Title: Problems and Consequences of Bilateral Notions of (Meta-)Derivability Show Chinese title

Title: 双边可推导性（元）导出的問題與後果

Abstract: A bilateralist take on proof-theoretic semantics can be understood as demanding of a proof system to display not only rules giving the connectives' provability conditions but also their refutability conditions. On such a view, then, a system with two derivability relations is obtained, which can be quite naturally expressed in a proof system of natural deduction but which faces obstacles in a sequent calculus representation. Since in a sequent calculus there are two derivability relations inherent, one expressed by the sequent sign and one by the horizontal lines holding between sequents, in a truly bilateral calculus both need to be dualized. While dualizing the sequent sign is rather straightforwardly corresponding to dualizing the horizontal lines in natural deduction, dualizing the horizontal lines in sequent calculus, uncovers problems that, as will be argued in this paper, shed light on deeper conceptual issues concerning an imbalance between the notions of proof vs. refutation. The roots of this problem will be further analyzed and possible solutions on how to retain a bilaterally desired balance in our system are presented. Show Chinese abstract

Abstract: 对证明论语义的双边主义观点可以理解为要求一个证明系统不仅展示连接词的可证明条件，还要展示它们的可反驳条件。 在这种观点下，得到一个具有两种可推导关系的系统，这在自然演绎的证明系统中可以很自然地表达，但在序列演算表示中则面临障碍。 因为在序列演算中存在两种固有的可推导关系，一种由序列符号表示，另一种由序列之间的水平线表示，在真正的双边演算中，这两种都需要被对偶化。 虽然对偶化序列符号相当直接地对应于自然演绎中水平线的对偶化，但对偶化序列演算中的水平线却揭示了问题，这些问题将如本文所论证的那样，揭示出关于证明与反驳概念之间不平衡的更深层次的概念性问题。 这个问题的根源将进一步分析，并提出了如何在我们的系统中保持双边期望的平衡的可能解决方案。