deduction - A method of reasoning by which one infers a conclusion from a set of sentences by employing the axioms and rules of inference for a given logical system. See abduction, induction.
Deductive syllogisms in quantificational predicate calculus are of the following form:
All beans from this bag are white
These beans are from this bag.
Therefore, these beans are white.
More formally, deduction can be characterized as (Cambridge Dictionary of Philosphy, p. 183):
For any sentence S, relative to a set of sentences K, a finite sequence of sentences whose last sentence is S (the one said to be deduced) and which is such that each sentence in the sequence is an axiom or an element of K, or follows from preceding sentences in the sequence by a rule of inference.
Deductions are relative to particular sets of axioms and rules of inference, as a given sequence of sentences may be a deduction relative to one set of axioms and rules and not to another.
Some use the term 'deduction' in a general sense to denote the fact that a conclusion follows necessarily from the premises.
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