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Abduction, or abductive reasoning, is the process of inference to the best explanation.
"Abduction" is sometimes used to mean just the generation of hypotheses to explain observations or conclusions, but the former definition is more common both in philosophy and computing.
The semantics and the implementation of abduction cannot be reduced to those for deduction, as explanation cannot be reduced to implication.
Applications include fault diagnosis, plan formation and default reasoning.
Negation as failure in logic programming can both be given an abductive interpretation and also can be used to implement abduction. The abductive semantics of negation as failure leads naturally to an argumentation-theoretic interpretation of default reasoning in general.
A more formal definition of abduction
In the context of knowledge level modeling discussed in [1], abduction is a way to find assumptions A which, when combined with a theory T, achieves a set of goals OUT without contradiction:
- EQ1: T ∪ A ∴ OUT
- EQ2: T ∪ A ¬∴ OUT
See examples of logical reasoning.
["Abductive Inference", John R. Josephson <jj@cis.ohio-state.edu>].
Charles Sanders Peirce
C. S. Peirce actually introduced this concept into modern logic. In his works before 1900 he mostly uses the term hypothesis meaning the selection of a known rule to explain a fact, e.g. discovering that the grass is wet and by using the known rule "if it rains, the street will get wet" to deduce that it has been raining.
In his later works he sees that in quite a few examples there was actually a different process described, namely that of making up a "new" rule to explain a new or surprising fact. This is the form he uses abduction from then on, and emphasises that abduction is the only logical inference which actually creates anything "new", thereby allowing creativity to enter.
He describes the process of science as abduction, deduction and implication,
and stresses that only in the abductive part new knowledge enters the process.
This is contrary to the use of abduction by a lot of people e.g. in the social science, who say that any puzzle solving is abducive reasoning, even if it is only choosing and trying out known rules. Abduction is creating new rules, not checking which of the known ones might fit a situation!
And, in contrast to many uses of the word abduction in the social science or artificial intelligence he also says that the actual process of generating a new rule is not "hampered" by logic rules. He keeps referring to an inbred ability of humans to get to a right inference, referring to an evolutionary biologists perspective that man has developed in nature and thereby developed an "instinct" to understand nature.
For Peirce, progress in science depends on the observation of the right facts by minds furnished with appropriate ideas (Tursman, 1987). Definitely, the intuitive judgment made by an intellectual is different from that made by a high school student. Peirce cited several examples of remarkable correct guesses. All success is not simply luck. Instead, the opportunity was taken by the people who were prepared:
a). Bacon's guess that heat was a mode of motion;
b). Young's guess that the primary colors were violet, green and red;
c). Dalton's guess that there were chemical atoms before the invention of microscope (cited in Tursman, 1987).
By the same token to continue the last example, the cosmological view that "atom" is the fundamental element of the universe, introduced by ancient philosophers Leucippus and Democritus, revived by Epicurus, and confirmed by modern physicists, did not result from a lucky guess. Besides the atomist theory, there were numerous other cosmological views such as the Milesian school, which proposed that the basic elements were water, air, fire, earth, etc. Atomists were familiar with them and provided answers to existing questions based on the existing framework (Trundle, 1994).
Peirce stated that classification plays a major role in making a hypothesis, that is the characters of phenomenon are placed into certain categories (Peirce, 1878b). Although Peirce is not a Kantian (Feibleman 1945), Peirce endorsed Kant's categories in Critique of Pure Reason (Kant, 1781/1969) to help us to make judgments of the phenomenal world. According to Kant, human thought and enlightenment are dependent on a limited number of a priori perceptual forms and ideational categories, such as causality, quality, time and space. Also, Peirce agreed with Kant that things have internal structure of meaning. Abductive activities are not empirical hypotheses based on our sensory experience, but rather the very structure of the meanings themselves (Rosenthal, 1993). Based on the Kantian framework, Peirce (1867/1960) later developed his "New list of categories." For Peirce all cognition, ranging from perception to logical reasoning, is mediated by "elements of generality." (Peirce, 1934/1960). Based upon the notion of categorizing general elements, Hoffman (1997) viewed abduction as a search for a mode of perception while facing surprising facts.
See also
References
[1] T. Menzies. Applications of Abduction: Knowledge-Level Modeling. November 1996.
[2] Yu, C. H. (1994, April). Induction? Deduction? Abduction? Is there a logic of EDA? Paper presented at the Annual Meeting of American Educational Researcher Association, New Orleans, LA. (ERIC Document Reproduction Service No. ED 376 173)
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