that one event e1 can be a proper part of another event e2 in two distinct ways: it can be that
- (i) ithe temporal trace of e1, τ(e1), is a proper part of the temporal trace of e2, τ(e2), or that
- (ii) the temporal trace is the same but e1 is otherwise 'smaller' than e2
(for example, an event of singing a choir piece can have a proper part of the same type, say, if this is an event of singing the piece in the second soprano voice). This is the reason that the telicity definition (T) cannot just be about proper event parts but must be about something like final parts, which are in turn defined through temporal traces, also called runtimes.
Think of (T) as saying that if a telic VP is true of an event running over a certain time interval, it is false of any part of that event running over a proper sub-interval. You cannot 'shrink' the event.
It is a fact about natural language that VPs that are not telic tend to be not just atelic but the opposite, anti-telic. This is usually captured in a notion of divisive reference (the 'sub-interval property' in early work like Dowty 1979).
(D) A property of events P is divisive if and only if for all e and w, if Pw(e),
(T) any part of e e' is such that Pw(e').
This only works down to, and should be restricted to, a certain threshold level of granularity (for example, a swimming has parts so small that they do not qualify as swimmings).
There are many properties of events that are neither telic nor divisive, but few if any of them are expressed by VPs, in context anyway, where what is said tends to be one or the other.
Telic / Anti-telic diagnostics: measure adverbials with different prepositions, across languages
To a considerable extent, the telic or anti-telic aktionsart of a VP depends on its buildup, in particular on whether the argument is quantized – see Krifka (2001) The mereological approach to aspectual composition.
As opposed to aktionsart, aspect proper – also called viewpoint aspect – is a grammatical add-on.
When we do semantic composition, we normally consider one world at a time, writing w as an arbitrary constant for the current world of evaluation. Accordingly, what we treat is not the property of events expressed by a VP (its intension) but the set of events denoted by it at w (its extension at w). When this set of events creeps up the syntactic tree, it encounters an Aspect head (which can be covert in a language like Mainland Scandinavian).
Aspects relate events to times. Specifically – while still generally – what an aspect (or a reading of an underspecified aspect) does is transform the set of events coming from the VP into a set of times, sent off to a tense. The main distinction here is between the case where the output times include the runtimes of the input events and the case where it is the other way around – perfective versus (a sense of) imperfective.
Compare the English progressive with the simple past:
(1) In June 2018 she was writing her dissertation.
(2) In June 2018 she wrote her dissertation.
The difference is accounted for by a standard analysis of the progressive as an imperfective aspect and the simple, non-progressive as a perfective aspect:
(3) IPF denotes the function that maps a set of events E to the set of times t such that
(3) E has a member e such that t ⊑ τ(e)
(3) – formally: [[IPF]] = λEλt Ǝe E(e) ∧ t ⊑ τ(e)
(4) PF denotes the function that maps a set of events E to a set of times t such that
(3) E has a member e such that τ(e) ⊑ t
(4) – formally: [[PF]] = λEλt Ǝe E(e) ∧ τ(e) ⊑ t
The imperfective paradox...
Dowty, David (1979) Word Meaning and Montague Grammar. Dordrecht: Reidel.
Krifka, Manfred (1998) The origins of telicity. In Susan Rothstein (ed.) Events and Grammar, Dordrecht: Kluwer, 197–235.