Talk:Structural rule

resolution

I have updated the resolution link to Resolution (logic). feel free to change it if you know a better place to redirect the link to. STHayden ^{[ Talk ]} 04:15, 21 August 2006 (UTC)

Simple-language section needed

This article, like many mathematics articles, is written in a language that is entirely inaccessible to non-mathematicians. The subject matter, however, appears simple and could be made clear to the novice through simple, concrete examples of each rule. The article badly needs a general-audience section in simple language, placed before the formal-logic formulation. -- 169.230.94.21 17:53, 4 January 2007 (UTC)

mistake in weakening?

I'm pretty sure (but pretty tired, so i didn't just change the article) that the second version of weakening should not be

${\frac {\Gamma \vdash \Sigma }{\Gamma \vdash A,\Sigma }}$

but

${\frac {\Gamma \vdash A,\Sigma }{\Gamma \vdash \Sigma }}$

80.109.45.190 (talk) 22:47, 14 April 2008 (UTC)

I agree (and I'm not tired at the moment), so I fixed it. Pi zero (talk) 15:18, 25 May 2008 (UTC)

... and then I unfixed it. The right side of a sequent should be understood as a disjunction, so $\Gamma \vdash A,\Sigma$ is weaker than $\Gamma \vdash \Sigma$. Pi zero (talk) 15:31, 25 May 2008 (UTC)

I can confirm, the correct rule is ${\frac {\Gamma \vdash \Sigma }{\Gamma \vdash A,\Sigma }}$

The justification is—as observed—that $P\vee Q$ is weaker than $P$, and that a sequent $\Gamma \vdash \Sigma$ can be read as "Assuming the conjunction of $\Gamma$, we can show the disjunction of $\Sigma$".

For reference, see The Open Logic Text, Complete Version, §9.3 2001:8003:232E:CD01:3F:C4E8:D8AB:41AD (talk) 04:01, 4 October 2021 (UTC)