The Completeness of Linear Logic for Petri Net Models
The Completeness of Linear Logic for Petri Net Models
复制标题
Petri 网模型线性逻辑的完备性
DOI：
10.1093/jigpal/9.4.549
复制
发表时间：
1998
期刊：
影响因子：
--
通讯作者：
K. Hiraishi
中科院分区：
文献类型：
--
作者：
Keiko Ishihara;K. Hiraishi
线性逻辑和Petri Nets之间的完整性已显示出几种线性逻辑的版本。例如，Engberg和Winskel考虑了命题直觉线性逻辑的无t片段，而无需指数级！证明完整命题直觉的线性逻辑的完整性的困难之一在于u超过t，这在线性逻辑中无效。 Engberg和Winskel构建的量子是分布晶格，即分布始终是有效的。在本文中，我们首先使用封闭操作构建了来自Petri Nets的非分配数量，并证明了完整的线性逻辑的完整性，而无需指数。接下来，我们将量化的构造扩展到指数！我们还与Engberg和Winskel相比，对拟议的Petri Net模型的逻辑含义给人留下了深刻的印象。
The completeness between linear logic and Petri nets has been shown for several versions of linear logic. For example, Engberg and Winskel considered the t-free fragment of propositional intuitionistic linear logic without exponential !, and showed soundness and completeness of the logic for a Petri net model. One of difficulties in proving completeness for full propositional intuitionaistic linear logic lies in distributivity of u over t, that is not valid in linear logic. The quantales constructed by Engberg and Winskel are distributive lattices, i.e., distributivity is always valid. In this paper, we first construct non-distributive quantales from Petri nets by using a closure operation, and prove completeness of full linear logic without exponential for them. Next we extend the construction of the quantales to those with exponential !, and prove completeness of linear logic with exponential for the quantales. We also give an impression on the meaning of the logic on the proposed Petri net model, comparing with that by Engberg and Winskel.