Despite the tendency to be otherwise, some non-classical logics are known to validate formulas that are invalid in classical logic. A subclass of such systems even possesses pairs of a formula and its negation as theorems, without becoming trivial. How should these provable contradictions be understood? The present paper aims to shed light on aspects of this phenomenon by taking as samples the constructive connexive logic C, which is obtained by a simple modification of a system of constructible falsity, namely N4, as well as its non-constructive extension C3. For these systems, various observations concerning provable contradictions are made, using mainly a proof-theoretic approach. The topics covered in this paper include: how new contradictions are found from parts of provable contradictions; how to characterise provable contradictions in C3 that are constructive; how contradictions can be seen from the relative viewpoint of strong implication; and as an appendix an attempt at generating provable contradictions in C3.

尽管有相反的趋势，但已知一些非经典逻辑可以验证在经典逻辑中无效的公式。此类系统的子类甚至拥有成对的公式及其否定作为定理，而不会变得微不足道。应该如何理解这些可证明的矛盾呢？本文旨在通过以构造性连接逻辑C为样本来阐明这一现象的各个方面，该逻辑 C 是通过对可构造虚假系统N4及其非构造性扩展C3进行简单修改而获得的。对于这些系统，主要使用证明理论方法，对可证明的矛盾进行了各种观察。本文涵盖的主题包括：如何从部分可证明的矛盾中发现新的矛盾；如何描述C3中可证明的建设性矛盾；如何从强蕴涵相对的角度看待矛盾；并作为附录尝试在C3中产生可证明的矛盾。