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UID:5172@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20240530T110000
DTEND;TZID=Europe/Paris:20240530T123000
DTSTAMP:20240703T140303Z
URL:https://www.i2m.univ-amu.fr/evenements/regular-samplers-and-the-de-fin
 etti-construction-in-integrable-cones/
SUMMARY:Raphaëlle Crubilllé (LIS): Regular samplers and the De Finetti co
 nstruction in Integrable Cones
DESCRIPTION:Raphaëlle Crubilllé: The starting point of this talk is the s
 tructure of the object\n!Bool in probabilistic coherent spaces. For the pu
 rpose of building a\nsemantics interpretation for PCF_proba\, it is enough
  to consider elements of\n!Bool that are promotions of elements in Bool\, 
 but !Bool contains also\nmore exotic elements\, that can nonetheless be se
 en as probabilistic samplers\n(in the sense that they can handle any numbe
 r of query from a program !Bool → σ\nto its argument\, seen as a random
  oracle). In this work\, we present a\ncaracterisation of all total elemen
 ts in !Bool: we show that they can all be\nseen as continuous mixture of p
 romotions. The central element of this proof\nis an extension to the categ
 ory of integrable cones of the categorical\nversion[1] of the De Finetti t
 heorem (that says that there is a one-to-one\ncorrespondance between the c
 ontinuous probability distributions on [0\,1]\, and\nthe infinite exchange
 able sequence of discrete random variables on booleans).\n\n[1] B. Jacobs 
 and S. Staton. De finetti’s construction as a categorical limit\, CMCS 2
 020.
CATEGORIES:Séminaire,Logique et Interactions
LOCATION:I2M Luminy - TPR2\, Salle de Séminaire 304-306 (3ème étage)\, 1
 63 Avenue de Luminy\, Marseille\, 13009\, France
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 e de Séminaire 304-306 (3ème étage):geo:0,0
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