A Bicategorical Model for Finite Nondeterminism
A Bicategorical Model for Finite Nondeterminism
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有限非确定性的双分类模型
DOI：
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发表时间：
2021
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通讯作者：
Z. Galal
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作者：
Z. Galal
Ehrhard引入了线性空间，作为线性逻辑关系模型的一种改进。一个有限性空间是一个集合配备了一类有限子集，可以认为是子集的行为像有限集。有限性空间之间的态射是保持有限性结构的关系。该模型为有限非决定性提供了一种语义，并为微分线性逻辑和泰勒展开的句法概念提供了一种语义动机。在本文中，我们提出了一个bicategorical扩展这个结构的关系模型被替换为模型的广义物种的结构Fiore等人。有限性属性现在依赖于有限的presentability。2012年ACM学科分类计算理论→线性逻辑;计算理论→范畴语义学
Finiteness spaces were introduced by Ehrhard as a refinement of the relational model of linear logic. A finiteness space is a set equipped with a class of finitary subsets which can be thought of being subsets that behave like finite sets. A morphism between finiteness spaces is a relation that preserves the finitary structure. This model provided a semantics for finite non-determism and it gave a semantical motivation for differential linear logic and the syntactic notion of Taylor expansion. In this paper, we present a bicategorical extension of this construction where the relational model is replaced with the model of generalized species of structures introduced by Fiore et al. and the finiteness property now relies on finite presentability. 2012 ACM Subject Classification Theory of computation → Linear logic; Theory of computation → Categorical semantics