Deduction:To find conclusions
that follow from given assumptions in the
sense that if the assumptions are true then the conclusions must be true
as well. This is the type of reasoning on
which mathematics is based and that logic tries to
explain and formalize. If some conclusion C does follow deductively from premisses P1 .. Pn then the conclusion C cannot fail to be true if the premisses are true.
That all the premisses are true one often does not know, but then any deductive consequence C that fails to be the case is the ground for a deductive proof that then at least one of the premisses P1 .. Pn must false as well.
Incidentally, what is popularly called deduction  Sherlock Holmes, Hercule Poirot  seldomly is, and to give a really valid deductive proof of something is often not easy, especially if one knows nothing about formal logic.
See Natural Deduction for an outline of deductive techniques in formal logic.
