A method of reasoning by which one infers to the best explanation. See induction, deduction.

This notion was first introduced by Peirce (CP 2.511, 623; 5.270) in an attempt to classify a certain form of syllogism. Abductive syllogisms are of the following form:
All beans from this bag are white
These beans are white.
Therefore, these beans are from this bag.
This inference results in an explanation of the observation in the second premise. Though this form of reasoning is logically unsound (as the beans may be from a different source), Peirce argues that scientists regularly engage in this sort of syllogistic reasoning. Though scientific hypotheses are not valid by virtue of how they are abduced, abductive reasoning was thought to constitute a "logic of discovery" in one of Peirce's four steps of scientific investigation. These steps are:
  1. observation of an anomaly 
  2. abduction of hypotheses for the purposes of explaining the anomaly
  3. inductive testing of the hypotheses in experiments
  4. deductive confirmation that the selected hypothesis predicts the original anomaly.
Abduction is not currently thought to be well understood and Peirce's formulation has been criticized as being restricted to language-like mediums (Shelley, 1996). It should be noted that for Peirce, abduction was restricted to the generation of explanatory hypotheses. The more general characterization of abduction as inference to the best explanation is a more recent interpretation.
Chris Eliasmith