Jean Goubault-Larrecq (Paris, France), Probability and Nondeterminism in Domain Theory, Part II
Schedule
- Feb. 23, 2012, 15:20 - 16:20
Abstract
As the title indicates, this is a follow-up
on Daniele Varacca's talk. We shall first talk
about the very intuitive denotational model
of probabilistic choice given by so-called
continuous random variables, and will explain
the relation to indexed valuations, as seen
in Part I. We shall then explore a few
solutions to the problem of giving semantics
to mixed non-deterministic and probabilistic
higher-order functional programs. While
indexed valuations and continuous random
variables solve the problem by changing
the model of probabilistic choice,
previsions and the Mislove-Ouaknine-Worrell
and Tix-Kleimel-Plotkin models solve it
by changing the model of non-deterministic
choice to convex non-determinism.
We shall conclude by returning to some of
the goals stated at the beginning of Part I,
and shall establish a few full abstraction
results for variants of PCF with choice,
exhibiting the differences in observable
properties that each model exhibits.
Attachments
As the title indicates, this is a follow-up on Daniele Varacca's talk. We shall first talk about the very intuitive denotational model of probabilistic choice given by so-called continuous random variables, and will explain the relation to indexed valuations, as seen in Part I. We shall then explore a few solutions to the problem of giving semantics to mixed non-deterministic and probabilistic higher-order functional programs. While indexed valuations and continuous random variables solve the problem by changing the model of probabilistic choice, previsions and the Mislove-Ouaknine-Worrell and Tix-Kleimel-Plotkin models solve it by changing the model of non-deterministic choice to convex non-determinism. We shall conclude by returning to some of the goals stated at the beginning of Part I, and shall establish a few full abstraction results for variants of PCF with choice, exhibiting the differences in observable properties that each model exhibits.