Logic and linear algebra: an introduction · HackerPapers discussions

Logic and linear algebra: an introduction — HN submission

Mon, 28 Nov 2022 14:27:38 GMT

Logic and Linear Algebra: An Introduction

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Logic and linear algebra: an introduction — mentioned by bitdizzy

Fri, 19 Jun 2020 21:41:15 GMT

The reasoning is sort of a technical analogy. Linear Logic was discovered by an analysis of the structure of Coherent Spaces, which are a model of Intuitionistic logic distilled from Scott domains. Jean-Yves Girard realized that function spaces A => B can be decomposed into two finer constructions as !A -o B where `A -o B` is a space of functions whose properties resemble linear functions between vector spaces and `!A` resembles the Fock space construction on a vector space. There are two ways this resemblance manifests. First off, the basic elements of a coherent space are called cliques…

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Logic and linear algebra: an introduction — mentioned by dmurfet

Mon, 29 Jan 2018 10:41:42 GMT

Author here. The theoretical background can be found in: https://arxiv.org/abs/1407.2650 https://arxiv.org/abs/1701.01285 http://therisingsea.org/notes/MScThesisJamesClift.pdf As neel_k notes, a good way to understand this picture is in terms of differential linear logic (a refinement of simply-typed differential lambda calculus). I did not provide references in the talk as unfortunately I did not understand the subject at the time, but the introduction to the second paper above hopefully serves to remedy that omission. Suffice to day that Ehrhard and Regnier discovered something quite…

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