differential linear logic. Differential Linear Logic Linearity revisited in Logic Linear hypotheses, to be used exacly once in Computer Science Linear inputs, to be used exactly once in Analysis Linear arguments occurring in linear position We will see some of the consequences that this approach brings in the top areas.
Cofree coalgebras and differential linear logic - Volume 30 Issue 4 - James Clift, Daniel Murfet We extend Ehrhard–Regnier’s differential linear logic along the lines of Laurent’s polarization. 1.4 but you need to know it already to see it).
Linear? We provide a denotational semantics of this new system in the well-known relational model of linear logic, extending canonically the semantics of both differential and polarized linear logics: this justifies our choice of cut elimination rules. We present a proof-net syntax for Differential Linear Logic and a categorical axiomatization of its denotational models. We present a proof-net syntax for Dif- ferential Linear Logic and a categorical axiomatization of its denotational models.
Thomas Ehrhard, An introduction to differential linear logic: proof-nets, models and antiderivatives.
We extend Ehrhard-Regnier's differential linear logic along the lines of Laurent's polarization.
We prove that the category of vector bundles over a fixed smooth manifold and its corresponding functional analytic category of convenient modules are models for intuitionistic differential linear logic in two ways.
Abstract.
Differential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. Mathematical Structures in Computer Science 28(7):995-1060, 2018. (It is funny that even this paper fails to include an explicit definition of the sequent calculus of DiLL.
A model of differential linear logic Once the exponential modality of linear logic has been interpreted asA7→SymA, it appears that the model of distributors does not just provide a mathe- matical interpretation of linear logic (LL) but also of differential linear logic (DiLL). … The first uses the jet comonad to model the exponential modality. The exponential modality is modelled by composing the jet comonad, whose Kleisli category has linear differential operators as morphisms, with the more familiar distributional comonad, whose Kleisli category has smooth maps as morphisms… In this case the Kleisli category is the category of convenient modules with linear differential operators as morphisms. In fact, it is implicitly given in Sect. Abstract Dierential Linear Logic enriches Linear Logic with additional logical rules for the exponential connectives, dual to the usual rules of derelic- tion, weakening and contraction.
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