标题： 命题逻辑的证明论语义学带有断言和否定 显示英文标题

标题： Proof-theoretic Semantics for Classical Propositional Logic with Assertion and Denial

摘要： 证明理论语义学（P-tS）领域提供了一种替代逻辑意义的方法，该方法基于推理和论证（而非模型中的真值）。 它已被成功应用于各种逻辑；特别是，Sandqvist为经典逻辑和直觉主义逻辑发展了这种语义学。 在经典逻辑的情况下，P-tS提供了一种避免对二值原则做出\emph{事前}承诺的后果概念，解决了Dummett所识别出的逻辑中的一个重要基础性挑战。 在本文中，我们提出了一个经典逻辑的替代P-tS，该语义学本质上通过操作文字而不是原子命题来扩展直觉主义逻辑的P-tS。 重要的是，文字是原子的，并不是通过否定定义的，而是通过推理关系定义的。 这种语义学展示了这样的观点，即经典逻辑可以被理解为补充了对偶原则的直觉主义逻辑，为这两种系统之间的关系提供了新的见解。 显示英文摘要

摘要： 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 \emph{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 defined by inferential relationships. 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.