The definition of Abhidhamma, from the Pali Text Society dictionary is as follows...
Abhidhammahttp://dsal.uchicago.edu/cgi-bin/philol ... :1726.pali
Abhidhamma [abhi + dhamma] the "special Dhamma," i. e., 1
. theory of the doctrine, the doctrine classified, the doctrine pure and simple (without any admixture of literary grace or of personalities, or of anecdotes, or of arguments ad personam), Vin i.64, 68; iv.144; iv.344. Coupled with abhivinaya, D iii.267; M i.272. -- 2
. (only in the Chronicles and Commentaries) name of the Third Piṭaka, the third group of the canonical books. Dpvs v.37; PvA 140. See the detailed discussion at DA i.15, 18 sq. [As the word abhidhamma standing alone is not found in Sn or S or A, and only once or twice in the Dialogues, it probably came into use only towards the end of the period in which the 4 great Nikāyas grew up.]
-- kathā discourse on philosophical or psychological matters, M i.214, 218; A iii.106, 392. See dhammakathā.
As can be seen, the PTS Dictionary cites two clearly distinct definitions for the term abhidhamma and the contexts in which each unique definition is used in different parts of the the Pali Canon and ancient commentaries.
Just as in English where one word can have multiple meanings, so it is in Pali. Classic examples of this in Pali include words like dukkha, dhamma, loka, the prefix abhi- and so on. When one of the words is used, it does not imply each-and-every-possible-definition as applicable or relevant in that instance. Likewise, when the word abhidhamma appears in the texts it does not relate to all possible definitions of that word simultaneously.
Thus, the quotations kindly provided by Kevin above which use the word abhidhamma, should be understood with respect to the definition provided by the Pali Text Society. Thus, they are definitions 2, 1, 1 and 1 respectively. Note also, that the capitalisation of the term in the second and fourth quotations is a little misleading as it is indicative of title case (and thus implying definition 2) when in actuality it is definition 1 that is appropriate as confirmed by the PTS reference.