论文标题
线性逻辑的分类模型具有公式的固定点
Categorical models of Linear Logic with fixed points of formulas
论文作者
论文摘要
我们开发了Mull的典型语义，Mull是一种命题线性逻辑的版本，最少，最大的固定点扩展了David Baelde的命题Mumall和指数。我们的一般分类环境是基于Seely类别的概念和作用于它们的强函数的概念。我们展示了此设置的两个简单实例。在第一个基于集合和关系类别的第一个中，最少和最大的固定点以相同的方式解释。在第二个中，基于配备了整体概念（不一致的总空间）和保留它们的关系的集合，最少和最大的固定点具有不同的解释。后一个模型表明，Mull享有证明正常化的指示形式。
We develop a denotational semantics of muLL, a version of propositional Linear Logic with least and greatest fixed points extending David Baelde's propositional muMALL with exponentials. Our general categorical setting is based on the notion of Seely category and on strong functors acting on them. We exhibit two simple instances of this setting. In the first one, which is based on the category of sets and relations, least and greatest fixed points are interpreted in the same way. In the second one, based on a category of sets equipped with a notion of totality (non-uniform totality spaces) and relations preserving them, least and greatest fixed points have distinct interpretations. This latter model shows that muLL enjoys a denotational form of normalization of proofs.
