NII Technical Report (NII-2006-011E)：Uniqueness of D-normal Proofs

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This paper presents the notion of D-normal proofs, which is defined syntactically and gives one of the weakest condition for uniqueness of normal proofs. This paper proves the following results: (1) beta eta D-normal proofs of a formula are unique. (2) A beta-normal proof of a PNN-formula is D-normal. (3) A beta-normal proof of a minimal formula in BCK logic is D-normal. These results give other proofs of uniqueness of beta eta-normal proofs of a PNN-formula, and uniqueness of beta eta-normal proofs of a minimal formula in BCK logic.

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