Variations
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. This form is needed to obtain calculi for intuitionistic logic. 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 multisets or sets instead of sequences. Thus one disregards the order or even the number 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 does not depend on these data. In substructural logic, however, this may become quite important.
Read more about this topic: Sequent
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