deductive logic

In philosophical logic, natural deduction is an approach to proof theory that attempts to provide a formal model of logical reasoning as it "naturally" occurs.
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a way of reasoning from one set of statements to another.  It has the form: If this is the case and this is the case, then we can conclude tha this other thing is the case, too.  People use deductive logic in a loose way when they think and talk, but it is used in a highly formalized way in philosophy circles.  There, in the last century especially, the rules of logic become quite complex and the deduction (the reasoning leading to the conclusion) follows rules that are so formal that they are often thought to be, or hoped to be, a kind of mathematical calculus.  Note that deduction does not require any factual or observed information.  One can deduce something false if one reasons with false ideas or premises.  Contrast "deductive logic" with "inductive logic."