What is abduction in context of philosophy of science? Is it alternative to deduction and induction? Is it some sort of combination of both? And what is it used for?
I presuppose the references to SEP for the definition of abductive reasoning.
A typical example of abductive reasoning is to make a conjecture from the symptom of an disease to its possible causes.
This kind of reasoning is formalized by the mathematical model of Bayesian nets. A Bayesian net has the possible causes and theirs symptoms as vertices and a directed edge from a cause to each of its symptoms. The edge is weighted with the probability that the cause induces the symptom. Due to the Bayesian formula one can invert the probabilities and compute the conditioned probability that a certain observed symptom is induced by a certain cause.
Bayesian nets are used in diagnostics, in a medical as well as in a technical context, e.g. in the domain of automotive.
N. R. Hanson regarded abduction as a significant kind of logic of discovery that differs from both deduction and induction. The term abduction was coined by Peirce to describe the inference from a phenomenon to a theory that if true would explain the phenomenon.
Some philosophers use the term abductive inference to signify inference to the best explanation. But others treat abduction as distinct from inference to the best explanation: abduction, they say, concerns a single theory and reasons for taking the theory as a candidate for further exploration; inference to the best explanation rather involves the comparison of several theories and reasons for believing that one of the theories is probable or true.
See the online Stanford Encyclopedia for further introductory overview: http://plato.stanford.edu/entries/abduction/ And http://plato.stanford.edu/entries/scientific-discovery/