@article{paquet_continuous_2018,
series = {Proceedings of the {Thirty}-{Fourth} {Conference} on the {Mathematical} {Foundations} of {Programming} {Semantics} ({MFPS} {XXXIV})},
title = {Continuous {Probability} {Distributions} in {Concurrent} {Games}},
volume = {341},
issn = {1571-0661},
url = {http://www.sciencedirect.com/science/article/pii/S1571066118300975},
doi = {10/ggdmwv},
abstract = {We present a model of concurrent games in which strategies are probabilistic and support both discrete and continuous distributions. This is a generalisation of the probabilistic concurrent strategies of Winskel, based on event structures. We first introduce measurable event structures, discrete fibrations of event structures in which each fibre is turned into a measurable space. We then construct a bicategory of measurable games and measurable strategies based on measurable event structures, and add probability to measurable strategies using standard techniques of measure theory. We illustrate the model by giving semantics to an affine, higher-order, probabilistic language with a type of real numbers and continuous distributions.},
language = {en},
urldate = {2019-11-28},
journal = {Electronic Notes in Theoretical Computer Science},
author = {Paquet, Hugo and Winskel, Glynn},
month = dec,
year = {2018},
note = {ZSCC: 0000002},
keywords = {Game semantics, Interactive semantics, Probabilistic programming, Programming language theory},
pages = {321--344}
}
@inproceedings{castellan_concurrent_2018,
address = {Oxford, United Kingdom},
title = {The concurrent game semantics of {Probabilistic} {PCF}},
isbn = {978-1-4503-5583-4},
url = {http://dl.acm.org/citation.cfm?doid=3209108.3209187},
doi = {10/ggdjfz},
abstract = {We define a new games model of Probabilistic PCF (PPCF) by enriching thin concurrent games with symmetry, recently introduced by Castellan et al, with probability. This model supports two interpretations of PPCF, one sequential and one parallel. We make the case for this model by exploiting the causal structure of probabilistic concurrent strategies. First, we show that the strategies obtained from PPCF programs have a deadlock-free interaction, and therefore deduce that there is an interpretation-preserving functor from our games to the probabilistic relational model recently proved fully abstract by Ehrhard et al. It follows that our model is intensionally fully abstract. Finally, we propose a definition of probabilistic innocence and prove a finite definability result, leading to a second (independent) proof of full abstraction.},
language = {en},
urldate = {2019-11-26},
booktitle = {Proceedings of the 33rd {Annual} {ACM}/{IEEE} {Symposium} on {Logic} in {Computer} {Science} - {LICS} '18},
publisher = {ACM Press},
author = {Castellan, Simon and Clairambault, Pierre and Paquet, Hugo and Winskel, Glynn},
year = {2018},
note = {ZSCC: 0000018},
keywords = {Denotational semantics, Game semantics, Interactive semantics, Probabilistic programming, Programming language theory},
pages = {215--224}
}
@article{abramsky_geometry_2002,
title = {Geometry of {Interaction} and {Linear} {Combinatory} {Algebras}},
volume = {12},
issn = {0960-1295},
url = {http://dx.doi.org/10.1017/S0960129502003730},
doi = {10/fcsmhm},
abstract = {We present an axiomatic framework for Girard's Geometry of Interaction based on the notion of linear combinatory algebra. We give a general construction on traced monoidal categories, with certain additional structure, that is sufficient to capture the exponentials of Linear Logic, which produces such algebras (and hence also ordinary combinatory algebras). We illustrate the construction on six standard examples, representing both the ‘particle-style’ as well as the ‘wave-style’ Geometry of Interaction.},
number = {5},
urldate = {2019-11-28},
journal = {Mathematical. Structures in Comp. Sci.},
author = {Abramsky, Samson and Haghverdi, Esfandiar and Scott, Philip},
month = oct,
year = {2002},
note = {ZSCC: 0000162},
keywords = {Interactive semantics, Linear logic},
pages = {625--665}
}
@inproceedings{danos_probabilistic_2000,
title = {Probabilistic game semantics},
volume = {3},
isbn = {978-0-7695-0725-5},
doi = {10/b6k43s},
abstract = {A category of HO/N-style games and probabilistic strategies is developed where the possible choices of a strategy are quantified so as to give a measure of the likelihood of seeing a given play. A 2-sided die is shown to be universal in this category, in the sense that any strategy breaks down into a composition between some deterministic strategy and that die. The interpretative power of the category is then demonstrated by delineating a Cartesian closed subcategory which provides a fully abstract model of a probabilistic extension of Idealized Algol},
author = {Danos, Vincent and Harmer, Russell},
month = feb,
year = {2000},
note = {ZSCC: NoCitationData[s1]},
keywords = {Denotational semantics, Game semantics, Interactive semantics, Probabilistic programming, Programming language theory},
pages = {204--213}
}
@inproceedings{girard_geometry_1995,
address = {Berlin, Heidelberg},
series = {{NATO} {ASI} {Series}},
title = {On {Geometry} of {Interaction}},
isbn = {978-3-642-79361-5},
doi = {10/fr557p},
abstract = {The paper expounds geometry of interaction, for the first time in the full case, i.e. for all connectives of linear logic, including additives and constants. The interpretation is done within a C*-algebra which is induced by the rule of resolution of logic programming, and therefore the execution formula can be presented as a simple logic programming loop. Part of the data is public (shared channels) but part of it can be viewed as private dialect (defined up to isomorphism) that cannot be shared during interaction, thus illustrating the theme of communication without understanding. One can prove a nilpotency (i.e. termination) theorem for this semantics, and also its soundness w.r.t. a slight modification of familiar sequent calculus in the case of exponential-free conclusions.},
language = {en},
booktitle = {Proof and {Computation}},
publisher = {Springer},
author = {Girard, Jean-Yves},
editor = {Schwichtenberg, Helmut},
year = {1995},
note = {ZSCC: NoCitationData[s0]},
keywords = {Interactive semantics, Linear logic},
pages = {145--191}
}