Understanding perfective aspect

[Ephraim]

You and others have given examples where the exact same action is described as telic or atelic, which suggests at the least that telicity involves the speaker taking a viewpoint. This can easily be conditioned by the language involved.

To put it succinctly: If you ask whether or not the sentence "John hit the bear" is telic, you're asking me if John's action had an innate conclusion. [...]

I agree as well; this is nicely put.

I definitely think telicity involves the speaker taking a viewpoint, as Zompist put it. I don't think the important part here is whether John's action in the real world had any innate conclusion. I would maybe say that the sentence "John hit the bear" is telic if it construes the action as having an innate conclusion. This is an important distinction.

Aktionsart is certainly not a property of real-world (or imagined-world) events by themselves. You can't really point to something and say "look, something telic is happening over there!" (well, I guess you could...). There are typically many different ways to describe the same real-world event linguistically. For example, "he is a smoker" and "he smokes every day" may very well describe the same state-of-affairs, but the first one construes it as a state and the second as a (recurring) activity (in Vendler's sense).

However, I wouldn't really consider Aktionsart to be a be a property of the linguistic expression itself either, even if it can have a lot of influence over grammar and word choice (and you could say that it can be encoded in the grammar or lexicon to some extent). For one thing, as has already been shown in this thread, the same exact linguistic expression can often have both telic and atelic interpretations, and the only way to tell which one is intended is from context.

Also note that the scenario construed by a linguistic expression can sometimes be broken up into multiple occasions, events or phases that may themselves have a different Aktionsart. The sentence "I used to eat up an entire bag of candy every day." probably construes an atelic scenario, since the same procedure is repeated every day without any innate conclusion, but the event that happens every day ("I ate up an entire bag of candy") does have an innate conclusion and should probably be called telic.

I'm not sure that I can really articulate this in an easy-to-understand way—and probably I don't fully understand this myself—but Aktionsart seems more than anything else to be a part of the way that we conceptualize or construe events through language. Or I guess the way we structure and package information about things that are and things that happen in a complex world, into something that can more easily be encoded in human language. It might be said to exist on a layer between the real world (or our perception of it), and the grammar and lexicon. It doesn't necessarily follow from this that concepts such as telicity are universal, they may be, at least in part, language-dependent or not fully coherent within one language.

Now, I don't think this is in any way a unique property of Aktionsart, this may be how semantics work in general. Someone who is more well-versed in cognitive linguistics than I am may have something clever to say about this (and possibly object to the way I use the term "construe").

I don't know if other conlangers had the same thought, but I had understood that Finnish used the partitive or accusative cases for objects because a phrase was telic/atelic. Instead, it seems that the phrase would telic/atelic due to which one was used, much in the same way that adding the definite article or time adverbials changes telicity in English. This, plus the understanding of telicity rising from an entire phrase rather than just from a given verb and the form used made me much more comfortable with the concept (even though I still struggle with it a bit!).

Well, given what I expressed above, I would generally favour the approach where, for the speaker/writer, the conceptualization of the scenario as atelic comes first (and at that point, it's not really a "phrase" since it's pre-linguistic in a sense) and the linguistic expression comes after this. With this approach, the choice of the partitive case is because the scenario construed is atelic (if that is the way Finnish works here). For the addressee, who interprets the linguistic expression, it's obviously the other way round.

If this has any basis in how human cognitive processes works, I do not know, I just find it to be a helpful way to think about this (and this might actually be a controversial topic at which I'm far from an expert).

I also find it fascinating that within the conlanging community, the Finnish accusative–partitive distinction seems to be the go-to example of telicity. I can only imagine that this is because of the prominent role that this distinction has on the Wikipedia article on telicity (it used to be more or less the only part of that article, see the history). I seem to recall that the podcast Linguitect referenced the bear-shooting examples as the standard examples when it comes to telicity (which I don't think is true in the wider linguistics community). Although the Finnish distinction is certainly interesting, I'm not sure that it's an ideal starting point for understanding telicity (if such a thing is possible), especially since Wikipedia talks about "telicity as an aspect".

Oh this helps a lot. Thanks. I should find the paper by Vendler that Ephrain alludes to.

It's a classic article from 1957 which can be found here:
https://semantics.uchicago.edu/scalarch ... dler57.pdf

Or here, which I think is the 1967 version ("with only minor changes"):
https://www.cs.brandeis.edu/~jamesp/con ... er-LOT.pdf

The article was highly influential, and it is definitely worth reading. Vendler's somewhat confusing terminology ("activity", "accomplishment", "achievement" and "state") is still used, although many authors have since expanded upon the model.

[Vardelm]

I'm not sure that I can really articulate this in an easy-to-understand way—and probably I don't fully understand this myself—but Aktionsart seems more than anything else to be a part of the way that we conceptualize or construe events through language. Or I guess the way we structure and package information about things that are and things that happen in a complex world, into something that can more easily be encoded in human language. It might be said to exist on a layer between the real world (or our perception of it), and the grammar and lexicon. It doesn't necessarily follow from this that concepts such as telicity are universal, they may be, at least in part, language-dependent or not fully coherent within one language.

That makes a good deal of sense, actually. I'd say there has to be some packaging of information in order to encode it in language.

I also find it fascinating that within the conlanging community, the Finnish accusative–partitive distinction seems to be the go-to example of telicity. I can only imagine that this is because of the prominent role that this distinction has on the Wikipedia article on telicity (it used to be more or less the only part of that article, see the history). I seem to recall that the podcast Linguitect referenced the bear-shooting examples as the standard examples when it comes to telicity (which I don't think is true in the wider linguistics community). Although the Finnish distinction is certainly interesting, I'm not sure that it's an ideal starting point for understanding telicity (if such a thing is possible), especially since Wikipedia talks about "telicity as an aspect".

I'd say it's just because of the way they encode it: through noun case. That makes it fairly explicit and easy to point to the morphological feature that encodes (or determines) telicity.

[Ephraim]

This thread is, or was originally, about understanding perfective aspect, so I was hoping that I might be able to contribute something on this subject. However, I don't think it's possible to understand aspect without understanding actionality, so I'm going to start with this subject.

Something about actionality

As mentioned above, I tend to think of the events or states construed by a linguistic expression as being somewhat separate both from the real or imagine world and from the linguistic expression itself.

The terminology for referring to the action construed by a linguistic expression is very disparate. Your can find terms such as event, situation, eventuality, action, state-of-affairs, scenario, process among others used with a variety of meanings. I will mostly use my preferred terminology here, and sometimes give examples of terminological variation. If you want to read more about this subject, be aware that different authors use different terminology.

The situation is the basic unit of action. This is more or less the action construed by a single verb constellation, with singular participants, and with no form of repetition, i.e. the action happens only once (see the basic-level verb constellation of Smith 1997). However, there can still be singular situations with multiple participants or on multiple locations, perhaps because many participants act together in some way (collectively).

Situations can be classified into different types based on their actionality. Actionality is actually my preferred to for what has been to referred to as Aktionsart earlier in this thread. Other terms for more or less the same basic idea are time schemata (Vendler 1957), lexical aspect, aspectual types (Croft 2012) and situation types (Smith 1997).

There are many different models of actionality. A common model, which I will more or less follow here, is to basically adapt Vendler's categories (Vendler 1957) and recognize three basic features: dynamicity, durativity and telicity. Situations can then be divided into states (static situations) and events (dynamic situations). Events can be further divided into activities (durative and atelic), accomplishments (durative and telic) and achievements (punctual and telic). Whether punctual events can be atelic or not kind of depends on your definitions of telicity, but some authors recognize semelfactives as a distinct separate type (Comrie 1976, Smith 1997). States are typically durative but point states ("It is 5 o’clock", "The sun is at its zenith") have also been recognized (see Croft 2012 p. 43, citing Mittwoch 1988). Some interesting overviews of different classifications are found in Christensen (1995) and Croft (2012).

Situations can have internal structure and involve a repetition of phases (see Cusic 1981). This is probably not that important for understanding aspect.

Situations can also be repeated themselves. Multiple situations may be repeated on one occasion, where they are in some way connected to each other. Situations may also be repeated over multiple occasions (again, see Cusic 1981). It is actually possible to introduce even more levels of repetition ("I used to eat two bags of candy every thursday of every other week of every other month of every third year"). It may also be necessary to distinguish habituality from other forms of repetition.

I use the term scenario to refer to the entirety of action. This is not a widely used term, and it doesn't seem to be that common to use a special term to distinguish the totality of action from a single situation (Cusic 1981 has the term "history", Hollenbaugh 2021 seems to use the term "eventuality").

It is very important to recognize that repetition can change the actionality of the scenario (see Smith 1997 ch. 2.1). "I knocked once at the door" construes a punctual scenario but "I knocked at the door for two hours" construes a durative scenario involving a repetition of punctual situations. "I ate up a bag of candy" construes a telic situation but "I ate up a bag of candy every day" construes an atelic scenario involving the repetition of telic situations.

Something about aspect systems

The term aspect is unfortunately used with a variety of meanings. The type of aspect that this thread is mostly about is what Smith (1997, especially ch. 4) refers to as viewpoint aspect. She describes viewpoint aspect as functioning like a camera to make the scenario (or situation in her words) visible to the receiver. Note that while explicit marking of actionality can frequently operate on the level of the situation (cf English "I ate up a bag of candy every day"), I think viewpoint aspect tend to operate on the level of the scenario. This is probably not without exceptions, though.

Now, we should recognize that even if the same label is used for some aspect found in different languages, there is obviously going to be differences between how they are used. I think we may broadly be able to recoginize the following idealized systems, but I do not claim that any language exactly follows any of these idealized systems and there may well be further types:

• Slavic-style perfective–imperfective, which is very sensitive to actionality. Punctual scenarios require the perfective (but note that repeated punctual events make a durative scenario). Durative atelic scenarios require the imperfective. Durative telic scenarios can take either the imperfective or the perfective. Static and habitual scenarios typically require the imperfective (since they are atelic and durative).
• Romance-style perfective–imperfective (or aorist–imperfect), which is less sensitive to actionality, although punctual scenarios still require the perfective. However, durative scenarios can take either aspects regardless of telicity, and this also includes static and habitual scenarios.
• English-style simple–progressive, which is very similar to Romance-style aspect, but static and habitual scenarios don't take the progressive.

The distinction between Romance-style and Slavic-style aspect is due to Dahl (1985). This is not a claim that Slavic or Romance languages have ideal Slavic-style or Romance-style aspect systems, and English probably doesn’t have an ideal English-style system either. From what I understand, the Russian aspect system is among the most Slavic-style, while I think Western Slavic languages may have more Romance-style characteristics. Some Slavic languages, most notably Bulgarian, have been claimed to combine both systems in the past tense (Lindstedt 1995), so that both Slavic-style perfective and imperfective verbs can be used with the imperfect (Romance-style past imperfective) and aorist (Romance-style past perfective) for a four-way contrast.

While I claimed above that in the ideal Romance-style system, static and habitual scenarios can take either perfective or imperfective aspect, some languages may require the imperfective here. There could also be some kind of dedicated stative or habitual marking.

Despite the cross-linguistic differences, the similarities between different perfectives (and the English style "simple") and imperfectives (or progressives) should be recognized.

Approaches to viewpoint aspect

As mentioned above, languages may require a specific viewpoint aspect for some actional types. But there are often some types of scenarios that can take more than one aspect, with some difference in meaning. So what is this difference? There are many approaches to this question.

One common approach to viewpoint aspect is to say that "the perfective looks at the situation from outside, without necessarily distinguishing any of the internal structure of the situation, whereas the imperfective looks at the situation from inside, and as such is crucially concerned with the internal structure of the situation" (Comrie 1976: 4). Dahl (1985: 74) calls this the 'totality' view of perfectivity. This view was mentioned by bradrn in the initial post of the thread, and I tend to agree that it's a bit hard to understand what this means in practice.

Below, I will instead present my favourite approach to viewpoint aspect – which from what I was able to tell is missing from this thread. There are nevertheless other approaches which are also interesting and worth checking out, see for example Smith (1997) and Johanson (2000). A honourable mention goes to the chronogenetic approach of for example Hewson & Bubenik (1997) and Hewson (2012), among other works by especially Hewson, although the approach goes back to Gustave Guillaume. I honestly don't think I understand this approach, especially its distinction between ascending and descending time, but I nevertheless find it fascinating.

One approach

Another very common approach, and also the one that I find the most enlightening, is to see viewpoint aspect as the relationship between some different time intervals. If I'm not mistaken, this is what is often called the Neo-Reichenbachian Model, following Klein (1994), but adopted from Reichenbach (1947). Let's first define the following:

• T_s: Scenario time, the time from and including the start of the scenario up to and including the end of the scenario. Huddleston (2002) calls this the time of situation or T_sit. It can also be called eventuality time, event time or E.
• T_r: Reference time, which is basically the viewpoint of the viewpoint aspect. This can be a single point in time or a duration of time. The reference time can be explicitly marked for example by a time adverb ("I ate some candies yesterday") or an adverbial clause ("I was eating some candies when he arrived"). The reference time of an answer might follow from a question (Q: "What were you doing when he arrived?" A: "I was eating some candies!"). However, the reference time is not always explicit. Huddleston (2002) uses the term time referred to or T_r. It is also frequently labelled simply as R. The terms topic time, T_T, or assertion time, T_A are also used (see Hollenbaugh 2021: 54 ff).
• T_o or T_d: Orientation time or deictic time. This is a point in time which is typically the time of the utterance, and for simplicity, we should assume that this is the case and only use the term orientation time or T_o. But see Huddleston (2002: 125 ff) for instances where this is not the case, and for the distinction between T_o and T_d. Terms such as utterance time T_u, speech time, speech event time, T_s or S, and origo, evaluation time or perspective time are also used (and distinguished), alongside O and T₀ (Hollenbaugh 2021: 54 ff).

With this approach, absolute tense marks the relationship between the reference time and the orientation time. The past tense marks that the reference time is anterior to the orientation time (T_r < T_o), the present that the reference time is simultaneous with the orientation time (T_r ⊇ T_o) and the future that the reference time is posterior to the orientation time (T_r > T_o).

Viewpoint aspect (and relative tense) mark the relationship between the scenario time and the reference time. Basically, the perfective aspect is used if if scenario time is entirely contained within the reference time (T_s ⊆ T_r), or at least if the endpoint of the scenario time is contained within it. If instead, the reference time is contained within the scenario time (T_s ⊇ T_r), the imperfective (or progressive) aspect is used. Languages may differ in how they treat scenario times that are equal to the reference time (T_s = T_r, see Hollenbaugh 2021: 68 ff and Gvozdanović 2012: 795). An anterior relative tense may be used when the scenario time is anterior to the reference time (T_s < T_r) while a posterior relative tense may be used then the scenario time is posterior to the reference time (T_s > T_r). The model can also be expanded to include the perfect/restrospective and prospective aspects.

The following illustrations from Glottopedia may be helpful (T_sit is my T_s):



Under this approach, it may also be said that the Slavic-style perfective requires not only that the reference time contains the scenario time, but also that the endpoint of the scenario time is material rather than simply temporal (cf. Lindstedt 1995). In other words, the scenario has to be telic, and when the scenario ends (within the reference time), it should have reached its telos and thus be finished rather than simply stopped. With a Romance-style perfective or English-style "simple", a temporal endpoint is sufficient.

For examples of this approach, see Klein (1994), Huddleston (2002), Gvozdanović (2012), and Hollenbaugh (2021).

References

• Christensen, Lisa (1995) Svenskans aktionsarter: En analys med särskild inriktning på förhållandet mellan aktionsarten och presensformens temporala referens
• Comrie, Bernard (1976) Aspect: An Introduction to the Study of Verbal Aspect and Related Problems
• Croft, William (2012) Verbs: Aspect and Causal Structure
• Cusic, David Dowell (1981) Verbal Plurality and Aspect (Dissertation)
• Dahl, Östen (1985) Tense and Aspect Systems (read here)
• Glottopedia, the articles on Aspect and Perfective.
• Gvozdanović, Jadranka (2012) Perfective and imperfective aspect, in Binnick, Robert I., The Oxford Handbook of Tense and Aspect (chapter 27)
• Hollenbaugh, Ian Benjamin (2021) Tense and aspect in Indo-European: A usage-based approach to the verbal systems of the Rigveda and Homer (read here
• Huddleston, Rodney (2002) The verb, in Huddleston, Rodney & Pullum, Geoffrey K. The Cambridge Grammar of the English Language
• Johanson, Lars (2000) Viewpoint operators in European languages, in Dahl, Östen, Tense and Aspect in the Languages of Europe
• Klein, Wolfgang (1994) Time in Language
• Lindstedt, Jouko (1995) Understanding perfectivity - understanding bounds (read here), in P M Bertinetto, V Bianchi , Ö Dahl & M Squartini (eds), Temporal reference, aspect and actionality
• Hewson, John & Bubenik, Vit (1997) Tense and Aspect in Indo-European Languages: Theory, Typology, Diachrony
• Hewson, John (2012) Tense, in Binnick, Robert I., The Oxford Handbook of Tense and Aspect (chapter 17)
• Mittwoch, Anita (1988) Aspects of English aspect: on the interaction of perfect, progressive and durational phrases. Linguistics and Philosophy 11:203–54
• Reichenbach, Hans (1947) Elements of Symbolic Logic
• Smith, Carlota S. (1997) The Parameter of Aspect, second edition (first edition published in 1991)
• Vendler, Zeno (1957) Verbs and Times, in The Philosophical Review, Vol. 66, No. 2. (Apr., 1957), pp. 143-160 (read here), also reproduced with only minor changes in Vendler, Zeno (1967) Linguistics in Philosogy (read here)

[bradrn]

This thread is, or was originally, about understanding perfective aspect, so I was hoping that I might be able to contribute something on this subject. However, I don't think it's possible to understand aspect without understanding actionality, so I'm going to start with this subject.

As always, thanks so much for the amazingly informative post! (You should write a tutorial at some point.) I mostly understand perfectivity at this point, but even so it really helped clarify things.

Now, we should recognize that even if the same label is used for some aspect found in different languages, there is obviously going to be differences between how they are used. I think we may broadly be able to recoginize the following idealized systems, but I do not claim that any language exactly follows any of these idealized systems and there may well be further types:

• Slavic-style perfective–imperfective, which is very sensitive to actionality. Punctual scenarios require the perfective (but note that repeated punctual events make a durative scenario). Durative atelic scenarios require the imperfective. Durative telic scenarios can take either the imperfective or the perfective. Static and habitual scenarios typically require the imperfective (since they are atelic and durative).
• Romance-style perfective–imperfective (or aorist–imperfect), which is less sensitive to actionality, although punctual scenarios still require the perfective. However, durative scenarios can take either aspects regardless of telicity, and this also includes static and habitual scenarios.
• English-style simple–progressive, which is very similar to Romance-style aspect, but static and habitual scenarios don't take the progressive.

The distinction between Romance-style and Slavic-style aspect is due to Dahl (1985). This is not a claim that Slavic or Romance languages have ideal Slavic-style or Romance-style aspect systems, and English probably doesn’t have an ideal English-style system either. From what I understand, the Russian aspect system is among the most Slavic-style, while I think Western Slavic languages may have more Romance-style characteristics. Some Slavic languages, most notably Bulgarian, have been claimed to combine both systems in the past tense (Lindstedt 1995), so that both Slavic-style perfective and imperfective verbs can be used with the imperfect (Romance-style past imperfective) and aorist (Romance-style past perfective) for a four-way contrast.

While I do like the terminology, my own view is that aspectual systems are not discrete but rather span over a whole continuum. Some events are prototypically perfective (they tend to be punctual, telic and involve change-of-state, Dahl p78), while others are prototypically imperfective (durative and atelic); aspectual systems are then just different choices in how to divide up the in-between space. Slavic-style systems draw the dividing line near prototypically perfective events, English-style systems draw it near prototypically imperfective events, and Romance-style systems are in-between, but of course there are many different possibilities for exactly where to draw the line. (I think Dahl’s Table 3.2 (p71) shows the continuum particularly nicely.)

Viewpoint aspect (and relative tense) mark the relationship between the scenario time and the reference time. Basically, the perfective aspect is used if if scenario time is entirely contained within the reference time (T_s ⊆ T_r), or at least if the endpoint of the scenario time is contained within it. If instead, the reference time is contained within the scenario time (T_s ⊇ T_r), the imperfective (or progressive) aspect is used. Languages may differ in how they treat scenario times that are equal to the reference time (T_s = T_r, see Hollenbaugh 2021: 68 ff and Gvozdanović 2012: 795). An anterior relative tense may be used when the scenario time is anterior to the reference time (T_s < T_r) while a posterior relative tense may be used then the scenario time is posterior to the reference time (T_s > T_r). The model can also be expanded to include the perfect/restrospective and prospective aspects.

I really like this approach! It’s elegant and fits the data well. Also, it seems to corroborate my ideas of prototypically perfective and imperfective events: the prototypically perfective event would be one where T_s is of negligible length, so T_s ≪ T_r always, whereas the prototypically imperfective event would have T_s such that T_s ≫ T_r always.

(One oddity in that last claim is that, when thinking of events of maximal T_s, stative events immediately come to mind, whereas my ‘prototypical imperfective’ is closest to the English progressive. But that can be resolved by noting that stative events uniquely can be of any length, from point to infinity — in a way, they are midway between the prototypical events. By contrast, progressive events are those where you just don’t need to refer to the event as a whole, guaranteeing that T_s ≫ T_r.)

[Ephraim]

The idea that some types of scenarios are prototypically used with the perfective or imperfective, based on their actionality, is of course not incompatible with the idea that the perfective and imperfective have some sort of prototypical semantics that's not related to the actionality of the scenario.

If we start with a Neo-Reichenbachian model for the prototypical semantics of the perfective and imperfective, we may be able to give some explanation for why certain types of scenarios are typically used with certain aspects. Let's assume that:

• The prototypical perfective aspect is used if the scenario time is properly included in the reference time (T_s ⊂ T_r).
• The prototypical imperfective aspect is used if the scenario time properly includes the reference time (T_s ⊃ T_r).

By 'properly includes', I mean that T_s and T_r are not coextensive (T_s = T_r), i.e. they are not exactly equal, one has to be smaller than the other. The case when they are coextensive may be assigned to either aspect, depending on the language, or could potentially be assigned to a third aspect (not sure if there are any good natlang examples of this). We may hypothesize that T_s = T_r is more likely to be assigned to the least marked aspect, but I'm not sure if this is actually true. There is also the case when only one endpoint of the scenario time (the start or the end but not both) is included in the reference time, but let's leave that aside for the moment.

From the assumption above, we can conclude that punctual scenarios are incompatible with the prototypical imperfective since a scenario that is construed as a single point in time can't properly include the reference time. This is obviously in line with what we observe in natural languages. This also largely explains the rarity of present perfectives (sometime referred to as 'the present perfective paradox'). But note that if a language uses the imperfective for the coextensive case (T_s = T_r), the the imperfective is actually compatible with punctual scenarios if the reference time is also punctual.

We may also conclude that atemporal or permanent scenarios that don't really have a beginning or an end are incompatible with the prototypical perfective, since they can't be properly included in the reference time even if it is infinite (but they may be coextensive).

However, apart from this, most scenarios are actually compatible with both the prototypical perfective and imperfective. While static scenarios lack an inherent or natural endpoint, they may still have a beginning and an end. States are not necessarily even that long-lasting, some ("she is hungry") may be quite transitory. Static scenarios that have a beginning and an end are compatible with both the prototypical imperfective and perfective, and are not that different from atelic dynamic scenarios. However, it may be necessary to distinguish between different types of states because some ("she is from France") may last at least over the life-time of the subject, and possibly beyond that. Cf the distinction between stage-level predicates and individual-level predicates.

Now, even though most scenarios are in principle compatible with both the prototypical perfective and imperfective, they are certainly not equally likely to occur with a given aspect. If we were to analyse some actual discourse and try assign a prototypical perfective or imperfective to different scenarios, we would probably find significant statistical differences.

This is more of a guess on my part, but perhaps we could come up with a hierarchy similar to this one, from statistically most likely to use the prototypical imperfective to most likely to use the prototypical perfective:

• scenarios involving permanent states, properties or generic statements
• > habitual scenarios or long-lasting static scenarios
• > scenarios involving repetition over an unbounded number of occurrences ('frequentatives')
• > short-lasting static scenarios
• > scenarios involving unbounded repetition on a single occurrence ('iteratives')
• > durative atelic dynamic scenarios (activities), not involving repetition
• > durative telic dynamic scenarios (accomplishments)
• > punctual scenarios (achievements and semelfactives)

This hierarchy probably strongly resembles the idea of starting from 'prototypically perfective and imperfective events/scenarios', the difference being that it should (properly) be derived statistically from use of the Neo-Reichenbachian prototypes, rather than from a priori assumptions.

Of course, a language could deviate from the Neo-Reichenbachian prototype above, where the choice of aspect is in principle unrelated to actionality and only based on the relationship between T_s and T_r, and have some actionalities require the perfective or imperfective regardless of the relationship between T_s and T_r. This could possibly be based on the actionality of the situation rather than the entire scenario or even be a lexical property inherent in the verb. If this is the case, we may expect that the split or splits should occur somewhere along the hierarchy above and that the types of scenarios that are in the middle are more likely to allow for a 'free aspect' based on the relationship between T_s and T_r.

For the types of scenarios at either end of the hierarchy, there are at least three possible strategies for a 'fixed aspect':
1. Always assign the most likely aspect. For example, habitual scenarios, states and atelic dynamic scenarios may always take the imperfective. If I'm not mistaken, this is what Russian does most of the time.
2. Always assign the least marked aspect. It may be counter-intuitive that English should not use the progressive (imperfective-like) with states and habitual scenarios, but we may make sense of this from the perspective that the English progressive is highly marked, and it may be uneconomical to use it in cases where the prototypical perfective would be rare.
3. Always assign some sort of special aspect, like a dedicated habitual or stative aspect.

Note that languages may be quite flexible about allowing for readings with different actionalities without any special marking. This is certainly the case with English. The choice of aspect may influence what readings are available for a scenario. For example, in English the progressive may force a durative reading of the scenario, often through event repetition in the case of semelfactive events ("she was knocking on the door") or by referring to the run-up phase of achievements rather than the punctual event itself ("he was dying"). A perfective may have 'inceptive' or 'ingressive' uses, especially to refer to entering into a state (a telic punctual or possibly durative event) rather than to the state itself. What reading are made available by the different aspects can be explained within the Neo-Reichenbachian model, but it is important to distinguish this phenomenon from the prototypical use of the aspect.

While I do like the terminology, my own view is that aspectual systems are not discrete but rather span over a whole continuum. Some events are prototypically perfective (they tend to be punctual, telic and involve change-of-state, Dahl p78), while others are prototypically imperfective (durative and atelic); aspectual systems are then just different choices in how to divide up the in-between space. Slavic-style systems draw the dividing line near prototypically perfective events, English-style systems draw it near prototypically imperfective events, and Romance-style systems are in-between, but of course there are many different possibilities for exactly where to draw the line. (I think Dahl’s Table 3.2 (p71) shows the continuum particularly nicely.)

Right, I didn't mean to suggest that all aspect systems can be neatly categorized into these three idealized systems, it's possible that most can't. In any case, I think the ideal Romance-style system described in my previous post more or less has the a Neo-Reichenbachian prototypical perfective or imperfective (but maybe not both).

And as mentioned, I think the hierarchy derived above may resemble your idea of a continuum between 'events that are prototypically perfective' and 'events that are prototypically imperfective', except that it is starting from other assumptions.

However, feel free to elaborate on your approach to aspectual systems. For example, is there some way to handle the 'free choice' of aspect, e.g. English "I was the bag of candy" vs "I was eating the bag of candy"?