More on arthApatti...

This page: http://www.kamakoti.org/hindudharma/part13/chap3.htm has the Late Kanchi swami justify why arthApatti is not subsumed under anumAna. He writes:
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Our Sastras give a clear idea of arthapatti through an illustration. "Pino Devadatto diva na bhunkte". What does the statement mean? "The fat Devadatta doesn't eat during daytime". Though Devadatta does not eat during daytime, he still remains a fat fellow. How? We guess that he must be eating at night. There is something contradictory about an individual not eating and still not being thin. Here arthapatti helps us to discover the cause of Devadatta being fat. Our guess that he eats at night does not belong to the category of anumana. To make an inference there must be a hint or clue in the original statement itself. There must be a "linga" like smoke from fire, thunder from clouds. Here there is no such linga.
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There are two wrong points: one is the wrong expectation that there must be a hint or clue in the original statement itself. Strictly speaking, the naiyyAyika doesn't expect this. The naiyyAyika expects pakShadharmatA, hetu among other things. Technically, there is no such thing as a 'clue' or 'hint'.

Secondly, it is wrong to say that there is an absence of hetu (linga) in the case of arthApatti. The linga in this case is: the impossibility of a normal man not eating at all, and still being fat. That could be used for a dUShanAnumAna. For sAdhanAnumAna, it could be: man eating at night is fat. It shouldn't be difficult to put this in the proper vibhaktyanta to make it a hetu. Strictly speaking, a hetu or linga is NOT a clue or hint.

Therefore arthApatti is a different form of anumAna.