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