TY - CONF
TI - The Geometry of Bayesian Programming
AU - Dal Lago, Ugo
AU - Hoshino, Naohiko
DA - 2019/06/01/
PY - 2019
DO - 10/ggdk85
DP - ResearchGate
SP - 1
EP - 13
KW - Bayesian inference
KW - Denotational semantics
KW - Linear logic
KW - Probabilistic programming
KW - Programming language theory
KW - Rewriting theory
KW - Transition systems
ER -
TY - CONF
TI - Higher-Order Distributions for Differential Linear Logic
AU - Kerjean, Marie
AU - Pacaud Lemay, Jean-Simon
A2 - Bojańczyk, Mikołaj
A2 - Simpson, Alex
T3 - Lecture Notes in Computer Science
AB - Linear Logic was introduced as the computational counterpart of the algebraic notion of linearity. Differential Linear Logic refines Linear Logic with a proof-theoretical interpretation of the geometrical process of differentiation. In this article, we construct a polarized model of Differential Linear Logic satisfying computational constraints such as an interpretation for higher-order functions, as well as constraints inherited from physics such as a continuous interpretation for spaces. This extends what was done previously by Kerjean for first order Differential Linear Logic without promotion. Concretely, we follow the previous idea of interpreting the exponential of Differential Linear Logic as a space of higher-order distributions with compact-support, which is constructed as an inductive limit of spaces of distributions on Euclidean spaces. We prove that this exponential is endowed with a co-monadic like structure, with the notable exception that it is functorial only on isomorphisms. Interestingly, as previously argued by Ehrhard, this still allows the interpretation of differential linear logic without promotion.
C1 - Cham
C3 - Foundations of Software Science and Computation Structures
DA - 2019///
PY - 2019
DO - 10/ggdmrj
DP - Springer Link
SP - 330
EP - 347
LA - en
PB - Springer International Publishing
SN - 978-3-030-17127-8
KW - Denotational semantics
KW - Differential Linear Logic
KW - Differentiation
KW - Linear logic
ER -
TY - CONF
TI - Probabilistic game semantics
AU - Danos, Vincent
AU - Harmer, Russell
T2 - ACM Transactions on Computational Logic - TOCL
AB - 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
DA - 2000/02/01/
PY - 2000
DO - 10/b6k43s
DP - ResearchGate
VL - 3
SP - 204
EP - 213
SN - 978-0-7695-0725-5
KW - Denotational semantics
KW - Game semantics
KW - Interactive semantics
KW - Probabilistic programming
KW - Programming language theory
ER -
TY - CONF
TI - Bisimulation for probabilistic transition systems: A coalgebraic approach
AU - de Vink, E. P.
AU - Rutten, J. J. M. M.
A2 - Degano, Pierpaolo
A2 - Gorrieri, Roberto
A2 - Marchetti-Spaccamela, Alberto
T3 - Lecture Notes in Computer Science
AB - The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendier in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation.
C1 - Berlin, Heidelberg
C3 - Automata, Languages and Programming
DA - 1997///
PY - 1997
DO - 10/fcqzmk
DP - Springer Link
SP - 460
EP - 470
LA - en
PB - Springer
SN - 978-3-540-69194-5
ST - Bisimulation for probabilistic transition systems
KW - Categorical probability theory
KW - Coalgebras
KW - Denotational semantics
KW - Probabilistic transition systems
KW - Transition systems
ER -