The Deductive reasoning reference article from the English Wikipedia on 24-Jul-2004
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Deductive reasoning

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Deductive reasoning is the process of reaching a conclusion that is guaranteed to follow, if the evidence provided is true and the reasoning used to reach the conclusion is correct. The conclusion also must be based only on the evidence previously provided; it cannot contain new information about the subject matter. Deductive reasoning was first described by the ancient Greek philosophers such as Aristotle.

Deductive is a descriptor for one type of logical reasoning. In logic, there are two broad methods of reaching a conclusion. The alternative to deductive reasoning is inductive reasoning.

Both types of reasoning are routinely employed. One difference between them is that in deductive reasoning, the evidence provided must be a set about which everything is known before the conclusion can be drawn. Since it is difficult to know everything before drawing a conclusion, deductive reasoning has little use in the real world. This is where inductive reasoning steps in. Given a set of evidence, however incomplete the knowledge is, the conclusion is likely to follow, but one gives up the guarantee that the conclusion follows. However it does provide the ability to learn new things that are not obvious from the evidence.

Many incorrectly teach that deductive reasoning goes from the general to the specific and that inductive reasoning travels in the opposite direction.

Deductive reasoning is supported by deductive logic, for example:

All apples are fruit.
All fruits grow on trees.
Therefore all apples grow on trees.

Or

All apples are fruit.
Some apples are red.
Therefore some fruit is red.

Reference

Zarefsky, David, Argumentation: The Study of Effective Reasoning Parts I and II, The Teaching Company 2002