Cut-Elimination by Resolution
In Chapter 5 we analyzed methods which eliminate cuts by stepwise reduction of cut-complexity. These methods always identify the uppermost logical operator in the cut-formula and either eliminate it directly (grade reduction) or indirectly (rank reduction). Here it is typical that, during grade reduction, the cut formulas are “peeled” from outside. These methods are local in the sense that only a small part of the whole proof is analyzed, namely the derivation corresponding to the introduction of the uppermost logical operator. As a consequence many types of redundancy in proofs are left undetected in these reductive methods, leading to bad computational behavior.
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