Linear logic in normed cones: probabilistic coherence spaces and beyond

Ehrhard, Pagani and Tasson proposed a model of probabilistic functional programming in category normed positive cones stable measurable cone maps, which can be seen as coordinate-free generalization coherence spaces. However, unlike the case spaces, it remained unclear if could refined to classical linear logic. In this work we consider somewhat similar gives indeed full propositional logic with nondegenerate interpretation additives sound exponentials. Objects are dual pairs satisfying certain specific completeness properties, such existence norm-bounded monotone weak limits, morphisms bounded (adjointable) maps. Norms allow us distinct additive connectives product coproduct. Exponential modelled using real analytic functions distributions that have representations power series coefficients. Unlike familiar there is no reference or need for preferred basis; sense invariant. Probabilistic spaces form subcategory, whose objects, posets, lattices. Thus get fitting tradition interpreting algebraic setting, arguably free from drawbacks its predecessors. Relations constructions Tasson's left future research.