natural deduction

Natural deduction refers to related proof systems for several different kinds of logic, intended to be similar to the way people actually reason. Unlike many other proof systems, it has many rules and few axioms. Sequents in natural deduction have only one formula on the right side.

Typically the rules consist of one pair for each connective, one of which allows the introduction of that symbol and the other its elimination.

To give one example, the proof rules $\rightarrow I$ and $\rightarrow E$ are:

\frac{\Gamma,\alpha\Rightarrow\beta}{\Gamma\Rightarrow\alpha\rightarrow\beta}(% \rightarrow I)

and

\frac{\begin{array}[]{cc}\Gamma\Rightarrow\alpha\rightarrow\beta&\Sigma% \Rightarrow\alpha\end{array}}{[\Gamma,\Sigma]\Rightarrow\beta}(\rightarrow E)

Title	natural deduction
Canonical name	NaturalDeduction
Date of creation	2013-03-22 13:05:14
Last modified on	2013-03-22 13:05:14
Owner	Henry (455)
Last modified by	Henry (455)
Numerical id	5
Author	Henry (455)
Entry type	Definition
Classification	msc 03F03
Related topic	GentzenSystem