The concept of substructural logic was originally introduced in relation to limitations of Gentzen’s structural rules of Contraction, Weakening and Exchange. Recent years have witnessed the development of substructural logics also challenging the Tarskian properties of Reflexivity and Transitivity of logical consequence. In this introduction we explain this recent development and two aspects in which it leads to a reassessment of the bounds of classical logic. On the one hand, standard ways of defining the notion of logical consequence in classical logic naturally induce substructural logics when admitting more than two truth values; on the other hand, these substructural logics give rise to hierarchies of metainferences that can be used to approximate classical logic at different levels.

子结构逻辑的概念最初是针对 Gentzen 的收缩、弱化和交换结构规则的限制而引入的。近年来见证了子结构逻辑的发展，也挑战了逻辑结果的自反性和传递性的塔斯基属性。在本导言中，我们解释了这一最新发展以及它导致对经典逻辑界限进行重新评估的两个方面。一方面，当承认两个以上的真值时，经典逻辑中定义逻辑后果概念的标准方法自然会引入子结构逻辑；另一方面，这些子结构逻辑产生了元引用的层次结构可用于在不同层次上逼近经典逻辑。