Natural deduction systems are more suited to practical theorem-proving.
2.
He wrote that the intuitionistic natural deduction system NJ was somewhat ugly.
3.
He wrote important papers on free logic, general modal logic, and natural deduction systems.
4.
Natural deduction systems resemble Hilbert-style systems in that a deduction is a finite list of formulas.
5.
Similar but more complex translations to and from algebraic logics are possible for natural deduction systems as described above and for the sequent calculus.
6.
These logical frameworks are themselves always specified as natural deduction systems, which is a testament to the versatility of the natural deduction approach.
7.
Natural deduction systems use single-consequence conditional assertions, but they typically do not use the same sets of inference rules as Gentzen introduced in 1934.
8.
This can be ensured ( along with stronger conditions ) by, e . g ., placing certain restrictions on the rules of a natural deduction system.
9.
The original natural deduction system ( due to Gerhard Gentzen ), which uses an extra stack, is an example of a system that cannot be implemented with Metamath.
10.
Gentzen asserted a sharp distinction between his single-output natural deduction systems ( NK and NJ ) and his multiple-output sequent calculus systems ( LK and LJ ).
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