# Abductive reasoning

Abduction, or abductive reasoning, is reasoning based on the principle 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 in artificial intelligence 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.

 Contents

## 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:

[itex]EQ_1: T \cup A \to OUT[itex]
[itex]EQ_2: T \cup A \neg \to OUT[itex]

See examples of logical reasoning.

["Abductive Inference", John R. Josephson <jj@cse.ohio-state.edu>].

## History of the concept

The American philosopher C. S. Peirce introduced this concept into modern logic. In his works before 1900, he mostly uses the term hypothesis to mean 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. This is an example of inference to the best explanation.

In his later works, he realises that in quite a few examples a different reasoning process is involved: namely that of making up a "new" rule to explain a new or surprising fact. This is the sense in which he used abduction from then on, emphasising 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 sciences, who say that any puzzle solving is abductive reasoning, even if it is only choosing and trying out known rules. Abduction according to Peirce is about 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 communities 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 produce a correct inference, referring to the evolutionary theory 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 armed with the appropriate ideas (Tursman, 1987). Obviously, 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 our last example, the cosmological view that the 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).

This article was originally based on material from the Free On-line Dictionary of Computing, which is licensed under the GFDL.

## 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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