One experience with the workshop (and in the above mentioned
discussion) is that the terms induction and abduction are very
overloaded. As written in the report, in the workshop two main schools
emerged. These schools use the same terminology (induction,
abduction) to cover different forms of reasoning. In particular,
"abduction" in one, more "philosophically" oriented school covers a
spectrum of different forms of reasoning including "induction"
according to this first school and both "abduction" and "induction"
considered in the other, "empirically" oriented school.
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 [1] 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.
Best regards,
-- Marc Denecker
[1] Marc Denecker, Bern Martens and Luc De Raedt, "On the
Difference between Abduction and Induction: A Model Theoretic
Perspective", ECAI96 workshop on Abductive and Inductive Reasoning,
1996.