Date of Original Version

2001

Type

Article

Published In

Journal of Logic and Algebraic Programming (2001), 49: 15-30.

Rights Management

All Rights Reserved

Abstract or Description

Algebraic proofs of the cut-elimination theorems for classical and intuitionistic logic are presented, and are used to show how one can sometimes extract a constructive proof and an algorithm from a proof that is nonconstructive. A variation of the double-negation translation is also discussed: if phi is provable classically, then ¬(¬phi)nf is provable in minimal logic, where θnf denotes the negation-normal form of θ. The translation is used to show that cut-elimination theorems for classical logic can be viewed as special cases of the cut-elimination theorems for intuitionistic logic.

DOI

10.1016/S1567-8326(01)00009-1

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