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Logic and linear algebra: an introduction

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Author: Daniel Murfet
Url: http://arxiv.org/abs/1407.2650
Format: Ps, Pdf
Year: 2015
Category: Logic
Pages: 42
Clicks: 114

Description
We give an introduction to computation and logic tailored for algebraists, and use this as a springboard to discuss geometric models of computation and the role of cut-elimination in these models, following Girard's geometry of interaction program. We discuss how to represent programs in the λ-calculus and proofs in linear logic as linear maps between infinite-dimensional vector spaces. The interesting part of this vector space semantics is based on the cofree cocommutative coalgebra of Sweedler.

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