Editing Sequent (section)

== Variations ==
{{Refimprove section|date=June 2014}}
The general notion of sequent introduced here can be specialized in various ways. A sequent is said to be an '''intuitionistic sequent''' if there is at most one formula in the succedent (although multi-succedent calculi for intuitionistic logic are also possible). More precisely, the restriction of the general sequent calculus to single-succedent-formula sequents, ''with the same inference rules'' as for general sequents, constitutes an intuitionistic sequent calculus. (This restricted sequent calculus is denoted LJ.)

Similarly, one can obtain calculi for [[dual-intuitionistic logic]] (a type of [[paraconsistent logic]]) by requiring that sequents be singular in the antecedent.

In many cases, sequents are also assumed to consist of [[multiset]]s or [[Set (mathematics)|sets]] instead of sequences. Thus one disregards the order or even the numbers of occurrences of the formulae. For classical [[propositional logic]] this does not yield a problem, since the conclusions that one can draw from a collection of premises do not depend on these data. In [[substructural logic]], however, this may become quite important.

[[Natural deduction]] systems use single-consequence conditional assertions, but they typically do not use the same sets of inference rules as Gentzen introduced in 1934. In particular, [[System L|tabular natural deduction]] systems, which are very convenient for practical theorem-proving in propositional calculus and predicate calculus, were applied by {{harvtxt|Suppes|1999}} and {{harvtxt|Lemmon|1965}} for teaching introductory logic in textbooks.