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What is the difference between deduction and inference?
My guess is that deduction is a more concrete and restricted opinion because it involves logic every time whereas inference is a mere guess on the given evidences or situations and it involves logic sometime.
What does Sherlock Holmes do? Is it deduction or inference?
To deduce and infer are largely interchangeable, but...
deduce is more likely to be used where you arrive at some conclusion after a more prolonged logical analysis of relevant factors (which may not even be readily apparent until actively sought out).
Whereas you often infer a conclusion almost instantly, from directly-observable factors.
Since Sherlock is the archetypal solver of complex/non-obvious mysteries, he tends to deduce...
Holmes deduced [something] (about 709 results in Google Books)
Sherlock deduced it. (186 results)
Holmes inferred it (100 results)
Sherlock inferred it (5 results)
I personally don't recognise OP's formal logical reasoning vs inspired guess distinction, except insofar as it may reflect the above tendency for deduction to sometimes be a more lengthy process.
"Deduction," is the logical process of prediction based on a large number of samples or experience.
"Inference," is the logical process of prediction based on anecdotal, or a relatively small sample.
They are not at all interchangeable.
Deduction is most often used in closing a case, corresponding most often with the Conclusion phase of the Scientific Method. Inference can be used anywhere and even at multiple times throughout the study, often in the hypothesis stage. And it can occur even after the conclusion is presented, thus opening the case for subsequent studies.
