双边逻辑中强否定的可定义性
On the Definability of Strong Negation in Bilateral Logics
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中文总结 AI 辅助
本文研究双边逻辑中强否定的可定义性，通过四类结果明确了不同构造性联结词及组合对强否定的定义能力，为N4相关片段提供了单联结词基础并刻画了特定联结词组合的定义条件。
中文摘要 AI 辅助
双边逻辑领域的近期研究关注，在缺乏强否定（用于在断定和否定之间“切换”）的双边系统中，强否定是否可定义以及可定义的程度。本文给出了关于双边系统中强否定可定义性的一系列结果：首先，证明了构造性纳尔逊式谢弗竖可将公式A的强否定定义为(A|(A|A))|A，该谢弗竖还可定义构造性纳尔逊蕴涵，从而为N4的强否定与蕴涵片段提供了单联结词基础；其次，全面刻画了8种由单个“聚合”联结词与单个纳尔逊式联结词组成的组合，这些组合足以共同定义强否定且二者均无法单独定义它，其中一种组合是实质条件与构造性共蕴涵；第三，证明了构造性和共存的万辛式谢弗竖（近期被称为“共存排除”）同样可将A的强否定定义为(A|(A|A))|A，还可定义共存蕴涵；第四，证明了与纳尔逊式联结词不同，若万辛式联结词与聚合联结词均无法单独定义强否定，则不存在二者的组合可共同定义强否定。
英文摘要
Recent work in bilateral logic has concerned itself with whether and to what extent strong negation, which "toggles" between assertion and denial, is definable in bilateral systems that lack it. This paper presents a number of results about the definability of strong negation in bilateral systems. First, I show that a constructive Nelson-style Sheffer stroke defines the strong negation of A as (A|(A|A))|A. The same stroke defines the constructive Nelson implication, thus providing a single-connective basis for the strong-negation-and-implication fragment of N4. Second, I provide an exhaustive characterization of the eight combinations of a single "aggregative" connective and a single Nelson-style connective that suffice to jointly define strong negation, with neither defining it individually. One such combination is the material conditional together with constructive co-implication. Third, I show that a constructive and connexive Wansing-style Sheffer stroke (recently referred to as "connexive exclusion") likewise defines the strong negation of A as (A|(A| A))|A and also defines connexive implication. Fourth, I show that, unlike with the Nelson-style connectives, there are no combinations of Wansing-style and aggregative connectives that jointly define strong negation if neither connective defines it individually.
