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52
The Measurement Process in Domain Theory
 Proceedings of the 27 th International Colloquium on Automata, Languages and Programming (ICALP), Lecture Notes in Computer Science
, 2000
"... We introduce the measurement idea in domain theory and then apply it to establish two fixed point theorems. The first is an extension of the Scott fixed point theorem which applies to nonmonotonic mappings. The second is a contraction principle for monotone maps that guarantees the existence of uniq ..."
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Cited by 30 (20 self)
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We introduce the measurement idea in domain theory and then apply it to establish two fixed point theorems. The first is an extension of the Scott fixed point theorem which applies to nonmonotonic mappings. The second is a contraction principle for monotone maps that guarantees the existence of unique fixed points. 1
A Partial Order on Classical and Quantum States
, 2002
"... We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information ..."
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Cited by 27 (8 self)
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We introduce a partial order on classical and quantum states which reveals that these sets are actually domains: Directed complete partially ordered sets with an intrinsic notion of approximation. The operational significance of the orders involved conclusively establishes that physical information has a natural domain theoretic structure. In the same
Epistemic actions as resources
 Journal of Logic and Computation
, 2007
"... We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, ..."
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Cited by 22 (17 self)
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We provide algebraic semantics together with a sound and complete sequent calculus for information update due to epistemic actions. This semantics is flexible enough to accommodate incomplete as well as wrong information e.g. deceit. We give a purely algebraic treatment of the muddy children puzzle, which moreover extends to situations where the children are allowed to lie and cheat. Epistemic actions, that is, information exchanges between agents A, B,... ∈ A, are modeled as elements of a quantale, hence conceiving them as resources. Indeed, quantales are to locales what monoidal closed categories are to Cartesian closed categories, respectively providing semantics for Intuitionistic Logic, and for noncommutative Intuitionistic Linear Logic, including Lambek calculus. The quantale (Q, � , •) acts on an underlying Qright module (M, � ) of epistemic propositions and facts. The epistemic content is encoded by appearance maps, one pair f M A: M → M and f Q A: Q → Q of (lax) morphisms for each agent A ∈ A. By adjunction, they give rise to epistemic modalities [12], capturing the agents ’ knowledge on propositions and actions. The module action is epistemic update and gives rise to dynamic modalities [20] — cf. weakest preconditions. This model subsumes the crucial fragment of Baltag, Moss and Solecki’s [6] dynamic epistemic logic, abstracting it in a constructive fashion while introducing resourcesensitive structure on the epistemic actions. Keywords: Multiagent communication, knowledge update, resourcesensitivity, quantale, Galois adjoints, dynamic epistemic logic, sequent calculus, Lambek calculus, Linear Logic.
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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Cited by 13 (0 self)
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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.
A domain of spacetime intervals in general relativity
, 2004
"... Beginning from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special c ..."
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Cited by 13 (4 self)
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Beginning from only a countable dense set of events and the causality relation, it is possible to reconstruct a globally hyperbolic spacetime in a purely order theoretic manner. The ultimate reason for this is that globally hyperbolic spacetimes belong to a category that is equivalent to a special category of domains called interval domains. 1
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.
Presenting dcpos and dcpo algebras
 Proceedings of the 24th Conference on the Mathematical Foundations of Programming Semantics (MFPS XXIV), Electronic Notes in Theoretical Computer Science
"... Dcpos can be presented by a preorder of generators and inequational relations expressed as covers. Algebraic operations on the generators (possibly with their results being ideals of generators) can be extended to the dcpo presented, provided the covers are “stable ” for the operations. The resultin ..."
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Cited by 9 (1 self)
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Dcpos can be presented by a preorder of generators and inequational relations expressed as covers. Algebraic operations on the generators (possibly with their results being ideals of generators) can be extended to the dcpo presented, provided the covers are “stable ” for the operations. The resulting dcpo algebra has a natural universal characterization and satisfies all the inequational laws satisfied by the generating algebra. Applications include known “coverage theorems ” from locale theory. 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 6 (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
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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Cited by 6 (1 self)
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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
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 6 (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.