Talk:Sequent calculus

message: In fact, since Wikipedia has changed its layout recently, the tabular layout of the rule system included here looks awfully. Please feel free to typeset it in LaTeX... --Markus Krötzsch 22:49, 8 Jun 2004 (UTC)
replies: text: A good layout for derivations as a wiki-table/TeX hybrid is given in the example derivation. The html-or does not display well on many browsers, so I prefer the TeX version. --Markus Krötzsch 14:48, 27 Jul 2004 (UTC)

text: I am typesetting all the derivations on (La)TeX my version --Miguel Pagano 20:35, 25 July 2005 (UTC)
thread_title: Untitled

message: I am experiencing some html (i.e. not png) rendering problems on the sequent calculus page on Firefox (Windows) for quite some time. I have tried to fix this, but it has been without results so far.
The problem is in the html rendering of ∧, \and and \land. In Firefox, they show up as a small square (∧) most of the times.
I have been able to reproduce this problem in the sandbox, but this generates unpredictable results: sometimes the results are displayed correctly, and sometimes not! Refreshing the page can even toggle between right and wrong results.
The problem is also present at other pages such as natural deduction and first-order logic.
I have confirmed this problem on a number of machines running Windows.
I am aware of the fact this is possibly not the best place to post this problem, but I have no idea where to post it elsewhere.
Cheers, eboy 15:02, 7 November 2006 (UTC)
thread_title:  HTML rendering problems on Firefox (Windows) of <tt>&amp;and;</tt>, <tt><nowiki><math>\and</math></nowiki></tt> and <tt><nowiki><math>\land</math></nowiki></tt> 

message: The intuitive explanations of the rules were very helpful - but the section on 
Structural Rules lists Weakening, PR, and Contraction, gives intuitive explanations of PR and Contraction but skips Weakening -- can anyone add to this?
Zero sharp 06:36, 19 December 2006 (UTC)
replies: text: You are in error.  The rule actually says that if \Gamma \vdash \Delta, then \Gamma \vdash A,\Delta for any formula A -- what's important is that the formulas \Delta remain in the conclusion.  In terms of the standard classical semantics of sequents described in the introduction, this rule can be justified by saying that it is possible to weaken an assertion ("the conjunction of the \Gamma implies the disjunction of the \Delta") by adding an extra disjunctive possibility ("the disjunction of the \Delta or A"). Noamz (talk) 03:26, 22 October 2012 (UTC)
thread_title: Weakening?

message: I cut the discussion following "This very rigid reasoning may at first be difficult to understand, but it forms the very core of the difference between syntax and semantics in formal logics".  First of all, it doesn't.  Finite sequences are no more formal than finite multisets (so I added a sentence about the possibility of giving a multiset presentation, which seems to have been discussed in a previous version of the article anyways, referenced in "Minor structural alternatives").  Second, the rest of the paragraph built on a confusion between the permutation rule and the disjunction right rules -- in this presentation of sequent calculus, A ∨ B is different from B ∨ A because there are two different right rules for disjunction, regardless of whether permutation is treated explicitly. Noamz (talk) 06:32, 17 October 2009 (UTC)
thread_title:  An example derivation 

message: Considering space is not an issue for wikipedia, it would be kind to be explicit about the modified rules for LJ. 
Perhaps create a new page LJ inference rules and place them there.
86.5.129.198 (talk) 20:43, 24 January 2013 (UTC)
thread_title:  LJ Rules 

message: Substituted at 02:35, 5 May 2016 (UTC)
thread_title: Assessment comment

message: After the rules for the quantifiers, the entry says:
Restrictions: In the rules ({\forall}R) and ({\exists}L), the variable y must not occur free within \Gamma and \Delta. Alternatively, the variable y must not appear anywhere in the respective lower sequents.
How come the second part is an alternative to the first?
In Gentzen's original paper, only the alternative was included.
Also, and please correct me if I am wrong, the part before "Alternatively" seems insufficient:
if this is the only restriction, that you can derive
\Rightarrow\forall x.x=y from \Rightarrow y=y by taking A to be x=y.
If there isn't any mistake in this argument, I propose to include only the "alternative" restriction.  — Preceding unsigned comment added by Yoni206 (talk • contribs) 18:48, 18 November 2017 (UTC)
thread_title:  Are the restrictions in the quantifier rules correct?