FLOC 2018: FEDERATED LOGIC CONFERENCE 2018
Models of Linear Logic based on the Schwartz epsilon product

Authors: Marie Kerjean and Yoann Dabrowski

Paper Information

Title:Models of Linear Logic based on the Schwartz epsilon product
Authors:Marie Kerjean and Yoann Dabrowski
Proceedings:Linearity/TLLA Pre-proceedings
Editors: Maribel Fernandez, Valeria de Paiva, Thomas Ehrhard and Lorenzo Tortora De Falco
Keywords:Differential Linear Logic, star-autonomous categories, Functional Analysis
Abstract:

ABSTRACT. In this talk we want to present the recent results of \cite{DK}. We construct several smooth classical denotational models of Linear Logic: they are smooth as non-linear proofs are interpreted as infinitely differentiable functions, and they feature an involutive linear negation. The starting point of this work consists in noticing that the multiplicative disjunction \$\parr\$ corresponds to the well-known Schwartz' epsilon product. Requiring its associativity then asks for a completeness notion, while the linear involutive negation is ensured by considering a good topology (the Arens topology) on the dual, ensuring that the linear involutive negation works as an orthogonality relation.

Pages:5
Talk:Jul 08 12:00 (Session 38K)
Paper: