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Topological Games in Domain Theory
 Topology Appl
"... We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximal elements in a domain is always complete in a sense rst introduced by Choquet. ..."
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We prove that a metric space may be realized as the set of maximal elements in a continuous dcpo if and only if it is completely metrizable by showing more generally that the space of maximal elements in a domain is always complete in a sense rst introduced by Choquet.
Consistent partial model checking
 Electronic Notes in Theoretical Computer Science
, 2004
"... We propose assertionconsistency (AC) semilattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multipleviewpoint and multiplevalued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those or ..."
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We propose assertionconsistency (AC) semilattices as suitable orders for the analysis of partial models. Such orders express semantic entailment, multipleviewpoint and multiplevalued analysis, maintain internal consistency of reasoning, and subsume finite De Morgan lattices. We classify those orders that are finite and distributive and apply them to design an efficient algorithm for multipleviewpoint checking, where checks are delegated to singleviewpoint models — efficiently driven by the order structure. Instrumentations of this algorithm enable the detection and location of inconsistencies across viewpoint boundaries. To validate the approach, we investigate multiplevalued models and their compositional property semantics over a finite distributive AC lattice. We prove that this semantics is computed by our algorithm above whenever the primes of the AC lattice determine ‘projected’ single viewpoints and the order between primes is preserved as refinements of singleviewpoint models. As a case study, we discuss a multiplevalued notion of statemachines with firstorder logic plus transitive closure. 1
The Space of Maximal Elements in a Compact Domain
, 2001
"... In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scott domain must be Cechcomplete. An important consequence is that any metric space homeomorphic to the max ..."
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Cited by 4 (3 self)
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In this paper we try to improve the current state of understanding concerning models of spaces with Scott domains. The main result given is that any developable space which has a model by a Scott domain must be Cechcomplete. An important consequence is that any metric space homeomorphic to the maximal elements of a Scott domain must be completely metrizable. 1
Ideal Models of Spaces
 Theoretical Computer Science
, 2000
"... Ideal domains have an elementary order theoretic structure: Every element is either compact or maximal. Despite this, we establish that (1) They can model any space currently known to possess a countably based model, and (2) The metric spaces with ideal models are exactly the completely metrizab ..."
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Cited by 3 (2 self)
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Ideal domains have an elementary order theoretic structure: Every element is either compact or maximal. Despite this, we establish that (1) They can model any space currently known to possess a countably based model, and (2) The metric spaces with ideal models are exactly the completely metrizable spaces.
Unique Fixed Points in Domain Theory
, 2001
"... We unveil new results based on measurement that guarantee the existence of unique fixed points which need not be maximal. In addition, we establish that least fixed points are always attractors in the topology, and then explore the consequences of these findings in analysis. In particular, an exten ..."
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Cited by 1 (0 self)
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We unveil new results based on measurement that guarantee the existence of unique fixed points which need not be maximal. In addition, we establish that least fixed points are always attractors in the topology, and then explore the consequences of these findings in analysis. In particular, an extension of the Banach fixed point theorem on compact metric spaces [3] is obtained. 1