Abstract
AbstractNatural deduction is a philosophically as well as pedagogically important logical proof system. This chapter introduces Gerhard Gentzen’s original system of natural deduction for minimal, intuitionistic, and classical predicate logic. Natural deduction reflects the ways we reason under assumption in mathematics and ordinary life. Its rules display a pleasing symmetry, in that connectives and quantifiers are each governed by a pair of introduction and elimination rules. After providing several examples of how to find proofs in natural deduction, it is shown how deductions in such systems can be manipulated and measured according to various notions of complexity, such as size and height. The final section shows that the axiomatic system of classical logic presented in Chapter 2 and the system of natural deduction for classical logic introduced in this chapter are equivalent.
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