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UID:8626@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20250417T110000
DTEND;TZID=Europe/Paris:20250417T123000
DTSTAMP:20250325T092554Z
URL:https://www.i2m.univ-amu.fr/evenements/double-indexed-differential-lin
 ear-logic-reconciling-resources-and-differential-operators/
SUMMARY:Simon Mirwasser (LIPN\, Sorbonne Paris Nord): Double indexed differ
 ential linear logic reconciling resources and differential operators
DESCRIPTION:Simon Mirwasser: Graded Linear Logic is a central development o
 f Linear Logic\, quantifying the use of resources in proofs and programs. 
 Differential Linear Logic\, on the other hand\, dualises this focus on res
 ources by adding co-structural rules defining proof differentiation. In th
 is paper we use the Laplace transform as the final building block to recon
 cile co-structural rules with graded exponential. We define a graded diffe
 rential linear logic where structural and co-structural rules act on four 
 different exponential connectives. Contrarily to previous work\, this proo
 f calculus goes higher-\norder by including a promotion rule\, and also pr
 ovides a sound syntax for the recently introduced co-promotion rule. We pr
 ovide two different models for this syntax: the first extends a previously
  known first-order model to higher order thanks to Köthe spaces\, where t
 he indices are either polynomials or linear partial differential operators
 . The second arises from the literature in functional analysis\, the indic
 es being Young functions and their convex conjugate.
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Sall
 e de Séminaire 304-306 (3ème étage):geo:0,0
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