This paper concerns a stochastic construction of probabilistic coherent spaces by employing novel ingredients (i) linear exponential comonads arising properly in the measure-theory (ii) continuous orthogonality between measures and measurable functions. A linear exponential comonad is constructed over a symmetric monoidal category of transition kernels, relaxing Markov kernels of Panangaden's stochastic relations into s-finite kernels. The model supports an orthogonality in terms of an integral between measures and measurable functions, which can be seen as a continuous extension of Girard-Danos-Ehrhard's linear duality for probabilistic coherent spaces. The orthogonality is formulated by a Hyland-Schalk double glueing construction, into which our measure theoretic monoidal comonad structure is accommodated. As an application to countable measurable spaces, a dagger compact closed category is obtained, whose double glueing gives rise to the familiar category of probabilistic coherent spaces.
翻译:本文涉及通过使用测量理论中适当产生的新成分(一) 线性指数共振,对概率一致性空间进行随机构建。一个线性指数共振,是测量和可测量函数之间连续的正反向共振。一个线性共振,是在一个对称的单向过渡内核类别上构造的,将Panangaden的随机关系的Markov内核放松为一定的内核。这个模型支持在测量和可测量功能之间的一个整体体积,这可以被视为Girard-Danos-Ehrhard的线性双向延伸,以预测一致性空间为一种连续的延伸。这个线性共振动共振通过一种Hyland-Schal 双层粘结构造形成,我们测量的理论性单向共聚体结构可以适应。作为一个可测量空间的应用,获得了一个匕项紧紧闭的类别,其双重粘合可以产生一个熟悉的概率一致空间类别。