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UID:7251@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20180906T110000
DTEND;TZID=Europe/Paris:20180906T123000
DTSTAMP:20241120T203848Z
URL:https://www.i2m.univ-amu.fr/evenements/the-algebraic-structure-of-clas
 sical-realizability-models/
SUMMARY:Etienne Miquey (IRIF\, Université de Paris): The algebraic structu
 re of classical realizability models
DESCRIPTION:Etienne Miquey: Implicative algebras\, developed by Alexandre M
 iquel\, are very simple algebraic structures generalizing at the same time
  complete Boolean algebras and Krivine realizability algebras\, in such a 
 way that they allow to express in a same setting the theory of forcing (in
  the sense of Cohen) and the theory of classical realizability (in the sen
 se of Krivine). Besides\, they have the nice feature of providing a common
  framework for the interpretation both of types and programs. The main def
 ault of these structures is that they are deeply oriented towards the λ-c
 alculus\, and that they only allows to faithfully interpret languages in c
 all-by-name. To remediate the situation\, we introduce two variants of imp
 licative algebras: disjunctive algebras\, centered on the “par” (⅋) 
 connective of linear logic (but in a non-linear framework) and naturally a
 dapted to languages in call-by-name\; and conjunctives algebras\, centered
  on the “tensor” (⊗) connective of linear logic and adapted to langu
 ages in call-by-value. Amongst other properties\, we will see that disjunc
 tive algebras are particular cases of implicative algebras and that conjun
 ctive algebras can be obtained from disjunctive algebras (by reversing the
  underlying order).\n\nhttps://www.irif.fr/~emiquey/
ATTACH;FMTTYPE=image/jpeg:https://www.i2m.univ-amu.fr/wp-content/uploads/2
 015/07/Etienne_Miquey.jpg
CATEGORIES:Séminaire,Logique et Interactions
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