I believe that the two schools provide useful and complementary perspectives on related forms of reasoning. Evidently, it would be preferable if the terminology would be disambiguated. The workshop did certainly an excellent job in pointing out these differences in the use of terminology. I will refer to "philosophical" respectively "empirical" "induction"/"abduction" whenever necessary (*though there are certainly also many different variants within each of the schools*).
According to John Josephson, exponent of the philosophical school, abduction is "inference to the best explanation". This is an extremely general definition and covers a spectrum of different forms of reasoning; even (human) scientific discovery or scientific theory formation can be and is viewed as "abduction". Einstein's creation of relativity theory is an inference to the best explanation (according to certain criteria, probably not easy to make explicit) and hence an abduction.
This is an interesting perspective, and it appears from the work of Josephson presented at the workshop (and other members of the philosophical school) that a number of interesting points can be make on this level of generality. One important point is about the relationship between "explanation" and "causality" (see also his recent comment on the relationship between flu and body aches). Another point is on how "induction" can be seen as a form of "abduction".
On the other hand, inevitably such a general notion of abduction covers forms of reasoning which can be intuitively and formally distinguished. A number of papers in the workshop attempt to provide more refined and less general frameworks to formalise and classify different forms of "philosophical abduction". This second school seems more empirically oriented in the sense that most of the work aims at studying and formalising abduction and induction as it appears in "empirical" AI-sciences; i.e. these domains of AI, where abduction and induction have been applied and have been implemented.
Our contribution to the workshop should be categorised within the second school. The notions of induction and abduction formalised in our abstract, can be seen both as instances of "philosophical abduction". Because we restrict to less general forms of reasoning, we are able to distinguish these more restricted notions of induction and abduction in an intuitively appealing model theoretic way, using a possible world semantics. The framework has not the ambition to cover (human) scientific theory discovery. Even though scientific discovery is being investigated within the machine learning community, this process in its full generality is not understood well, as it seems to involve many different forms of reasoning, including hypothesis formation, esthetical and empirical evaluation of hypotheses, knowledge acquisition, belief revision, paradigm switch, etc..
The philosophical school attempts to capture general characteristics of common forms of reasoning in a very general framework; the other aims at clearly and formally separating certain subforms of this reasoning. Obviously, both aims are respectable and complementary. For example, it is interesting that, as observed in our paper, in AI-applications of (empirical) abduction, the domain theory used in general does represent causality information. This is the case in typical abduction applications such as diagnosis, planning in the event calculus, natural language understanding. This observation supports the claims about the relation between abductive explanation and causality in the philosophical school.
The report mentions about the second school that "in this (perhaps extreme) view we should not expect that there are Platonic ideals of abduction and induction that we are trying to capture but rather that abduction and induction are simply processes that are needed for solving practical problems.".
I disagree. It is not because one limits the notions of abduction and induction to the ones that appear in "empirical AI-sciences", that there would not be a Platonic ideal underlying these frameworks. In our case, there is certainly a Platonic ideal: we use possible world semantics to formalise the differences between induction and abduction with a Platonic ideal in mind: one possible world is seen as a Platonic abstraction of a possible real state of the world and a possible world model is seen as a Platonic abstraction of the very notion of "knowledge" itself.