A Duality Theorem for Quantitative Semantics

A Duality Theory for Quantitative Semantics

A continuous predicate on a domain, or more generally a topological space, can be concretely described as an open or closed set, or less obviously, as the set of all predicates consistent with it. Generalizing this scenario to quantitative predicates, we obtain under certain well-understood hypotheses an isomorphism between continuous functions on points and supremum preserving functions on ope...

Duality Theorem for Motives

A general duality theorem for the category of motives is established, with a short, simple, and self-contained proof. Introduction Recently, due to the active study of cohomological invariants in algebraic geometry, “transplantation” of classical topological constructions to the algebraic-geometrical “soil” seems to be rather important. In particular, it is very interesting to study topological...

A Duality Theorem for Plastic Plates

Limit analysis studies the asymptotic behavior of elastic-plastic materials and structures. The asymptotic material properties exist for a class of ductile metals and are designed into optimal structural members such as I-beams and composite plates. The analysis automatically ignores the relatively small elastic deformations. Classical lower and upper bound theorems in the form of inequalities ...

A Duality Theorem for Dieudonné Displays ʙʏ

A Metrized Duality Theorem for Markov Processes

We extend our previous duality theorem for Markov processes by equipping the processes with a pseudometric and the algebras with a notion of metric diameter. We are able to show that the isomorphisms of our previous duality theorem become isometries in this quantitative setting. This opens the way to developing theories of approximate reasoning for probabilistic systems.