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UID:7195@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20181122T110000
DTEND;TZID=Europe/Paris:20181122T123000
DTSTAMP:20241120T203446Z
URL:https://www.i2m.univ-amu.fr/evenements/connecting-models-of-differenti
 al-linear-logic-with-reloids/
SUMMARY:Zeinab Galal (IRIF\, Université de Paris): Connecting models of di
 fferential linear logic with reloids
DESCRIPTION:Zeinab Galal: Species of structures were introduced by Joyal as
  a unified framework for the theory of generating series in enumerative co
 mbinatorics.\nSpecies are connected to Girard's normal functor semantics o
 f λ-calculus where terms are interpreted as power series with sets as coe
 fficients.\nFiore et al. presented a generalised definition that both enco
 mpasses Joyal's species and constitutes a model of differential linear log
 ic.\nFor generalised species of structures\, types are interpreted as grou
 poids which provides the connection with combinatorics whereas they are in
 terpeted as sets in Girard's normal functors and in the relational model. 
 To investigate how these models interact\, we introduce a variant of the r
 elational model where objects are setoids (sets equipped with an equivalen
 ce relation) and morphisms are relations. We obtain a new model of differe
 ntial linear logic (named Reloids) that allows for a less degenerate colla
 pse from species than the one to normal functors or relations. We then sho
 w how to construct functors preserving the linear logic structure between 
 these four models.
CATEGORIES:Séminaire,Logique et Interactions
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