The field of proof-theoretic semantics (P-tS) offers an alternative approach to meaning in logic that is based on inference and argument (rather than truth in a model). It has been successfully developed for various logics; in particular, Sandqvist has developed such semantics for both classical and intuitionistic logic. In the case of classical logic, P-tS provides a conception of consequence that avoids an a priori commitment to the principle of bivalence, addressing what Dummett identified as a significant foundational challenge in logic. In this paper, we propose an alternative P-tS for classical logic, which essentially extends the P-tS for intuitionistic logic by operating over literals rather than atomic propositions. Importantly, literals are atomic and not defined by negation but are related by a primitive duality encoded inferentially at the atomic level. This semantics illustrates the perspective that classical logic can be understood as intuitionistic logic supplemented by a principle of duality, offering fresh insights into the relationship between these two systems.

翻译：证明论语义学（P-tS）领域提供了一种基于推理与论证（而非模型中的真值）的替代性逻辑意义理论。该理论已成功应用于多种逻辑系统；特别是桑德奎斯特为经典逻辑与直觉主义逻辑分别构建了此类语义。在经典逻辑情形下，P-tS提供了一种避免先验承诺二值原则的后承概念，回应了达米特所识别的逻辑领域重大基础性挑战。本文提出一种经典逻辑的替代性P-tS方案，其本质是通过对文字（而非原子命题）进行运算来扩展直觉主义逻辑的P-tS。关键在于，文字本身是原子的，并非由否定定义，而是通过原子层面以推理方式编码的原初对偶性相关联。该语义阐释了"经典逻辑可理解为经对偶性原则补充的直觉主义逻辑"这一视角，为理解这两个系统之间的关系提供了新见解。