Abductive reasoning

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Abduction is a kind of logical inference described by Charles Sanders Peirce as "guessing".[1] The term refers to the process of arriving at an explanatory hypothesis. Peirce said that to abduce a hypothetical explanation a from an observed surprising circumstance b is to surmise that a may be true because then b would be a matter of course.[2] Thus, to abduce a from b involves determining that a is sufficient (or nearly sufficient), but not necessary, for b.

For example, the lawn is wet. But if it rained last night, then it would be unsurprising that the lawn is wet. Therefore, by abductive reasoning, it rained last night. (But note that Peirce did not remain convinced that a single logical form covers all abduction.)[3]

Peirce argues that good abductive reasoning from P to Q involves not simply a determination that, e.g., Q is sufficient for P, but also that Q is among the most economical explanations for P. Simplification and economy are what call for the 'leap' of abduction.[4]

There has been renewed interest in the subject of abduction in the fields of computer science and artificial intelligence research.[5]

Contents

Deduction, induction, and abduction

Formalizations of abduction

Logic-based abduction

In logic, explanation is done from a logical theory T representing a domain and a set of observations O. Abduction is the process of deriving a set of explanations of O according to T and picking out one of those explanations. For E to be an explanation of O according to T, it should satisfy two conditions:

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