Sri Jayatiirtha shows, in his pramANa paddhati, how arthApatti is not a separate pramANa but a different form of inference and is subsumable under inference. The proof is really simple and elegant.
Now, some issue silly comments, out of prejudices:
One such can be seen at the following in
http://lists.advaita-vedanta.org/archives/advaita-l/1996-July/005323.html :
"I think it is basically wrong to describe arthApatti as a special case of anumAna. A statement made as an arthApatti is something that *explains* the facts, not something that is directly inferred from the facts. But this will open up a completely different discussion on epistemology, so I don't want to go into it now".
arthApatti has been considered as a pramANa by advaita. pramANa is a means of knowledge (as generally accepted). So arthApatti, even in advaita, is not just an explanation of some facts, but a source of knowledge. Consider the standard example of arthApatti:
(i) Devadatta does not eat in day
(ii) he is not thin/weak etc.
(iii) Therefore Devadatta eats at night.
Now, to hold that (iii) is an explanation of facts (is it really?) and not a special case of inference is evidently wrong. Here's why: A Standard inference (in naiyyAyika's terms, not mAdhva) has five components (a loose translation):
a. pratijnA -- A Statement to be established. For example: This hill has fire on it.
b. hetu -- Reason. For, it has smoke.
c. udAharaNa -- Illustration. Just like the kitchen.
d. upanaya -- Generalization and application of the general rule to the pakSha. Wherever there is smoke, there is fire. and there is smoke on this hill.
e. nigamana -- Summary, conclusion. Therefore this hill has fire.
It is easy to see that the standard example given for arthApatti well fits this scheme of things:
a. pratijnA = Devadatta eats at night.
b. hetu = because he is not thin/weak though he does not eat in the day.
c. udAharaNa = just like a well-fed man (like me!)
d. upanaya = whoever eats well, is not weak.
e. nigamana = Therefore, Devadatta must be eating well, when it is not day i.e. night.
The essential point to note is this: In case of arthApatti, there is an application of a generic relation between two events/entities/qualities. This is true of inference too. There is no point in gimmicks saying that 'arthApatti is only explanative'. Every explanation, if not indulging in siddhasAdhanatA (establishing that which is already established), and if it aims to serve as a pramANa (means of knowledge), must bring out an inference.
Obviously, this elegance in approach is given up to accomodate prejudices.