Induction, Deduction, Abduction

[Cesare Tinelli]

You may want to have a look at Michalski's paper [1]. Although questionable at
times, it is a nice and comprehensive treatment of the issues you are
interested in.
Hope it helps.

Cesare

[1] R.S. Michalski, Toward a unified theory of learning,
Proc. of the 1st World Conference on the Fundamentals of AI, 1991

[Dan Ventura]

I am trying to understand at what level induction, deduction, and
abduction are different with respect to machine learning/intelligence.
Clearly, induction and deduction are unique techniques in the field
of mathematics. However, it seems to me that at least at some level
they are at least very similar when it comes to machine learning. For
example, both use a set of known "facts" to produce new facts/knowledge.
In some sense, both methods will have a "proof" for any new facts/knowledge
so produced. I know this is simplistic, but I need to start this discussion
somewhere.

Also, I am just becoming familiar with the term abduction. One definition
I have seen goes like this:
D is a set of facts
if H were true, it would explain D
no H' would explain D better
thus H must be true.
I am very fuzzy on this still, but this seems very much like an inductive
learning approach, where H is "better" that H' according to whatever bias
the learning employs.

Comments on any of this?
How about abduction and deduction?
Are there any other "uctions" out there to know about?

Dan Ventura
--
Dan Ventura | email: d...@axon.cs.byu.edu
Computer Science Department | phone: (801) 378-5498
2224 TMCB | fax: (801) 378-7775
Brighma Young University | web: http://synapse.cs.byu.edu/~dan/dan.html
Provo, UT 84602

[Edgar Sommer]

In <3smt33$c...@hamblin.math.byu.edu> Dan Ventura <dan@axon> writes:

>I am trying to understand at what level induction, deduction, and
>abduction are different with respect to machine learning/intelligence.

just a quick way of keeping the three apart that i've found
useful over the years:

inference involves 3 things: premise, implication & conclusion

A --> B
deduction = + + -
induction = + - +
abduction = - + +

i.e. in deduction, you are given the premise and the implication, and
you infer the conclusion.

in induction, you have both premise and conclusion, and infer the implication
(the rules).

hope this helps,
eddi

ps: it's just a mental aide -- not an excuse for disregarding all the literature

[Cameron Shelley]

I haven't the opportunity to respond to your post in detail, but you
may find it helpful to look at the bibliography on abductive inference
on the Computational Epistemology Lab Web site:

http://beowulf.uwaterloo.ca/

Check out the "bibliographies" section. Hope this helps!

</dev/cam
--
Cameron Shelley - Department of Philosophy - University of Waterloo
Email: cpsh...@watarts.uwaterloo.ca - Phone: (519) 888-1211 x2555
Me: <URL:http://watarts.uwaterloo.ca/~cpshelle>
CEL: <URL:http://beowulf.uwaterloo.ca/>
Dept: <URL:http://watarts.uwaterloo.ca/PHIL/cpshelle/philosophy.html>

[Darryl N Davis]

The simplest explanation I have:

Given the three sentences:
A. Socrates was a man
B. All men are mortal
C. Socrates was mortal.

Deduction infers C from A and B.
Induction infers B from A and C
Abduction infers A from B and C.

PS There are so many important 'uctions out there/here eg seduction, reduction...

--
Dr. Darryl Davis E-mail: d...@uk.ac.bham.cs
Dept. of Computer Science, Tel: (+44) 021 414 4773
University Of Birmingham, Fax: (+44) 021 414 4281
Birmingham, B15 2TT. UK. Telex: 333762 UOBHAM G

[John Josephson]

Have a look at

Josephson, J. R., & Josephson, S. G. (Eds.). (1994). Abductive
Inference: Computation, Philosophy, Technology. New York: Cambridge
University Press.

.. jj

[B Chandrasekaran]

If you are putting a bibliography together, don't forget the recent book,

Abductive Inference: Computation, Philosophy, Technology
by John and Susan Josephson, Cambridge University Press.