When including the following examples from Cicero in a too long! answer to a previous post, a terminological question came to my mind: How would one classify those constructions marked in bold below? As "Ablative Absolutes (AAs)"? According to Pinkster's (1990: 117-118; Latin syntax and semantics) definition of AA ("I assume that the ablative absolute construction is in reality nothing else than a Dominant participle construction functioning as a satellite <i.e. adjunct: Mitomino> with regard to the remainder of the predication"), it seems that these adjunct ("satellite", in his terms) dominant participle constructions could be said to fall under the set of AAs.

Ceteris enim semper bene gesta, mihi uni conservata re publica gratulationem decrevistis. (Cic. Catil. 4, 20) ‘For you have passed votes of congratulation to others for having governed the republic successfully, but to me alone for having saved it.' (C. D. Yonge, 1856, Perseus site).

Mihi togato senatus non ut multis bene gesta, sed ut nemini conservata re publica, singulari genere supplicationis deorum immortalium templa patefecit. (Cic. Pis. 6.6) ‘Though I was only clad in the garb of peace, the senate, by an unprecedented sort of supplication, opened the temples of the gods in my honour; not because I had successfully governed the republic, that being a compliment which had been paid to many, but because I had saved it, that being an honour which has never been conferred on any one.’ (C. D. Yonge, 1891, Perseus site).

However, intuitively speaking, these participial constructions do not seem to function as typical AAs like Urbe capta, hostes fugerunt (or like the ones that are typically found in Latin grammars: e.g. see here). It is true that both bene gesta re publica and urbe capta function as adjunct predications in the examples above but the former is not as "absolute" as the latter... It seems that the participial constructions exemplified above are to be descriptively classified as "causal adjuncts" but they are not as "peripheric" as the typical AAs: the former are Verb Phrase (VP) modifiers, whereas the latter ("true" AAs) are sentential modifiers. In this sense, these participial constructions are more similar to the interesting case discussed in this post than to the typical AAs: i.e. they are not sentential modifiers but rather XP(hrase) modifiers, where "XP" can be an Adjective Phrase (AdjP), like the one discussed in that post (victa serpente superbus), or a Verb Phrase (VP), like the ones discussed in the present question. For those of you who are teachers of Latin: please feel free to let me know your experience when you have to explain the syntax of examples like the ones above from Cicero. The former example is from IV Catilinarian, so probably some of you will have dealt with this example in (on?) some occasion. Thanks!