Differential Structure in Models of Multiplicative Biadditive Intuitionistic Linear Logic

Resource type
Authors/contributors
Title
Differential Structure in Models of Multiplicative Biadditive Intuitionistic Linear Logic
Abstract
In the first part of the paper I investigate categorical models of multiplicative biadditive intuitionistic linear logic, and note that in them some surprising coherence laws arise. The thesis for the second part of the paper is that these models provide the right framework for investigating differential structure in the context of linear logic. Consequently, within this setting, I introduce a notion of creation operator (as considered by physicists for bosonic Fock space in the context of quantum field theory), provide an equivalent description of creation operators in terms of creation maps, and show that they induce a differential operator satisfying all the basic laws of differentiation (the product and chain rules, the commutation relations, etc.).
Date
2007
Proceedings Title
Typed Lambda Calculi and Applications
Place
Berlin, Heidelberg
Publisher
Springer
Pages
163-177
Series
Lecture Notes in Computer Science
Language
en
DOI
10/c8vgx8
ISBN
978-3-540-73228-0
Library Catalog
Springer Link
Extra
ZSCC: NoCitationData[s1]
Citation
Fiore, M. P. (2007). Differential Structure in Models of Multiplicative Biadditive Intuitionistic Linear Logic. In S. R. Della Rocca (Ed.), Typed Lambda Calculi and Applications (pp. 163–177). Berlin, Heidelberg: Springer. https://doi.org/10/c8vgx8
DIFFERENTIAL CALCULUS
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