Structuring Logic with Sequent Calculus

Defects of Natural Deduction
The notion of cut is implicit, there is no explicit rule for the
cut;
ND is satisfying only for a fragment of intuitionistic logic (⇒,
∧, ∀).
Paradoxically, the connectives which are the most interesting
for intuitionistic logic are ∨ and ∃...
⇒ Natural Deduction lacks structure.
Sequent Calculus: Explicit Cut, Rules dedicated to the
management of the formulas, Deep left-right symmetry of the
system (introduction/elimination rules on the right are replaced by
left/right introduction rules).
Alexis Saurin – ENS Paris & École Polytechnique & CMI Structuring Logic with Sequent Calculus