[sci.logic] abduction vs. induction

marquis@crin.crin.fr (Pierre MARQUIS) (05/17/89)

Could somebody tell me what is the difference between "abduction" (this last
term was apparently introduced by Alan Bundy) and "induction" ?

Please, send the replies to my mail address.
Many thanks in advance,

Pierre Marquis
CRIN (Centre de Recherche en Informatique de Nancy)
Campus Scientifique
B.P. 239
54506 - Vandoeuvre-les-Nancy CEDEX
France

sarrett@ics.uci.edu (Wendy Sarrett) (05/17/89)

"abduction" can be thought of in two ways. The first is generating
explanations from a conclusion - taking a conclusion and using
background information to build a "proof tree" leading too the
conclusion. The second way to think about it is as the opposite of
deduction i.e. if you have A -> B then you turn the arrow around and
when you see B, you infer that A must be true.

"induction" is the process of generalizing from lots of examples. For
example, suppose you see a number of examples of ducks and they are
all grey ( isa-duck -> grey) then you would conclude for all ducks,
isa-duck -> grey.  Note that there is also induction in mathematics
where if you can show (where A is a set) (1 in A) and (n in A) -> (n+1
in A) then you can conclude for all n, n in A.

Note that both "abduction" and "induction" are not "safe" forms of
inference as "deduction" is. (i.e. you can't be 100% certain your
inference is correct)

Hope this answers your question,
Wendy 
(sarrett@ics.uci.edu)
Department of Information and Computer Science
University of California, Irvine

punch@melon.cis.ohio-state.edu (William F Punch) (05/17/89)

In article <1480@crin.crin.fr> marquis@crin.crin.fr (Pierre MARQUIS) writes:
>Could somebody tell me what is the difference between "abduction" (this last
>term was apparently introduced by Alan Bundy) and "induction" ?
>
>Please, send the replies to my mail address.
>Many thanks in advance,
>
>Pierre Marquis
>CRIN (Centre de Recherche en Informatique de Nancy)
>Campus Scientifique
>B.P. 239
>54506 - Vandoeuvre-les-Nancy CEDEX
>France


The first use of the term "abduction" was by the
philosopher/mathmatician Charles Sanders Peirce 1839-1914 (pronounced purse).
Unfortunately I don't have my Peirce stuff handy but I use the
following quote from his works in my work on abductive inference.


\begin{quote}
The first stating of a hypothesis and the entertaining of it, whether
as a simple interrogation or with any degree of confidence, is an
inferential step which I propose to call {\em abduction} [or {\em
retroduction}]. 

...

Long before I first classed abduction as an inference it was
recognized by logicians that the operation of adopting an explanatory
hypothesis--which is just what abduction is--was subject to certain
conditions. Namely, the hypothesis cannot be admitted even as a
hypothesis, unless it be supposed that it would account for the facts
or some of them. The form of inference, therefore, is this:

\begin{tabular}{l}
	The suprising fact, C, is observed;\\
	But if A were true, C would be a matter of course,\\
	Hence, there is reason to suspect that A is true.
\end{tabular}
\end{quote}

Excuse the tex-isms.

Other useful places to look for discussions are 


Gilbert Harmon,"Inference to the Best Explanation", Philosophical
Review (1965)

John Josephson, "Explanation and Induction", Dissertation, Ohio State,
1982. 


Charniak and McDermot make mention of abduction throughout their AI
book and a number of researchers do research in the area (Reggia,
Josephson, Charniak, Pearl etc.)

As for the difference between abduction and induction, the discussion
is more complicated. I think the most concise thing to say is that
abduction is a different cut on logic than induction or deduction.
Abduction is driven by trying to explain a set of facts based on
available hypotheses. It is often typified by method of a detective
solving a crime, i.e. here are the crime clues (to be explained) and
here are the facts I can use to explain them.  What is the best
explanation of these clues (in terms of plausiblity, consistency,
whatever parameters you choose) using these facts that I can come up
with.

In finding the explanation, one may use deduction (deriving true
conclusions from premises) or induction (populations from samples) but
one is driven by the process of explanation. How's that?
						>>>Bill<<<


p.s. An interesting, but not always easy to follow (or useful), book
on the detective, Peirce, abduction etc. is 

The Sign of Three, Edited by Eco and Sebeok, Indiana Universtiy Press, 1983
-=-
 There is no such thing as a problem    *	     >>>Bill Punch<<<
 without a gift for you in its hands. 	*	  punch@cis.ohio-state.edu
 You seek problems because you need	*         ...!att!osu-cis!punch
 their gifts.		R. Bach 	*  2036 Neil Ave;OSU;Columbus, OH 43210

rayt@cognos.UUCP (R.) (05/19/89)

In article <14820@paris.ics.uci.edu> Wendy Sarrett writes:
 
<>"induction" is the process of generalizing from lots of examples. For
<>example, suppose you see a number of examples of ducks and they are
<>all grey ( isa-duck -> grey) then you would conclude for all ducks,
<>isa-duck -> grey.  Note that there is also induction in mathematics
<>where if you can show (where A is a set) (1 in A) and (n in A) -> (n+1
<>in A) then you can conclude for all n, n in A.
 
<>Note that both "abduction" and "induction" are not "safe" forms of
<>inference as "deduction" is. (i.e. you can't be 100% certain your
<>inference is correct)

Clearly the first form of induction given is not a logically valid
deduction. I am surprised to here that the SECOND isn't, since MANY
mathematical proofs rest upon it. Have I perhaps misunderstood your
assertion?

						R.
-- 
Ray Tigg                          |  Cognos Incorporated
                                  |  P.O. Box 9707
(613) 738-1338 x5013              |  3755 Riverside Dr.
UUCP: rayt@cognos.uucp            |  Ottawa, Ontario CANADA K1G 3Z4

vdasigi@silver.wright.edu (Venu Dasigi) (05/20/89)

The following is the way Peirce himself characterized them [Peirce, 31].

Starting with

1. A --> B (if a sample is from this bag, the sample is white.)
2. A (this sample s is from this bag.)
3. B (the sample s is white.)

Deduction amounts to concluding 3 from 1 and 2.
Induction amounts to concluding 1 from 2 and 3.
Abduction amounts to concluding 2 from 1 and 3.

From this simple description, it may be observed that induction involves
generalizing from specific observations, while abduction involves plausibly
explaining facts or observations. While abductive and inductive "conclusions"
are not necessarily valid (and often referred to as "assumptions"), Peirce
notes that abduction and induction are constructive unlike deduction.

Peirce, C.S., 31: Collected Papers of Charles Sanders Peirce, Vol. 2:
Elements of Logic, Chapter 5, Hartsthorne, C. and P. Weiss (Eds.) Harvard
University Press, Cambridge, MA, 1931.

--- Venu Dasigi
Venu Dasigi      CSNet: vdasigi@cs.wright.edu
US Mail: Dept. of CS&Eng, Wright State U, 3171 Research Blvd, Dayton, OH 45420





Dr. Venu Dasigi      CSNet: vdasigi@cs.wright.edu
US Mail: Dept. of CS&Eng, Wright State U, 3171 Research Blvd, Dayton, OH 45420

flach@kubix.UUCP (Peter Flach) (05/24/89)

In article <526@thor.wright.EDU> vdasigi@silver.UUCP (Venu Dasigi) recalls
Peirce's beautiful characterisation of deduction, induction and abduction:

>Starting with
>
>1. A --> B (if a sample is from this bag, the sample is white.)
>2. A (this sample s is from this bag.)
>3. B (the sample s is white.)
>
>Deduction amounts to concluding 3 from 1 and 2.
>Induction amounts to concluding 1 from 2 and 3.
>Abduction amounts to concluding 2 from 1 and 3.

The formulation of induction given here, brings into mind a problem that
has been bothering me for some time. Given premises A and B, why should
I prefer the inductive conclusion A --> B over B --> A (any white sample
is from this bag)? The same problem arises with the prototypical
crows-argument: seeing a number of black crows might amount to the
inductive conclusion, that everything that is black is a crow. Of
course, this hypothesis would be falsified by the observation of a black
non-crow, rendering the set of premises non-symmetrical. But it seems to
me that any set of premises of the form
	{A(a)&B(a), A(b)&B(b), ...}
give equal evidence for two possible inductive hypotheses:
	forall(x) A(x) --> B(x), and
	forall(x) B(x) --> A(x).
Perhaps the introduction of a typed logic could help: if A is treated as
a type, the inductive conclusion would be
	forall(x:A) B(x)

Any comments on this?
--Peter

Peter A. Flach                             Institute for Language Technology
UUCP: ..!mcvax!kubix!flach                 and Artificial Intelligence (ITK)
BITNET: flach@htikub5                      Tilburg University,   PObox 90153
(+31) (13) 66 3119                         5000 LE  Tilburg, the Netherlands