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Additive function Categorical variable Probabilistic logic Coherence (philosophical gambling strategy) Differential (mechanical device) Differential calculus Mathematics Linear logic Lambda calculus Lambda Calculus (dental) Pure mathematics Algebra over a field Discrete mathematics Mathematical analysis Physics Statistics Medicine Dentistry Optics Thermodynamics

Thomas Ehrhard ·

YOU? · · 2023 · Open Access · · DOI: https://doi.org/10.1017/s0960129523000129 · OA: W3182522751

The categorical models of differential linear logic (LL) are additive categories and those of the differential lambda-calculus are left-additive categories because of the Leibniz rule which requires the summation of two expressions. This means that, as far as the differential lambda-calculus and differential LL are concerned, these models feature finite nondeterminism and indeed these languages are essentially non-deterministic. We introduce a categorical framework for differentiation which does not require additivity and is compatible with deterministic models such as coherence spaces and probabilistic models such as probabilistic coherence spaces.