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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
Semantic Domains for Combining Probability and NonDeterminism
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2005
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Topology, Domain Theory and Theoretical Computer Science
, 1997
"... In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from ..."
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Cited by 10 (2 self)
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In this paper, we survey the use of ordertheoretic topology in theoretical computer science, with an emphasis on applications of domain theory. Our focus is on the uses of ordertheoretic topology in programming language semantics, and on problems of potential interest to topologists that stem from concerns that semantics generates. Keywords: Domain theory, Scott topology, power domains, untyped lambda calculus Subject Classification: 06B35,06F30,18B30,68N15,68Q55 1 Introduction Topology has proved to be an essential tool for certain aspects of theoretical computer science. Conversely, the problems that arise in the computational setting have provided new and interesting stimuli for topology. These problems also have increased the interaction between topology and related areas of mathematics such as order theory and topological algebra. In this paper, we outline some of these interactions between topology and theoretical computer science, focusing on those aspects that have been mo...
Nonclassical Techniques for Models of Computation
 Topology Proceedings
, 1999
"... After surveying recent work and new techniques in domain theoretic models of spaces, we introduce a new topological concept called recurrence, and consider some of its applications to the model problem. ..."
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Cited by 9 (4 self)
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After surveying recent work and new techniques in domain theoretic models of spaces, we introduce a new topological concept called recurrence, and consider some of its applications to the model problem.
Extension of Valuations on Locally Compact Sober Spaces.
, 2000
"... We show that every locally finite continuous valuation defined on the lattice of open sets of a regular or locally compact sober space extends uniquely to a Borel measure. ..."
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Cited by 5 (0 self)
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We show that every locally finite continuous valuation defined on the lattice of open sets of a regular or locally compact sober space extends uniquely to a Borel measure.
On the calculating power of Laplace’s demon
"... Abstract. We discuss some of the choices that arise when one tries to make the idea of physical determinism more precise. Broadly speaking, ‘ontological ’ notions of determinism are parameterized by one’s choice of mathematical ideology, whilst ‘epistemological ’ notions of determinism are parameter ..."
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Abstract. We discuss some of the choices that arise when one tries to make the idea of physical determinism more precise. Broadly speaking, ‘ontological ’ notions of determinism are parameterized by one’s choice of mathematical ideology, whilst ‘epistemological ’ notions of determinism are parameterized by the choice of an appropriate notion of computability. We present some simple examples to show that these choices can indeed make a difference to whether a given physical theory is ‘deterministic’ or not. Keywords: Laplace’s demon, physical determinism, philosophy of mathematics, notions of computability. 1
Generalizing Domain Theory
"... Domain theory began in an attempt to provide mathematical models for highlevel programming languages, an area where it has proved to be particularly useful. It is perhaps the most widelyused method for devising semantic models for such languages. This paper is a survey of some generalizations of d ..."
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Domain theory began in an attempt to provide mathematical models for highlevel programming languages, an area where it has proved to be particularly useful. It is perhaps the most widelyused method for devising semantic models for such languages. This paper is a survey of some generalizations of domain theory that have arisen in efforts to solve related problems. In each case, a description is given of the problem and of the solution generalizing domain theory it inspired. The problems range from the relation of domain theory to other approaches for providing semantic models, particularly in process algebra, to issues surrounding the notion of a computational model, an approach inspired by the recent work of Abbas Edalat.
omegaQRBdomains and the probabilistic powerdomain
"... Is there any cartesianclosed category of continuous domains that would be closed under Jones and Plotkin’s probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higherorder languages. We relax the question, and look for quasico ..."
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Is there any cartesianclosed category of continuous domains that would be closed under Jones and Plotkin’s probabilistic powerdomain construction? This is a major open problem in the area of denotational semantics of probabilistic higherorder languages. We relax the question, and look for quasicontinuous dcpos instead. We introduce a natural class of such quasicontinuous dcpos, the