一个更普遍的证明理论

Q1 Mathematics

Journal of Applied Logic Pub Date : 2017-12-01 DOI:10.1016/j.jal.2017.01.002

Heinrich Wansing

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引用次数: 26

摘要

本文建议推广我们对一般(结构)证明理论的认识，把它看作是两类推导的一般理论，即证明和对偶证明。该建议由以下方面证实:(i)对断言、否认和双边主义的考虑，(ii)对证明论语义中的组合性的评论，以及(iii)对证伪和共同暗示的评论。本文的主要形式化结果是双直觉逻辑2Int的自然演绎证明系统N2Int的一个范式定理。该证明利用了2Int在有效性方面忠实嵌入直觉逻辑，并表明对偶证明的转换是可以回避的。

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A more general general proof theory

In this paper it is suggested to generalize our understanding of general (structural) proof theory and to consider it as a general theory of two kinds of derivations, namely proofs and dual proofs. The proposal is substantiated by (i) considerations on assertion, denial, and bi-lateralism, (ii) remarks on compositionality in proof-theoretic semantics, and (iii) comments on falsification and co-implication. The main formal result of the paper is a normal form theorem for the natural deduction proof system N2Int of the bi-intuitionistic logic 2Int. The proof makes use of the faithful embedding of 2Int into intuitionistic logic with respect to validity and shows that conversions of dual proofs can be sidestepped.

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