4 papers · 1 filter
Linear Logic and the Hilbert Scheme
William Troiani, Daniel Murfet
We introduce a geometric model of shallow multiplicative exponential linear logic (MELL) using the Hilbert scheme. Building on previous work interpreting multiplicative linear logi…
Linear Logic and Quantum Error Correcting Codes
Daniel Murfet, William Troiani
We develop a point of view on reduction of multiplicative proof nets based on quantum error-correcting codes. To each proof net we associate a code, in such a way that cut-eliminat…
Elimination and cut-elimination in multiplicative linear logic
Daniel Murfet, William Troiani
We associate to every proof structure in multiplicative linear logic an ideal which represents the logical content of the proof as polynomial equations. We show how cut-elimination…
Gentzen-Mints-Zucker duality
Daniel Murfet, William Troiani
The Curry-Howard correspondence is often described as relating proofs (in intutionistic natural deduction) to programs (terms in simply-typed lambda calculus). However this narrati…