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Logic and linear algebra: an introduction
We give an introduction to logic tailored for algebraists, explaining how proofs in linear logic can be viewed as algorithms for constructing morphisms in symmetric closed monoidal categories with additional structure. This is made explicit by showing how to represent proofs in linear logic as linear maps between vector spaces. The interesting part of this vector space semantics is based on the cofree cocommutative coalgebra of Sweedler.
Logical Complexity of Proofs
If you cannot find proofs, talk about them. Robert Reckhow with his advsior Stephen Cook famously started the formal study of the complexity of proofs with their 1979 paper. They were interested in…
Proof Explorer
Inspired by Whitehead and Russell's monumental Principia Mathematica, the Metamath Proof Explorer has over 26,000 completely worked out proofs in its main sections (and over 41,000 counting "mathboxes", which are annexes where contributors can develop additional topics), starting from the very foundation that mathematics is built on and eventually arriving at familiar mathematical facts and beyond.
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