A Proof-Theoretic Approach to the Semantics of Classical Linear Logic
Victor Barroso-Nascimento, Ekaterina Piotrovskaya, Elaine Pimentel
线性逻辑(LL)是一种资源感知的抽象逻辑编程语言,它既完善了经典逻辑,又完善了直觉逻辑。 线性逻辑语义通常以两种方式之一呈现:通过将每个公式与可用于证明它的所有上下文集(例如相位语义)或直接为证明(例如一致性空间)分配意义。 这项工作提出了通过采用证明理论视角为证明赋予意义的不同观点。 更具体地说,我们使用基础扩展语义(BeS)来表征基于基础支持的概念。 最近的发展表明,BeS足够强大,可以在结构丰富的逻辑(如直觉线性逻辑)中捕获证明理论概念。 在本文中,我们将这个框架扩展到经典案例,为线性逻辑(MALL)的乘法附加片段的语义提出了证明理论方法。
Linear logic (LL) is a resource-aware, abstract logic programming language that refines both classical and intuitionistic logic. Linear logic semantics is typically presented in one of two ways: by associating each formula with the set of all contexts that can be used to prove it (e.g. phase semantics) or by assigning meaning directly to proofs (e.g. coherence spaces). This work proposes a different perspective on assigning meaning to proofs by adopting a proof-theoretic perspective. More specif...