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natural deduction
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(Definition)
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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
 and
 are:
and
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"natural deduction" is owned by Henry.
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(view preamble)
Cross-references: connective, side, right, formula, sequents, axioms, similar, logic, proof
There are 4 references to this entry.
This is version 2 of natural deduction, born on 2002-10-02, modified 2004-04-11.
Object id is 3503, canonical name is NaturalDeduction.
Accessed 5451 times total.
Classification:
| AMS MSC: | 03F03 (Mathematical logic and foundations :: Proof theory and constructive mathematics :: Proof theory, general) |
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Pending Errata and Addenda
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![$\displaystyle \frac{\begin{array}{cc}\Gamma\Rightarrow\alpha\rightarrow\beta &\... ...a\Rightarrow\alpha\end{array}}{[\Gamma,\Sigma]\Rightarrow\beta} (\rightarrow E)$](http://images.planetmath.org:8080/cache/objects/3503/l2h/img4.png "$\displaystyle \frac{\begin{array}{cc}\Gamma\Rightarrow\alpha\rightarrow\beta &\... ...a\Rightarrow\alpha\end{array}}{[\Gamma,\Sigma]\Rightarrow\beta} (\rightarrow E)$")