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An Extension Result for Continuous Valuations
, 1998
"... We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel oealgebra of the dcpo with the Scott topology. It follows that every boun ..."
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Cited by 32 (4 self)
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We show, by a simple and direct proof, that if a bounded valuation on a directed complete partial order (dcpo) is the supremum of a directed family of simple valuations then it has a unique extension to a measure on the Borel oealgebra of the dcpo with the Scott topology. It follows that every bounded and continuous valuation on a continuous domain can be extended uniquely to a Borel measure. The result also holds for oefinite valuations, but fails for dcpo's in general. 1
Nondeterminism and Probabilistic Choice: Obeying the Laws
 In Proc. 11th CONCUR, volume 1877 of LNCS
, 2000
"... In this paper we describe how to build semantic models that support both nondeterministic choice and probabilistic choice. Several models exist that support both of these constructs, but none that we know of satisfies all the laws one would like. Using domaintheoretic techniques, we show how models ..."
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Cited by 25 (2 self)
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In this paper we describe how to build semantic models that support both nondeterministic choice and probabilistic choice. Several models exist that support both of these constructs, but none that we know of satisfies all the laws one would like. Using domaintheoretic techniques, we show how models can be devised using the "standard model" for probabilistic choice, and then applying modified domaintheoretic models for nondeterministic choice. These models are distinguished by the fact that the expected laws for nondeterministic choice and probabilistic choice remain valid. We also describe some potential applications of our model to aspects of security.
A Logic for Probabilities in Semantics
, 2003
"... Probabilistic computation has proven to be a challenging and interesting area of research, both from the theoretical perspective of denotational semantics and the practical perspective of reasoning about probabilistic algorithms. On the theoretical side, the probabilistic powerdomain of Jones and Pl ..."
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Cited by 9 (1 self)
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Probabilistic computation has proven to be a challenging and interesting area of research, both from the theoretical perspective of denotational semantics and the practical perspective of reasoning about probabilistic algorithms. On the theoretical side, the probabilistic powerdomain of Jones and Plotkin represents a significant advance. Further work, especially by AlvarezManilla, has greatly improved our understanding of the probabilistic powerdomain, and has helped clarify its relation to classical measure and integration theory. On the practical side, many researchers such as Kozen, Segala, Desharnais, and Kwiatkowska, among others, study problems of verification for probabilistic computation by defining various suitable logics for the classes of processes under study. The work reported here begins to bridge the gap between the domain theoretic and verification (model checking) perspectives on probabilistic computation by exhibiting sound and complete logics for probabilistic powerdomains that arise directly from given logics for the underlying domains. The category in which the construction is carried out generalizes Scott’s Information Systems by taking account of full classical sequents. Via Stone duality, following Abramsky’s Domain Theory in Logical Form, all known interesting categories of domains are embedded as subcategories. So the results reported here properly generalize similar constructions on specific categories of domains. The category offers a promising universe of semantic domains characterized by a very rich structure and good preservation properties of standard constructions. Furthermore, because the logical constructions make use of full classical sequents, the morphisms have a natural nondeterministic interpretation. Thus the category is a natural one in which to investigate the relationship between probabilistic and nondeterministic computation. We discuss the problem of integrating probabilistic and nondeterministic computation after presenting the construction of logics for probabilistic powerdomains.
On probabilistic coherence spaces
, 2008
"... We introduce a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambdacalculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation ..."
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Cited by 3 (0 self)
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We introduce a probabilistic version of coherence spaces and show that these objects provide a model of linear logic. We build a model of the pure lambdacalculus in this setting and show how to interpret a probabilistic version of the functional language PCF. We give a probabilistic interpretation of the semantics of probabilistic PCF closed terms of ground type.