Abductive Reasoning
This topic has come up multiple times in studying the math behind artificial intelligence / machine learning, so I want to know more about it.
References
Notes
Abductive reasoning (also called abduction, abductive inference, or retroduction) is a form of logical inference that seeks the simplest and most likely conclusion from a set of observations. It was formulated and advanced by American philosopher and logician Charles Sanders Peirce beginning in the later half of the 19th century.
- Abductive reasoning yields a plausible conclusion but does not definitely verify it. It does not eliminate uncertainty or doubt. Abductive conclusions are confined to the particular observations in question.
Deduction
Deductive reasoning allows deriving from where is formal logical consequence of . Deduction derives the consequences of the assumed.
Induction
Inductive reasoning is the process of inferring some general principle from a body of knowledge , where does not necessarily follow from . might give us a very good reasoning to accept but does not ensure .
Abduction
Abductive reasoning allows inferring as an explanation of . As a result of this inference, abduction allows the precondition to be abducted from the consequence . Properly used, abductive reasoning can be a useful source of priors in Bayesian statistics.
Abductive validation is the process of validating a given hypothesis through abductive reasoning. This can also be called reasoning through successive approximation. Under this principle, an explanation is valid if it is the best possible explanation of a set of known data. The best possible explanation is often defined in terms of simplicity and elegance. Subjective logic generalizes probabilistic logic by including degrees of epistemic uncertainty in the input arguments - instead of probabilities, the analyst can express arguments as subjective opinions.
The American philosopher Charles Sanders Pierce introduced abduction into modern logic. Over the years, he called such inference hypothesis, abduction, presumption, and retroduction. He considered it a topic in logic as a normative filed in philosophy, not in purely formal or mathematical logic, and eventually as a topic also in economics of research.
Applications of abduction in Artificial intelligence include fault diagnosis, belief revision, and automated planning. The most direct application of abduction is that of automatically detecting faults in systems: given a theory relating faults with their effects and a set of observed effects, abduction can be used to derive sets of faults that are likely to be the cause of the problem.