
Presenting convex sets of probability distributions by convex semilattices and unique bases
We prove that every finitely generated convex set of finitely supported ...
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On the Axiomatizability of Quantitative Algebras
Quantitative algebras (QAs) are algebras over metric spaces defined by q...
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Extending set functors to generalised metric spaces
For a commutative quantale V, the category Vcat can be perceived as a c...
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Composition of Credal Sets via Polyhedral Geometry
Recently introduced composition operator for credal sets is an analogy o...
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Distances between States and between Predicates
This paper gives a systematic account of various metrics on probability ...
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Theory Presentation Combinators
To build a scalable library of mathematics, we need a method which takes...
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An enriched category theory of language: from syntax to semantics
Given a piece of text, the ability to generate a coherent extension of i...
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Monads and Quantitative Equational Theories for Nondeterminism and Probability
The monad of convex sets of probability distributions is a wellknown tool for modelling the combination of nondeterministic and probabilistic computational effects. In this work we lift this monad from the category of sets to the category of metric spaces, by means of the Hausdorff and Kantorovich metric liftings. Our main result is the presentation of this lifted monad in terms of the quantitative equational theory of convex semilattices, using the framework of quantitative algebras recently introduced by Mardare, Panangaden and Plotkin.
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