Mike Aubrey works for Logos Bible Software and Wycliffe Bible Translators, and he blogs at Koine-Greek. He wrote the chapter on the Perfect Tense in the book Linguistics and New Testament Greek (see also here). This post mostly summarizes his contribution, which you can also find in draft form at his academia.edu page.
There is debate about what the semantics of the perfect tense (mentioned also in my previous post), which is why there is a chapter on it in a book on NT Greek. Another new publication also deals entirely with the perfect tense, presenting different viewpoints (Porter, Fanning, Campbell): Perfect Storm.
Just for comparison’s sake, here is what von Siebenthal says about the perfect:
Generally speaking, the (augmentless) indicative perfect combines the (conspicuous or marked) resultative aspect (194k) with the present tense. Basically, the focus is on a “situation” in the present (as seen from the speaker’s/writer’s vantage point). In most cases this “situation” is a result: something that took place in the past continues to have an effect in the present, an effect usually connected with either the subject entity or the object entity. [There are exceptions, but…] Generally speaking, however, the indicative perfect refers not only to the present result but also to the past “action” that has led to it.p. 329
The Cambridge Grammar of Classical Greek defines it this way:
The perfect indicative signifies that an action has been completed in the past and that the effects of that action are in some way relevant in the present; frequently it expresses a more or less permanent state in the present which exists as the result of a completed action in the past.p. 420, §33.34
It seems to me that these two definitions basically agree with the traditional view of the perfect: past action with present results. Aubrey surveys different definitions (not those above), and finds that several NT scholars (Wallace, Black, Croy) echo this common definition, while other scholars (Porter and Decker) interpret the Greek perfect as conveying stative aspect without any attention to a past action that engendered the current state. And then there’s Constantine Campbell (see my previous post), who (in Aubrey’s words) classifies the perfect as “another imperfective aspect with the additional heightened proximity” (p. 59).
Aubrey introduces two concepts that he thinks will help explain the perfect: event structure and transitivity (pp. 59–65).
Aubrey uses the example of the Manipuri language (relying on this grammar), which is rich in verbal aspects. “English speakers can express these same phases, but we do so with lexical items—’begin,’ ‘become,’ ‘stop’—rather than aspect markers” (p. 63).
Aubrey (pp. 66–67) points out that some verbs do not usually form perfects: stative verbs (but some do: pp. 76–80), activity verbs, and semelfactive verbs (he provides lists for each category). “The remaining verbs, those that do inflect a perfect, nearly all involve a change of state: one participant is in a different state at the end of the event” (p. 67).
Then we get a lengthy section (pp. 68–80) with plenty of examples of the perfect of a verb compared to the same verb in the aorist and the present, and these examples are classified in terms of their transitivity: are they highly transitive (e.g., “smash”) or do they display low transitivity (e.g., “see”)? Aubrey shows how the perfect functions with these different verbs.
It’s hard to summarize those points rather than simply reproducing them, so I’ll just leave it there. I think this paper is a pretty good presentation of the perfect tense which helps explain some of its nuances.