论和谐与转换

Q1 Mathematics

Journal of Applied Logic Pub Date : 2017-05-01 DOI:10.1016/j.jal.2016.12.004

Nissim Francez

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引用次数: 4

摘要

本文通过将排列转换与和谐联系起来，揭示了(在自然演绎系统中)排列转换与这些系统在被称为证明论语义的意义理论中的作用的相关性，迄今为止仅与规范化相关。这是通过显示排列转换的连接，一般概念的规范，一旦应用于任意派生从开放的假设。在揭示排列转换与和谐关系的过程中，提出了前者的一般定义，概括了文献中考虑的析取和存在量词的具体情况。

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On harmony and permuting conversions

The paper exposes the relevance of permuting conversions (in natural-deduction systems) to the role of such systems in the theory of meaning known as proof-theoretic semantics, by relating permuting conversion to harmony, hitherto related to normalisation only. This is achieved by showing the connection of permuting conversion to the general notion of canonicity, once applied to arbitrary derivations from open assumption. In the course of exposing the relationship of permuting conversions to harmony, a general definition of the former is proposed, generalising the specific cases of disjunction and existential quantifiers considered in the literature.

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