Robert Furber
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View article: Interpreting Lambda Calculus in Domain-Valued Random Variables
Interpreting Lambda Calculus in Domain-Valued Random Variables Open
We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of eq…
View article: Scott Continuity in Generalized Probabilistic Theories
Scott Continuity in Generalized Probabilistic Theories Open
Scott continuity is a concept from domain theory that had an unexpected previous life in the theory of von Neumann algebras. Scott-continuous states are known as normal states, and normal states are exactly the states coming from density m…
View article: Probabilistic logics based on Riesz spaces
Probabilistic logics based on Riesz spaces Open
We introduce a novel real-valued endogenous logic for expressing properties of probabilistic transition systems called Riesz modal logic. The design of the syntax and semantics of this logic is directly inspired by the theory of Riesz spac…
View article: PROBABILISTIC LOGICS BASED ON RIESZ SPACES
PROBABILISTIC LOGICS BASED ON RIESZ SPACES Open
International audience
View article: Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras
Infinite-Dimensionality in Quantum Foundations: W*-algebras as Presheaves over Matrix Algebras Open
In this paper, W*-algebras are presented as canonical colimits of diagrams of matrix algebras and completely positive maps. In other words, matrix algebras are dense in W*-algebras.