Differential Structure in Models of Multiplicative Biadditive Intuitionistic Linear Logic

(Extended Abstract)
  • Marcelo P. Fiore
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4583)

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.).

Keywords

Categorical Model Natural Transformation Annihilation Operator Creation Operator Monoidal Category 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Marcelo P. Fiore
    • 1
  1. 1.Computer Laboratory, University of Cambridge 

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