<logic> the process of inference to the best explanation.
The term 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 notion was first introduced by Peirce (CP 2.511, 623; 5.270) in an attempt to classify a certain form of syllogism.
Abductive inferences are of the following form:
i) All beans from this bag are white. ii) These beans are white. iii) Therefore, these beans are from this bag.This inference results in an explanation of the observation in the second premise.
The semantics and the implementation of abduction cannot be reduced to those for deduction, as explanation cannot be reduced to implication.
Though this method of reasoning is not logically valid (as the beans may be from a different source), Peirce argues that scientists regularly engage in this sort of inferential reasoning. Though scientific hypotheses are not valid by virtue of how they are abducted, 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 currently thought not to be well understood and Peirce's formulation has been criticised 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 characterisation of abduction as inference to the best explanation is a more recent interpretation.
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.
Peirce, C. (1958) Volume 2, paragraph 511, 623; Volume 5, paragraph 270. In Hartshoren and Weiss.
Levesque (1989). A knowledge level account of abduction. In Sridharan 1989 pp. 1061-1067.
Shelley, C. (1996) Visual abductive reasoning in archaeology. Philosophy of Science Association, 63. 278-301.abscissa
<mathematics> The x coordinate on an (x, y) graph; the input f a function against which the output is plotted.
y is the "ordinate".
See Cartesian coordinates.
Based on [FOLDOC] and Chris Eliasmith - [Dictionary of Philosophy of Mind] Homepage
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