Talk:Admissible rule
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I replaced Admissible inference rule with a redirect to this page. I believe that the other article was incorrect: Admissibility is not about composing existing inference rules, but about facts that arise because those inference rules are the only ones in the system. For instance, one cannot generally construct the cut rule by composing other rules (then it would be derivable); rather, one must actually perform a computation on the derivations of the premises in order to form a derivation of the conclusion.
A while ago I wrote some information on admissibility in the article on inference rules. I think the material rightly belongs in that article, but surely the article "Admissible rule" shouldn't be a stub that's shorter than the discussion in some larger article. Thoughts? Brighterorange 22:04, 25 Apr 2005 (UTC)
I'm confused. This article states that the concept of an admissible rule was introduced in 1955, yet Gentzen showed Cut was admissible in LK in 1934, according to the article on the Cut elimination theorem. Am I confusing matters here? Are we talking about two different notion of admissibility, or what? DPMulligan (talk) 10:34, 19 May 2008 (UTC)
- Gentzen proved in 1934 the cut-elimination theorem for his sequent calculus. He did not isolate admissibility as a general concept, which entered the proof theory jargon only much later. There is no need or reason to refer to admissible rules in the statement of Gentzen's theorem. — EJ (talk) 12:52, 19 May 2008 (UTC)
