There are many books and internet tutorials about sequent calculus for classical first-order logic (LK – which, if I understood correctly, is the one that allows for any number of formulae on the right side). I am actually only concerned with propositional logic.
Some web pages list the ground rules including the cut rule; an example is Toman's lecture notes. Others exclude the cut rule; an example is Slaney's Logic Notes. The wikipedia page itself makes one list with, and another without: compare this section with this section.
Is it because of the cut-elimination theorem that some tutorials don't list the cut rule? But I have also read (eg wikipedia again) that without the cut rule some proofs would be unfeasibly long.
I would be thankful if you could explain me where these differences in presentation come from.
