Image:Comparison among deduction systems.png

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[edit] Summary

Description

Comparison between Hilbert-style deduction system and natural deduction, approached with the concept of judgment.

The image is drawn for illustration of an argumentation in a talk page debate. The factual correctness of the image can be disputed, see the later development of the thread . The (maybe obsolete) argumentation for which the image has been drawn was the following below:

In Hilbert-style deduction system,

For contrast, in natural deduction,

  • judgment is of a more sophisticated form, playing significant role in the machinery.
  • Implication-introduction (the correspondent of DT in HS) relies heavily on the notion of judgment
  • and is in the very kernel, incorporated as rule of inference, not just dropped onto the top of the already-built machinery.
Source

self-made
Date

6 Jan 2008
Author

Physis
Permission
(Reusing this image)

see below

[edit] Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license".

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File history

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Date/TimeDimensionsUserComment
current05:13, 6 January 2008816×1,056 (25 KB)Physis (Logical relationship between rule of inference "implication-introduction" and auxiliary concept "judgment" is not reciprocal)
04:40, 6 January 2008816×1,056 (25 KB)Physis ({{Information |Description=Comparison between Hilbert-styledeductionsystem and natural deduction, approached with the concept of judgment |Source=self-made |Date=6 Jan 2008 |Author= Physis |Permission= |other_versions= }} )
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