论文标题
锥线性结构
On the linear structure of cones
论文作者
论文摘要
为了涵盖概率相干空间的局限性，这些空间似乎无法提供对实际数据类型（例如真实线，ehrhard and al）的自然解释。引入了基于（正）锥的概率高阶计算模型，以及他们称为“稳定”的一类完全单调的函数。然后，Crubill {é}证明了该模型是早期概率相干空间模型的保守扩展。我们通过表明锥体类别，线性和连续连续功能是直觉线性逻辑的模型来继续进行这些研究。为了定义张量产品，我们使用特殊的伴随函子定理，并证明此操作是概率相干空间的标准张量产品的扩展。我们还表明，这些后者在锥体中是密集的，因此可以将概率相干空间的张量产物的主要特性提升为一般锥体。最后，我们以圆锥体的指数定义方式定义，并将可测量性扩展到这些新操作。
For encompassing the limitations of probabilistic coherence spaces which do not seem to provide natural interpretations of continuous data types such as the real line, Ehrhard and al. introduced a model of probabilistic higher order computation based on (positive) cones, and a class of totally monotone functions that they called "stable". Then Crubill{é} proved that this model is a conservative extension of the earlier probabilistic coherence space model. We continue these investigations by showing that the category of cones and linear and Scott-continuous functions is a model of intuitionistic linear logic. To define the tensor product, we use the special adjoint functor theorem, and we prove that this operation is and extension of the standard tensor product of probabilistic coherence spaces. We also show that these latter are dense in cones, thus allowing to lift the main properties of the tensor product of probabilistic coherence spaces to general cones. Last we define in the same way an exponential of cones and extend measurability to these new operations.
