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An introduction to differential linear logic: proof-nets, models and antiderivatives

Published online by Cambridge University Press:  09 February 2017

THOMAS EHRHARD
THOMAS EHRHARD*
Affiliation:
CNRS, IRIF, UMR 8243, Univ Paris Diderot, Sorbonne Paris Cité F-75205 Paris, France Email: thomas.ehrhard@pps.univ-paris-diderot.fr
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Abstract

Differential linear logic enriches linear logic with additional logical rules for the exponential connectives, dual to the usual rules of dereliction, weakening and contraction. We present a proof-net syntax for differential linear logic and a categorical axiomatization of its denotational models. We also introduce a simple categorical condition on these models under which a general antiderivative operation becomes available. Last, we briefly describe the model of sets and relations and give a more detailed account of the model of finiteness spaces and linear and continuous functions.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 28 , Special Issue 7: Differential Linear Logic, Nets and Other Quantitative and Parallel Approaches to Proof-Theory , August 2018 , pp. 995 - 1060
Copyright
Copyright © Cambridge University Press 2017 

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